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Maths Is Fun - Rod Pierce, mathsisfun.com
Math revision (review) pages, games, puzzles, and offline activities for age 11 through college algebra. A discussion forum and a newsletter are also available. The Illustrated Math Dictionary links definitions to further resources on the site. Maths
...more>>
Maths - Martin John Baker, EuclideanSpace
Originally intended to give enough maths information to allow physical objects to be simulated by a computer program, these pages now cover a broader range of mathematical topics. The pages that get the most hits on the site are those concerned with 3D
...more>>
MathsOnline - King's College
MathsOnline, from New Zealand, covers the entire mathematics curriculum for secondary school students from Year 8 (Year 9 in NZ) to Year 12 (Year 13 in
NZ). The site splits each year level into 50 topics and contains notes, examples, tests, exams, quizzes,
...more>>
MathSource - Wolfram Research
An extensive electronic library of Mathematica material and notebooks, with over 100,000 pages of immediately accessible Mathematica programs, documents, examples, and more. You may browse the archive or search by author, title, keyword, or item number.
...more>>
Math Trivia - FunTrivia.com
Online multiple-choice (MC) quizzes covering topics in algebra, geometry, statistics and probability, calculus, measurements, and more. Register to record your high scores on the site; Find out how many others have played a given game, and how they rate
...more>>
The Math Tutor Center - Addison Wesley Longman, Inc.
A service free for students who purchase a new Addison Wesley Longman math textbook included on the list of eligible textbooks and are enrolled in developmental, precalculus, calculus and introductory statistics courses. Qualified math instructors tutor
...more>>
MathWare Ltd.
Software and books for algebra, geometry and calculus: Derive, MathPert, Scientific Notebook, Cyclone; books for use with the TI Graphing Calculators, and a book and CD for Mathematica. Also an Interactive Math Dictionary on CD-ROM with biographical entries,
...more>>
Math Worksheets Center
Thousands of teacher-made K-12 math worksheets, lessons, homework assignments, quizzes, and tip sheets. Browse by grade level or student age; each math topic links to an index of the remedial math worksheets that point up the skills needed to get to that
...more>>
Math Worksheets Land
Thousands of downloadable math worksheets, aligned to the Common Core State Standards (CCSS) and with solutions, by a retired teacher: addition, algebra, area and perimeter, basic operations, complex numbers, counting, decimals, division, estimation,
...more>>
MathWorld Interactive - Carolynn S. Mortensen
Open-ended word problems and some answers from this now-defunct project. MathWorld began as MathMagic FidoNet in 1991, and was dedicated to helping educators and parents motivate their students to solve open-ended word problems, communicate mathematically,
...more>>
The Median Isn't the Message - Stephen Jay Gould
A personal story of statistics and "stretching the truth with numbers"; according to Steve Dunn, "the wisest, most humane thing ever written about cancer and statistics. It is the antidote both to those who say that, 'the statistics
don't matter,' andMichigan Math Scholars
A summer program for high school students at the University of Michigan. Program information, mathematics news, a student paper ("On the Problem of Dividing a Clock Face Into Equal Thirds"), several online courses (The Nature of Infinity; Chaos; Graph
...more>>
Microsoft Math Partnership
Through partnerships with eight area school districts and the Puget Sound Educational Service District, the Microsoft Math Partnership (MMP) provides support to schools to help students become critical thinkers and proficient in mathematical skills andOTIVATE - Univ. of Cambridge, UK
MOTIVATE is a project incorporating a series of videoconferences, run by the Millennium Mathematics Project at Cambridge. The objectives of MOTIVATE are: to enrich the mathematical experience of school students, to broaden their mathematical horizons,
...more>>
Musing Mathematically - Nat Banting
Thoughts from a high school mathematics teacher on the teaching of mathematics, and the learning of mathematics. Posts, which date back to May, 2011, have included "Playing with Mean, Median & Mode," "Attaching a 'Why' to the 'How," "The Mathematics
...more>>
My NMSI Story
Watch clips of U.S. students and teachers speaking about their participation in the National Math and Science Initiative's Advanced Placement Training and Incentive Program (APTIP). Upload your own video narrative about APTIP, which has expanded American
...more>> |
MTH 111 Mathematics as a Human
Pursuit Calendar Semester 112
Write out complete
answers NEATLY and CLEARLY.
For written
problem assignments:
Number each
exercise to the left.
Work only one problem across the page -- i.e. problems should proceed form top to bottom.
You must show your work! Correct mathematical notation must be
used. Partial credit is given when work is shown even if answer is
incorrect. However, correct answers without any work shown will in general
be given no credit.
If the problem is a computation leading to a final answer, box the answer.
Use pencil and eraser -- do not scratch out work.
Start homework
early and see me for help with problems you don't know how to work! It is
inappropriate to ask how to do a problem in class the day it is due!!!!
Staple your pages together before submitting. My office
is Core 257-- See my schedule
for office hours or call or send email for an appointment. I am always
delighted to help. |
Grade 8-12
This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.
2ALG.7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.
2ALG.8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
2ALG.9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b)2 + c.
2ALG.10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
2ALG.11.0 Students prove simple laws of logarithms.
2ALG.11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
2ALG.11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.
2ALG.12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
2ALG.13.0 Students use the definition of logarithms to translate between logarithms in any base.
2ALG.14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
2ALG.16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.
2ALG.17.0 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
2ALG.18.0 Students use fundamental counting principles to compute combinations and permutations.
2ALG.19.0 Students use combinations and permutations to compute probabilities.
2ALG.20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
2ALG.21.0 Students apply the method of mathematical induction to prove general statements about the positive integers.
2ALG.22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
2ALG.23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
2ALG.24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
2ALG.25.0 Students use properties from number systems to justify steps in combining and simplifying functions. |
Unit specification
Aims
The programme unit aims to introduce the basic ideas of real analysis (continuity, differentiability and Riemann
integration) and their rigorous treatment, and then to introduce the basic elements of complex analysis, with
particular emphasis on Cauchy's Theorem and the calculus of residues.
Brief description
The first half of the course describes how the basic ideas of the calculus of real functions of a real variable
(continuity, differentiation and integration) can be made precise and how the basic properties can be developed
from the definitions. It builds on the treatment of sequences and series in MT1242. Important results are the
Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the
Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.
The second half of the course extends these ideas to complex functions of a complex variable. It turns out
that complex differentiability is a very strong condition and differentiable functions behave very well.
Integration is along paths in the complex plane. The central result of this spectacularly beautiful part
of mathematics is Cauchy's Theorem guaranteeing that certain integrals along closed paths are zero. This
striking result leads to useful techniques for evaluating real integrals based on the `calculus of residues'.
Intended learning outcomes
On completion of this unit successful students will be able to:
understand the concept of limit for real functions and be able to calculate limits of standard functions and construct simple proofs involving this concept;
understand the concept of continuity and be familiar with the statements and proofs of the standard results about continuous real functions;
understand the concept of the differentiability of a real valued function and be familiar with the statements and proofs of the standard results about differentiable real functions;
appreciate the definition of the Riemann integral, and be familiar with the statements and proofs of the standard results about the Riemann integral including the Fundamental Theorem of Calculus;
understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations;
evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem and have seen an outline of the proof;
compute the Taylor and Laurent expansions of simple functions, determining the nature of the singularities and calculating residues;
use the Cauchy Residue Theorem to evaluate integrals and sum series.
Future topics requiring this course unit
Real analysis is needed in more advanced courses in analysis, functional analysis and topology and some
courses in numerical analysis.
Complex analysis is needed for advanced analysis, geometry and topology, but also has applications
in differential equations, potential theory, fluid mechanics, asymptotics and wave analysis. |
This textbook entitled Trigonometry (Notes) is a complete and detailed account of trigonometry, including numerous solved problems and formula derivations with each and every step included. Furthermore, the textbook presents the development of trigonometry in a logical manner, starting with the definitions of the six trigonometric ratios on a right-triangle, and later generalizing these definitions for the rectangular coordinate system. Finally, the six trigonometric functions are abstracted from the six trigonometric functions. The textbook is essentially divided into two parts:
Trigonometry developed from the right-triangle, and
Trigonometry derived from the rectangular coordinate system.
Trigonometry (Notes) is intended for the student who wants to learn trigonometry completely and thoroughly, with a complete understanding of the concepts and their relationships to one another.
Except for the Table of Contents, the textbook is hand-written as opposed to typed; thus the word Notes in parentheses in the title.
Originally formulated for the home-schooled student, this five hundred page text and study guide provides extremely detailed explanations in simple English with numerous example problems accompanied by narrative explanations for each topic presented. Reader friendly and logically organized, this volume serves as an all-inclusive high-school algebra text for the college bound student or as an excellent study guide to accompany any serious algebra or trigonometry course. Hundreds of practice problems complete with solutions are included in the text, covering every aspect of a high school or introductory level college algebra course. Also, it is perfect as summer reading for the student who wishes to get ahead or for adults participating in continuing education courses. |
Algebra (geometry helpful but not necessary),
All materials are available in the course or online; however, students who wish to have a supplementary book should have access to any standard school physics text
Course Requires a Media Kit to be Purchased by Course Sponsor
(see additional details below):
No
Description:
Note: This course is intended to teach and reinforce crucial academic skills to help students strengthen their background in the subject area prior to taking an advanced level course. Students who have already taken the Virtual High School course "Integrated Mechanical Physics with Logical Reasoning" should not take this course.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
So you plan to go to college and study physics, math, or engineering? DO THIS FIRST! This course will teach you HOW to figure out problems and how to judge whether or not your answers are reasonable. Save yourself a lot of time and trouble! This course will serve as an introduction to mechanical physics and the reasoning and problem-solving approaches utilized in physics, math and engineering disciplines. Emphasis will be placed on problem-solving approaches and on developing the student's ability to grasp the 'overall picture' of a problems in order to estimate and evaluate reasonable outcomes.
*This course may be appropriate for Gifted and Talented middle school students that meet all course prerequisites.* |
Materials Needed for Class
1. Notebook (3 ring binder with paper)
2. Pencil for quizzes/tests. (pen may be used for notes)
3. Textbook - book must have a paper cover on it
4. Scientific calculator or better (TI-30XS Multi-view or TI-30xIIs is recommended)
Attendance:
Absence: If you are absent, please get the assignments by one of the following methods:
1. asking me when you return to school 2. calling a reliable friend from class
3. checking the Milwaukee Lutheran website (
If you are absent for a long period of time, please contact the school so that assignments can be sent home. You are required to make up the missing work. When you get back, you need to make arrangements with me to get the work completed. If an absence is due to a field trip or other school activities, you must get assignments ahead of time and make arrangements for missing quizzes or test ahead of time. Tardies: You must be completely in the classroom by the end of the tone. Please get seated immediately.
How to be Successful: 1. Take notes (in a notebook) during class. Copy sample problems from board and try them as we go through them in class. Do the assignments in your notebook. If you have trouble with the problems, come in and get extra help. Notebooks will be collected and graded at the end of each chapter.
2. Use all given class time to begin your assignment.
3. Take announced quizzes. .
4. Take Chapter Tests. a. Chapter tests are cumulative. The last cumulative test of the semester will be the final exam.
On-Line Grades: To access grades go to the Milwaukee Lutheran website. Daily work will be posted within 2-3 days. Quizzes/Tests will be posted within 1 week. Miscellaneous: Cheating Policy: You will receive a zero along with the person who gave you the answers or work and parents will be notified.
Extra Help: Hours 3 and 8 (with a pass from me)
before school (7:35-7:50 Mondays; 7:20-7:50 Tuesdays, Wednesdays, Fridays)
before school (7:30-8:30 on Student Help Thursdays)
after school (3:06-3:35 ) (except when coaching)
Passes: Given for emergencies only. Planner and school ID required.
Classroom R's: Responsibility and Respect
You are responsible for your education. Others, like myself, are here to guide and help you. Please respect the right of others wanting to learn. |
Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C), and MAT 080 (min grade C), or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
30220
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MAT115 Principles of Modern Math
Prerequisite: MAT 076 (min grade C) or 1 year high school geometry (min grade C), and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
IAI#: M1904
30153
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3
MW
08:00-09:15
3G06
CR. Conderman
13
30554
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3
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11:00-12:15
2M05
JL. Horn
0
MAT121 College Algebra
Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C) and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement or ACT score of 21-22
30155
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$10
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2M05
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$10
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EA. Etter
15
$10
30385
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$10
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MAT122 Trigonometry
Prerequisite: MAT 121 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and apprpriate placement score or ACT score of 23-25
30158
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$10
MAT203 Calculus & Analytic Geometry I
Prerequisite: MAT 122 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and appropriate Placement score or ACT score of 23-25 |
How To Solve Word Problems In Geometry - 00 edition
Summary: The easiest way to solve the hardest problems! Geometry's extensive use of figures and visual calculations make its word problems especially difficult to solve. This book picks up where most textbooks leave off, making techniques for solving problems easy to grasp and offering many illustrative examples to make learning easy. Each year more than two million students take high school or remedial geometry courses. Geometry word problems are abstract and especially hard...show more to solve--this guide offers detailed, easy-to-follow solution procedures. Emphasizes the mechanics of problem-solving. Includes worked-out problems and a 50-question self-test with answers |
MATHEMATICS 0405 Study Skills: Math Anxiety 1 credit hour
Basic course designed for students who want to reduce or manage math anxiety. Students examine underlying issues that contribute to math anxiety; discuss various learning styles; assess own learning style; learn ways to accommodate an instructor's teaching style; and learn strategies and techniques to effectively cope with math anxiety. This course may be taken three times for credit.. This course can only be taken on a pass/fail basis. Prerequisite: Consent of instructor is required. (1 lecture hour)
MATHEMATICS 0408 Arithmetic Whole Numbers I 0.5 credit hours
Computation skills involving addition and subtraction of whole numbers and applications. This course can only be taken on a pass/fail basis. Prerequisite: Consent of instructor required. (.5 lecture hour)
MATHEMATICS 0410 Arithmetic of Whole Numbers 0.5 credit hour
Computation skills involving addition, subtraction, multiplication, division and applications of whole numbers. This course may be taken four times for credit. Prerequisite: Consent of instructor is required.(0.5 lecture hour)
MATHEMATICS 0412 Arithmetic of Fractions I 0.5 credit hour
Computation skills involving addition and subtraction of fractions and mixed numbers. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0413 Arithmetic of Fractions II 0.5 credit hour
Computation skills involving multiplication and division of fractions and mixed numbers. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0415 Arithmetic of Decimals 0.5 credit hour
Computation skills involving addition, subtraction, multiplication and division of decimals. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0417 Arithmetic of Percents 0.5 credit hour
Computation skills involving percents, conversions among fractions, decimals and percents including applications. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0418 Arithmetic of Ratio/Proportion 0.5 credit hour
Computation skills involving ratio and proportion. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0420 Arithmetic: Special Topics 0.5 credit hour
Topics include exponents, roots, rounding and estimating. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0422 Arithmetic of Signed Numbers 0.5 credit hour
Computation skills involving addition, subtraction, multiplication and division of signed numbers, and properties of numbers. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0430 Algebra: Factoring 0.5 credit hour
Factoring polynomials and its application in solving equations. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0432 Algebra: Fractions 0.5 credit hour
Computation skills involving addition, subtraction, multiplication and division of algebraic fractions and applications of algebraic fractions. This course may be taken four times for credit. Prerequisite: Consent of instructor is required. (0.5 lecture hour)
MATHEMATICS 0434 Algebra: Graphing 0.5 credit hour
Graph linear and quadratic equations and linear inequalities. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0436 Algebra: Systems of Linear Equations 0.5 credit hour
Solving systems of linear equations including applications by graphing, elimination and substitution. This course may be taken four times for credit..Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0440 Algebra: Quadratic Equations 0.5 credit hour
Solve quadratic equations by factoring and the quadratic formula. This course may be taken four times for credit. Prerequisite: Consent of instructor required. (0.5 lecture hour)
MATHEMATICS 0451 Essentials of Arithmetic I 2 credit hours
Fundamental skills in addition, subtraction, multiplication and division with respect to whole numbers, fractions, ratio and proportion, and decimals. Included are problem-solving techniques with practical application. Equivalent to the first half of Mathematics 0460. This course may be taken four times for credit. (2 lecture hours)
MATHEMATICS 0452 Essentials of Arithmetic II 2 credit hours
Principles of arithmetic, review of fractions, exponents, order of operations, percents and applications, ratio and proportion, and applications. This course may be taken four times for credit. (2 lecture hours)
MATHEMATICS 0455 Fundamentals of Algebra 2 credit hours
Covers essential fundamentals of algebra. Students begin with signed numbers, learn to solve equations and inequalities, apply properties of exponents, and perform fundamental operations with polynomials. Included are problem-solving techniques with practical application. This course may be taken four times for credit. (2 lecture hours)
MATHEMATICS 0460 College Arithmetic 3 credit hours
Principles of arithmetic. Fundamental operations with whole numbers, common fractions and decimals. Percents and applications in the world of business. Rational numbers, exponents and powers. This course may be taken four times for credit. (3 lecture hours)
MATHEMATICS 0485 Algebra Refresher Workshop 0.5 credit hours
Designed as a focused review of the elementary and intermediate algebra techniques and associated problem-solving skills required for a student to be successful in college level math. Students meeting mastery-level performance qualifications in the workshop can take a written departmental exit examination for potential placement. This course can only be taken on a pass/fail basis. Prerequisite: Consent of instructor (0.5 lecture hour)
MATHEMATICS 1100 Business Mathematics 3 credit hours
Applications of mathematics to business transactions. Analysis and solution of the business problems in profit and loss, interest, installment transactions, percent discounts, taxes and payroll. Prerequisite: Mathematics 0460 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test (3 lecture hours)
MATHEMATICS 1102 Mathematics for Health Sciences 3 credit hours
Designed for health science majors. Topics include systems of measurements, use of formulas, dimensional analysis, percents, decimals, fractions, ratio and proportion, direct and inverse variation, solutions, and dosage calculations. Prerequisite: Mathematics 0481 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test (3 lecture hours)
MATHEMATICS 1104 Mathematics for Horticulture 3 credit hours
Designed for horticulture majors only. Topics include fractions, decimals, percents, systems of measurement, dimensional analysis, use of formulas, ratio and proportion, linear equations, perimeter, area, volume, and surface area as related to landscape, mixtures as related to seed, fertilizer and chemicals, estimation, scale drawings, sales including discount and markup, construction as related to landscape, and estimates and bids on landscaping projects. (3 lecture hours)
MATHEMATICS 1108 Perspectives of Mathematics 3 credit hours
The course surveys some of the major ideas of mathematics and relationships to the arts, life sciences, physical sciences, social sciences, games, etc. Topics are selected from number systems, inductive and deductive reasoning, algebraic processes and methods, geometry, probability and statistics. Prerequisites: Demonstrated geometry competency (level 2), and Mathematics 0481 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test (3 lecture hours)
MATHEMATICS 1115 Technical Mathematics I 3 credit hours
For technical/occupational programs. Emphasizes problem-solving skills using elementary algebra, right angle trigonometry, and ratio and proportion. Prerequisite: 1. Mathematics 0481 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test (3 lecture hours)
MATHEMATICS 1120 Mathematical Foundations for Diagnostic Medical Imaging Sonographers 3 credit hours
Designed for Diagnostic Medical Imaging Sonography (DMIS) majors only. Mathematical applications and problem solving in the field of sonography are emphasized. Topics include systems of measurement, dimensional analysis, application of formulas, probability, and statistics. Prerequisite: Consent of Diagnostic Medical Imaging Sonography Coordinator and either Math 0482 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test or a qualifying A.C.T. math score (3 lecture hours)
MATHEMATICS 1218 (IAI M1 904) General Education Mathematics 3 credit hours
Designed to fulfill general education requirements and not designed as a prerequisite for any other college mathematics course. Focuses on mathematical reasoning and the solving of real-life problems, rather than routine skills. Logic and set theory are studied. Two other topics from the following list are to be studied in depth: counting techniques and probability, game theory, geometry, graph theory, statistics, and mathematics of finance. The regular use of calculators and/or computers are emphasized 1220 (IAI M1 901) Quantitative Literacy 3 credit hours
Designed to fulfill general education requirements, and not designed as a prerequisite for any other college mathematics course. Provides the basic numeracy needed by a college graduate to reason about quantities, their magnitudes, and their relationships between and among other quantities. Topics include linear systems, linear programming, analysis and interpretation of graphs, logic and reasoning, descriptive statistics, the normal distribution, statistical inference, estimation and approximation 1321 Mathematics for Elementary School Teachers I 4 credit hours
Designed for elementary education majors. Sets, logic and mathematical reasoning, problem solving, numeration systems, and elementary number theory. Properties, algorithms and computation with the sets of whole numbers, integers, rational and real numbers. One of the requirements for receiving credit in the course is an arithmetic proficiency test that must be passed with a score of at least 80 percent correct. Prerequisite: Demonstrated geometry competency (level 1), and Mathematics 0482 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test or a qualifying A.C.T. math score (4 lecture hours)
MATHEMATICS 1340 History of Mathematics 3 credit hours
The historical development of mathematics and certain mathematical concepts from ancient times to the present, with emphasis given to basic and intermediate mathematics concepts. The focus of this mathematics-driven course will be on the problems mathematicians have faced, and the theory and methodology that were developed to resolve these problems. Prerequisite: Mathematics 1218 (or college equivalent) with a grade of "C" or better (3 lecture hours)
MATHEMATICS 1428 College Algebra with Applications 3 credit hours
The study of algebra with emphasis on applications. This course should not be taken by students planning to enroll in calculus. Topics include, but are not limited to, matrices, functions, conic sections, polynomials, exponential and logarithmic functions, and sequences and series. Prerequisite: Demonstrated geometry competency (level 2), and Mathematics 0482 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test or a qualifying A.C.T math score (3 lecture hours)
MATHEMATICS 1533 (IAI M1 906) Finite Mathematics 4 credit hours
Designed primarily for students planning to major in business or the behavioral, social or biological sciences. Topics include sets, counting techniques, probability, modeling, systems of linear equations and inequalities, matrix algebra, linear programming, Markov chains and game theory. Applications are presented from business and the above sciences4 lecture hours)
MATHEMATICS 1635 (IAI M1 902) Statistics 4 credit hours
Elementary statistics: elements of descriptive and inferential statistics. Communication with data descriptions and graphs. Probability principles and their use in developing probability distributions. Binomial, normal, student-t, chi-square and F distributions. Hypothesis testing, estimation, contingency tables, linear regression and correlation, and one-way ANOVA. Prerequisite: Mathematics 1428 (or college equivalent) with a grade of "C" or better or Mathematics 1431 (or college equivalent) with a grade of "C" or better or Mathematics 1533 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test or a qualifying A.C.T. math score (4 lecture hours)
MATHEMATICS 1820 Selected Topics I 1 to 3 credit hours
Introductory exploration and analysis of selected mathematics 1840 Independent Study 1 to 4 credit hours
Exploration and analysis of topics within MathematicsMATHEMATICS 2115 (IAI M1 905) Discrete Mathematics 3 credit hours
An introduction to the formal study of discrete structures in mathematics. Topics include set theory, combinatorial mathematics, logic, graph theory, Boolean algebra, formal languages3 lecture hours)
MATHEMATICS 2134 (IAI M1 900-B) Calculus for Business and Social Sciences 4 credit hours
Designed primarily for students planning to major in business, or behavioral, social or biological sciences. The basic concepts of differential and integral calculus are taught with emphasis on a wide variety of applications. Prerequisite: Mathematics 1431 (or college equivalent) with a grade of "C" or better or a qualifying score on the mathematics placement test or a qualifying A.C.T. math score (4 lecture hours)
MATHEMATICS 2231 (IAI M1 900-1) Calculus and Analytic Geometry I 5 credit hours
Lines, circles, functions, limits, continuity, the derivative, rules for differentiation of algebraic, trigonometric, and the transcendental functions, related rates, mean value theorem, optimization and curve sketching, differentials, Newton's method, antiderivatives and integration, and the fundamental theorem of calculus. Prerequisite: Mathematics 1431 (or college equivalent) with a grade of "C" or better and Mathematics 1432 (or college equivalent) with a grade of "C" or better, or a qualifying score on the mathematics placement test, or a qualifying A.C.T. math score (5 lecture hours)
MATHEMATICS 2270 Differential Equations 4 credit hours
Equations of first order with applications, homogeneous linear equations of higher order with constant coefficients, non-homogeneous linear equations of higher order with constant coefficients, Laplace transform methods, applications of higher order differential equations, linear equations with variable coefficients, power series solutions, systems of linear equations, and numerical solutions of first order equations. Prerequisite: Mathematics 2233 with a grade of "C" or better (4 lecture hours)
MATHEMATICS 2820 Advanced Selected Topics I 1 to 3 credit hours
Advanced exploration and analysis of selected mathematical |
Product Description
From Amazon
A 1996 revision of a timeless classic originally published in 1941. Highly recommended for any serious student, teacher or scholar of mathematics.
Review
"Can...be read with great profit by anyone desiring general mathematical literacy."--Mathematics Abstracts
"A great book."--Ludwig Otto, Paul Quinn College
"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."--Albert Einstein
"Without doubt, the work will have great influence. It should be in the hands of everyone, professional or otherwise, who is interested in scientific thinking."--The New York Times
"A work of extraordinary perfection."--Mathematical Reviews
"It contains an excellent selection of material for students who have no desire to develop mathematical skills but who may be willing to look briefly into this field of intellectual activity....For the inquiring student who wishes to know what real mathematics is about, or for the trained engineer or physicist who has some interest in the justification of procedures he uses, it should prove a source of great pleasure and satisfaction."--Journal of Applied Physics
"This book is a work of art."--Marston Morse
"This is not a book in philosophy; but there are probably few philosophers who can not gain instruction and clarification from it. It succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods."Journal of Philosophy
"It is a work of high perfection, whether judged by aesthetic, pedagogical or scientific standards. It is astonishing to what extent What is Mathematics? has succeeded in making clear by means of the simplest examples all the fundamental ideas and methods which we mathematicians consider the life blood of our science."--Herman Weyl
"Still a book that all prospective mathematics teachers should read and experience. A rare book that has retained its "freshness" and readability for more than 50 years....Very readable."--Stephen Krulik, Temple University
Courant's 500-page text is not entirely suitable for the layman. Its target audience includes those who enjoy reading and studying mathematics and have a good background through precalculus or higher. "What is Mathematics?" is a mathematics book, not a book about mathematics.
"What is Mathematics?" is not a new book. It was first published in 1941. New editions appeared in 1943, 1945, and 1947. My soft cover fourth edition by Oxford University Press is in its 12 printing.
The authors indicate that it is no means necessary to "plow through it page by page, chapter by chapter". I fully agree. I have skipped around, jumping to chapters of particular interest, but I have now read nearly every chapter.
I initially skipped to page 165 and delved directly into projective geometry (chapter IV), proceeded to topology (chapter V), and then jumped backwards to the beginning to explore the theory of numbers. After moving to geometry, I finally returned to the later chapters on functions and limits, maxima and minima, and the calculus.
Courant engages the reader in discussions on mathematical concepts rather than focusing on applications and problem solving. "What is Mathematics?" is a great textbook for students that have completed a year or more of calculus and wish to pull all of their mathematical learning together before moving on to more advanced studies. I suspect that it would even be welcomed by students that have completed an undergraduate degree in mathematics.
I cannot resist quoting Albert Einstein's comment on What is Mathematics? - "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable."
Richard Courant was a highly respected mathematician. He taught in Germany and in Cambridge and was director of the Institute of Mathematical Sciences at New York University (now renamed the Courant Institute of Mathematical Sciences). Courant has authored other widely acclaimed mathematical texts including Methods of Mathematical Physics (co-authored with David Hilbert) and his popular Differential and Integral Calculus.
Einstein writes..."Easily understandable." And Herman Weyl,..."It is a work of high perfection." It is both for beginners and for scholars. The first edition by Courant and Robbins, has been revised, with love and care, by Ian Stewart. Of the sciences, math stands out in the way some central ideas and tools are timeless. Key math ideas from our first mathematical experiences, perhaps early in life, often have more permanence this way. While the fads do change in math, there are some landmarks that remain, and which inspire generations. And they are as useful now as they were at their inception, the fundamentals of numbers, of geometry, of calculus and differential equations, and more. Much of it is presented with an eye to applications. The book is a classic and a masterpiece. The co-authors are ambitious (and remarkably sucessful)in trying to cover the essetials within the span of 500 plus pages. You find the facts, presented in clear and engaging prose, and with lots of illustrations. The book has been used by generations of readers, and it still points to the future.
This is an interesting and wide ranging book. In the main it presents, develops and explains it's ideas very well, although I did not always find it, as one reviewer, a mister Albert Einstein described it, "easily understandable". I have two minor complaints about this book:
1) Print quality For no apparent reason the text size varies occasionally, and in places the printing is slightly blurred, so that sometimes the subscripts and superscripts on formulae are illegible. Perhaps they skimped on typesetting costs by photoreproducing formulae from the original printing?
2) Incompleteness If you bought this book because the front cover says "...representation of the fundamental concepts and methods of the whole field of mathematics" (another A.E. quote) you may be disappointed to find this is not the case. Trigonometry, for example, is not discussed, except where it crops up in other topics such as applying calculus to trig functions. |
What is applied mathematics?
Applied mathematics is mathematics applied to real world problems. Many areas of mathematics have applications to the world. Some areas of mathematics deal very heavily with application, for example numerical analysis (the mathematics of getting good approximations), differential equations (with lots of applications in physics and engineering, among other areas), and linear algebra.
What kinds of problems do applied mathematicians work on?
An applied mathematician starts with a real world problem posed by an engineer, a biologist, a business executive, or whoever else needs a problem solved. The Mathematician builds a mathematical model from the information surrounding the problem and uses it to get solutions. Then the model may be tested and improved. |
An intensive refresher course in basic mathematics with introductory algebra topics. This course prepares students for MAT 136, Mathematics for the Health Sciences. Topics include fractions, decimals, ratio and proportion, percents, solving linear equations and inequalities, graphing linear equations, and operations and polynomials. College credit will be awarded, but this credit will not count toward a degree. This course is designed to meet the mathematics prerequisite for MAT 136 ONLY and course enrollment is restricted to nursing and health students whose program or program prerequisites require(s) MAT 136. Skills prerequisites: MAT 011, ENG 020 and ENG 060. |
The Advanced Algebra Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers the transformations of functions in Algebra, including what a transformation of a function is and why it is important. Grades 9-College. 35 minutes on DVD. |
Vectors: Grade 10 Grade 10: Vectors. Are vectors physics? No, vectors themselves are not physics. Physics is just a description of the world around us. To describe something we need to use a language. The most common language used to describe physics is mathematics. Vectors form a very important part of the mathematical description of physics, so much so that it is absolutely essential to master the use of vectors. Author(s): Creator not set
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Rights not setCK-12 Geometry (CA Textbook) CK-12's Geometry delivers a full course of study in the mathematics of shape and space for the high school student, relating the ancient logic and modern applications of measurement and description to its essential elements, processes of reasoning and proof, parallel and perpendicular lines, congruence and similarity, relationships within triangles and among quadrilaterals, trigonometry of right triangles, circles, perimeter, area, surface area, volume, and geometric transformations.
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Rights not setEmpirical Research Methods Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl Author(s): Creator not set
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Rights not setAlgorithms The design of algorithms is studied, according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time coPersonalisation Services for Self e-Learning Networks This paper describes the personalisation services designed for self e-learning networks in the SeLeNe project. A self e-learning network consists of web-based learning objects that have been made available to the network by its users, along with metadata descriptions of these learning objects and of the network's users. The proposed personalisation facilities include: querying learning object descriptions to return results tailored towards users' individual goals and preferences; the ability to Author(s): Keenoy Kevin,Poulovassilis Alexandra,Christophides
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Darden MBA International Community and Opportunities Marie Skjold-Joergensen, Class of 2011, talks about the international student community at the University of Virginia Darden School of Business, as well as international opportunities offered through the Full-Time MBA program. Author(s): No creator set
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Bill of Rights On 12 September 1787, during the final days of the Constitutional Convention, George Mason of Virginia expressed the desire that the Constitution be prefaced by a Bill of Rights. Elbridge Gerry of Massachusetts proposed a motion to form a committee to incorporate such a declaration of rights; however the motion was defeated. This lesson examines the First Congress's addition of a Bill of Rights as the first ten amendments to the Constitution. Author(s): No creator set
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7.60 Cell Biology: Structure and Functions of the Nucleus (MIT) The goal of this course is to teach both the fundamentals of nuclear cell biology as well as the methodological and experimental approaches upon which they are based. Lectures and class discussions will cover the background and fundamental findings in a particular area of nuclear cell biology. The assigned readings will provide concrete examples of the experimental approaches and logic used to establish these findings. Some examples of topics include genome and systems biology, transcription, an Author(s): Sharp, Phillip,Young=B This book is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks. Author(s): No creator set
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Greetings from Kingan & Company, Ltd. The company's logo is in the upper left corner of the card. It shows a man at the wheel of a ship. In the center is a drawing of the Kingan & Company Indianapolis facility. It is near a river and has railroad tracks next to it. Some of the buildings are labeled, such as the canning factory and the curing warehouse. Above the picture of the plant, pigs are holding a banner that says "Greetings." Beneath the plant picture a family of pigs is playing on the ice. The father pig is helping the mother Author(s): Creator not set |
This program allows you
to look up formulas quickly, check out different problems and graph the
answers easily as well as put everything together for a lab report. You can
do all that and more using StudyWorks. There are different sections in the
software, which will allow you to do everything from problem solving to
preparing for the SAT IIís.
Click OK, and then follow the
instructions on the screen to install StudyWorks.
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Windows 3.1 or 3.11 you will need version 1.30 or later of the Win32
libraries to run StudyWorks.
The setup will install
StudyWorks on your computer in the directory labeled C:\STUDYWKS and create a
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Windows 95/98:
Insert the StudyWorks CD into
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When installation is
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You can access our sample Web site from the CD. Easy Install requires you to
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Web link feature so you can access the StudyWorks web site. You can also copy
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Calm down - it will be okay. The Algebra Helper software can help you with your homework. It makes your homework faster to do and easier to learn...so don't panic.
We've all been there. We've studied. Done the problems. Asked the parents. For hours we scribbled, calculated, erased, scribbled, calculated and erased some more. We've studied the books and asked the teachers, but we're still left confused. Many algebra tutorials teach you how to solve math equations that barely look like what you're trying to do. When you're done solving those, you're still left wondering how to solve yours.
How about a program that can help you solve the equations that you actually have to solve? Why not learn how to do do your own homework faster and more easily than hoping your parents remember how to do it from way back when they were in school? Cut the time it takes to do your homework in half and then some. Once you plug in your algebra equation, the program will go through it with you step by step. Instead of fighting to figure out where you went wrong, you can learn it at the same time you're doing your homework. No more math labs, tutoring sessions with the teacher, embarassement because you didn't know the answer or asking your parents if they remember how to do this stuff.
Stop chewing on your pencil and punching the number keys on your calculator. There's hope. Take a look at the demo and see how incredibly helpful this program is. Any reason in particular you're still reading this? No? Okay, give it a try and go finish your homework! You'll be amazed at how quickly you'll be done and how well you'll understand it.
Posted: Fri Mar 14, 2003 3:11 pm ; Post subject: trinomial solver
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Strategies to Improve Problem Solving Skills
1. Use Time and Resources Effectively
Work on courses regularly: keep up so you can build on past knowledge (sequential learning), and get help quickly for difficulties. Do all the questions assigned, rather than dividing questions among group members, as you will get more practice with the concepts your Professor expects you to know. Aim for accuracy, then speed. Start assignments at least a week ahead of the due date, so you have time for help if needed.
Use study groups to compare completed solutions to assigned problems. Teaching someone is a very effective learning and study technique.
Choose problems wisely: learn to apply a specific concept to solve a variety of related problems. Start with simpler ones, and work up. Identify the relevant concept and practice until you know when and how to apply it, i.e. you may not need to do all questions.
Set a time limit: attempt a new problem every @ 15-20 minutes. If you can't complete a problem, check your "thinking strategies" and change to a new problem. Get help with the problems you couldn't complete, at tutorial, etc.
Do some uncalculated solutions: If you are confident in your calculations-set up the solution but don't finish the calculation.
Learn the necessary background and skills: find out from professor, course outline, etc. what the course involves and upgrade before the course begins if you don't feel confident about the prerequisites.
Find and use help resources: use tutors, professors, TAs, friends, text, internet. For example: in accounting, economics, and finance texts, it is common to find examples that are quite similar to the problems at the end of the chapter. Work through the logic of the examples to develop a better understanding of how best to start the homework problems, if you run into trouble.
2. Develop Strategies to Organize Your Thinking
Quantitative Concept Summary Strategy
Concepts are general organizing ideas, are there are often very few of them taught in a course, along with their many applications (ie. the spiral of learning). Key concepts may be identified by:
reading the learning objectives on the course outline or the course description,
referring to the lecture outline to identify recurring themes,
thinking about the common aspects of problems you are solving.
Learn and understand the small amount of information essential to each concept. If in doubt, ask the professor what is important for you to "get".
General Problem Solving Method
Use a methodical, thorough approach to solve problems logically from first principles. Refer to the self-assessment questionnaire by Woods et al. (2000) in this guide to remind yourself of target activities you need to focus on.
Steps involve:
Engage with the problem
Define and understand the problem- what is being asked? Express your thinking in several ways, such as verbally, graphically or pictorially, and finally mathematically
Explore links between the current problem and related ones you have previously solved.
Decision Steps Strategy
This strategy is a specific application of the General Problem Solving Strategy described above, and is suitable for use in statistics, accounting and other applied problem solving situations.
During the lecture or when reading course notes, focus on the process of solving the problem, instead of on the computation. When your professor is lecturing, listen to their comments on how steps are inked from one to another. This helps you identify the "decision steps" that lead to correct application of a concept. Ask yourself "Why did I move from this step to this step?" |
Euclidean plane geometry is one of the oldest and most beautiful of subjects in mathematics, and Methods for Euclidean Geometry explores the application of a broad range of mathematical techniques to the solution of Euclidean problems.
The book presents numerous problems of varying difficulty and diverse methods for solving them. More than a third of the book is devoted to problem statements, hints, and complete solutions. Some exercises are repeated in several chapters so that students can understand that there are various ways to solve them.
The book offers a unique and refreshing approach to teaching Euclidean geometry, which can serve to enhance students' understanding of mathematics as a whole.
Having completed a survey of lines, polygons, circles, and angles, we come to another collection of well-known figures in the plane: ellipses, parabolas, and hyperbolas. In what situations do these figures appear? What is our motivation for studying them?
One way in which these figures arise quite naturally is when we try to find answers to questions of the type, "What is the set of all points (loci) of a plane that satisfy a given property?" Another is when we wish to understand the trajectory of a moving point. Yet a third situation occurs when we seek to describe the intersection of two surfaces in space. |
The Coffeecup Caustic - Roy Williams
You are drinking from a cylindrical cup in the sunshine. Sometimes, when the sun shines into the cup, you can see a crescent of light as the sunshine reflects from the inside of the cup onto the surface of the drink. This Java applet illustrates the optics
...more>>
Colégio de Gaia, Grupo de Matematica
Math resources in Portuguese: Galeria de Sketches - a gallery of JavaSketchpad and Geometer's Sketchpad problems and sketches including the Pythagorean theorem (o Teorema de Pitágoras), Vector Addition (Adicao de Vectores), cutting a cube/parallelepiped
...more>>
College Entrance Exam Math Prep - EduCAD
A free, interactive library of the most complex math problem types found on the SAT® or ACT® college entrance exams. The "show next step" button provides a hint about the strategy to take; a correct answer submitted with the "check answer" button
...more>>
Complex Numbers & Trig - Alan Selby
Complex Numbers and the Distributive Law for Complex Numbers, offering a short way to reach and explain trigonometry, the Pythagorean theorem, trig formulas for dot- and cross-products, the cosine law, and a converse to the Pythagorean theorem. A geometricnexions - Rice University
Connexions is a non-profit start-up launched at Rice University in 1999 that aims to reinvent how we write, edit, publish, and use textbooks and other learning materials. It is a global repository of educational content that can be described in four words
...more>>
Constructor - Soda
Constructor animates and edits two-dimensional models made out of masses and springs. The springs can be controlled by a wave to make pulsing muscles, and you can construct models that bounce, roll, walk, etc. Try some of the ready-made models or build
...more>>
Convex Hull Algorithms - Tim Lambert
An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from
...more>>
Cool School Tools - Tim Fahlberg
Shockwave whiteboard movies on algebra, geometry, probability, statistics, the mathematics of finance, and more. A whiteboard movie (WM) is a multimedia screen recording of writing on an electronic whiteboard (real or virtual) with or without voice and/or
...more>>
CopyCat - Jim Morey
A Java game that revolves around replicating a picture created by several patterned faces of a solid object (like a cube), challenging the mind to understand complex geometrical structures and symmetry. To do well at the game, the player must first become
...more>> |
College Math
In this section
About This Course
Course Name/Code: College Mathematics, ASMA 103 Catalog Description: Designed to equip the student with mathematical reasoning skills and to introduce the student to a diversity of mathematical areas. Topics will include problem solving, set theory, logic, data interpretation, the real number system, introduction to algebra, functions, and an introduction to geometry. *Prerequisites: This class is not open to students who have previously obtained a waiver of three mathematics credits of the general education requirements or have been awarded three credits by CLEP examination. Credits/Hours: 3
Instructors and Texts
Instructors Who Teach This Course:Mr. Melvin Cacayorin
Required Text(s) Students must purchase and possess the required text(s) by the first day of class. Order early:
Blitzer, Robert. Thinking Mathematically. 4th Edition
ISBN 10- 0-13-175204-9
ISBN 13- 978-0-13-175204-7
This book is also available in an e-version
ISBN 10- 0321646193
ISBN 13- 9780321646194
Course Workload Preview
The following preview of anticipated course workload is subject to instructor change. |
Math 8 for 7th Graders is an advanced seventh grade course designed to prepare students for the rigor of high school mathematics classes. This standards-based course completes the middle school curriculum's intent to help students make the transition from concrete arithmetic to abstract algebraic thinking. Math 8 for 7th Graders includes pre-algebra concepts and skills that set high expectations for all students. It makes provisions for enrichment and acceleration for advanced students. The course emphasizes algebraic thinking and applies it to other aspects of mathematics including geometry, measurement, probability, and statistics.
The content and pace of the course are rigorous. Tutoring schedule is posted on the Homework Calendar under Lists and Libraries.
Course Content Standards
This curriculum provides a close correlation to South Carolina 's eighth grade math standards where students make the transition from arithmetic to algebra. The standards are as follows:
Mathematical Processes
Standard 8-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation
8-1.5 Generalize mathematical statements based on inductive and deductive reasoning.
8-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.
8-1.7 Generalize connections among a variety of representational forms and real-world situations.
8-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.
Number and Operations
Standard 8-2: The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the approximation of cube and square roots, and the application of proportional reasoning.
8-3.3 Use commutative, associative, and distributive properties to examine the equivalence of a variety of algebraic expressions.
8-3.4 Apply procedures to solve multistep equations.
8-3.5 Classify relationships between two variables in graphs, tables, and/or equations as either linear or nonlinear.
8-3.6 Identify the coordinates of the x- and y-intercepts of a linear equation from a graph, equation, and/or table.
8-3.7 Identify the slope of a linear equation from a graph, equation, and/or table.
Geometry
Standard 8-4: The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane.
Indicators
8-4.1 Apply the Pythagorean theorem.
8-4.2 Use ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane.
8-4.3 Apply a dilation to a square, rectangle, or right triangle in a coordinate plane.
8-4.4 Analyze the effect of a dilation on a square, rectangle, or right triangle in a coordinate plane.
Measurement
Standard 8-5: The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.
Indicators
8-5.1 Use proportional reasoning and the properties of similar shapes to determine the length of a missing side.
8-5.2 Explain the effect on the area of two-dimensional shapes and on the volume of three-dimensional shapes when one or more of the dimensions are changed.
8-5.3 Apply strategies and formulas to determine the volume of the three-dimensional shapes cone and sphere.
8-5.4 Apply formulas to determine the exact (pi) circumference and area of a circle.
8-5.5 Apply formulas to determine the perimeters and areas of trapezoids.
8-5.6 Analyze a variety of measurement situations to determine the necessary level of accuracy and precision.
8-5.7 Use multistep unit analysis to convert between and within U.S. Customary System and the metric system.
Data Analysis and Probability
Standard 8-6: The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample.
Indicators
8-6.1 Generalize the relationship between two sets of data by using scatterplots and lines of best fit.
8-6.2 Organize data in matrices or scatterplots as appropriate.
8-6.3 Use theoretical and experimental probability to make inferences and convincing arguments about an event or events.
8-6.4 Apply procedures to calculate the probability of two dependent events.
8-6.5 Interpret the probability for two dependent events.
8-6.6 Apply procedures to compute the odds of a given event.
8-6.7 Analyze probability using area models.
8-6.8 Interpret graphic and tabular data representations by using range and the measures of central tendency (mean, median, and mode).
Homework Policy : To provide extra practice and mastery of skills, homework is given Monday through Thursday. Students should record daily assignments in an appropriate location. Homework grade reflects completeness. Problems are gone over in class, and students are expected to make their own corrections.
Missed Work/Make-up Policy: Students have five school days to make up tests or quizzes missed during an excused absence. It is the student's responsibility to ask the teacher when tests and quizzes can be made up.
Grading Scale:
93 – 100 A 86 – 92 B 77 – 85 C 70 – 76 D Below 70 F
Rules for Student Behavior :
1. Enter the room in a quiet and orderly manner. 2. Be seated and prepared to begin class promptly. 3. Bring all necessary materials and completed assignments. (Pencils are to be sharpened before class.) 4. Follow directions the first time they are given. 5. Raise your hand and wait to be recognized before speaking or leaving your seat. 6. Show respect and consideration for others. 7. No gum, candy food, drink, or hats allowed. 8. Obey all school and team rules.
Consequences for Violating Class and School Rules: The school-wide disciplinary steps will be followed:
Severe clause: Severe disruptions or violations will be referred immediately to an administrator. Steps start over second semester.
Tardy Policy and No ID Policy: refer to student handbook which is posted on the school website and printed in the student's agenda.
Presentation of Rules and Procedures : It is the student's responsibility to read and be aware of school rules, as stated in the student handbook. Additionally, teachers will explain, clarify, and emphasize rules during the first few days of school. Rules will also be posted in the room as a daily reminder of expectations.
Procedures for Non-Instructional Routines: Any student who needs to leave the room, for any reason, will receive teacher-issued cardstock to use as a pass. Any student who is absent is responsible for collecting their makeup work on the day they return to school.
Communication with Parents: If you have a question or concern, please let me know. You may …
· send a note or write a note in your child's agenda · call me at school at 355-2172 · send an email to [email protected] · call 7th grade guidance counselor, at 355-2117 to schedule a conference |
This book presents a wide range of problems connected with rational approximations of numbers and analytic functions. These problems touch on many topics in contemporary analysis, such as analytic functions, orthogonal polynomials, spectral theory of operators, and potential theory. Motivated by the development of the theory of Padé approximants and the current application of this theory in related disciplines, the authors present an introduction to this circle of ideas. The book is intended for students and future researchers interested in function theory and number theory.
Reviews
"A comprehensive introduction for students and future researchers to topics that are nowadays undergoing intensive development." |
mathway
Mathway is a Web calculator that not only solves math problems for you, but also shows you how it got to the answer with step-by-step directions. It's the kind of service that would have utterly ruined me in middle school if I had wanted to cruise through the stacks of homework without doing any of the actual computations.
Mathway covers several types of math genres, including high school level stuff like trigonometry and calculus. It'll also take any "basic math," like what you'd do with a calculator, although it's kind of a waste since … Read more |
A good physics book besides Giancoli?
A good physics book besides Giancoli?
Hey!
I'm a junior in high school who's curious and determined to figure and (and retain the knowledge afterwards) how the world works. I'm enrolled in AP physics (i think it was B) but i don't really like how things are explained in our Giancoli book. By no means is it a bad book but I think he focuses too much emphasis on algebraic proofs than explanations (i don't think memorizing formulas is a good way to understanding physics). So what are your recommendations? I'm taking calculus A right now and am proficient in that course.
is conceptual physics by Hewitt any good? I only have enough money to buy 1 book right now. Thanks for your input.A good physics book besides Giancoli?
Quote by Kwally3Feynman uses intuition and philosophy, it is not very mathematically emphasized. It would let you "understand" physics.
there's philosophy in physics??
I'm now super hyped. Unless no one else suggests anything by this afternoon, I'm going to purchase them.
When you say it's not mathematically emphasized, do you mean he provides you with the knowledge to derive formulas yourself?
And, just to suppress a side thought, it's definitely not one of those books that you have a great time reading but have no idea how
to apply the knowledge afterwards right? |
Lecture 30: Solving a quadratic by factoring
Embed
Lecture Details :
factoring quadratics
Course Description :
This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II. |
cise Calculator Tutorial
The format for the tutorial is different. It is more 'show and tell'. The calculator is a Scientific Programmable Calculator (usually people are concerned and do not like the math or advanced calculators). The idea is to give the problems with how to do, then they can just change the variables (where you put A= 5 - or some number and then all they need to do is change the variables - [the number where A= ??] and it will work the problem. Or see how the calculator is programmed and write their own programs. The easier the calculator is to use, the more chance they will use it (the calculator is FREE).
- How can I change it to make it better (all areas). You can download the calculator and use it (FREE). More examples will be posted as I get time.
-
Thank You
falcon
My error. The site is the page Precise Calculator Manual (the link) The Calculator is the link in the banner 'Precise Calculator Download' also there is 'Precise Calculator Examples'. These should make it easier to use and understand. My goal is to make it easy, so anything that needs to be clarified is what I am looking for. I have been programming and setting up calculators (different makes and models) so I miss the concepts or areas that you don't understand because many I take for granted. Mostly using TI calculators and programming in Basic, But many free ones are able to achieve the same results and this is one of the better FREE ones and is easy to program and use (also is better than some expensive ones). I didn't write the calculator program, just trying to help students be able to use it to calculate some advanced math.
-
Thank You
falcon
Good idea! At this stage it's like BASIC with some buttons around.
To make really quick improvements, alter it's syntax:
1. To automatically PRINT raw expressions (i.e. "2+2" line should print "4")
2. To automatically ASK for unknown variables (i.e. "2*X+5" should ask with popup for X value and then print the result).
In general, you should do this as web service for people to calculate online and share common library of macroses.
Check top of page 'Related Articles' "Download Precise Calculator". There you should see many Macros that you can 'copy and paste' to the calculator and run. Then add to your stored Macros. We are adding to the Macros every week, plus we intend to add some line-by-line descriptions for some of the Macros. Make it as easy a possible to use this FREE Programmable Scientific Calculator.
- Thank You
falcon |
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An equation is a formal mathematical equation (with an optional rather than a required title).
If the MathML Module is used, equation can also contain the mml:math element.
Processing expectations
Formatted as a displayed block. For an inline equation, use inlineequation.
Processing systems that number equations or build a table of equations at the beginning of a document may have difficulty correctly formatting documents that contain both equations with titles and equations without titles. You are advised to use informalequation for equations without titles. |
This course examines an important and interesting part of the history of mathematics and, more generally, the intellectual history of human kind: the history of mathematics in the Islamic world. Some of the most fundamental notions in modern mathematics have their roots here, such as the modern number system, the fields of algebra and trigonometry, and the concept of algorithm, among others. In addition to studying specific contributions of medieval Muslim mathematicians in the areas of arithmetic, algebra, geometry, and trigonometry in some detail, we will examine the context in which Islamic science and mathematics arose, and the role of religion in this development. The rise of Islamic science and its interactions with other cultures (e.g., Greek, Indian, and Renaissance Europe) tell us much about larger issues in the humanities. Thus, this course has both a substantial mathematical component (60-65 percent) and a significant history and social science component (35-40%), bringing together three disciplines: mathematics, history, and religion. The course is a part of the Islamic Civilization and Cultures Program, and fulfills the QR requirement. No prerequisite is needed beyond high school algebra and geometry (but a solid knowledge in algebra and geometry is needed).
This course focuses on choosing, fitting, assessing, and using statistical models. Simple linear regression, mulitple regression, analysis of variance, general linear models, logistic regression, and discrete data analysis will provide the foundation for the course. Classical interference methods that rely on the normality of the error terms will be thoroughly discussed, and general approaches for dealing with data where such conditions are not met will be provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, will be presented. Students will use statistical software throughout the course to write and present statistical reports. The culminating project will be a complete data analysis report for a real problem chosen by the student. The MATH 106-206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science, and many other fields. Prerequisite: MATH 106 or MATH 116. Offered every springThis course introduces students to mathematical reasoning and rigor in the context of set-theoretic questions. The course will cover basic logic and set theory, relations--including orderings, functions, and equivalence relations--and the fundamental aspects of cardinality. Emphasis will be placed on helping students in reading, writing, and understanding mathematical reasoning. Students will be actively engaged in creative work in mathematics. Students interested in majoring in mathematics should take this course no later than the spring semester of their sophomore year. Advanced first-year students interested in mathematics are encouraged to consider taking this course in their first year. (Please see a member of the mathematics faculty if you think you might want to do this.) Prerequisite: MATH 213 or permission of instructor. Offered every semester.
This course will focus on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are highly useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising often in fields such as computer science, physics, chemistry, biology, and economics. In this course, we will use a computer algebra system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality, and diagonalization. Applications will be included throughout the course. Prerequisite: MATH 213. Offered every fall.
Looking at a problem in a creative way and seeking out different methods toward solving it are essential skills in mathematics and elsewhere. In this course, students will build their problem-solving intuition and skills by working on challenging and fun mathematical problems. Common problem-solving techniques in mathematics will be covered in each class meeting, followed by collaboration and group discussions, which will be the central part of the course. The course will culminate with the Putnam exam on the first Saturday in December. Interested students who have a conflict with that date should contact the instructor. Prerequisite: MATH 112 or equivalent.
This course will explore the theory, structure, applications, and interesting consequences when probability is introduced to mathematical objects. Some of the core topics will be random graphs, random walks and Markov processes, as well as randomness applied to sets, permutations, polynomials, functions, integer partitions, and codes. Previous study of all of these mathematical objects is not a prerequisite, as essential background will be covered during the course. In addition to studying the random structures themselves, a concurrent focus of the course will be the development of mathematical tools to analyze them, such as combinatorial concepts, indicator variables, generating functions, discrete distributions, laws of large numbers, asymptotic theory, and computer simulation. Prerequisite: MATH 112 or permission of the instructor. Offered every other year.
Patterns within the set of natural numbers have enticed mathematicians for well over two millennia, making number theory one of the oldest branches of mathematics. Rich with problems that are easy to state but fiendishly difficult to solve, the subject continues to fascinate professionals and amateurs alike. In this course, we will get a glimpse at both the old and the new. In the first two-thirds of the semester, we will study topics from classical number theory, focusing primarily on divisibility, congruences, arithmetic functions, sums of squares, and the distribution of primes. In the final weeks we will explore some of the current questions and applications of number theory. We will study the famous RSA cryptosystem, and students will be reading and presenting some current (carefully chosen) research papers. Prerequisite: MATH 222. Offered every other year.
Abstract algebra is the study of algebraic structures that describe common properties and patterns exhibited by seemingly disparate mathematical objects. The phrase "abstract algebra" refers to the fact that some of these structures are generalizations of the material from high school algebra relating to algebraic equations and their methods of solution. In Abstract Algebra I, we focus entirely on group theory. A group is an algebraic structure that allows one to describe symmetry in a rigorous way. The theory has many applications in physics and chemistry. Since mathematical objects exhibit pattern and symmetry as well, group theory is an essential tool for the mathematician. Furthermore, group theory is the starting point in defining many other more elaborate algebraic structures including rings, fields, and vector spaces. In this course, we will cover the basics of groups, including the classification of finitely generated abelian groups, factor groups, the three isomorphism theorems, and group actions. The course culminates in a study of Sylow theory. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math, and elementary number theory. There will also be a couple of projects illustrating how a formal algebraic structure can empower one to tackle seemingly difficult questions about concrete objects (e.g., the Rubik's cube or the card game SET). Finally, there will be a heavy emphasis on the reading and writing of mathematical proofs. Prerequisite: MATH 222 or permission of the instructor. Junior standing is usually recommended. Offered every other fall. |
Mathematics (MATH)
MATH 066 Pre-Algebra (3 credits)
This course is a comprehensive study of foundational mathematical skills which should provide a strong mathematical underpinning for further study. Topics include principles and applications of decimals, fractions, the number line, ratio, signed operations, properties of operations, order of operations, numerical factoring, measurement, unit conversion, perimeter, and area. Upon completion, students should be able to perform fundamental computations and solve multistep mathematical problems using the four problems solving steps in Polya's How To Solve It.
MATH 086 Math 086 – Introductory Algebra (3 credits)
This course establishes a foundation in algebraic concepts and problem solving. Topics include signed numbers, exponents, order of operations, variables, algebraic expressions, proportions, introductory planar geometry, simplifying, linear equations, graphing lines in the plane, formulas, polynomial operations, and factoring. Upon completion, students should be able to apply the above concepts in problem solving using Polya's four steps.
MATH 102 Survey of Mathematics (3 credits)
Prerequisite: MATH 096, or Placement test
Introduces students to a broad variety of mathematical applications. Emphasis on topics that are applicable to students' lives. Develops students' understanding of topics such as problem solving, geometry and measurement, personal finance, counting techniques, probability and statistics.
MATH 110 College Algebra (3 credits)
Prerequisite: MATH 096, or Placement test
Builds on the fundamentals of Algebra developed in basic and intermediate algebra courses. This course is to extend the students knowledge and skills in Algebra through practical applications related to real world situations.
MATH 120 College Trigonometry (3 credits)
Prerequisite: MATH 110
Designed for students interested in pursuing other courses in mathematics, sciences, or engineering. It develops proficiency in trigonometry and its underlying concepts. It relies on technology and critical thinking in solving and analyzing real world problems. |
Riverside, RI Precalculus...I ...It's not unusual for some courses to include solid geometry and advanced algebra, such as synthetic division, sequences, and series. These subjects form the foundations of calculus, and not mastering these topics will haunt students when they get into calculus, particularly integral calculus and... |
Download "All Aboard for Kindergarten Math " by Alison Cancilliari for FREE. Read/write reviews, email this book to a friend and more...
All Aboard for Kindergarten MathComments for "All Aboard for Kindergarten Math "
As I was writing my e book 365 v 10 fun activities for kids at home, I came across this e book. So interesting, practical and easy to do, not only helped my kg son but also helped me in fine tuning my own writing!
Most descriptions of physical systems, as used in physics, engineering and, above all, in applied mathematics, are in terms of partial differential equations. This text, presented in three parts, introduces all the main mathematical ideas that are needed for the construction of solutions. The material covers all the elements that are encountered in any standard university study: first-order equati... |
Mathematics is the academic discipline that involves the study of such concepts as quantity, structure, space and change. Mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been a part of individual and group life.
For classes slated to graduate in 2009, 2010, or 2011, the math courses taken by a student will depend on whether the student is pursuing a college prep or tech prep diploma. These courses are based on Georgia's Quality Core Curriculum objectives. They include:
Pre-Algebra (Tech & Career)
Algebra I (College Prep)
Algebra I (Tech & Career)
Euclidean Geometry (Either level)
Algebra II (College Prep)
Algebra III (College Prep)
Trigonometry (College Prep)
Math Money Management (Either level)
Pre-Calculus (College Prep)
AP Calculus (College Prep)
For classes scheduled to graduate in 2012 and after, students will be taking courses aligned with Georgia's Performance Standards. Those courses include: |
Summary: Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's BASIC MATHEMATICS FOR COLLEGE STUDENTS, Fourth Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, mathematics is like a foreign language. They have difficulty translating the words, their meanings, and how they apply to problem solving. Emphasizing the "language of mathematics," the text's fu...show morelly ...show less
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How long does it take on avg. to finish Spivak's Calculus book?
How long does it take on avg. to finish Spivak's Calculus book?
i would like to gain a deeper understanding of Calculus so i'm planning on self-studying more on the side. i will do majority of my studies during winter break but i'd like to know long it takes a student who has already taken Calculus 2 to finish his book?
i know it's dependent on the person, but i'm committed and would just like to know.
Why not just get a regular analysis book like Pugh? He explains things very well. I don't think Spivak covers metric spaces or topology. Spivak is more like a half calculus/ half analysis book. In my opinion, it is pretty overrated.Here is the book.
It's not something you really want to do for speed...figure first pass over the course of a few months, maybe? Not full time, obviously. You don't want to do it as a block, anyway, you need time to digest & rest. |
This course is designed to provide a study in mathematical ideas suitable for education majors and those needing course work for teacher re-certification. The topics covered will include number sense, concepts and operations, measurement, geometry and spatial sense, algebraic thinking, data analysis and probability. The topics are in alignment with the National Council of Teachers of Mathematics standards, the Sunshine State Standards, math curriculum of Marion, Citrus and Levy counties, and the FCAT. |
Pre-Algebra: Percents (Resource Book Only) eBook
Grade 6|Grade 7|Grade 8|Grade 9|Grade 10|Grade 11|Grade 12
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Price:5.00$4.25MathSkills reinforces math in three key areas: Pre-Algebra, Geometry, and Algebra. These reproducible activities supplement any math textbook. Pages can be used in the classroom as lesson previews or reviews. The activities are perfect for homework or end-of-unit quizzes. |
2011-11-02 11:00 - 11:45
Location: Ämnestorget för matematik - rum 1
Lecturers: Emmanuel Schanzer.
Description
Researchers and educators have viewed algebraic functions as a foundational concept in mathematics since the turn of the century, but many students struggle to master the concept. Starting in the 1960s, some have viewed computer programming as a vehicle for exploring functions, but the results have been mixed at best. This talk will use current research in the field of mathematical education and cognitive science to analyze previous attempts, and discuss the novel approach taken by Bootstrap, a curriculum that teaches children to program their own videogames using an algebraic programming language and mathematical activities to drive their learning. |
Monroe Township Schools
Monroe Township Schools
Curriculum Management System
Algebra 1 A/B
Grade 9
July 2010
* For adoption by all regular education programs Board Approved:
as specified and for adoption or adaptation by
all Special Education Programs in accordance
with Board of Education Policy # 2220.
Table of Contents
Monroe Township Schools Administration and Board of Education Members Page 3
Acknowledgments Page 4
District Vision, Mission, and Goals Page 5
Introduction/Philosophy/Educational Goals Pages 5-6
Core Curriculum Content Standards Page 7
Scope and Sequence Pages 8-11
Algebra I Core Content Overview Pages 12-14
Goals/Essential Questions/Objectives/Instructional Tools/Activities Pages 15-67
Benchmarks Page 68
2
MONROE TOWNSHIP SCHOOL DISTRICT
ADMINISTRATION
Dr. Kenneth Hamilton, Superintendent
Mr. Jeff Gorman, Assistant Superintendent
Ms. Sharon M. Biggs, Administrative Assistant to the District Superintendent
BOARD OF EDUCATION
Mr. Lew Kaufman, President
Mr. Marvin I. Braverman, Vice President
Mr. Ken Chiarella
Mr. Mark Klein
Ms. Kathy Kolupanowich
Mr. John Leary
Ms. Kathy Leonard
Mr. Louis C. Masters
Mr. Ira Tessler
JAMESBURG REPRESENTATIVE
Ms. Patrice Faraone
Student Board Members
Ms. Reena Dholakia
Mr. Jonathan Kim
3
Acknowledgments
The following individuals are acknowledged for their assistance in the preparation of this Curriculum
Management System:
Writers Names: Jaclyn E. Varacallo
Technology Staff: Al Pulsinelli
Reggie Washington
Secretarial Staff: Debby Gialanella
Gail Nemeth
4
Monroe Township Schools
Vision, Mission, and Goals
Vision Statement
The Monroe Township Board of Education commits itself to all children by preparing them to reach
their full potential and to function in a global society through a preeminent education.
Mission Statement
The Monroe Public Schools in collaboration with the members of the community shall ensure that all
children receive an exemplary education by well trained committed staff in a safe and orderly
environment.
Goals
Raise achievement for all students paying particular attention to disparities between subgroups.
Systematically collect, analyze, and evaluate available data to inform all decisions.
Improve business efficiencies where possible to reduce overall operating costs.
Provide support programs for students across the continuum of academic achievement with an
emphasis on those who are in the middle.
Provide early interventions for all students who are at risk of not reaching their full potential.
5
INTRODUCTION, PHILOSOPHY OF EDUCATION, AND EDUCATIONAL GOALS
Philosophy
Monroe Township Schools are committed to providing all students with a quality education resulting in life-long learners who can
succeed in a global society. The mathematics program, grades K-12, is predicted on that belief and is guided by the following six
principals as stated by the National Council of Teachers of Mathematics (NCTM) in the Principles and Standards for School
Mathematics, 2000. First, a mathematics education requires equity. All students will be given worthwhile opportunities and strong
support to meet high mathematical expectations. Second, a coherent mathematics curriculum will effectively organize, integrate, and
articulate important mathematical ideas across the grades. Third, effective mathematics teaching requires the following: a) knowing
and understanding mathematics, students as learners, and pedagogical strategies, b) having a challenging and supportive classroom
environment and c) continually reflecting on and refining instructional practice. Fourth, students must learn mathematics with
understanding. A student's prior experiences and knowledge will actively build new knowledge. Fifth, assessment should support the
learning of important mathematics and provide useful information to both teachers and students. Lastly, technology enhances
mathematics learning, supports effective mathematics teaching, and influences what mathematics is taught.
As students begin their mathematics education in Monroe Township, classroom instruction will reflect the best thinking of the
day. Children will engage in a wide variety of learning activities designed to develop their ability to reason and solve complex problems.
Calculators, computers, manipulatives, technology, and the Internet will be used as tools to enhance learning and assist in problem
solving. Group work, projects, literature, and interdisciplinary activities will make mathematics more meaningful and aid understanding.
Classroom instruction will be designed to meet the learning needs of all children and will reflect a variety of learning styles.
In this changing world those who have a good understanding of mathematics will have many opportunities and doors open to
them throughout their lives. Mathematics is not for the select few but rather is for everyone. Monroe township Schools are committed
to providing all students with the opportunity and the support necessary to learn significant mathematics with depth and understanding.
This curriculum guide is designed to be a resource for staff members and to provide guidance in the planning, delivery, and assessment
of mathematics instruction.
Educational Goals
Algebra I is the first course of the college preparatory sequence. It is designed to provide an in-depth analysis of the real world
system and introduce process of algebra. Topics included are: data analysis, roots and powers, simplify mathematical expressions,
linear equations, graphing linear equations, theoretical and experimental probability, linear inequalities, systems of equations and
inequalities, polynomial equations, quadratic functions, graphing quadratic functions, mathematical models, functions, matrices, and
solve rational equations. The A/B curriculum is designed to teach and remediate with the same instructor so as to aid students in
meeting all the standards and requirements to pass the End of Course Algebra 1 Exam.
6
New Jersey State Department of Education
Core Curriculum Content Standards
A note about Common Core State Standards for Mathematics
The Common Core State Standards for Mathematics were adopted by the state of New Jersey in 2010. The standards referenced in
this curriculum guide refer to these new standards and may be found in the Curriculum folder on the district servers. A complete copy
of the new Common Core State Standards for Mathematics and the end of year algebra 1 test content standards may also be found at:
7
Algebra 1 A/B
Scope and Sequence
Quarter I
Big Idea I: Representation and Modeling with Variables Big Idea II: Equivalence
I. Variables in Algebra I. Absolute Value
a. Writing and Evaluating Variable Expressions II. Graphing and Comparing Real Numbers on a Number Line
b. Evaluating Simple Interest III. Addition and Subtraction of Real Numbers
II. Expressions Containing Exponents IV. Multiplication and Division of Real Numbers
III. Order of Operations V. Distributive Property
IV. Equations and Inequalities
a. Checking and Solving Equations
b. Checking Solutions of Inequalities
V. Translating Verbal Phrases to use in Algebraic Models
a. Translating verbal phrases into Algebra
b. Using verbal models
VI. Functions
a. Input-Output tables
b. Domain and Range
Big Idea III: Connections and Data Analysis Big Idea IV: Equivalence/ Representation & Modeling with
Variables
I. Construct and Interpret Data Displays
a. Line Graph I. One-Step Equations
b. Bar Graph II. Multi-Step
c. Box and Whisker Plots a. Combining like terms
d. Stem and Leaf Plots b. Distribution
II. Probability and Odds c. Multiplying by reciprocals
a. Experimental vs. Theoretical d. Variables on Both Sides
b. Combinations and Permutations e. Rational Coefficients
i. Using a Graphing Calculator f. Reciprocal Property and Cross Products
III. Measures of Central Tendency III. Using Linear Equations for Problem Solving
IV. Rates, Ratios, Proportions, Percents a. Translating verbal models
b. Drawing a diagram
c. Using tables to solve
d. Using graphs to solve
IV. Transforming Formulas
Course Quarterly Benchmark Assessment: (Higher level 5-10 questions,
45 minutes)
8
Quarter II
Big Idea V: Representation & Modeling with Big Idea VI: Linearity
Variables/Linearity
I. Slope-Intercept Form
I. Plotting Cartesian Coordinates II. Point- Slope Form
II. Scatterplots III. Writing an Equation
a. Graphing Data a. Given two points
III. Graphing Linear Equations b. Given a point and slope
a. Using Input-Output Table c. Given a point and a line parallel
b. Using Intercepts d. Given a point and a line perpendicular
c. Using Slope and y-intercept IV. Converting to Standard Form
d. Horizontal and Vertical Lines V. Reintroducing Scatterplots and Predicting with Linear Models
e. Using a Graphing Calculator a. Graphing Data
IV. Solving Linear Equations Using Graphs b. Calculate Line of Best Fit by Hand
a. Graphical Check for a Solution c. Calculate Line of Best Fit with Graphing Calculator
b. Solving an Equation Using a Graph VI. Graphing Absolute Value Equations
c. Approximating Solutions Using a Graph a. Using Input-Output Table
V. Functions vs. Relations b. Using Vertex and Slope
a. Using a graph to determine c. Using a Graphing Calculator
b. Using a table to determine
c. Vertical Line Test
Big Idea VII: Linearity Big Idea VIII: Linearity
I. Solving and Graphing Inequalities in One Variable I. Solving Linear Systems
a. One Step a. Checking Validity of Solutions
b. Multi Step i. Substituting in values
c. Compound ii. Using a Graphing Calculator
d. Absolute Value b. Determining the Number of Solutions
II. Graphing Linear Inequalities in Two Variable c. By Graphing
a. Checking Solutions d. By Substitution
b. Using a Graphing Calculator e. By Elimination (Linear Combination)
II. Solving Systems of Linear Inequalities
a. Graphing by Hand
b. Using a Graphing Calculator
III. Applications of Linear Systems
Course Quarterly Benchmark Assessment: (Higher level 5-10 questions)
9
Quarter III
Big Idea IX: Non-linear Relationships Big Idea X: Representation and Modeling with Variables
I. Properties of Exponents I. Radicals
a. Multiplication a. Simplification
b. Power of Power b. Multiplication
c. Power of Product c. Division
d. Zero and Negative Exponents d. Rationalizing Denominators
e. Division e. Addition and Subtraction of Rational Expressions
II. Scientific Notation II. Solving Radical Equations
a. Converting from Expanded Form to Scientific Notation III. Evaluating a Discriminant
b. Converting from Scientific Notation to Expanded Form IV. Distance Formula (Pythagorean Theorem)
c. Computations with Scientific Notation V. Graphing a Quadratic Function
III. Exponential Graphs a. Determine the Vertex and Axis of Symmetry
a. Growth and Decay Functions and their Graphs b. Using an Input-Output Table
i. Growth and Decay Factor c. Using a Graphing Calculator
ii. Interpreting Using Graphing Calculator d. Identify Domain and Range
b. Determining Domain and Range Using a Graph VI. Solving Quadratic Equations using the Quadratic Formula
c. Compound Interest VII. Application of the Discriminant
Course Quarterly Benchmark Assessment: (Higher level 5-10 questions)
10
Quarter IV
Big Idea XI: Representations and Modeling with Variables Big Idea XII: Nonlinear Relationships
VIII. Polynomial Functions XI. Direct and Inverse Variation
a. Naming a. Using a Model to Solve Application Problems
b. Addition/Subtraction i. Using a Graphing Calculator
c. Multiplication XII. Simplifying Rational Expressions
d. Solving in Factored Form a. By Factoring
IX. Solving Quadratic Equations by Factoring b. By Using Greatest Common Factor
a. With a Leading Coefficient of 1 c. Finding Values Where a Rational Expression is Undefined
b. With a Leading Coefficient other than 1 d. Using Addition and Subtraction
c. With a Greatest Common Factor e. Using Multiplication and Division
d. Special Products XIII.Solving Rational Equations
e. Grouping
X. Finding Zeros/Intercepts of an Quadratic Equation
a. By Solving Quadratic Equations
b. Graphically
c. Using a Graphing Calculator
Big Idea XIII: Connections and Extensions
XIV. Operations with Radical Expressions (Chapter 12) Course Quarterly Benchmark Assessment: (Higher level 5-10 questions)
XV. Pythagorean Theorem and its Converse (Chapter 12)
XVI. Identifying Patterns (External Resources – HSPA Review Packet)
XVII. Application Problems
11
Algebra I Core Content Overview
O1.B1 Using variables in different ways.
Big Idea I: L1.a Representing linear functions in multiple ways.
Representation and Modeling L1.b Analyzing linear functions.
L1.d Using linear models.
O1.a Reasoning with real numbers.
Big Idea II: O1.b Using ratios, rates, and proportions.
D1.b Comparing data using summary statistics.
Connections and Data D1.c Evaluating data-based reports in the media.
Analysis D2.a Using counting principles.
D2.b Determining probability.
O1.a Reasoning with real numbers.
L1.a Representing linear functions in multiple ways.
L1.b Analyzing linear functions.
Big Idea III:
L1.d Using linear models.
Equivalence L2.a Solving linear equation and inequalities.
L2.e Modeling with single variable linear equations, one or two variable inequalities, or
systems of equations.
O1.B1 Using variables in different ways.
Big Idea IV: L1.a Representing linear functions in multiple ways.
Representation and Modeling L1.b Analyzing linear functions.
L1.d Using linear models.
L1.a Representing linear functions in multiple ways.
L1.b Analyzing linear functions.
Big Idea V:
L1.d Using linear models.
Linearity L2.c Graphing linear functions involving absolute value.
L2.e Modeling with single variable linear equations, one or two variable inequalities, or
systems of equations.
12
Algebra I Core Content Overview
L2.a Solving linear equation and inequalities.
L2.b Solving equations involving absolute value.
Big Idea VI:
L2.c Graphing linear inequalities.
Linearity L2.e Modeling with single variable linear equations, one or two variable inequalities, or
systems of equations.
L1.b Analyzing linear functions.
L1.d Using linear models.
Big Idea VII: L2.c Graphing linear functions involving absolute value.
Linearity L1.d Using linear models.
L2.e Modeling with single variable linear equations, one or two variable inequalities, or
systems of equations.
O1.c Using numerical exponential expressions.
Big Idea VIII:
O2.a Using algebraic exponential expressions.
Relationships N2.B1 Solving simple exponential equations.
O1.d Using numerical radical expressions.
O2.d Using algebraic radical expressions.
Big Idea IX: O2.b Operating with polynomial expressions.
Relationships N1.a Representing quadratic functions in multiple ways.
N1.c Using quadratic models.
N2.b Solving quadratic equations.
O2.b Operating with polynomial expressions.
Big Idea X: O2.c Factoring polynomial expressions.
Representation and Modeling N1.b Distinguishing between function types.
N1.c Using quadratic models.
N2.b Solving quadratic equations.
13
Algebra I Core Content Overview
O1.b Using ratios, rates, and proportions.
Big Idea XI:
L2.e Modeling with single variable linear equations, one or two variable inequalities, or
Relationships systems of equations.
O1.d Using numerical radical expressions.
Big Idea XII: O2.d Using algebraic radical expressions.
Connections and Extensions L2.e Modeling with single variable linear equations, one or two variable inequalities, or
systems of equations.
14
BIG IDEA I 6
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
Variables can be used to describe Equations are used to describe patterns. Write and evaluate a variable expression.
1.1
number relationships. Operations are used to represent verbal models. Evaluate Simple Interest.
Symbols can be manipulated using different operations to
Exponents are tools to model model and communicate relationships. Evaluate and write expressions containing
1.2
patterns. exponents
Order of operations is a standardized Sample Conceptual Understandings Use order of operations to evaluate
1.3
method to evaluate expressions. One room in Jean's apartment is a square measuring 12.2 algebraic expressions with and without a
feet along the base of each wall. How many square feet calculator.
Verbal sentences can be translated of wall-to-wall carpet does Jean need to carpet the room? Check solutions to equations and
into mathematical sentences. inequalities.
Mathematical sentences represent Use verbal and algebraic models to
1.4
Make a table for the powers of 8. Describe any patterns.
verbal sentences. represent real-life situations.
Solutions allow number sentences to You are shopping for a mountain bike. A store sells two
make a true statement. different models. The model that has steel wheel rims
Problem solving can be achieved costs $220. The model with aluminum wheel rims costs Explain modeling using algebraic
through a system of verbal models $480. You have a summer job for 12 weeks. You save expressions.
1.5
labelsalgebraic $20 per week, which would allow you to buy the model
modelsolvingand a solution with the steel rims. You want to know how much more
check.
15
Functions are one-to-one and onto. money you would have to save each week to be able to Identify a function.
Functions can be represented in buy the model with the aluminum wheel rims. Functions can be described using an
multiple ways to model real-life o Write a verbal model and an algebraic model for input-output table, verbal description, in
situations. how much more money you would have to save symbols, and a graph.
Domain is the set of all input values each week. Describe the relationship between the
that go into a function. This results in o Use mental math to solve the equation. What domain and range of a function.
the range – the set of all output does the solution represent?
values.
If you place one marble in a measuring cup that contains
200 milliliters of water, the measure on the cup indicates
1.7
that there is a one millimeter increase in volume. How
much does the volume increase when you place from 1 to
10 marble in the measuring cup?
o Write an equation to represent the function.
o Compute an input-output table for the function
with the domain 0,1,2,3,4,5,6,7,8,9,10.
o Describe the domains and range of the function
whose values are shown in the table.
o Graph the data in the table. Use this graph to
graph the function Concept Activity: Finding Patterns (Chapter 1 Resource Books, p.56)
Chapter 1 Project: Watch It Disappear (Chapter 1 Resource Books, p.117)
11.3 Graphing Calculator Activity (Chapter 11 Resource Books, p.40)
Tiered Activity Example Big Idea #1: Tiered Example
16 You are making candles to sell at your school's art festival. You melt paraffin wax in a cubic container. Each edge is 6 inches in length.
The container is one-half full. Design a cubic candle mold that will hold all of the melted wax. Draw a diagram of the mold. Explain
why your mold will hold all of the melted wax. (McDougal-Littell: Algebra 1, pg. 14)
1.1 Real-Life Applications: Freshman Class Officer Duties (Chapter 1 Resource Books, p.21)
1.5 Real-Life Applications: Taiwan Vacation (Chapter 1 1: Alternative Assessment and Math Journal (Chapter 1 Resource Books, p.115)
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
17
BIG IDEA II: Equivalence 8
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
Absolute value of a number is the Real numbers are communication tools that express Graph and compare real numbers
distance of a value from zero on the important ideas. using a number line.
2.1
number line. Addition and subtraction of real numbers are directly Find the absolute value of a number.
Real numbers are all values that are related to one another. Find the opposite value of a number.
found on a number line. Multiplication and division of real numbers are directly
The sum of two positive integers is related to one another. Add real numbers using a number line
positive. or addition rules.
The sum of two negative integers is Sample Conceptual Understandings
2.2
negative. A star's brightness as it appears to a person on Earth is
The sum of a positive integer and a measured by its apparent magnitude. A bright start has
negative integer can be positive, negative, a lesser apparent magnitude than a dim star.
or zero. Star Magnitude
To subtract two quantities, add the Canopus -0.72 Subtract real numbers using the
2.3
opposite. The result is the difference of Altair 0.77 subtraction rule.
the two quantities.
Sirius -1.46
When multiplying, if the signs of two Multiply real numbers using properties
Vega 0.03
factors are the same, the product will be of multiplication.
2.5
positive. If the signs of two factors are o Which star looks the brightest?
different, the product will be negative. o Which star looks the dimmest?
18
The distributive property is used when a o Which star looks dimmer than Altair? Use the distributive property to
factor is multiplied by a polynomial and multiply a factor and a polynomial.
the factor must be distributed to each In a game that decides the high school football
term in a polynomial. championship, your team needs to gain 14 years to score
2.6
Like terms in an expression have the same a touchdown and win. Your team's final four plays result
variable raised to the same power. in a 9-yard gain, a 5-yard loss, a 4-yard gain, a 5-yard
Constant terms are terms without a gain as time runs out. Use a number line to model the
variable. gains and losses and explain whether your team won.
The product of a nonzero number and its Divide real numbers.
reciprocal is 1. You and a friend decide to leave a 15% tip for restaurant
To divide, multiply dividend by the service. You compute the tip as , where
reciprocal of the divisor. represents the cost of the meal. Your friend claims that
Division by zero is undefined. an easier way to mentally compute the tip is to calculate
10 % of the cost of the meal plus one half of 10% of the
2.7
cost of the meal.
o Write an equation that represents your friend's
method of computing the tip.
o Simplify the equation.
o Will both methods give the same results? Explain 2.3 Visual Approach Lesson Opener (Chapter 2 Resource Books, p.42 Big Idea #2: Tiered Example
19Assessment Models
Open-Ended Assessment:
2.2 Real-Life Applications: Stockholders (Chapter 2 Resource Books, p.36)
2.5 Real-Life Applications: Hot-Air Balloons (Chapter 2 Resource Books, p.7820
BIG IDEA III: Connections and Data Analysis can odds and probability help to analyze information to interpret data?
How can you use data displays in the real world?
Describe the relationship between mean, median, mode, and outliers.
Suggested Blocks for Instruction: 10
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
Data is information, fact, or numbers that Graphs represent data in an organized manner to help Use a table to organize data into
describe something. analyze information. meaningful groupings.
1.6
Tables and graphs are used to organize Mean, median, and mode are measures of central Make and interpret a bar graph.
data. tendency of a data set. Make and interpret a line graph.
Probability of an event is the likelihood Probability is used to analyze information and Find the probability of an event and
that the event will occur. interpret significance. determine its likelihood.
Ratios are used to make inferences about large Find the odds of an event.
2.8
The odds of an event are the ratio of the population using small samples. Calculate theoretical probability of an
number of favorable outcomes divided by Percents are used to analyze and compare data from event.
the number of unfavorable outcomes. graphs. Calculate experimental probability of an
Experimental Probability uses Unit rates are factors that help to model and scale event.
A unit rate is a rate per one given unit. proportions to desired quantities. Use rates and ratios to model and solve
real-life problems.
3.8
Sample Conceptual Understandings Use percents to solve real-life
The table shows the number of commercial television problems.
A stem and leaf plot is used to organize stations for different years. Make a line graph of the Make and use a stem-and-leaf plot to
data. data. Discuss what the line graph shows. put data in order.
6.6
Find the mean, median, and mode of
data.
21
A Box and whisker plot is a data display Draw a box-and-whisker plot to
that divides a set of data into four parts. organize data.
The median separates the set into two Read and interpret a box-and-whisker
halves (50%). Suppose you randomly choose a marble from a bag plot.
The first quartile is the median of the holding 11 green, 4 blue, and 5 yellow marbles. Use
lower half (25%) and the third quartile is probability and odds to express how likely it is that you
the median of the upper half (75%) of the choose a yellow marble. If you find one (probability or
data. If a measure of position is shared odds) easier to understand or more useful than the
between two data entries, the average is other, explain why.
6.7
taken to represent that position. In that You are conducting a survey on the use of air-plane
case, those two averaged data entries are phones. You survey 320 adults and find that 288 of
included in calculating the quartiles. them never made a phone call from an airplane. If you
surveyed 3500 adults, how many of them would you
predict have made a phone call from an airplane?
Explain.
If someone said that the mean age of everyone in your
algebra class is about 16 ½ years old, do you think the
age of the teacher was included in the calculation?
Explain Cooperative Learning Activity (Chapter 1 Resource Books, p.90)
Activity Lesson Opener (Chapter 6 Resource Books, p.94 Example
22 Interdisciplinary Application (Chapter 2 Resource Books, p.120)
Real-Life Application: Skyscrapers(Chapter 3 Resource Books, p.118)
Real Life Application: Good Health and Test Scores (Chapter 6 Resource Books, p.102 should Alternative Assessment and Math Journal Multistep Problem (#2 only)(Chapter 6 Resource Books, p.112)
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
23
BIG IDEA IV equations useful in everyday life?
How is an equation that has no solution different than an equation that is an identity?
How can drawing diagrams, using a table, and using a graph can be useful problem solving tools?
How are formulas similar and different to equations?
Why are ratios useful for architectural design?
How do percentages relate to you?
Suggested Blocks for Instruction: 14
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
A linear equation is when the Equations model patterns that occur in real life Solve linear equations using addition and
variable is raised to the first power problems and are used to solve for unknown subtraction.
and does not occur in a quantities.
denominator, inside a square root Diagrams help to model problems and draw
symbol, or inside an absolute value conclusions.
symbol. A graph and its equation are in an interdependent
3.1
Inverse operations are operations relationship.
that undo each other, which help Formulas are direct representations of real life
to isolate the variable on one side applications that help to solve for an unknown
of the equation. quantity.
The goal of solving a linear
equation is isolating the variable on
one side of the equation.
Dividing by a number is the Solve linear equations using multiplication
3.2
equivalent to multiplying by its Sample Conceptual Understandings and division.
reciprocal. The table shows the number of Digital Versatile Disc
To solve a multi-step equation, first (DVD) players sold in the first ten month after their Use two or more transformations to solve
simplify both sides of the equation release in 1997. an equation.
3.3
and then use inverse operations to Combine like terms in an equation.
isolate the variable.
24
Translate word problems (verbal models)
into equations.
An identity is an equation that is Collect variables on both sides of the
true for all values of the variable. equation.
3.4
Some linear equations have no
solution.
Graphs are the visualization of Draw diagrams to problem solve.
equations. Use graphs and tables to gather and/or
3.5
check answers.
o For each month, write a sales equation
Round-off error is a consequence relating cumulative and monthly sales. Let Find exact and approximate solutions of
3.6
of rounded solutions. represent the number of players sold that equations that contain decimals.
month.
A formula is an algebraic equation o Solve your sales equations to fill in the Solve a formula for one of its variables.
that relates two or more real-life monthly sales column. Rewrite an equation in function form.
3.7
quantities. o Suppose a DVD player manufacturer started
Function form is when a variable is an advertising campaign in September. Use
isolated on one side of the formula. your table to Judge the campaign's effect on
A proportion is an equation that sales. Write a brief report explaining whether Use the reciprocal property to solve
11.1
states two ratios are equal. the campaign was successful. proportions for unknown quantities.
Use the cross product property to solve
Write and solve an equation to find your average proportions for unknown quantities.
Percents can be described using speed on a trip from St. Louis to Dallas. You drove Use equations to solve problems involving
percentages, decimals, or ratios. miles in 10 ½ hours. percents.
Two student volunteers are stuffing envelopes for a
local food pantry. The mailing will be sent to 560
possible contributors. Luis can stuff 160 envelopes per
hour and Mei can stuff 120 envelopes per hour.
o Working alone, what fraction of the job can
11.2
Luis complete in one hour? In hours? Write
the fraction in lowest terms.
o Working alone, what fraction of the job can
Luis complete in hours?
o Write an expression for the fraction of the job
that Luis and Mei can complete in hours if
they work together.
o To find how long it will take Luis and Mei to
complete the job if they work together, you
25
can set the expression you wrote in part (c)
equal to 1 and solve for . Explain why this will
work.
o How long will it take Luis and Mei to complete
the job if they work together? Check your
solution.
Train A leaves the downtown station for the other end
of the line at 55 mi/h. Train B leaves the other end of
the line on a parallel route and heads downtown at 65
mi/h.
o Use the graph to tell how many minutes it will
be before the trains pass one another.
o Write and solve an equation to check your
answer.
Suppose another town has 15,860 people aged 25
years or older that 7581 of these people have
completed at least 4 years of college. Explain how you
can find out whether the number of college graduates
in that town is typical for a town of that size.
You are shopping and find a coat that is on sale for
26
30% off. It is regularly prices at $80. Your friend tells
you that she saw the same coat that she saw the same
coat for $80 in another store, but it was 20% off plus
an additional 10% off. Will you save by going to the
other store? Explain 3.1 Activity Lesson Opener (Chapter 3 Resource Books, p.13)
3.3 Application Lesson Opener(Chapter 3 Resource Books, p.37)
11.1 Application Lesson Opener(Chapter 11 Resource Books, p.12)
Tiered Learning ActivityAssessment Models
Open-Ended Assessment:
3.1 Real-Life Application: College Football Stadiums (Chapter 3 Resource Books, p.20)
3.2 Interdisciplinary Application: Pony Express(Chapter 3 Resource Books, p.32)
3.4 Real-Life Application: Recycling (Chapter 3 Resource Books, p.62)
3.5 Real-Life Application: Tunnels(Chapter 3 Resource Books, p.76)
3.6 Interdisciplinary Application: Magnification(Chapter 3 Resource Books, p.105)
11.2 Interdisciplinary Application: Markup and Cost(Chapter 11 Resource Books, p.34Sample Conceptual Understanding section. (Synthesis, Analysis, Evaluation)
27 3: Project: Ice Rescue (Chapter 1 Resource Books, p.130)
Chapter 11 Project: Miniature Room (Chapter 1128
BIG IDEA V scatterplot useful in making predictions?
How is a line a useful tool for interpreting data?
Describe an occupation in which slope plays an important role.
Suggested Blocks for Instruction: 10
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
A coordinate plane is formed by two real Scatterplot enable analysis of patterns and the Plot points in a coordinate plane.
number lines that intersect at the relationship between two quantities by yielding a visual Draw a scatter plot and make
origin, . representation of data. predictions.
Each point in the plane corresponds to an Real life situations can be modeled using an equation.
4.1
ordered pair . Equations can be used to describe real life situations to
A scatterplot is a graph of ordered data form predictions.
pairs on a coordinate plane that allow
analysis between two quantities. Sample Conceptual Understandings
A point is on the graph of an equation if it The table below shows the number of rolls developed Graph a linear equation using a table or
satisfies the statement when the values for the United States media at the Winter Olympics. a list of values.
4.2
are substituted in. Graph horizontal and vertical lines.
Describe the situation presented using
a graph of the data.
The -intercept is the value of o Construct a scatter plot of the data. Find the intercepts of a graph of a
when . Describe the pattern of the number of rolls linear equation.
4.3
The -intercept is the value of of film developed for the Winter Olympics Use intercepts to make a quick graph of
when . from 1984 to 1998. a linear equation.
Draw appropriate scales.
29
The ratio "rise to run" describes the o Predict the number of rolls of film that will Find the slope of a line using two of its
steepness of a slope. be developed for the Winter Olympics in the points.
The slope of a non-vertical line is the year 2002. Explain how you made your Interpret slope using real life contexts.
number of units the line rises or falls for prediction.
4.4
each unit of horizontal change from left Use a table of values to graph the equation:
to right. .
A vertical slope is undefined. Your school drama club is putting on a play next
Rate of change compares two different month. By selling tickets for the play, the club hopes
quantities that are changing. to raise $600 for the drama fund for new costumes,
Slope intercept is of the form scripts, and scenery for future plays. Let represent Graph a linear equation in slope-
where is the slope and is the - the number of adult tickets they sell at $8 each, and intercept form.
intercept. let represent the number of student tickets they Graph and interpret equations in slope-
4.6
sell at $5 each. intercept form that model real life
o Write a linear function to model the situations.
situation. Identify parallel lines.
o Graph the linear function. Solve a linear equation graphically.
4.7
o What is the -intercept? What does it Use a graphing calculator to
represent in this situation? approximate a solution.
o What are three possible number of adult
A relation is any set of ordered pairs. Identify when a relation is a function
and student tickets to sell that will make the
A relation is a function of the horizontal graphically and looking at sets of
drama club reach its goal?
axis variable if and only id no vertical line ordered pairs.
Draw a ramp and label its rise and run. Explain what
passes through two or more points on the
is meant by the slope of the ramp.
graph.
The volume of blood pumped from your heart
is called function notation.
each minute varies directly with your pulse rate .
Each time your heart beats, it pumps approximately
liter of blood.
o Find an equation that relates and .
4.8
o Take your pulse and find out how much
blood your heart pumps per minute.
Graph the situation: You start from home and drive
55 miles per hour for 3 hours, where is your
distance from home.
21st Century Skills
30
Critical Thinking and Problem Solving Critical Thinking and Problem Solving Communication and Collaboration
Media Literacy Media Literacy ICT Literacy
Technology Based Activities Technology Based Activities
Learning Activities
4.1 Graphing Calculator Activity(Chapter 4 Resource Books, p.15)
4.1 Activity Lesson Opener (Chapter 4 Resource Books, p.12)
4.7 Graphing Calculator Lesson Opener (Chapter 4 Resource Books, p.98)
4.8 Application Lesson Opener (Chapter 4 Resource Books, p.111)
Tiered Learning Activity Big Idea V: Tiered 4.1 Interdisciplinary Application: Mammals (Chapter 4 Resource Books, p.22)
4.4 Interdisciplinary Application: Minimum Wage(Chapter 4 Resource Books, p.62)
4.5 Real-Life Application: Gasoline Prices (Chapter 4 Resource Books, p.74)
4.6 Interdisciplinary Application: Mount Everest (Chapter 4 4: Alternative Assessment and Math Journal(Chapter 4 Resource Books, p.128)
Chapter 4 Project: Carnival Time(Chapter 4 Resource Books, p.131)
31
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
32
BIG IDEA VI: Linearity linear model used to approximate a real life situation?
Explain how to use a linear model to make predictions from given data.
Describe the differences between parallel and perpendicular lines.
How do the different forms of linear functions and the concept of slope help solve real world situations?
Suggested Blocks for Instruction: 14
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
Slope-intercept form of the equation of Equations describe the relationship between a dependent Use the slope-intercept form to
the line is: . and an independent variable. write an equation of a line.
A linear model is a linear function that Best-fit line represents the relationship between two Write an equation of a line from a
is used to model a real-life situation. variables. graph.
5.1
When a linear model is used to Point-intercept form, point-slope form, and standard form Model a real life situation with a
approximate a situation, slope models are interdependently related. linear function.
the rate of change and -intercept is
the initial amount or the fixed amount. Sample Conceptual Understandings
Parallel lines have the same slope. A rental company charges a flat fee of $30 and an additional Use slope and any point on a line to
"If and only if" is a bi-conditional $.25 per mile to rent a moving van. Write an equation to write an equation of the line.
5.2
statement that means if model the total charge (in dollars) in terms of , the Use a linear model to make
. number of miles driven. predictions about a real-life
The cost of a taxi ride is an initial fee plus $1.50 for each situation.
The slope of a line can be found using mile. Your fare for 9 miles is $15.50. Write an equation that Write an equation of a line given
two points on the line. models the total cost of a taxi ride in terms of the number two points on the line.
The product of a number and its of miles . How much is the initial fee?
multiplicative inverse, its reciprocal, is Write an equation in slope-intercept form of the line that
5.3
equal to -1. passes through the points: .
Perpendicular lines are two lines that A mountain climber is scaling a 300-foot cliff at a constant
intersect at a angle. rate. The climber starts at the bottom at 12:00 PM by 12:30
Perpendicular lines have slopes that are PM, the climber has moved 62 feet up the cliff. Write an
opposite reciprocals.
33
The best-fitting line is a line that models equation that gives the distance (in feet) remaining in the Find a linear equation that
the trend through a set of data points. climb in terms of the time (in hours). What is the slope of approximates a set of data points
Correlation is a number satisfying the line? At what time will the mountain climber reach the manually.
that indicates the strength top of the cliff? Find a linear equation that
of the best fit line. Write the equation in standard form of the line that passes approximates a set of data points
5.4
Positive correlation is data that has a through the given point and has the given using a graphing calculator.
trend line with a positive slope. slope: Determine whether there is a
Negative correlation is data that has a Graph using an input output table. positive or negative or no
trend line with a negative slope. Describe the graph. correlation in a set of data.
No correlation is data that cannot be
modeled by a trend line.
The point-slope form of the equation of Use the point-slope form to write an
the non-vertical line that passes equation of a line.
5.5
through a given point with a Use the point-slope form to model a
slope of is: . real life situation.
The standard form of the equation is Write a linear equation in standard
form.
5.6
Standard form linear equations can be Use the standard form of an
useful for modeling situations involving equation to model real-life
a combination of items. situations.
The vertex of an absolute value Graph absolute value equations
6.4 Extension
equation, is the point using an input-output table.
Graph absolute value equations
using a vertex and slope.
Graph absolute value equations
using a graphing calculator.
External Resources required
21st Century Skills
Critical Thinking and Problem Solving Critical Thinking and Problem Solving Communication and Collaboration
Media Literacy Media Literacy ICT Literacy
Technology Based Activities Technology Based Activities
Learning Activities
34
Algebra: Real-Life Investigations in a Lab Setting – Leah P. McCoy,
(Reprinted from Barbara Moses, ed., Algebraic Thinking,
Grades K-12: Readings from NCTM's School-Based Journals and Other Publications (Reston, Va.: National Council of Teachers of Mathematics, 2000), pp.
202-5.
5.1 Graphing Calculator Lesson Opener(Chapter 5 Resource Books, p.12)
5.2 Activity Lesson Opener(Chapter 5 Resource Books, p.24)
5.4 Application Lesson Opener(Chapter 5 Resource Books, p.52)
5.4 Cooperative Learning Activity (Chapter 5 Resource Books, p.60)
Tiered Learning Activity 5.1 Interdisciplinary Application: Break-Even Analysis (Chapter 5 Resource Books, p.19)
5.2 Real-Life Application: Sports Participation (Chapter 5 Resource Books, p.32)
5.3 Interdisciplinary Application: Bald Eagles(Chapter 5 Resource Books, p.46)
5.5 Interdisciplinary Application: Advertising(Chapter 5 Resource Books, p.73)
5.6 Real-Life Application: Saving Money(Chapter 5 Resource Books, p.9035
BIG IDEA VII 14
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
The inequality symbol is reversed when Linear inequalities describe a range of possible Write linear inequalities.
both sides of an inequality are multiplied solutions to a situation. Graph linear inequalities in one variable.
or divided by a negative number. Solve one-step linear inequalities.
The graph of a linear inequality in one
variable is the set of points on a number
6.1
line that represent all solutions of the
Sample Conceptual Understandings
inequality. After two games of bowling, Brenda has a total
score of 475. To win the tournament, she
Solid dot represents inclusion of the
needs a total score of 684 or higher. Let
point and an empty circle represents the
represent the score she needs for her third
exclusion of the point.
game to win the tournament. Write an
means is more than . Solve multi-step linear inequalities.
inequality for . What is the lowest score she
means is less than . Use linear inequalities to model and solve real-
6.2
can get for her third game and win the
means is at least . tournament?
life problems.
means is at most . Write an inequality for the values of
A compound inequality consists of two Write, solve, and graph compound inequalities.
inequalities connected by "and" or "or". Model a real life situation with a compound
6.3
inequality.
36
Solve absolute-value equations.
Absolute value are grouping symbols. Solve absolute value inequalities.
6.4
o "Less thAND"
o "greatOR" On your basketball team, the starting players'
scoring averages are between 8 and 22 points
per game. Write an absolute value inequality
An ordered pair, is a solution of a describing the scoring averages for the players. Graph a linear inequality in two variables.
linear inequality if the inequality is true
You have $12 to spend on fruit for a meeting. Check solutions of a linear inequality.
when the values of and are
Grapes cost $1 per pound and peaches cost Model a real-life situation using a linear
6.5
substituted into the inequality. inequality in two variables.
$1.50 per pound. Let represent the number
of pounds of grapes you can buy. Write and
graph an inequality to model the amounts of
grapes and peaches you can buy 6.1 Application Lesson Opener(Chapter 6 Resource Books, p.12)
6.2 Visual Approach Lesson Opener(Chapter 6 Resource Books, p.24)
6.3 Activity Lesson Opener(Chapter 6 Resource Books, p.36)
Tiered Activity Example Example
37 6.1 Real-Life Application: Golf(Chapter 6 Resource Books, p.19)
6.2 Interdisciplinary Application: People in Flight(Chapter 6 Resource Books, p.31)
6.3 Real-Life Application: The Value and Cost of Education(Chapter 6 Resource Books, p.45)
6.4 Real-Life Application: Compact Disc (CD) Players (Chapter 6 Resource Books, p.60)
6.5 Interdisciplinary Application: Japan (Chapter 6 Resource Books, p.73 6 Project: Dinosaur Activity
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
38
BIG IDEA VIII 10
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
A solution of a system of linear A solution of a system of linear equations models a Solve a system of linear equations by
equations in two variables is an ordered unique outcome for two real-life situations. graphing on a coordinate plane.
pair, , that satisfies each equation Systems of linear equations model real life situations to Solve a system of linear equations by
in the system. make predictions given certain conditions. graphing on a graphing calculator.
7.1
A solution of a linear system is the Systems of linear inequalities model all possible Check the intersection point to verify it is a
intersection point of the two lines. outcomes for two or more real-life situations. solution of the system.
Model a real-life problem using a linear
Sample Conceptual Understandings system.
When using substitution, you will get the You do 4 loads of laundry each week at a launderettte Use substitution to solve a linear system.
same solution whether you solve for where each load costs $1.25. You could buy a washing
7.2
first or first. machine that costs $400. Washing 4 loads at home will
You should begin by solving for the cost about $1 per week for electricity. How many loads
variable that is easier to isolate. of laundry must you do in order for the costs to be
Linear combination of two equations is equal? Use linear combinations to solve a system
an equation obtained by adding one of of linear equations.
7.3
You exercised on a treadmill for 1.5 hours. You ran at a
the equations (or a multiple of one of rate of 5 miles per hour, then you sprinted at a rate of 6
the equations) to the other equation.
39
Graphing is a useful method for miles per hour. If the treadmill monitor says that you Choose the best method to solve a system
approximating a solution, checking the ran and sprinted 7 miles, how long did you run at each of linear equations.
reasonableness of a solution, and speed?
providing a visual model. You have a necklace and a matching bracelet with 2
Substitution is a useful method when types of beads. There are 30 small beads and 6 large
one of the variables has a coefficient of 1 beads on the necklace. The bracelet has 10 small beads
7.4
or -1. and 2 large beads. The necklace weighs 3.6 grams and
Linear combination is a useful method the bracelet weighs 1.2 grams. If the chain has no
when none of the variables has a significant weight, can you find the weight of one large
coefficient of 1 or -1. bead? Explain.
To avoid fractional or decimal A monthly magazine is hiring reporters to cover school
coefficients, multiply the equation by a events and local events. In each magazine, the
constant first before solving. managing editor wants at least 4 reporters covering
A solution to a system of linear local news and at least 1 reporter covering school news. Identify linear systems as having one
equations is the intersection of the two The budget allows for not more than 9 different solution, no solution, or infinitely many
lines. reporters' articles to be in one magazine. Graph the solutions.
A solution to a system of linear region that shows the possible combinations of local
equations that are parallel, has no and school events covered in the magazine.
7.5
intersection, thus has no solution.
A solution to a system of linear
equations that turns out to be the same
line, has infinite intersections, thus has
infinitely many solutions.
Two or more linear inequalities form a Solving a system of linear inequalities by
system of linear inequalities. graphing using a coordinate plane.
A solution of a system of linear Solving a system of linear inequalities by
inequalities is an ordered pair that is a graphing using a graphing calculator.
solution of each inequality in the system. Use a system of linear inequalities to
The graph of a system of linear model a real-life situation.
inequalities is the graph of all solutions
that satisfy the system.
7.6
A solid line is used when the inequality is
composed of the symbols: .
A dotted line is used when the inequality
is composed of the symbols: .
40 7.4 Cooperative Learning Activity (Chapter 7 Resource Books, p.60)
7.5 Graphing Calculator Lesson Opener (Chapter 7 Resource Books, p.66 7.1 Real-Life Application: Newspaper Routes(Chapter 7 Resource Books, p.21)
Assessment Models
7.2 Interdisciplinary Application: Amphibians(Chapter 7 Resource Books, p.34)
7.3 Real-Life Application: The Juan Fernandez Islands (Chapter 7 Resource Books, p.46)
7.3 Math and History Application (Chapter 7 Resource Books, p.47)
7.4 Interdisciplinary Application: Brass Instruments(Chapter 7 Resource Books, p.61)
7.5 Interdisciplinary Application: Four Corners in Allegheny National Forest (Chapter 7 7: Alternative Assessment and Math Journal(Chapter 7 Resource Books, p.102)
Chapter 7 Project: Going Up (Chapter 7 Resource Books, p.105)
41
Resources
Additional McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
42
BIG IDEA IX why it is essential to have a like base in order to use any of the exponential properties.
Describe a real-life situation that might require using exponents.
Explain why scientific notation may be particularly useful in certain occupations.
How does exponential growth and decay apply to you and your future?
Suggested Blocks for Instruction: 12
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
To multiply powers having the same Exponential functions model percentages of Use properties of exponents to multiply
base, add the exponents. change over time. exponential expressions.
To find the power of a power, multiply Exponential functions model real-life Use powers to model real-life problems.
8.1
the exponents. applications and are used to make predictions.
To find a power of product, find the Scientific notation is an efficient method of
power of each factor and multiply. representing and calculating very large and very
A non-zero number to the zero power is small numbers. Evaluate powers that have zero and
1. negative exponents.
8.2
; Sample Conceptual Understandings Graph exponential functions using an input-
Exponential function is of the form: You are offered a job that pays dollars or output table.
. dollars for hours of work. Assuming you must
Quotient of powers property states to work at least 2 hours, which method of payment Use the division properties of exponents to
divide powers having the same base, would you choose? Explain your reasoning. evaluate powers and simplify expressions.
subtract exponents. Sketch the graphs of and . Use the division properties of exponents to
8.3
Power of a quotient property states to How are the graphs related? find a probability.
find the power of the quotient, find the The racing shells (boats) used in rowing
power of the numerator and the power competition usually have 1,2,4, or 8 rowers. Top
of the denominator and divide.
43
Scientific notation is of the form speeds for racing shells in the Olympic 2000- Use scientific notation to represent
where and is an integer. meter races can be modeled by numbers.
where is the speed in Rewrite from scientific notation into decimal
kilometers per hour and is the number of form.
rowers. Use the model to estimate the ratio of Rewrite from decimal form into scientific
8.4
the speed of an 8-rower shell to the speed of a notation.
2-rower shell. Computing with scientific notation by hand.
The distance between the ninth "planet" Computing with scientific notation by hand
Pluto and the sun is of kilometers. using a calculator.
Light travels at a speed of about Use scientific notation to describe real-life
kilometers per second. How long does it take situations.
Exponential growth is when a light to travel from the Sun to Pluto. Write and use models for exponential
quantity grows by the same percent The population of 30 mice is released in a growth.
in each unit of time and is of the wildlife region. The population doubles each Graph models for exponential growth.
form: year for 4 years. What is the population after 4
years.
8.5
Exponential growth models have a Each year in the month of March, the NCAA
variable used as an exponent. Their basketball tournament is held to determine the
value will eventually change much national champion. At the start of the
more rapidly than those of linear tournament there are 64 teams, and after each
models. round, one half of the remaining teams are
eliminated.
Exponential growth is when a Write and use models for exponential decay.
o Write an exponential decay model
quantity decreases by the same Graph a model for exponential decay.
showing the number of teams left in
percent in each unit of time and is of the tournament after round .
the form: o How many teams remain after 3
rounds? 4 rounds?
A quantity that decreases by a factor
less than 1 can be modeled by an
8.6
exponential equation that
represents exponential decay.
21st Century Skills
44 8.4 Application Lesson Opener(Chapter 8 Resource Books, p.55)
8.4 Cooperative Learning Activity(Chapter 8 Resource Books, p.63)
8.5 Application Lesson Opener (Chapter 8 Resource Books, p.70)
8.6 Cooperative Learning Activity(Chapter 8 Resource Books, p.94 8.1 Real Life Application: Telephone Numbers (Chapter 8 Resource Books, p.21)
Assessment Models
8.2 Interdisciplinary Application: Carbon 14 Dating (Chapter 8 Resource Books, p.35)
8.3 Real Life Application: Internet Usage (Chapter 8 Resource Books, p.49)
8.4 Interdisciplinary Application: Sahara Desert (Chapter 8 Resource Books, p.64)
8.5 Real Life Application: Investing for College (Chapter 8 Resource Books, p.79)
8.6 Real Life Application: Record Albums (Chapter 8 Resource Books, p.95 8: Alternative Assessment and Math Journal(Chapter 8 Resource Books, p.107)
Chapter 8 Project: City Growth (Chapter 8 Resource Books, p.109)
45
Resources
Additional McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
46
BIG IDEA X perfect squares and square roots related?
Explain how quadratic equations can be used to model real-life situations.
How are the coefficients of a quadratic equation and its graph related?
How is the quadratic formula more useful in solving quadratic equations than solving using radicals to solve?
Describe the relationship between the quadratic formula, the discriminant, and the number of solutions.
Suggested Blocks for Instruction: 24
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
If , the is the square root of . Quadratic equations are used in physics to model paths Evaluate and approximate square
All positive real numbers have two square of objects through the air (with little air resistance). roots.
roots: a positive and negative square The quadratic formula, the discriminant, and the Solve quadratic equation by finding
root. The positive square root is called the number of solutions are in an interdependent square roots.
principle square root. relationship.
The number or expression inside a radical
symbol is the radicand. Sample Conceptual Understandings
The square root of a negative number is The sales (in millions of dollars) of computer software
undefined. in the United States from 1990 to 1995 can be modeled
9.1
Numbers whose square roots are integers by , where is the number of
or quotients of integers are called perfect years since 1990. Use this model to estimate the year
squares. in which sales of computer software will be $7200
million.
47
An irrational number is a number that Find the area of the given figure.
cannot be written as the quotient of two
integers.
A radical expression involves square
roots.
means .
A quadratic equation is an equation that
can be written in the following standard Suppose a table-tennis ball is hit in such a way that its
form: path can be modeled by , where
is the leading coefficient. is the height in meters above the table and is the
When the quadratic equation is of time in seconds.
the form . o Estimate the maximum height reached by the
o If , then has two table-tennis ball.
solutions: . o About how many seconds did it take for the
o If , then has one table tennis ball to reach its maximum height
solution: after its initial bounce?
o If , then has no real o About how many seconds did it take for the
solution. table-tennis ball to travel from the initial
bounce to land on the other side of the net?
The product property states that the The number of recreational vehicles (RVs) sold in the Use properties of radicals to simplify
square root of a product equals the Unites States from 1985 to 1991 can be modeled by radicals.
product of the square roots of the , where represents the Use quadratic equations to model
factors. number of vehicles sold (in thousands) and real-life problems.
where and represents the number of years since 1985.
o Sketch a graph of the model for positive values
9.2
The quotient property states that the
of and .
square root of a quotient equals the
o Use the graph to estimate a positive root of the
quotient of the square roots of the
equation .
numerator and denominator.
o According to the model, in what year will the
where and number of RVs sold in the Unites States drop to
0?
48
You can predict the shape of the graph o Do you think the prediction is realistic? What Sketch the graph of a quadratic
of , if it opens up or factors might explain a decrease or an increase function using a coordinate plane.
down, and its general position by in the number of sales of recreational vehicles? Sketch the graph of a quadratic
examining A falcon dives toward a pigeon on the ground. When function using a graphing calculator.
The shape of a quadratic function is the falcon is at a height of 1000 feet, the pigeon sees Use quadratic models in real-life
called a parabola. the falcon, which is diving at 220 feet per second. situations.
The vertex is the highest point of a Estimate the time the pigeon has to escape.
parabola that opens up or the lowest You see a firefighter aim a fire hose from 4 feet above
9.3
point of a parabola that opens down. the ground at a window that is 26 feet above the
The vertex of the equation ground. The equation
can be found: models the path of the water when equals the height
Vertex = in feet. Estimate, to the nearest whole number, the
possible horizontal distances (in feet) between the
The line that passes through the vertex firefighter and the building.
that divides the parabola into two
symmetric parts is called the axis of
symmetry: .
The quadratic formula, , Use the quadratic formula to solve a
quadratic equation.
9.5
can be used to solve for the roots of any
quadratic equation in standard form
.
The discriminant, , is a part of
the quadratic formula that helps to
determine the number of roots or
solutions in a quadratic equation.
o If , the equation has
9.6
two solutions.
o If , the equation has
one solution.
o If , the equation has no
real solutions49
Learning Relationships
BIG IDEA XI: Activities
Curriculum Management System
Algebra 1 A/B : Grade 9
9.3 Graphing Calculator Lesson Opener (Chapter 9 Resource Books, p.37)
9.3 Graphing Calculator Activity (Chapter 9 Resource Books, p.40)
9.4 Visual Approach Lesson Opener (Chapter 9 Resource Books, p.55)
9.6 Activity Lesson Opener (Chapter 9 Resource Books, p.85 9.1 Interdisciplinary Application: Right Circular Cylinder (Chapter 9 Resource Books, p.20)
9.2 Interdisciplinary Application: Centripetal Acceleration (Chapter 9 Resource Books, p.32)
Assessment Models
9.3 Real Life Application: Ballet Recital(Chapter 9 Resource Books, p.40)
9.4 Interdisciplinary Application: Air Pollution (Chapter 9 Resource Books, p.65)
9.5 Interdisciplinary Application: Current in Electric Circuit (Chapter 9 Resource Books, p.79)
9.6 Real Life Application: Factory Sales (Chapter 9 9: Alternative Assessment and Math Journal(Chapter 9 Resource Books, p.133)
Chapter 9 Project: Light Square(Chapter 9 Resource Books, p.135)
Parachute Jump
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
50
BIG IDEA XI10.2
o Degree = 0 constant long as the length of the house.
o Degree = 1 linear
51 A polynomial named by the number of
terms is as follows: o Write an expression for the area of the land surrounding
o one term is called a monomial the house.
o two terms is called a binomial o If feet, what is the area of the house? What is the
o three terms is called a trinomial area of the entire property?
FOIL is a double distributing method of An investment of dollars that gains percent of its Multiply two polynomials.
multiplication for two binomials value in one year is worth at the end of that Use polynomial multiplication in real-
: year. An investment that loses percent of its value in life situations. Multiplying vertically follows the
o If the investment gains percent the first year
traditional (multi-digit) x (multi-digit)
and loses percent the second year, what is
number pattern.
the increase or decrease in the value of the
10.2
Multiplying horizontally follows the
investment?
distributive pattern where each term in
You sell hot dogs for $1.00 each at your concession
the polynomial on the left is distributed
stand at a baseball park and have about 200 customers.
to each term in the polynomial to the
You want to increase the price of a hot dog. You
right.
estimate that you will lose three sales for every $.10
The box method is a visual method that
increase. The following equation models your hot dog
organizes the multiplication of a
sales revenue , where is the number of $.10
(polynomial) x (polynomial)
increases.
. Concession stand revenue model:
o To find your revenue from hot dog sales, you
multiply the price of each hot dog sold by the
number of hot dogs sold. In the formula above,
52
Sum and difference pattern: what does represent? What does Use special product patterns for the
10.3 represent? product of a sum and a difference, and
Square of a binomial pattern: o How many times would you have to raise the for the square of a binomial.
price by $.10 to reduce your revenue to zero?
Make a graph to help find your answer.
o Decide how high you should raise the price to
A polynomial is in factored form if it is Solve a polynomial equation in factored
make the most money. Explain how you got
written as the product of two or more form.
your answer.
linear factors. Relate factors and x-intercepts.
10.4
Consider a circle whose radius is greater than 9 and
Zero product property states that if
whose area is given by . Use
then or .
factoring to find an expression for the radius of the
The zeros of a polynomial are the circle.
x - intercepts of the graph.
Deciding whether a trinomial can be Solve by factoring, finding the square roots, or by using Factor a quadratic expression of the
factored with the use of the form: .
10.5
the quadratic formula: .
discriminant.
An object is propelled from the ground with an initial Solve quadratic equations by factoring.
A polynomial equation must be set equal upward velocity of 224 feet per second. Using the
to zero in order to solve for the zeros. vertical motion equation , will the object
A polynomial expression is a sum of reach a height of 784 feet? If it does, how long will it Factor a quadratic expression of the
10.6
terms. take the object to reach that height? Solve by factoring. form: .
A polynomial equation is an equation Using the vertical motion equation , you Solve quadratic equations by factoring.
made up of a sum of terms. toss a tennis ball from a height of 96 feet with an initial
Difference of two squares pattern velocity of 16 feet per second. How long will it take for Use special product patterns to factor
the tennis ball to reach the ground? quadrcoefficients.
10.8535455
BIG IDEA XI: Representations1
0
1
1
1
0
1
1
0
2
.
.
.o Degree = 0 constant long as the length of the house.
o Degree = 1 linearo Write an expression for the area of the land surrounding
56
A polynomial named by the number of the house.
terms is as follows: o If feet, what is the area of the house? What is the
o one term is called a monomial area of the entire property?
10.1 continued
o two terms is called a binomial An investment of dollars that gains percent of its
o three terms is called a trinomial value in one year is worth at the end of that
year. An investment that loses percent of its value ino If the investment gains percent the first year
FOIL is a double distributing method of and loses percent the second year, what is Multiply two polynomials.
multiplication for two binomials the increase or decrease in the value of the Use polynomial multiplication in real-
: investment? life situations.
You sell hot dogs for $1.00 each at your concession
stand at a baseball park and have about 200 customers.
You want to increase the price of a hot dog. You
estimate that you will lose three sales for every $.10
increase. The following equation models your hot dog
Multiplying vertically follows the sales revenue , where is the number of $.10
traditional (multi-digit) x (multi-digit) increases.
Concession stand revenue model:
number pattern.
10.2
Multiplying horizontally follows the o To find your revenue from hot dog sales, you
distributive pattern where each term in multiply the price of each hot dog sold by the
the polynomial on the left is distributed number of hot dogs sold. In the formula above,
to each term in the polynomial to the what does represent? What does
right. represent?
The box method is a visual method that o How many times would you have to raise the
organizes the multiplication of a price by $.10 to reduce your revenue to zero?
(polynomial) x (polynomial) Make a graph to help find your answer.
. o Decide how high you should raise the price to
make the most money. Explain how you got
your answer.
Consider a circle whose radius is greater than 9 and
whose area is given by . Use
57
Sum and difference pattern: factoring to find an expression for the radius of the Use special product patterns for the
10.3 circle. product of a sum and a difference, and
Square of a binomial pattern: for the square of a binomial.
Solve by factoring, finding the square roots, or by using
the quadratic formula: .
An object is propelled from the ground with an initial
A polynomial is in factored form if it is Solve a polynomial equation in factored
upward velocity of 224 feet per second. Using the
written as the product of two or more form.
vertical motion equation , will the object
linear factors. Relate factors and x-intercepts.
10.4
reach a height of 784 feet? If it does, how long will it
Zero product property states that if
take the object to reach that height? Solve by factoring.
then or .
Using the vertical motion equation , you
The zeros of a polynomial are the
toss a tennis ball from a height of 96 feet with an initial
x - intercepts of the graph.
velocity of 16 feet per second. How long will it take for
Deciding whether a trinomial can be Factor a quadratic expression of the
the tennis ball to reach the ground?
factored with the use of the form: .
10.5
discriminant. Solve quadratic equations by factoring.
A polynomial equation must be set equal
to zero in order to solve for the zeros.
A polynomial expression is a sum of Factor a quadratic expression of the
10.6
terms. form: .
A polynomial equation is an equation Solve quadratic equations by factoring.
made up of a sum of terms.
Difference of two squares pattern Use special product patterns to factor
quadr10.8
coefficients.21st Century Skills
585960
BIG IDEA XII a real life situation that has a model that varies inversely and directly.
Explain the difference between a rational expression and a fraction.
Suggested Blocks for Instruction: 14
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
Direct variation is when the Inverse and direct variation model real-life patterns to make Use direct and inverse variation.
variable and vary directly if predictions. Use direct and inverse variations to model
for a constant ; or Rational expressions are used to model real-life situations real-life situations.
and can be used to make predictions.
Inverse variation is when the
variable and vary inversely if Sample Conceptual Understandings
for a constant ; or Decide if the data in the table show direct or inverse
. variation. Write an equation that relates the variables.
is the constant of variation.
1 3 5 10 0.5
11.3
5 15 25 50 2.5
You are designing a game for a school carnival. Players
will drop a coin into a basin of water, trying to hit a target
on the bottom. The water is kept moving randomly, so
the coin is equally likely to land anywhere. You use a
rectangular basin twice as long as it is wide. You place
the blue rectangular target an equal distance from each
end.
o Express the two dimensions of the target in
61
A rational number is a number terms of the variables and . Simplify a rational expression.
that can be written as the o Write a model that gives the probability that the
quotient of two integers. coin will land on the target.
A fraction whose numerator, Simplify:
denominator, or both Find an expression for the perimeter of the rectangle:
numerator and denominator are
nonzero polynomials is a
rational expression.
11.4
A rational expression is
simplified if its numerator and
denominator have no factors in
common (other than ). After 50 times at bat, a major league baseball player has
Simplifying fractions: a batting average of 0.160. How many consecutive hits
Let be nonzero numbers. must the player get to raise his batting average to 0.250?
=
To multiply rational expressions, Multiply and divide rational expressions.
let be nonzero Use rational expressions as real-life models.
polynomials, multiply the
numerators and denominators:
To divide rational expressions,
let be nonzero
polynomials, multiply by the
11.5
reciprocal of the divisor:
62
To add with a like denominator, Add and subtract rational expressions that
add the numerators and keep have like denominators.
the denominators the same: Add and subtract rational expressions that
have unlike denominators.
To subtract with a like
denominator, subtract the
11.6
numerators and keep the
denominators the same:
The least common denominator
(LCD) that you use is the least
common multiple of the original
denominators.
A rational equation is an Solve rational equations.
equation that contains rational
expressions.
11.8
Cross multiplication can only be
used when each side of the
equation is a single fraction 11.3 Graphing Calculator Activity (Chapter 11 Resource Books, p.40)
Tiered Activity Example Big Idea XII: Tiered Example
63 oral
reports, booklets, or other formats of measurement used by the teacher.
Open-Ended Assessment:
Assessment Models
11.3 Real Life Application: Light Bulbs (Chapter 11 Resource Books, p.49)
11.4 Interdisciplinary Application: Social Studies (Chapter 11 Resource Books, p.63)
11.5 Interdisciplinary Application: Health (Chapter 11 Resource Books, p.76)
11.6 Real Life Application: Television (Chapter 11 Resource Books, p.89)
11.8 Interdisciplinary Application: Medicine and Children (Chapter 11 topics.(Synthesis,
Analysis� Chapter 11: Alternative Assessment and Math Journal (Chapter 11 Resource Books, p.127)
Resources
Additional
McDougal-Littell: Algebra 1 2004
McDougal-Littell: Algebra 1 Chapter Resource Books
64
BIG IDEA XIII: Connections and Extensions how drawing a diagram, using a table, and using a graph can help with problem solving in the real world?
Suggested Blocks for Instruction: 10
KNOW UNDERSTAND DO
Students will know that: Students will understand that: Students will be able to:
The distributive property is used Drawing a diagram, using a table, and using a graph Add, subtract, multiply, and divide radical
to simplify the sums and model real life situations to help demonstrate expressions.
differences of radical expressions reasoning and model the situation. Use radical expressions in real life situations.
when the expressions have the
12.2
same radicand.
The expressions and
are conjugates.
65
The Pythagorean Theorem states: Sample Conceptual Understandings Use the Pythagorean Theorem and its converse.
if a triangle is a right triangle, At Barton High School, 45 students are taking Use the Pythagorean Theorem and its converse in
then the sum of the squares of real-life problems.
Japanese. The number has been increasing at a rate
the lengths of the legs and of 3 students per year. The number of students
equals the square of the length of taking German is 108 and has been decreasing at a
the hypotenuse rate of 4 students per year. At these rates, when will
the number of students taking Japanese equal the
Converse of the Pythagorean number taking German? Write and solve an
Theorem states: If a triangle has equation to answer the question. Check your
side lengths and such answer with a table or graph.
that, , then the
triangle is a right triangle. Find the area:
12.5
You are surveying a triangular-shaped piece of land.
You have measured and recorded two lengths on a
plot plan. What is the length of the property along
the street?
66 12.5 Visual Approach Lesson Opener (Chapter 12 Resource Books, p.67Assessment Models
oral reports, booklets, or other formats of measurement used by the teacher.
Open-Ended Assessment:
12.2 Real Life Application: Plywood (Chapter 12 Resource Books, p.33)
12.5 Real Life Application: Kites (Chapter 1267
Algebra 1 A/B
COURSE BENCHMARKS
1. The student will be able to understand that equations are used to describe patterns, operations are used to represent verbal models and symbols can
be manipulated using different operations to model and communicate relationships.
2. The student will be able to understand that real numbers are communication tools that express important ideas with addition and subtraction of real
numbers are directly related to one another and multiplication and division of real numbers are directly related to one another.
3. The student will be able to understand that graphs are used to represent data in an organized manner to help analyze information using the mean,
median, and mode as measures of center of a data set. Percents and probability are used to analyze information and interpret significance and ratios
are used to make inferences about large population using small samples. Unit rates are factors that help to model and scale proportions to desired
quantities.
4. The student will be able to understand that equations model patterns that occur in real life problems and are used to solve for unknown quantities and
formulas are direct representations of real life applications that help to solve for an unknown quantity. Diagrams help to model problems and draw
conclusions. A graph and its equation are in an interdependent relationship.
5. The student will be able to understand that scatterplots enable analysis of patterns and the relationship between two quantities by yielding a visual
representation of data. Real life situations can be modeled using an equation. Equations can be used to describe real life situations to form predictions.
6. The student will be able to understand that inverse and direct variation model real-life patterns to make predictions. Equations describe the
relationship between a dependent and an independent variable. Best-fit line represents the relationship between two variables. Point-intercept form,
point-slope form, and standard form are interdependently related.
7. The student will be able to understand that linear inequalities describe a range of possible solutions to a situation.
8. The student will be able to understand that a solution of a system of linear equations models a unique outcome for two real-life situations. Systems of
linear equations model real life situations to make predictions given certain conditions. Systems of linear inequalities model all possible outcomes for
two or more real-life situations.
9. The student will be able to understand that exponential functions model percentages of change over time. Exponential functions model real-life
applications and are used to make predictions. Scientific notation is an efficient method of representing and calculating large numbers.
10. The student will be able to understand that quadratic equations are used in physics to model paths of objects through the air (with little air resistance).
The quadratic formula, the discriminant, and the number of solutions are in an interdependent relationship.
11. The student will be able to understand that the factors and x-intercepts of a polynomial are directly related and multiplying polynomials and factoring
polynomials are reverse processes of each other.
12. The student will be able to understand that inverse and direct variation model real-life patterns to make predictions and rational expressions are used
to model real-life situations and can be used to make predictions.
13. The student will be able to understand that drawing a diagram, using a table, and using a graph, model real life situations to help demonstrate reasoning
and model the situation.
68
BIG IDEA I: Tiered Assignment
[back to Big Idea #I]69
2. If they qualified for the group rate, how many "student" Chens were present?
3. Use the data from Exercise 1 to determine how much could have been saved if the Chens arrived
after 3:00 PM.
4. Use the data from Exercise 2 to determine how much could have been saved if the Chens arrived
after70Write a Verbal Model: ______________________________________________________________
Algebraic
Let x = number of adults and y = number of children.
Evaluate
71
2. If they qualified for the group rate, how many "student" Chens were present?
Write a Verbal Model: ______________________________________________________________
Algebraic
Let x = number of adults and y = number of children.
Evaluate
3. Use the data from Exercise 1 to determine how much could have been saved if the Chens arrived
after 3:00 PM.
Write a Verbal Model for after 3:00 PM: _________________________________________________
Algebraic for 3:00 PM
Let x = number of adults and y = number of children.
Evaluate for 3:00 PM
Calculate Savings
72
4. Use the data from Exercise 2 to determine how much could have been saved if the Chens arrived
after 3:00 PM.
Let x = number of adults and y = number of children.
Evaluate for 3:00 PM
Calculate SavingsWhat is the ratio of NT to U.S. Dollars?____________________________________________________
Convert your answer to Exercise 1 to U.S. Dollars
73 opportunityVerbal
Algebraic
+ =
Let x = number of adults and y = number of children.
Evaluate
+ =
74
2. If they qualified for the group rate, how many "student" Chens were present?
Verbal
Algebraic
+ =
Let x = number of adults and y = number of children.
Evaluate
+ =
3. Use the data from Exercise 1 to determine how much could have been saved if the Chens arrived
after 3:00 PM.
Answer from Exercise 1 1 and if they arrived after 3:00 PM.
75
4. Use the data from Exercise 2 to determine how much could have been saved if the Chens arrived
after 3:00 PM.
Answer from Exercise 2 2 and if they arrived afterWrite the exchange rate for NT to U.S. dollars as a fraction:___________________________________
Answer in NT from Exercise 1: __________________________________________________________
Use the exchange rate to convert from NT to U.S dollars:
Answer in U.S. Dollars _________________________________________________________________
76
BIG IDEA II: Tiered Assignment
[back to Big Idea #II] (When would
you have made the greatest profit from selling your share?)
77
4. Suppose you do not sell your share and watch the market for another fiveday period. The results are: loses 3
cents, gains 5 cents, gains 7 cents, loses 2 cents, and gains 9 cents. Find the net profit or loss for this five-day
period.
5. Using your answer from Exercise 2, find the value of your share after the ten-day period.
6. After the ten-day period, did you make a profit or suffer a loss? How much?
78 List the profit79 Find What was the starting value of your stock?______________________________________________
c. How much of a profit/loss did your stock take?
80 Write a number that represents the number of the profit or loss for each day.
a. Day 1:__________________
b. Day 2:__________________
c. Day 3: __________________
d. Day 4: __________________
e. Day 5: __________________
d. Find your net profit or loss for this five-day period by adding together your profits and losses over the five
days.
2. You paid $8.54 for your share. After the five-day period, how much is your share worth?
a. How much money did you pay for the share? ____________________________________________
b. Did you make or lose money in part d)? _________________________________________________
c. Add together your starting amount and your answer from part d).
81
3. As you look back over the five-day period, when would have been the best time for you to sell? List the "profit" Find How much of a profit/loss did your stock take?
i. What was the starting value of your stock? __________________________________________
ii. What is the ending value of your stock? ____________________________________________
iii. Find the difference of your starting and ending value of the stock. Is it a gain or loss? Why?
82
BIG IDEA III: Tiered Assignment
[Back to Big Idea III]2. Find the probability that a female from the 18–20 age group is not a registered voter.
3. Find the probability that a female registered voter chosen at random is 25 to 44 years old.
4. Find the probability that a female registered voter chosen at random is not 21 to 24 years old.
5. Find the odds of randomly choosing a female registered voter that is 65 years and older.
6. Find the odds of randomly choosing a female registered voter that is 25 to 64 years old.
7. Find the odds of randomly choosing a female ages 21 to 24 years old that is not a registered voter.
83a. Number of Females that are registered to vote in 18-20 age group: _____________________________________
b. Number of Females 18 to 20 years old : ____________________________________________________________
c. Number of Females that are NOT registered to vote in 18-20 age group: _________________________________
d84
4. Find the probability that a female registered voter chosen at random is not 21 to 24 years old.
5. Find the odds of randomly choosing a female registered voter that is 65 years and older.
favorable outcomes
odds
unfavorable outcomes
6. Find the odds of randomly choosing a female registered voter that is 25 to 64 years old.
7. Find the odds of randomly choosing a female ages 21 to 24 years old that is not a registered voter.
85e. Number of Females that are registered to vote in 18-20 age group: _____________________________________
f. Number of Females 18 to 20 years old : ____________________________________________________________
g. Number of Females that are NOT registered to vote in 18-20 age group: _________________________________
ha. Number of Females that are in the 25 – 44 age group: _____________________________________
b. Number of Females total: ____________________________________________________________
c. Divide a) and b) to find the probability that a female is aged 25 to 44: ______________________
86
4. Find the probability that a female registered voter chosen at random is not 21 to 24 years old.
a. Number of Females that are in the 21 – 24 age group: _____________________________________
b. Number of Females that are NOT in the 21 – 24 age group: _____________________________________
c. Number of Females total: ____________________________________________________________
d. Divide b) and c) to find the probability of a female not aged 21 to 24 years old:______________________
5. Find the odds of randomly choosing a female registered voter that is 65 years and older.
favorable outcomes
odds
unfavorable outcomes
a. Number of Females that are 65 years or older age group: _____________________________________________
b. Number of Females that are NOT in the 65 years or older age group: ____________________________________
c. The odds of randomly choosing a female registered voter that is 65 years or older: _________________________
6. Find the odds of randomly choosing a female registered voter that is 25 to 64 years old.
favorable outcomes
odds
unfavorable outcomes
a. Number of Females that are in the 25 to 64 age group that is a registered voter: _________________________
b. Number of Females that are NOT registered to vote in the 25 to 64 years age group: _______________________
c. The odds of randomly choosing a female registered voter that is 25 to 64 years age: ________________________
7. Find the odds of randomly choosing a female ages 21 to 24 years old that is NOT a registered voter.
favorable outcomes
odds
unfavorable outcomes
d. Number of Females that are in the 21 to 24 age group that are not registered to vote: _____________________
e. Number of Females that are in the 21 to 24 age group that are registered to vote: _________________________
f. The odds of randomly choosing a female ages 21 to 24 years old that is NOT a registered voter:
_____________________________________________________________________________________________
87
BIG IDEA IV: Tiered Assignment
[Back to Big Idea IV]
88
BIG IDEA V: Tiered Assignment
[Back to Big Idea V]
89
BIG IDEA VI: Tiered Assignment
[Back to Big Idea VI]
90
BIG IDEA VII: Tiered Assignment
[Back to Big Idea VII]
91
BIG IDEA VIII: Tiered Assignment
[Back to Big Idea VIII]
92
BIG IDEA IX: Tiered Assignment
[Back to Big Idea IX]
93
BIG IDEA X: Tiered Assignment
[Back to Big Idea X]
94
BIG IDEA XI: Tiered Assignment
[Back to Big Idea XI]
95
BIG IDEA XII: Tiered Assignment
[Back to Big Idea XII]966. Write an algebraic expression to find the percent of physicians who are pediatric doctors in the
United States.
7. Use your algebraic expression to find the percent of physicians who were pediatric doctors in
1999.
97 obtain1990: t =
1993: t =
1996: t =
981990: t =
1993: t =
1996: t = 1990: t =
1993: t =
1996: t =
99Number of physicians in 1999 =
Number of orthopedic surgeons in 1999=
6. Write an algebraic expression to find the percent of physicians who are pediatric doctors in the
United States.
7. Use your algebraic expression to find the percent of physicians who were pediatric doctors in
1999.
Number of physicians in 1999 = ___________________________________________________
Number of pediatric doctors in 1999=_______________________________________________
100620.9 7.9t
1990: t =___________ D
1 0.01t
620.9 7.9t
1993: t =___________ D
1 0.01t
620.9 7.9t
1996: t =___________ D
1 0.01t
10114.7 0.25t
1990: t =___________ D
1 0.01t
14.7 0.25t
1993: t =___________ D
1 0.01t
14.7 0.25t
1996: t =___________ D
1 0.01t26.9 0.48t
1990: t =___________ D
1 0.03t
26.9 0.48t
1993: t =___________ D
1 0.03t
26.9 0.48t
1996: t =___________ D
1 0.03t
102Let x represent the number of orthopedic surgeons and let y represent the number of
physicians.
5. Use your algebraic expression to find the percent of physicians who were orthopedic surgeons
in 1999.
a. Number of physicians in 1999 =_________________________________________________
620.9 7.9t
1999: t =___________ D
1 0.01t
b. Number of orthopedic surgeons in 1999=_________________________________________
14.7 0.25t
1999: t =___________ D
1 0.01t
c. Calculate the percentage using your answer from #4.
103
6. Write an algebraic expression to find the percent of physicians who are pediatric doctors in the
United States.
Number of Pediatric Doctors
Total Number of Physicians
100
Let z represent the number of pediatric doctors and let y represent the number of physicians.
7. Use your algebraic expression to find the percent of physicians who were pediatric doctors in
1999.
d. Number of physicians in 1999 =________________________________________________
620.9 7.9t
1999: t =___________ D
1 0.01t
e. Number of pediatric doctors in 1999=___________________________________________
26.9 0.48t
1999: t =___________ D
1 0.03t
f. Calculate the percentage using your answer from #6.
104
BIG IDEA XIII: Tiered Assignment
[Back to Big Idea XIII]
105 |
Mathematical Modeling
By
Mark Meerschaert, Michigan State University, East Lansing, MI, USA
Meerschaert's new edition strengthens his position as the survey text of choice for mathematical modeling courses, adding ample instructor support and leveraging on-line delivery for solutions manuals and software ancillaries.
From genetic engineering to hurricane prediction, mathematical models guide much of the decision-making in our society, and if the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor, as recent events have proved. Since mathematical modeling is a rapidly growing specialty with applications in so many scientific and technical disciplines, there is a need for mathematically rigorous treatments of the subject, and particularly for texts that expose students to a range of possible approaches.
Audience Advanced undergraduate or beginning graduate students in mathematics and closely related fields. Formal prerequisites consist of the usual freshman-sophomore sequence in mathematics, including one-variable calculus, multivariable calculus, linear algebra, and differential equations. Prior exposure to computing and probability and statistics is useful, but is not required.
Reviews
"I think this is the best book in its genre. I haven't been tempted to use another. The mathematics in it is interesting, useful, and still within reach of typical undergraduates." --John E. Doner, Department of Mathematics, University of California, Santa Barbara |
1800 118 002 [Toll Free]
Download CBSE Important Questions Class 10: Mathematics
Table Of Contents
Number Systems
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Euclid's Division Lemma, The
Fundamental Theorem of Arithmetic, Revisiting Irrational Numbers, Revisiting
Rational Numbers and Their Decimal Expansions.
Polynomials
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Geometrical Meaning of the
Zeroes of a Polynomial, Relationship between Zeroes and Coefficients of a
Polynomial, Division Algorithm for Polynomials.
Pair of Linear Equations in Two Variables
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Pair of Linear Equations in
TwVariables, Graphical Method of Solution of a Pair of Linear Equations,
Algebraic Methods of Solving a Pair of Linear Equations, Substitution
Method, Elimination Method, Cross-Multiplication Method, Equations Reducible
ta Pair of Linear Equations in TwVariables.
Quadratic Equations
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Quadratic Equations, Solution of
a Quadratic Equation by Factorisation, Solution of a Quadratic Equation by
Completing the Square, Nature of Roots.
Arithmetic Progressions
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Arithmetic Progressions, nth
Term of an AP, Sum of First n Terms of an AP.
Trigonometry
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Trigonometric Ratios,
Trigonometric Ratios of Some Specific Angles, Trigonometric Ratios of
Complementary Angles, Trigonometric Identities.
Heights and Distances
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Heights and Distances.
Co-Ordinate Geometry
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Distance Formula, Section
Formula, Area of a Triangle.
Similar Triangles
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Similar Figures, Similarity of
Triangles, Criteria for Similarity of Triangles, Areas of Similar Triangles,
Pythagoras Theorem.
Circles
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Tangent ta Circle, Number of
Tangents from a Point on a Circle.
Constructions
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Division of a Line Segment,
Construction of Tangents ta Circle.
Areas Related tCircles
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Perimeter and Area of a Circle A
Review, Areas of Sector and Segment of a Circle, Areas of Combinations of
Plane Figures.
Surface Areas and Volumes
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Surface Area of a Combination of
Solids, Volume of a Combination of Solids, Conversion of Solid from One
Shape tAnother, Frustum of a Cone.
Statistics
CBSE Important Questions for class 10 Mathematics. The following topics and
points are given for download Introduction, Mean of Grouped Data, Mode of
Grouped Data, Median of Grouped Data, Graphical Representation of Cumulative
Frequency Distribution.
Probability
CBSE Important Questions for class 10 Mathematics. The following topics
and points are given for download Introduction, Probability A Theoretical
Approach. |
mathematics
Mathematics Tools is a tools that help people in solving Mathematical problems such as: - Solving quadratic equation and cubic equation - Solving System of equations (2 or 3 unknowns) - Working in the Base Numbe The applications are many and reach from education over science to productive use in your company: in exampleCur One thing is to study and try to solve problems on Plane Analytic... Icons are carefully created pixel by pixel by the hand of a professional artist. They shine with a bright palette of colors, smooth and well-rounded edges. Superb in their quality, icons will help a developer to... Field-level Online Help is included as well as an effective variety of Themes.... by less intricate equations. The problems presented are...
This bilingual problem-solving mathematics software allows you to work through 36319 arithmetic and pre-algebra problems with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation option offers a way to learn math lexicon in a foreign language. Test preparation options...
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Calculate tedious and difficult Statistics and Discrete Mathematics formulas accurately, quickly, and with ease! Combinatorics (permutations and combinations, etc.), probabilities, expected values, confidence intervals, data analysis, hypothesis testing and more.Statistics Pro does more than simply give you the correct answer! It helps to ensure your understanding of the formulas and concepts involved by showing, and explaining, the actual formula you're using, all with a simple click of the...
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For searches similar to mathematics see "Related Downloads" under the categories listing. |
The author supports a spiral method of learning by introducing the basics (more).(less)
Advance discrete structure is a compulsory paper in most of computing programs (M.Tech, MCA, M.
Sc, B.Tech, BCA, B.
Sc etc.).
This book has been written to fulfill the requirements of graduate and post-graduate students pursuing courses in mathematics as well as in computer engineering. This book covers the topics from Sets, Relations, Functions, Propositional logic, Techniques of proof, Lattice, Algebraic structures, Boolean algebra Combinatorics, Discrete numeric function, generating function and recurrence relation and Graph theory.
In this book each chapter starts with a clear statement of pertinent definitions, principles and theorems with illustrative and descriptive material. A large number of solved
"This book explains the basic principles of discrete Mathematics and structures in a clear systematic manner. A contemporary approach is adopted throughout the book.
The book is divided in five sections. First section discusses set theory, relations and functions, probability and counting techniques; second section is about recurrence relations and prepositional logic; third section is related to Lattices and Boolean algebra; fourth section includes study of graph and trees and the last section is about algebraic structures and finite state machines.
Suitable examples, illustrations and exercises are included throughout the book to facilitate an easier understanding of the subject. The book would serve as a comprehensive text for |
Groups
The Algebra One course begins with a fast-paced review of the previous year. The beauty, clarity, and utility of algebraic reasoning are explored through practical and not so practical challenges. We will conclude with a study of the quadratic formula, and introduce formal logical reasoning.
This section contains information for our Explorer Tournament El Toro Boat Building Project. Documents for this project are listed below. Not all documents are publicly available. For full access, login or create an account.
In eighth grade, students begin bulding functional furniture using
traditional tools and techniques. They often build a threee-legged stool, a
small table, or a bench. More complex use of mallots and gauges is required
in these projects, as well as a greatly expending set of other tools. Mortise
and tennon joints are used to join the legs to the top |
Equations and Solvers Loaded
Thank you for considering our selection of TI calculators and associated products. These new calculators from TI are exactly what you can buy in the store, with one exception. When you purchase a calculator from our online store, we will open your new calculator and load equations and solvers into your calculator's memory which can easily be used to solve many problems on the ACT test. A packet explaining the use of each program (including screen shots) will be included with every calculator purchase.
Area Solver for Triangles, Rectangles, Parallelograms, Trapezoids, and Squares
Equation of a Line, Slope of a Line, Y-Intercept, and X intercept solver given two points, slope and a point, or slope and Y-Intercept
Equation of a Circle
Slope, Distance (in decimal and Simplified Radical form), and Midpoint Solver given any two points
Distance Formula
Equation Solver for any Linear or Quadratic equation of 1 variable, 2 equations and two unknowns, or 3 equations and 3 unknowns.
Prime Factorization Finder
Perimeter, Area, and Diagonal Solver for Squares and Rectangles
Circumference and Area Solver for Circles
Perimeter and Area Solver for Triangles
Volume and Surface area Solver for Box, Cylinder, Sphere, Cone, and Doughnut
Volume Solver for Pyramid and Prism
Formulas for Area of a Trapezoid, Area and Circumference of a Circle, Volume and Surface Area of a Cylinder, Cone, and Sphere
Greatest Common Factor Solver given any two numbers
Logarithm Solver for base, term, or equal
Midpoint Formula
Midpoint Solver for Missing End when given one end and the midpoint but having to find the other end
Polygon Solver - When the number of sides is entered, the program produces the sum of interior angles, sum of exterior angles, total unique diagonal, diagonal per vertex, triangles, interior angle, exterior angle, and central angle
Quadratic equation and quadratic equation solver. When you enter A, B, and C, this program produces the values of X in simplified radical form and it handles imaginary numbers too.
Radical Reducer - This program reduces any positive radical to its simplified form
Definition of Rational and Irrational numbers
Right Triangle Solver - This program solves for the lengths of the three sides and the measure of the interior angles given any two sides, two angles, or a side and an angle
Sequence and Series Solver - This program analyzes the five elements of any sequence or series: 1st Term, Last Term, Distance Between Term, Number of Terms, and Sum of Terms. Given any three of the above five critical elements, the program produces the answer to the other two
Law of Sines and Cosines
Sine, Cosine, and Tangent
Solver using Sine, Cosine, or Tangent to find lengths of sides or angles
ACT® is the registered trademark of ACT, Inc.
Cargill Consulting®, Inc. has no affiliation with ACT, Inc., and is not approved or endorsed (nor would we want to be) by ACT, Inc. |
In maths A Level, you have 4 core modules (C1, C2, C3, C4) and 2 applied modules (S, D, and M).
In further maths A Level, you have 2 or 3 further pure modules (FP1 and FP2 and/or FP3), and then either 3 or 4 applied modules, depending on how many further pure units you took.
There shouldn't be any mechanics in the other modules, so if you just want mechanics, I'd just stick to M1, M2 and M3. |
Algebra II expands on the mathematical content of Algebra I and Geometry. While the topics in Algebra II are interesting and important in their own right, they also serve as a basis for the material presented in subsequent mathematics courses, e.g. trigonometry and calculus. Emphasis will be on functions and algebraic solu- tions to various types of problems. Abstract thinking skills (including some proofs, and the notion of 'generality of a statement') will be introduced and cultivated.
No ELL version
1 Credit
American Government – Credit Recovery
American Government is the study of the historical backgrounds, governing princi- ples, and institutions of the government of the United States. The focus is on the principles and beliefs upon which the United States was founded and on the struc- ture, functions, and powers of government at the national, state, and local levels. The principles of popular sovereignty, separation of powers, checks and balances, republicanism, federalism, and individual rights will be examined as will the roles of individuals and groups in the American political system. Students will compare the American system of government with other modern systems and assess the strengths and problems associated with the American system. |
This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs.
In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages.
This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
An instructor's manual for this title is available electronically. Please send email to [email protected] for more information.
Readership
Undergraduate and graduate students interested in applied mathematics and scientific computing. |
QAX - The Complete Mathematics Solution
What is QAX?
QAX Mathematics can be used for your school's entire mathematics program. It covers the secondary curriculum for each Australian state, negating the need for other teaching resources. Each topic within the curriculum has a supply of questions and an introduction including examples of questions with full working out.
Teachers can create work programs or question sets (called Q Sets) for each topic from the 50,000 available questions.
Students complete questions online or as printed worksheets.
The program assists students by providing example questions, hints and solutions.
A fully worked solution is shown to students once they have answered the question correctly or made two incorrect attempts.
Students who have answered incorrectly are shown the correct solution and then given similar questions to answer. |
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
Interactive Tutorial exercises: MathXL's homework and practice exercises are based on the same concepts tested in end-of-section and end-of-chapter questions in the textbook, and they regenerate algorithmically to give you unlimited opportunity for practice and mastery. Most exercises are free-response and provide an intuitive math symbol palette for entering math notation. Exercises include guided solutions and sample problems, and they offer helpful feedback when you enter incorrect answers.
Study plan for self-paced learning: MathXL's study plan helps you monitor your own progress, letting you see at a glance exactly which topics you need to practice. MathXL generates a personalized study plan for you based on your test results, and the study plan links directly to interactive, tutorial exercises for topics you haven't yet mastered. You can regenerate these exercises with new values for unlimited practice, and the exercises include guided solutions to give you the extra help you need.
Access Code info.
Register for MathXL
To access MathXL, you must complete an easy, one-time registration process.
3. If your instructor has set up an online course for your class, click Enrol in my instructor's course, and then choose your school, instructor, and course name. Otherwise, click to choose your textbook |
Written for advanced undergraduates and beginning graduate students, this exceptionally clear text treats both the engineering and mathematical aspects of elasticity. It is especially useful because it offers the theory of linear elasticity from three standpoints: engineering, Cartesian tensor, and vector-dyadic. In this way the student receives a more complete picture and a more thorough understanding of engineering elasticity. Prerequisites are a working knowledge of statics and strength of materials plus calculus and vector analysis. The first part of the book treats the theory of elasticity by the most elementary approach, emphasizing physical significance and using engineering notations. It gives engineering students a clear, basic understanding of linear elasticity. The latter part of the text, after Cartesian tensor and dyadic notations are introduced, gives a more general treatment of elasticity. Most of the equations of the earlier chapters are repeated in Cartesian tensor notation and again in vector-dyadic notation. By having access to this threefold approach in one book, beginning students will benefit from cross-referencing, which makes the learning process easier. Another helpful feature of this text is the charts and tables showing the logical relationships among the equations--especially useful in elasticity, where the mathematical chain from definition and concept to application is often long. Understanding of the theory is further reinforced by extensive problems at the end of of each chapter. |
Career and Starter Opportunities for Mathematics Students
When somebody says, "I'm going to be an
electrical engineer," or "I'm going to be a physicist," we have
some idea of what they might do, but who has ever heard of a
mathematician, outside of the academic profession. It is not that
mathematics doesn't get used every day, but its use is often hidden
from view. Complex economic and planning decisions, scientific
discoveries that improve our lives, and new technologies and
products are often possible only after mathematical or statistical
analysis, or computer visualization, simulation, design and
implementation based on mathematics. So, often people whose first
love is mathematics masquerade as systems analysts, data analysts,
operations researchers, engineers, quality control experts,
actuaries, statisticians, and financial analysts in business,
government and industry. They combine their interest in mathematics
with tough real world problems that need talent and creativity to
solve. Thus, lots of mathematically based careers exist that math
majors will find enjoyable and rewarding.
The purpose of this page is to give you some ideas about career
options by listing employers of successful Rose math grads, some
career info sites, graduate schools where Rose math grads have gone
and sources of information for mathematics based supper
opportunities. Deciding whether and when to go to grad school is a
topic your math profs would be happy to discuss with you.
Employers
Our mathematics graduates, who do not immediately go on to
graduate school, have obtained rewarding employment at
various companies and organizations. Here is a list of
employers and initial positions held by our alumni, during the last
10 years. |
Pre-Algebra
March 3, 2012
This course is designed to help students who have previously
shown a weakness in the fundamentals of mathematics as well as to
give all students a solid foundation in the fundamental concepts
of Algebra. Pre-Algebra is very helpful to incoming freshmen by
giving them a head start in their first year of high school
mathematics. |
Calculus Books
Calculus Books
calculus books. Are you looking for books for calculus students to better understand calculus topics?
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We have hundreds of books for calculus students to practice. This page lists books on calculus. You can navigate through these pages to locate our calculus books.
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique.
If you are preparing for the AP Calculus AB or BC exam, you'll find all the techniques and information you need in this guide. Cracking the AP Calculus AB & BC Exams, 2010 Edition comes from the test-prep experts at The Princeton Review, and it includes:
Functions Modeling Change: A Preparation for Calculus
The third edition of this ground-breaking text continues the authors' goal - a targeted introduction to precalculus that carefully balances concepts with procedures. Overall, this text is designed to provide a solid foundation to precalculus that focuses on a small number of key topics thereby emphasizing depth of understanding rather than breath of coverage. Developed by the Calculus Consortium, FMC 3e is flexible enough to be thought-provoking for well-prepared students while still remaining accessible to students with weaker backgrounds. As multiple representations encourage students to reflect on the material, each function is presented symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples and problems enable students to create mathematical models that will help them understand and interpret the world in which they live.
Math Subjects: Calculus
Low Price: $132.32
calculus book
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I am working on my first online precalculus course so I am interested in websites that can enhance the textbook presentation of material. |
Cecilton Microsoft ExcelAlgebra 1 can be very confusing when it is not explained properly. It is not a hard subject matter, it just demands a good teacher. I use basic formulas and equations in algebra 1 on a daily basis, and believe this can help me to help you understand the subject matter using real world examples. |
I have recieved many emails saying that there have been problems opening the documents. When you click on the link for the document, you need to choose to save it and then type in .docx (for word documents) at the end of the file name and under file type change it from zip file to all files (.xslx for excel documents). Please let me know if there are anymore problems!
Advanced Algebra
Advanced Algebra is an in-depth study of topics covered in Algebra I. A good understanding of Algebra I topics is required. Other topics include the study of roots, rational and irrational numbers, conics, solving and graphing quadratic functions, and an introduction to exponential and logarithmic functions. Students are introduced to the graphing calculator and learn how it is used in problem solving situations.
This course is designed for those with a strong background in mathematics. Topics covered include a thorough review of linear and quadratic functions and an in-depth study of polynomial functions. The study of functions in the abstract is facilitated through the study of their graphs using both pen and pencil and technology in the form of graphing calculators and computers. Topics covered include exponential and logarithmic functions and their applications in the real world; trigonometric functions, their equations, graphs and identities and their applications; sequences and series, functions and limits, and their relationship to calculus. Finite topics developed include matrices, combinatorics and probability. |
Mathematical Modeling
By
Mark Meerschaert, Michigan State University, East Lansing, MI, USA
Meerschaert's new edition strengthens his position as the survey text of choice for mathematical modeling courses, adding ample instructor support and leveraging on-line delivery for solutions manuals and software ancillaries.
From genetic engineering to hurricane prediction, mathematical models guide much of the decision-making in our society, and if the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor, as recent events have proved. Since mathematical modeling is a rapidly growing specialty with applications in so many scientific and technical disciplines, there is a need for mathematically rigorous treatments of the subject, and particularly for texts that expose students to a range of possible approaches.
Audience Advanced undergraduate or beginning graduate students in mathematics and closely related fields. Formal prerequisites consist of the usual freshman-sophomore sequence in mathematics, including one-variable calculus, multivariable calculus, linear algebra, and differential equations. Prior exposure to computing and probability and statistics is useful, but is not required.
Reviews
"I think this is the best book in its genre. I haven't been tempted to use another. The mathematics in it is interesting, useful, and still within reach of typical undergraduates." --John E. Doner, Department of Mathematics, University of California, Santa Barbara |
Dedicated to increasing and disseminating mathematical knowledge
Ross Program
Introduction
The Ross Program at the Ohio State University is an intensive course in mathematics
for pre-college students. This Program is sponsored by the University in partnership
with the Clay Mathematics Institute. During the eight weeks of this summer program, students are immersed in a world of mathematical
discovery. The first year students (ranging in age from 14 to 18) take the basic
course in number theory. For most of the students this is the first time they
will be asked to consider entirely new questions, to develop methods that they
have not seen before, and to justify every answer.
The central goal of the Ross Program has always been to instruct and encourage
bright young students in the art of abstract thinking and to inspire them to
discover for themselves that abstract ideas are valuable and important. The
Ross Program strives to achieve this goal in an eight week summer residential
program for talented high school students. It is a multi-level academic program
with an emphasis on mathematics. Spurred by the launch of the Sputnik and the
subsequent surge of interest in science education, Dr. Arnold Ross founded his
Program at Notre Dame in 1957. The Program moved to Ohio State in 1964 and has
run every summer since then.
The value of a mathematics education lies not only in obtaining proficiency
in computational tasks, but also in providing a foundation for critical thinking.
American high schools typically teach computational skills with little mathematical
theory. This emphasis on computation alone too often produces students who have
never practiced thinking for themselves, who have never asked why things work
the way they do, who are not prepared to lead the way to future scientific innovation.
It is precisely this independence of thought and questioning attitude that the
Ross Program strives to nurture.
First Year Students
The first year course in the Ross Program is organized around a series of
daily problem sets in number theory. These sets invite the students to contemplate
a variety of seemingly simple questions about numbers and their relationships.
As the summer progresses the students are encouraged to investigate these questions
in increasing depth, and to return to them periodically as their skill at abstract
reasoning and their collection of available tools become more powerful.
This spiraling of concepts is summarized in the Ross Program's motto:
"Think deeply of simple things."
Beginning with everyday knowledge of familiar numbers students observe some
curious properties and then search for satisfactory explanations of them. For
example, the students investigate topics involving prime numbers and modular
arithmetic. The early questions are numerical in nature and give the students
a chance to become familiar with the basic ideas. As soon as they have made
some computations, however, they are asked to formulate more general statements
that include their numerical examples as special cases. Students then try to
explain their new observations, thus returning to the original questions at
a different level. After mastering these more complex issues, they encounter
versions of those questions in other contexts and begin to appreciate them from
a deeper perspective. Some of these investigations eventually lead to significant
insights about the structure of number systems, the underpinnings of algebraic
formalism and the relationship between numbers and geometry. By considering
simply stated questions from several directions and depths, these young students
attain an understanding of how professional mathematicians and scientists work:
gathering data, looking for patterns and analogies, making conjectures, and
finally testing and proving those conjectures.
Advanced Students and Counselors
In order for this intensely problem-based approach to succeed, the students
must be given careful and personal feedback on their work. This role is played
by the counselors, who live in the dormitories along with the younger participants.
The counselors are graduates of the Ross Program who are studying mathematics
and science as undergraduates in some of the best colleges and universities
of the United States. Each counselor works directly with several first year
students, contributing a tremendous amount of time and energy to their students.
The counselors contribute to the overall atmosphere of excitement at the Ross
Program by working on challenging advanced courses or on other topics they find
of interest. Their enthusiasm is contagious and their dedication is inspiring
for the younger students. The counselors work to bring the program participants
together to form a true community, but ultimately much of this task falls to
the students. It is the students themselves who must devote their energy to
meet the challenges set for them.
Beginning students who do well are invited back for a second summer, and may
return as junior counselors or counselors in subsequent summers. Returning students
and counselors also take advanced courses which vary from year to year.
Enthusiasm for the Ross Program is evident in comments posted
on the Ross
Program Alumni Home Page.
Costs and Financial Aid
The $2500 fee pays for eight weeks of room and board in a college dormitory. Some financial aid is available for qualified students.
Eligibility
Ambitious pre-college students with strong interests in mathematics are invited
to apply. The first year students range in age from 14 to 18, although exceptions
are made in some cases. Admission decisions are based on several criteria, including:
the applicant's solutions to some interesting mathematical problems included
with the application; teacher recommendations; school transcripts; and a short
essay describing the student's interest in mathematics and in the Ross Program.
Requests for Applications
Anyone interested in applying to the Ross Program should print a paper copy
of the application form, answer the questions, work on the mathematical problems,
and send it all to the address below. Electronic submissions will not be accepted.
Paper copies of the application form are also available by mail. To get a copy,
send a letter to the address above or call the Ross Program office at (614)
292-1569. Further information about this summer mathematics program is available
at [email protected]. |
Book 14017 section of the "Next Step" manual for adults demonstrates the mathematics applications for Number Operations; Fractions, Decimals, and Percent; Percent and Ratio; Measurement, Integers; Equations: Equalities and Inequalities; Graphs.
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The Book 14018 section of the "Next Step" manual for adults demonstrates the mathematics applications for Number Operations; Fractions, Decimals, and Percent; Percent, Ratio, and Proportion; Geometry; Measurement, Integers; Equations: Equalities and Inequalities; Graphs.
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The Book 14011 section of the "Next Step" manual for adults demonstrates the mathematics applications for Whole Numbers (Number/Word Recognition, Place Value, Counting, Addition, Subtraction) and Measurement (Time). |
Functions Modeling Change: A Preparation for Calculus, 3rd Edition
The third edition of this ground-breaking text continues the authors' goal - a targeted introduction to precalculus that carefully balances concepts with procedures. Overall, this text is designed to provide a solid foundation to precalculus that focuses on a small number of key topics thereby emphasizing depth of understanding rather than breath of coverage. Developed by the Calculus Consortium, FMC 3e is flexible enough to be thought-provoking for well-prepared students while still remaining accessible to students with weaker backgrounds. As multiple representations encourage students to reflect on the material, each function is presented symbolically, numerically, graphically and verbally (the Rule of Four). Additionally, a large number of real-world applications, examples and problems enable students to create mathematical models that will help them understand and interpret the world in which they live.
for Functions Modeling Change: A Preparation for Calculus, 3rd Edition. Learn more at WileyPLUS.com
Exceptional Problems: Examples and problems based on real data help students create mathematical models to help them understand their world. An appropriate number of drill problems are included to assist students in learning techniques. The problems are varied and some are more challenging. Most cannot be done by following a template in the text.
Allows for a broad range of teaching styles. This text is flexible enough for use in large lecture halls, small classes, or in group or lab settings.
Focuses on fewer topics than is customary, but each topic is treated in greater depth. Only those topics essential to the study of calculus are included.
Reflects the spirit of the standards established by the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC), and meets the recommendations of the National Council of Teachers of Mathematics (NCTM).
Assumes technology has a place in modern mathematics. This text takes full advantage of technology when appropriate, although no specific technology is emphasized. It is important for students to learn how and when to use technology as a tool, as well as its limitations. However the focus of the text is on conceptual understanding not technology.
The Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally. |
Book Description: Mathematics for Veterinary Medical Technicians provides a one-semester course in the basics of mathematics needed for Veterinary Technicians and Assistants. This revised edition has incorporated suggestions for improvement; some material has been reordered to improve presentation. The course covers fractions, decimals and percentages without the use of calculators as is the case on many State Board Exams. In addition to basic mathematical computations, several chapters are devoted to application problems involving dosage, concentration, dilution and the computation of infusion rates. An introduction to reading graphs is presented as well as a chapter on basic statistical concepts and measures. The language is designed to be readable and in terms of everyday usage rather than formal and strict mathematical terms. The workbook style of the text allows students the freedom to move at a pace that ensures mastery of the material as well as flexibility for covering topics in any prescribed manner. In many programs, this may be the only math course students are required to take. The material will be valuable and useful in other courses such as chemistry and clinical practices labs. A teacher's manual that includes complete solutions, quizzes, tests (including a pretest and final exam) and additional worksheets is available. For the benefit of students, the answers to odd numbered exercises are provided in the Answer Keys. |
Ringoes Algebra often, strategies that allow learners to visualize concepts and instruction that slows down processing time proves to be just the action needed for success. Remedial work on basic skills with an eye on current home work and classroom assignments is important to keep a struggling student feeling confident. Building self-confidence in math is a key to achievementLearn how to manipulate the formulas using the list of the trigonometric identities to solve complex problems. Lean about the physiology and anatomy of the human body. All the different systems, how they function, and how they can be affected by your nutrition |
The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English!
Synopsis
Whether you need help solving equations or determining the slope of a line, this guide gives you the tools you need to find your answers! Beginning with the basics, you will learn and practice all the skills needed to enhance your algebra expertise.
This comprehensive guide covers all the key concepts, including:
Variables and expressions
Linear equations and inequalities
Monomials and polynomials
Exponents
Rational expressions
The Pythagorean theorem
Area and perimeter
Graphs and charts
Inside you'll find hundreds of examples to illustrate the basics and plenty of exercises to ensure mastery of these fundamentals. No matter if you're a student looking for a companion to your textbook, or a curious learner who's been away from the classroom too long, this will be your indispensable algebra |
College Algebra and Trigonometry
Study Guide with Student Solution Manual for Aufmann/Barker/Nation's College Algebra and Trigonometry, 7th
Summary
Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Seventh Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Seventh Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts. |
Multimedia Algebra: What Is an Equation?
Content on this page requires a newer version of Adobe Flash Player.
In this lesson, we explore what an equation is.
Using the Multimedia Algebra Lessons:
Click on the left/right navigation buttons to scroll through the lesson.
Click on the Audio Play button to start the audio. The audio will not play automatically. Press the Pause button to pause the audio and resume the audio by pressing the Play button. If you press the Stop button, the audio will cease playing and the next time you press Play, the audio will start from the very beginning.
If a page has a video, the video controller works the same way as the audio controller. Furthermore, in the case where there are both video and audio buttons, clicking on on the audio button shuts off the video, and vice-versa.
If a page has an interactive component, use the Reset button to clear the screen.
Click the Practice button to launch the practice worksheet for a lesson.
The Multimedia Algebra Library is a comprehensive collection of multimedia lessons for Algebra 1, Algebra 2, Developmental Math, and other algebra-focused math courses. Each lesson in the Multimedia Algebra Library covers a key concept from algebra, providing text and audio instruction, real-world examples of algebra, and interactive math tools. Each lesson includes a practice worksheet.
Each chapter of the Multimedia Algebra Library includes mid- and end-of-chapter assessments provided in an interactive format.
The Multimedia Algebra Library currently consists of the following lessons (more will be added throughout 2012). The full library consisting of 12 chapters will launch in the fall of 2012 and will become a full subcription service. In the meantime, we offer this preview version of the full site free.
Let us know what you think. Send us a message at [email protected]. |
For Dummies Store
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The fun and easy way to learn pre-calculus Getting With this guide's help you'll quickly and painlessly get a handle on all of the concepts — not just ... Read More
Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common ... Read More |
... edu
...Probably one of the most challenging parts of learning and teaching is mastering a concept. This step requires going through more examples but in potentially greater depth and complexity. An Annotated Example of these steps:
(Calculus--Derivatives)
1. |
Unit specification
Aims
To give an introduction to the basic ideas of geometry and
topology.
Brief description
This course unit introduces the basic ideas of the geometry of
curves and surfaces in Euclidean space, differential forms and elementary
topological concepts such as the Euler characteristic. These ideas
permeate all modern mathematics and its applications.
Intended learning outcomes
On successful completion of this module students will have acquired
an active knowledge and understanding of the basic concepts of the geometry
of curves and surfaces in three-dimensional Euclidean space and will be
acquainted with the ways of generalising these concepts to higher dimensions.
Future topics requiring this course unit
The ideas in this course unit will be developed further in third
and fourth level course units in geometry and topology.
Syllabus
Recollection of lines and planes in R3.
Equations in various forms, normal vector to a plane, distance from a
point to a plane.
Differential forms in R2 and R3.
Geometrical meaning of differential forms. Examples: area of
parallelogram, volume of parallelipiped. |
You will be completing math assignments pertaining to the probability and statistics. Tasks will include watching videos, playing math games online, writing journals, completing discussions, and performing math computation and application skill problems. |
Lattices and Ordered Algebraic Structures provides a lucid and concise introduction to the basic results concerning the notion of an order. Although as a whole it is mainly intended for beginning postgraduates, the prerequisities are minimal and selected parts can profitably be used to broaden the horizon of the advanced undergraduate. The treatment is modern, with a slant towards recent developments in the theory of residuated lattices and ordered regular semigroups.
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course.
This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijk's lectures offer a detailed introduction to dendroidal sets, which were introduced by himself and Weiss as a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it also reveals new phenomena.
The third book of a three-part series, Algebraic, Graphics, and Trigonometric Problem Solving, Second Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and the accompanying practice exercises. Along with the activities and the exercises within the text, MathXL® and MyMathLab® have been enhanced to create a better overall learning experience for the reader. Technology integrated throughout the text helps readers interpret real-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops readers' mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines.
This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues.
This book constitutes the refereed proceedings of the Third International Conference on Algebraic Informatics, CAI 2009, held in Thessaloniki, Greece, in May 2009. The 16 full papers were carefully reviewed and selected from 25 submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraic aspects of cryptography. |
The Probability & Statistics Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers the addition rules of probability in Probability and Statistics, including what the addition rules of probability really mean and why they are important. Grades 9-12. 63 minutes on DVD.
Customer Reviews for Addition Rules of Probability DVD
This product has not yet been reviewed. Click here to continue to the product details page. |
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Without a basic understanding of maths, students of any science discipline are ill-equipped to tackle new problems or to apply themselves to novel situations. This book covers essential topics that will help encourage an understanding of... |
Complex Analysis
9780387950693
ISBN:
0387950699
Pub Date: 2001 Publisher: Springer Verlag
Summary: The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of to...pics designed to complete the coverage of all background necessary for passing Ph.D. qualifying exams in complex analysis.[read more]
Ships From:Secaucus, NJShipping:Standard, Expedited, Second Day, Next DayComments: This item is printed on demand. An introduction to complex analysis for students with some knowl... [more] This item is printed on demand. An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The r. [less] |
. T. (P) Caribbean Mathematics: Review Test & Ans Bk. 1
Average rating
5 out of 5
Based on 1 Ratings and 1 Reviews
Book Description con... More content of some chapters for which extra testing seemed necessary. The majority of these basic tests will require 20-40 minutes depending on the pupil's ability. The interim review tests are appropriately placed to ensure that students are able to review at regular intervals work previously covered. The suggested time required for these tests is 40 minutes. A comprehensive major test appears at the end and this covers the content of the text. The recommended time for this is 45-50 minutes. A separate sheet of answers is provided. |
Choose your search criteria in the right column.
lecture
Highlights the utility of mathematics in everyday life; increasing proficiency in advanced formula and problem solving, including real world applications. Prerequisite: MTH090 or satisfactory score on the Math placement test.
Highlights the utility of mathematics in everyday life; increasing proficiency in advanced formula and problem solving, including real world applications. Prerequisite: MTH090 or satisfactory score on the Math placement test.
Introduction to the theoretical and practical basis for mathematics taught in grades Pre-K-6. The organization of the course comes from the Principles and Standards of the National Teachers of Mathematics (NCTM). Topics include Calculation and Estimation, Statistics and Probability, Algebraic Relationships, Measurement, Geometric Concepts, and Mathematical Problem Solving. Prerequisite: Mth 110. |
Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently r [more]
Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill |
Chambers Adult Learners' Guide to Numeracy By N/A
Chambers
Detailed Description
Written in an exceptionally clear style, illustrated by diagrams and examples Covers all essential numeracy, from whole numbers to fractions and percentages Applies the knowledge to everyday skills such as taking measurements and performing financial calculations Exercises help the reader to consolidate the knowledge and skills Additional notes throughout provide tips, pointers to common mistakes and hints for using a calculator Chambers Adult Learners��� Guide to Numeracy is a completely new book aimed at adults who lack confidence in their numeracy skills. The book provides users with an understanding of the key concepts and methods, then applies them in real-world situations such as calculating distances or working out interest payments. The two-colour text is clearly and spaciously laid out, and plentiful examples, diagrams, and exercises reinforce all the learning points. The typeface has the approval of the British Dyslexia Association. The book is based around the 'Skills for Life' numeracy curriculum created by the Department for Education and Skills and its author, Geoff Mainwaring, is a highly experienced teacher and lecturer in numeracy. What it says on the back of the book Chambers Specially written for adult students by an experienced tutor Covers all the essential aspects of numeracy Spacious two-colour text features illustrations and diagrams Includes examples and exercises to reinforce the learning points Suitable for self-study or to complement basic-skills teaching |
Mathematics is a compulsory subject until the end of Year 11 and is one of the few subjects taught banded, with high-expectation groups extended and accelerated. Students with needs in numeracy are also targeted with extra support.
Homework
Students will receive homework on a daily basis except on assessment days; this is checked and feedback is given. Homework has a tremendous impact on student achievement and thus gets taken very seriously.
Assessment
Year 9 and 10 students study the units from the 3 strands of the New Zealand Mathematics Curriculum over their schooling. Assessment is aligned as closely to the structure of NCEA as possible. So a unit may be assessed as "Internal" (a project style assessment assessed during the year) or "External" (assessed at the end of the year in an examination).
Senior courses are entered in a combination of Unit Standards (best grade is achieved) and Achievement Standards (can also achieve with Merit and Excellence)
Structure
Year 9
Four Bands. Students are assessed in term 1 and placed appropriately in 1 of these 4 bands.
Year 10
Four Bands. Students are placed according to their final results in Year 9.
Year 11
Four courses to cater for the different needs of all students. The content and assessed standards in these courses is carefully selected to be give each student the chance to achieve well and be challenged.
Year 12
Three different courses to cater for the needs of all students - regular holiday workshops
Year 13
Mathematics with Statistics : Two courses
Mathematics with Calculus : Two courses
More information about each course can be found in the student handouts that all students receive at the beginning of their course.
Maths Publication
Maths Uncensored is a delightful read, put together entirely by students and aimed at introducing Maths at Springs to the community. |
References
Using GPS to Teach More than Accurate Positionspart of SERC Print Resource Collection Undergraduate science majors need practice in critical thinking, quantitative analysis, and judging whether their calculated answers are physically reasonable. We have developed exercises using ...
This website is devoted to different methods of approximation. The site describes using orders of magnitude, scaling, simplifying numbers, exponential notation, and Fermi questions. Included with the ...
The Mathematical Association of America (MAA) has sought to improve education in collegiate mathematics. This report outlines standards set forth by the MAA to improve college mathematics education. ... |
Information Portals
Mathematics
Mathematics
Math Forum
The leading online resource for improving math learning, teaching, and communication since 1992.
Math on the Web
Site and journal AMS - American Mathematical Society, journal ZBMATH (Zentralblatt MATH) in full text.
Mathematik.de
German site for improving math learning (you can choose level). Part of it goes without registration and gives an explanation of the selected topic.
MathGuide
The MathGuide is an Internet-based subject gateway to scholarly relevant information in mathematics, located at the Lower Saxony State and University Library, Göttingen (Germany).
Math-net
Math-Net intends to coordinate the electronic information and communication activities of the global mathematical community with the aim to enhance the free-flow of information within the community. Math-Net is a global electronic information and communication system for mathematics. |
"The Barnett, Ziegler, Byleen College Algebra" series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and ...
College Algebra: Concepts and Models provides a solid understanding of algebra, using modeling techniques and real-world data applications. The text is effective for students who will continue on in ...
David Cohen's COLLEGE ALGEBRA, Fifth Edition, focuses on teaching mathematics, using a graphical perspective throughout to provide a visual understanding of college algebra. The author is known for ... |
Calculus B, the second of a two-semester course, focuses on how to calculate and graph anti-derivatives and integrals, as well as how to apply these techniques to real-world problems. In addition, students also study topics in sequences and series. Students find the derivatives of several different functions and apply these derivatives in application problems. They also calculate volume, surface area, and arc length by working with applications of the integral. Finally, students differentiate and integrate multidimensional functions. |
Short film on alternativ energy production in Austria, by Lebensministerium Austria (duration 2 min.).
Author(s): No creator set
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Related contentNASA CONNECT Proportionality: Modeling the Future In NASA CONNECT Proportionality: Modeling the Future, students learn why scaling and proportion are important in the design of small aircraft transportation systems. Mathematical patterns are described through practical applications such as the growth of transportation, the Golden Ratio, and the Fibonacci sequence. Grades 4-8.The Development and Use of Representations in Teaching and Learning about Problem Solving: Exploring Tim Boerst has explored instructional approaches that foster the development of representational skill and routine use of multiple representations in problem solving. In particular he has used the 'Rule of 3' (a structure employed in calculus reform materials that highlights the use of numerical, algebraic, and/or graphic representations in mathematical learning) to see whether an emphasis on multiple representations would deepen mathematical learning opportunities for a wide variety of students
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Mathematics Under the Microscope This book inevitably asks the question "How does the mathematical brain work?" The author tries to reflect on the explosive development of mathematical cognition, an emerging branch of neurophysiology which purports to locate structures and processes in the human brain responsible for mathematical thinking. PDF file. Author(s): No creator set
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Basic Analysis: Introduction to Real Analysis This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course woulSkyMath: Mathematics for a Blue Planet SkyMath is a set of middle school mathematics modules incorporating weather data. TheHelping Your Child Learn Mathematics and Statistics This site features dozens of fun activities parents can use to help children (K-5th grade) have fun learning geometry, algebra, measurement, statistics, probability and other important mathematical concepts. Activities relate math to everyday life and can be done at home, at the grocery store, or while traveling. It includes sections for parents on what math is like in schools today and a parents' booklist for helping children learn math |
CCEA Foundation GCSE Mathematics
Neill Hamilton, Rosi MacCrea
Summary: This book covers the complete Foundation GCSE Mathematics course for years 11 and 12. Each chapter begins with Learning Objectives and pre-requisite knowledge. There are worked examples and full and clear explanations as well as teaching and learning tips throughout. Non-calculator and calculator questions are clearly indicated. Each chapter ends with a 'You should know' list of what has been covered in that chapter, and a summary exercise, as well as past exam questions.
Written especially by Northern Ireland authors to match the 2010 GCSE Mathematics specification from CCEA.
Complete coverage of the Foundation tier modules and completion paper. |
Holt McDougal Mathematics
The new Tables of Contents for Holt McDougal Mathematics for Grades 6, 7, and 8 math textbooks reflect a new focus on concepts that are taught in depth.
Holt McDougal Mathematics textbooks implement the Standards for Mathematical Practice into student learning and teacher resources, resulting in a deeper understanding of math strategies and concepts.
Embedded Response to Intervention resources within the Grade 6–8 math textbooks ensures every student gets the help they need.
More than just a print edition, our Grade 6–8 math textbooks are also available as an online textbook and eTextbook, downloadable on any mobile device.
Teacher and student resources are available in print, online, and mobile—providing the kind of anytime/anywhere access to resources that today's teaching environment demands and today's students deserve.
You can even customize your book to the distinct needs of your school or district.
No other math program empowers students to develop the core skills they need like Holt McDougal Mathematics does. A new era and a new approach for reaching all students! |
Other Materials
Description
Middle School Math 1 continues to build on concepts introduced in the elementary school. Most seventh grade students should be enrolled in this course, as it provides the foundation for Algebra and beyond. Students will explore and solve mathematical problems, think critically, work cooperatively with others, and communicate their ideas clearly as they work through mathematical concepts. A summary of the major concepts and procedures learned in this course follows. In seventh grade, students will add, subtract, multiply, and divide rational numbers, including positive and negative fractions, decimals and integers. Students will also extend their work with ratios to solve problems involving a variety of proportional relationships, such as making conversions between measurement units or finding the percentof increase or decrease of an amount. Students will explore proportional relationships found in similar figures, graph proportional relationships and identify slope in situations, tables,graphs, and equations. They will extend their understanding of surface area and volume to include finding surface area and volume of cylinders and volume of cones and pyramids. Students will broaden their understanding of probability. They will revisit how to interpret data, using more sophisticated types of data graphs and thinking about the meaning of certain statistical measures. Finally, students will extend their coordinate graphing skills, and begin their use of exponents |
Introduction Casio have had the school scientific calculator market pretty much sewn up for as long as I can remember. Back when I was doing my GCSEs - shortly after we'd stopped carving notches on mammoth tusks - I had one of the original fx-82 models, and variants of that trusty machine served me well for the rest of school and beyond. The spiritual successor to that calculator is this one, officially dubbed the fx-83GT PLUS. Why Casio felt the need to use that idiotic ALL CAPS formatting is beyond me, but given that car-like "GT" moniker maybe it can be considered the equivalent of go ...
more |
This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic models concurrent with the development of distribution theory while also introducing the reader to basic statistical inference. In this way, the major stochastic processes are blended with coverage of probability laws, random variables, and distribution theory, equipping the reader to be a true problem solver and critical thinker.
Deliberately conversational in tone, Probability is written for students in junior- or senior-level probability courses majoring in mathematics, statistics, computer science, or engineering. The book offers a lucid and mathematicallysound introduction to how probability is used to model random behavior in the natural world. The text contains the following chapters:
* Modeling
* Sets and Functions
* Probability Laws I: Building on the Axioms
* Probability Laws II: Results of Conditioning
* Random Variables and Stochastic Processes
* Discrete Random Variables and Applications in Stochastic Processes
* Continuous Random Variables and Applications in Stochastic Processes
* Covariance and Correlation Among Random Variables |
Calculus And Its Applications - 11th edition
Summary: This text is geared towards a one semester course in applied calculus.
This extremely readable, highly regarded, and widely adopted text presents...show more tried and true formula--pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises--has proven to be tremendously successful with both students and instructors.
Features
Exercise sets:
Carefully designed, building in level of difficulty so that instructors can chose those exercises appropriate for their students.
Thoroughly tested and very diverse.
Technology exercises offered at the ends of each section.
Applications: Contain up-to-date and realistic data to illustrate to students the relevance of these concepts.
Examples: Contains many more worked examples than is customary, many of which include real data.
Practice Problems: Each section concludes with ~5 problems that focus on concepts that are potentially confusion. Complete solutions are provided.
''Warnings!'' which provide tips on common pitfalls and mistakes appear at relevant times.
0.1 Functions and Their Graphs 0.2 Some Important Functions 0.3 The Algebra of Functions 0.4 Zeros of Functions--The Quadratic Formula and Factoring 0.5 Exponents and Power Functions 0.6 Functions and Graphs in Applications
1 The Derivative
1.1 The Slope of a Straight Line 1.2 The Slope of a Curve at a Point 1.3 The Derivative 1.4 Limits and the Derivative 1.5 Differentiability and Continuity 1.6 Some Rules for Differentiation 1.7 More About Derivatives 1.8 The Derivative as a Rate of Change
2 Applications of the Derivative
2.1 Describing Graphs of Functions 2.2 The First and Second Derivative Rules 2.3 The First and Second Derivative Tests and Curve Sketching 2.4 Curve Sketching (Conclusion) 2.5 Optimization Problems 2.6 Further Optimization Problems 2.7 Applications of Derivatives to Business and Economics
3 Techniques of Differentiation
3.1 The Product and Quotient Rules 3.2 The Chain Rule and the General Power Rule 3.3 Implicit Differentiation and Related Rates |
Engineering Mathematics By Grewal
Mental Arithmetic 2.0
Mental Arithmetic has been designed to provide pupils with unlimited practice in the fundamentals of mathematics by teachers David Benjamin and Justin Dodd, the UK's leading experts on the use ...
Racing Academy 1.0
The sole purpose of this game is to educate users in engineering concepts by playing the game. The concept is creating a racing game with realism in physics, engine management, and other factors in the ...
MathGenius 0.1
MathGenius is a graphical tool intended to simplify your work in mathematics. By now it includes a graphical function plotter, a mechanism (still in development) to derive functions, and an equation solver.
20sim Viewer 4.2.1.1
This helps you to enter models as in an engineering scheme: by choosing components from the library and connecting them, your engineering scheme is actually built without entering a single line of math!
Engineering - Mystery Of The Ancient 1.0.0.1Engineering - Mystery of the ancient clock is a matching game in which you must repair a chronometer by collecting its different parts that are scattered around the world. Throughout the game, you will ...
SciPy 0.9.0 RC 1
SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy ...
FRED Optical Engineering Software 9.1
The FRED Optical Engineering Software is capable of simulating the propagation of light through any optomechanical system by raytracing. Whether the design is imported from CAD, a lens design program, ...
Visual Mathematics 1
Visual Mathematics is a highly interactive visualization software (containing -at least- 67 modules) addressed to High school, College and University students. This is a very powerful tool that helps ...
MBSS Gravity Wells 2.0
MBSS Gravity Wells is the quintessential celebration of color, motion and mathematics as particles fill the screen in brilliant patterns as influenced by wandering gravity wells.Setup properties of the ...
Cumulative Probability Plot 3.0
Cumulative Probability Plot does all of the statistical mathematics for you and outputs the data in a visual format that can be easily interpreted by people with a limited knowledge of statistics. DownloadView Info
EasyBlank 1. 3. 4000
EasyBlank® is a software program developed by AutoForm Engineering and uses the AutoForm-OneStep solver to mesh, tip and calculate a flat layout. The purpose of the EasyBlank® software is to calculate ...
CheckStressPDMS 6.0
checkSTRESS is a unique solution to the old problem of project delays caused by 'back and forth' piping layout design reviews between the Design and Engineering departments. Simple and elegant, checkSTRESS' ...
Uconomix Encryption Engine 1.0.2441
The Uconomix Encryption Engine is a encryption/decryption software for protecting files by using powerful mathematics algorithm for encryption and a personal password.
IFileplay 1.0
iFileplay is a free utility developed by Global Engineering Security Systems. With iFileplay you can play the recorded .irf files by "File Play" in CMS. It allows you to change the ...
Mine Conveyor 3.5
Providing unique material handling engineering software written by and for engineers. Main features: - Get capacity results without entering power data. - Full load is always calculated for comparison.
Python - Scipy 0.9
Python - scipy is open-source program for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy library depends on NumPy, ...
Tilt-DesignNS 2.1
Tilt-DesignNS was developed by a practicing engineer, and designed exclusively for use by engineering professionals. In order to provide functionality well beyond what you would find in a typical, simple ...
Watch Window Professional 1.6
Watch Window Professional is an engineering and troubleshooting tool, typically used by service engineers for loading new Woodward GAP Application software, and viewing the "Debug" variables ...
Eurostag 4.3
EUROSTAG® is a software developed by Tractebel Engineering GDF SUEZ and RTE for accurate and reliable simulations of power systems dynamics. EUROSTAG® is used worldwide for studies, research, ...
SLOC Metrics 3.0
SLOC Metrics measures the size of your source code based on the Physical Source Lines of Code metric recommended by the Software Engineering Institute at Carnegie Mellon University Specifically, the ...
ThermoSolver 1.0
ThermoSolver is a software program which accompanies the textbook Engineering and Chemical Thermodynamics by Milo Koretsky . This software allows students to perform complex thermodynamics calculations, ...
Lernen Experimental 2.3
Catchy, easy-to-remember experiments for practice and understanding mathematical problems on all topics covered by the curricula of school mathematics., − the innovative mathematics learning ...
ETF Pong 0.1
ETF Pong is a Video game made by group of enthusiasts from School of Electrical Engineering, University of Belgrade. It is very simple to play. It has a very attractive interface. Try and play it. You ...
YagnaQBuilder-Chemistry-KCET 3.0
The Karnataka CET (KCET) examination, since 1984, has been conducted every year by the Government of Karnataka for admission in the Engineering and Medical Colleges of this state. The admission process ...
Arduino2Lego 2008
Arduino2Lego is a project developed at the Politecnico of Milan by a Computer Science Engineering student.It aims to make all Lego NXT peripherals (motors, sensors,...) easily usable from Arduino.
ASCEND Modelling Environment 0.9.8
ASCEND is a modelling environment and solver for large or small systems of non-linear equations, for use in engineering, thermodynamics, chemistry, physics, mathematics and biology. Solvers for both steady ...
Boundalyzer 1.0
The Boundalyzer is a tool for building and analyzing boundary specifications for software artifacts, inspired by the Black Box Specification of Harlan Mills, which is also one element of the Cleanroom Software Engineering process.
ChemProV 1.11.4.0
ChemProV is a tool used by chemical engineering students to solve material balance problems. The project is maintained by Washington State University. For more information on how to install ChemProV, ... |
College Algebra
MAT 120 with minimum grade of C or appropriate score on Mathematics Placement Test, and MAT 053 or geometry proficiency.
III. Course (Catalog) Description
Course surveys algebraic and exponential functions. Content includes polynomial,
rational, exponential, logarithmic, and special functions systems of equations
and inequalities, sequences and series, and the binomial theorem.
IV. Learning Objectives
A. Understand the concepts of relation and function. B. Understand the use of function notation. C. Understand the relationship between a function and its inverse. D. Graph and recognize the basic characteristics for the following functions: linear, quadratic, polynomial, rational, exponential, and logarithmic. E. Solve systems of linear and nonlinear equations and inequalities. F. Apply the concepts of sequence and series. G. Use technology for graphing and evaluating functions. 1. Generate the complete graph for the elementary functions. 2. Solve equations involving elementary functionsMethods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate. Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
(To be completed by instructor.)
Methods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate.
IX. Instructional Materials
Textbook information for each course and section is available on Oakton's Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".
Textbooks can also be found at our Mathematics Textbooks page.
A graphics calculator is required. A TI-83 will be used for instructional purposes.
X. Methods of Evaluating Student Progress
(To be completed by instructor.) Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam |
GraspMath Learning Systems Introductory Algebra (8) VHS Combo
Please Note: Pricing and availability are subject to change without notice.
The Introductory Algebra Video Tutor series consists of 8 tapes containing approximately 12 hours of video instruction. Topics include fractions, real numbers, exponents, solving linear equations and inequalities and application, polynomials, factoring, rational expressions, ratio and proportions, graphing linear equations and inequalities and equations of lines, functions, systems of linear equation and inequalities, radicals, rational exponents, solving quadratic equations. Many of the topic titles are the same as for the intermediate algebra series, but at a level consistent with beginning algebra courses.
Video 1 -Operations on Fractions & Real Numbers, Like Terms
Operations on Fractions.
This segment covers simplest form as well as addition, subtraction, multiplication and division of fractions.
Operations on Real Numbers.
This segment covers Addition, subtraction, multiplication, and division of signed numbers. Absolute value and opposites are also included.
Exponents, order of Operations, and Introduction to Variables.
This segment covers an introduction of exponents by raising signed numbers (including fractions) to positive integral powers. Order of operations is also covered as well as an introduction to variables. Evaluating an expression by substituting given replacement values for variables is included.
Combining Like Terms.
This segment covers the definition of a term, like terms, and numerical coefficients. The distributive property is used to combine like terms.
Video 2
Applications of Linear Equations.
This segment covers steps that may be used to solve applications. Translating phrases into expressions is included as well as solving applications by setting up and solving linear equations.
Solving Linear Inequalities.
This segment covers solving linear inequalities by isolating the unknown using methods similar to those for linear equations. The reversal of the inequality symbol when multiplying both sides of an inequality by a negative number is also covered.
Exponents.
This segment covers the laws of exponents and their use in simplifying algebraic expressions. This segment includes negative exponents.
Video 3 -Polynomials, Factoring, Quadratic Equations.
Operations on Polynomials.
This segment covers addition, subtraction, multiplication, and long division of polynomials. The First, Outer, Inner, Last (FOIL) method for multiplying a pair of binomials is also covered.
Factoring, Part I the case of polynomials with four or more terms, the method of factoring by grouping is covered.
Factoring, Part II
Solving Quadratic Equations by Factoring.
This segment covers the method of solving quadratic equations by first rearranging terms so as to force one side of the equation to be identically zero and then factoring the resulting trinomial or binomial. The factors are then used to obtain linear equations for the solutions.
Video 4 -Rational Expressions, Ratio and Proportions.
Rational Expressions - I.
This segment covers multiplication and division of rational expressions as well as reducing to lowest terms by factoring both numerator and denominator. In case of multiplication the use of dividing out common factors before multiplication to simplify work is covered.
Rational Expressions - II.
This segment covers addition and subtraction of rational expressions by finding the least common denominator after factoring all denominators. This segment also covers simplifying complex fractions.
Equations with
Ratio and Proportion.
This segment covers a definition of ratio as well as three ways of writing ratios. Proportions are solved by setting cross products equal, and applications are solved by setting up and solving proportions.
Video 5 -Graphing Linear Equations, Inequalities, Slope
Applications with Rational Expressions.
This segment covers solving applications by setting up and solving equations that contain rational expressions.
Graphing Linear Equations.
This segment covers graphing lines in the plane using rectangular coordinates via the method of tabulating and plotting points which satisfy the equation of the line.
Slope and Equations of Lines.
This segment covers the slope formula and finding the slope of a line by using the slope-intercept form of a line. Horizontal and vertical lines are included.
Slope and Graphing Inequalities.
This segment covers the slope-intercept and point-slope forms for the equation of a line. The relationship of slope to steepness and methods of calculating slope via rise over run as well as rearrangement into slope-intercept form is covered. Parallel and perpendicular lines are also covered as well as graphing inequalities by graphing their boundary equations and using a test point off the boundary to determine the solution region.
Video 6 -Systems of Equations, Word Problems, Radicals
Systems of Equations.
This segment covers the solution of systems of pairs of linear equations by both the method of elimination (sometimes called the method of addition or the method of row reduction for large systems) and the method of substitution. Graphical representations and notations of dependence and of inconsistency of parallel pairs are also covered.
This segment covers solving systems of linear inequalities in two variables by graphics.
Rational Exponents.
This segment covers the definition of a rational exponent. Also, expressions containing rational exponents are simplified using laws of exponents. The problems covered here are at the beginning algebra level of difficulty.
Video 8-Solving and Graphing Quadratic Equations
Solving Quadratic Equations by Completing the Square.
This segment covers solving quadratic equations by the square root method, as well as solving quadratic equations by completing the square. The problems covered here are at the beginning algebra level of difficulty.
Solving Quadratic Equations by the Quadratic Formula.
This segment covers the quadratic formula and its use in solving quadratic equations. This segment also covers writing a quadratic equation in standard form in order to identify appropriate coefficient in the quadratic formula.
This segment covers an introduction to complex numbers, operations on complex numbers, and complex solutions of quadratic equations. This segment also covers graphing quadratic equations in two variables by including methods for finding the vertex and x and y intercepts. |
1, 2007
MIND middle-school algebra
The MIND Research Institute has released a new courseware package, ST Math: Algebra Readiness Supplemental. The software targets teachers of middle-schoolers, helping them prepare students for algebra through a series of visually-oriented game modules. These concentrate on a variety of basic, underlying concepts, such as variables, long division, fractions and exponents, and are geared towards meeting both state and national government standards. Students playing the modules only advance at their own rate, as they must master each module before moving on.
The courseware pack is now on sale, shipping in a hybrid PowerPC/Windows format. Licenses are sold on a perpetual or subscription basis, the latter costing $89 per student, or $120 per sequential user, including training and support. Owners of of a license can track student status reports online. |
Chapter 3: Linear Equations and Inequalities in Two Variables; Functions
3.1 Reading Graphs; Linear Equations in Two Variables 3.2 Graphing Linear Equations in Two Variables 3.3 The Slope of a Line 3.4 Equations of a Line Summary Exercises on Linear Equations and Graphs 3.5 Graphing Linear Inequalities in Two Variables 3.6 Introduction to Functions
2007-01-12 Hardcover Good In Good Condition! Pearson/ Addison Wesley; Beginning Algebra: Tenth Edition (Hardcover). Copyright-2008, ISBN: 0321437268. We Ship Daily, Mon-Sat. (KC)We will not process...show more or accept International Orders! These orders will be cancelled automatically! Thank you for your cooperation! ...show less
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The course followed is MEI (OCR) for both Mathematics and Further Mathematics. Courses leading to AS Mathematics, A-level Mathematics, A-level Mathematics and AS Further Mathematics, and A-levels in both Mathematics and Further Mathematics are available, dependent upon demand.
At the beginning of year 12 all students are given a test on their basic algebra skills. If their performance in this test is not satisfactory they will be warned that they are unlikely to be successful in AS Mathematics, and counselled to consider an alternative subject.
In year 12 there is one 'double maths' set; these students will sit C1, C2, FP1, M1, S1 and D1, taking C1, C2 and one applied module in January and the remaining modules in June.
The remaining 'single maths' students are placed into one of six sets for pure mathematics – C1 and C2 – based on ability. C1 will be sat in January and C2 in June. A free choice of applied modules M1, S1 or D1 is available; advice is given on the most appropriate option for each student. This module will also be sat in June.
In the period following the AS examinations all students will complete the coursework for C3.
Progress into year 13 is dependent on satisfactory performance in the AS examination.
It is at this stage that those double mathematicians who only which to gain AS Further Mathematics will move to one of the single maths sets. The remaining double mathematicians will continue with C3, C4, FP2, DE, M2 and S2, with the option to study an additional module if time permits. C3 and at least one other module will be sat in January; the remainder will be sat in June.
There will be five sets for pure mathematics, taking C3 in January and C4 in June. Again, there are free choices for the applied module, this time M2, S2, (subject to having taken the appropriate 1-module in year 12) or to switch applied disciplines with M1 or S1. (N.B. D1 is not offered in year 13.) Option choices are dependent on there being sufficient numbers. The applied module will be sat in June.
At the end of year 12/13 students will have
1. completed appropriate assignments and assessments for each module.
2. been given regular feedback on the standard of their work.
3. been set extra work when remediation was needed.
4. been put on report if work was not satisfactory.
5. been prepared for the examination in each module by use of past papers, with at least one being sat under examination conditions.
Resit strategy
AS Mathematics: Students not continuing to A2 need to see Dr Ogden if they wish to resit any modules. She will then provide past papers and time to go over them with individual students, who need to see her to arrange a convenient time.
A2 Mathematics: Students on the A2 course should discuss with their main teacher the AS results. The general pattern is to resit the applied module in January and any Core modules in June of year 13. In March, when the results for January are known, all students need to discuss their results with their main teacher using a spreadsheet summary provided by Dr Ogden. They will use this to decide whether to enter any additional resits in order to achieve the best possible grade.
Resit support can be provided in a number of ways. The main teacher should ensure that students still have all the revision material they need for the module they are resitting. Dr Ogden will provide the most recent past papers and she can arrange a mutually convenient time to go over them. Help may also be available from the teacher who taught them in year 12.
AS/A2 Mathematics and Further Mathematics: Any resists needing to be taken by students taking both Mathematics and Further Mathematics to AS or A2 should be discussed with their class teacher who will also provide materials and support for them.
Websites
To practice some decision mathematics algorithms then click on the links below: |
al·ge·bra
the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.
2.
any of several algebraic systems, especially a ring in which elements can be multiplied by real or complex numbers (linear algebra) as well as by other elements of the ring.
3.
any special system of notation adapted to the study of a special system of relationship: algebra of classes.
1550s, from M.L. from Arabic al jebr "reunion of broken parts," as in computation, used 9c. by Baghdad mathematician Abu Ja'far Muhammad ibn Musa al-Khwarizmi as the title of his famous treatise on equations ("Kitab al-Jabr w'al-Muqabala" "Rules of Reintegration and Reduction"), which also introduced
Arabic numerals to the West. The accent shifted 17c. from second syllable to first. The word was used in Eng. 15c.-16c. to mean "bone-setting," probably from the Arabs in Spain.
algebra (āl'jə-brə) Pronunciation Key
A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or quantities and express general relationships that hold for all members of a specified set.
algebra definition
mathematics, logic 1. A loose term for an algebraic structure. 2. A vector space that is also a ring, where the vector space and the ring share the same addition operation and are related in certain other ways. An example algebra is the set of 2x2 matrices with real numbers as entries, with the usual operations of addition and matrix multiplication, and the usual scalar multiplication. Another example is the set of all polynomials with real coefficients, with the usual operations. In more detail, we have: (1) an underlying set, (2) a field of scalars, (3) an operation of scalar multiplication, whose input is a scalar and a member of the underlying set and whose output is a member of the underlying set, just as in a vector space, (4) an operation of addition of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a vector space or a ring, (5) an operation of multiplication of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a ring. This whole thing constitutes an `algebra' iff: (1) it is a vector space if you discard item (5) and (2) it is a ring if you discard (2) and (3) and (3) for any scalar r and any two members A, B of the underlying set we have r(AB) = (rA)B = A(rB). In other words it doesn't matter whether you multiply members of the algebra first and then multiply by the scalar, or multiply one of them by the scalar first and then multiply the two members of the algebra. Note that the A comes before the B because the multiplication is in some cases not commutative, e.g. the matrix example. Another example (an example of a Banach algebra) is the set of all boundedlinear operators on a Hilbert space, with the usual norm. The multiplication is the operation of composition of operators, and the addition and scalar multiplication are just what you would expect. Two other examples are tensor algebras and Clifford algebras. [I. N. Herstein, "Topics in Algebra"]. (1999-07-14) |
Here you will be able to find out about exams, homework/classwork assignments along with many other items that may help you in my class. I will keep the homework assignments current here so you will have time to complete them before they are due. I will go over homework at the beginning of each class. The Math support lab is designed to help you succeed in your Algebra class and on your required statewide test. It is also a time where you can complete your Algebra assignments before you get home. You should have at least 30 minutes of class time for homework, but usually it is longer. Most problems require you to show how you got to the final answer. If you cannot demonstrate how you worked the problem, you will receive no credit for that problem. In other words, an answer alone will still count as a 0 (zero). For VOCABULARY quiz word go to math dictionary for the definitions. |
Discrete Mathematics with Proof 2nd Edition
0470457937
9780470457931 Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications.The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include:An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofsNew sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distributionImportant examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databasesNumerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theoremExtensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercisesCombinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems.Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics. «Show less... Show more»
Rent Discrete Mathematics with Proof 2nd Edition today, or search our site for other Gossett |
Mathematics for Physics
9780199289295
ISBN:
0199289298
Pub Date: 2007 Publisher: Oxford University Press, Incorporated
Summary: Mathematics is the essential language of science. It enables us to describe abstract physical concepts, and to apply these concepts in practical ways. Yet mathematical skills and concepts are an aspect of physics that many students fear the most. Mathematics for Physics recognizes the challenges faced by students in equipping themselves with the maths skills necessary to gain a full understanding of physics. Working ...from basic yet fundamental principles, the book builds the students' confidence by leading them through the subject in a steady, progressive way. As its primary aim, Mathematics for Physics shows the relevance of mathematics to the study of physics. Its unique approach demonstrates the application of mathematical concepts alongside the development of the mathematical theory. This stimulating and motivating approach helps students to master the maths and see its application in the context of physics in one seamless learning experience. Mathematics is a subject mastered most readily through active learning. Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding. Mathematics for Physics is the perfect introduction to the essential mathematical concepts which all physics students should master |
Math 142: Precalculus II
Common Course Number
Prior to Summer 2009, this course was known as Math 132; only the course number has changed.
Course Description
Math 142 is the second course in a two-quarter precalculus sequence that also includes Math 141. Topics include: polynomial, rational, trigonometric, and inverse trigonometric functions; and applications involving these functions and functions from Math 141.
Who should take this course?
Generally, students seeking to take the 151–152–153 calculus sequence take the 141–142 precalculus sequence first. You should consult the planning sheet for your program and consult an advisor to determine if this sequence is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 141 with a grade of 2.0 or higher required 141.
What else is required for this course?
Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended. |
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