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-#  
+# A Level Mathematics  
 
-![HAS TO BE PROCESSED - three column table](images/img_1.png)  
+![Image of two origami pine cones, one brown and one tan.](images/img_1.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_2.png)  
+# Specification  
 
-![HAS TO BE PROCESSED - three column table](images/img_3.png)  
+Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0)  
 
-![HAS TO BE PROCESSED - three column table](images/img_4.png)  
+# Summary of Pearson Edexcel Level 3 Advanced GCE in Mathematics Specification Issue 4 changes.  
 
-![HAS TO BE PROCESSED - three column table](images/img_5.png)  
+![HAS TO BE PROCESSED - two column table](images/img_2.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_6.png)  
+![Image description unavailable](images/img_3.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_7.png)  
+Earlier issues show previous changes.  
 
-![HAS TO BE PROCESSED - three column table](images/img_8.png)  
+If you need further information on these changes or what they mean, contact us via our website at: qualifications.pearson.com/en/support/contact-us.html.  
+
+# Contents  
+
+1 Introduction 2   
+Why choose Edexcel A Level Mathematics? 2   
+Supporting you in planning and implementing this qualification 3   
+Qualification at a glance. 5   
+2  Subject content and assessment information. 7   
+Paper 1 and Paper 2: Pure Mathematics 11   
+Paper 3: Statistics and Mechanics 30   
+Assessment Objectives 40   
+3 Administration and general information 42   
+Entries 42   
+Access arrangements, reasonable adjustments, special consideration and malpractice 42   
+Student recruitment and progression 45   
+Appendix 1: Formulae 49   
+Appendix 2: Notation 53   
+Appendix 3: Use of calculators 59   
+Appendix 4: Assessment Objectives 60   
+Appendix 5: The context for the development of this qualification 62   
+Appendix 6: Transferable skills 64   
+pendix 7: Level 3 Extended Project qualification 65   
+Appendix 8: Codes 67  
+
+# 1 Introduction  
+
+# Why choose Edexcel A Level Mathematics?  
+
+We have listened to feedback from all parts of the mathematics subject community, including higher education. We have used this opportunity of curriculum change to redesign a qualification that reflects the demands of a wide variety of end users, as well as retaining many of the features that have contributed to the increasing popularity of GCE Mathematics in recent years.  
+
+We will provide:  
+
+Simple, intuitive specifications that enable co-teaching and parallel delivery. Increased pressure on teaching time means that it's important you can cover the content of different specifications together. Our specifications are designed to help you co-teach A and AS Level, as well as deliver maths and further maths in parallel..   
+Clear, familiar, accessible exams. Our new exam papers will deliver everything you'd expect from us as the leading awarding body for maths. They'll take the most straightforward and logical approach to meet the government's requirements. They'll use the same clear design that you've told us makes them so accessible, while also ensuring a range of challenge for all abilities. A wide range of exam practice to fully prepare students and help you track progress. With the new linear exams your students will want to feel fully prepared and know how they're progressing. We'll provide lots of exam practice to help you and your students understand and prepare for the assessments, including secure mock papers, practice. papers and free topic tests with marking guidance.. Complete support and free materials to help you understand and deliver the specification. Change is easier with the right support, so we'll be on hand to listen and give advice on how to understand and implement the changes. Whether it's through our Launch, Getting Ready to Teach, and Collaborative Networks events or via the renowned Maths Emporium, we'll be available face to face, online or over the phone throughout the lifetime of the qualification. We'll also provide you with free materials such as schemes of work, topic tests and progression maps..   
+The published resources you know and trust, fully updated for 2017. Our new A Level Maths and Further Maths textbooks retain all the features you know and love about the current series, while being fully updated to match the new specifications. Each textbook comes packed with additional online content that supports independent learning and they all tie in with the free qualification support, giving you the most coherent approach to teaching and learning.  
+
+# Supporting you in planning and implementing this qualification  
+
+# Planning  
+
+Our Getting Started guide gives you an overview of the new A Level qualification to help you to get to grips with the changes to content and assessment, as well as helping you understand what these changes mean for you and your students.   
+We will give you a course planner and scheme of work that you can adapt to suit your department.   
+Our mapping documents highlight the content changes between the legacy modular specification and the new linear specifications.  
+
+# Teaching and learning  
+
+There will be lots of free teaching and learning support to help you deliver the new qualifications, including:  
+
+.topic guides covering new content areas   
+. teaching support for problem solving, modelling and the large data set   
+. a student guide containing information about the course to inform your students and their parents.  
+
+# Preparing for exams  
+
+We will also provide a range of resources to help you prepare your students for the assessments, including:  
+
+specimen papers written by our senior examiner team. practice papers made up from past exam questions that meet the new criteria secure mock papers marked exemplars of student work with examiner commentaries..  
+
+# ResultsPlus and exam wizard  
+
+ResultsPlus provides the most detailed analysis available of your students' exam. performance. It can help you identify the topics and skills where further learning would benefit your students.  
+
+Exam Wizard is a data bank of past exam questions (and sample paper and specimen paper questions) allowing you to create bespoke test papers..  
+
+# Get help and support  
+
+# Mathematics Emporium - support whenever you need it  
+
+The renowned Mathematics Emporium helps you keep up to date with all areas of maths throughout the year, as well as offering a rich source of past questions and, of course,. access to our in-house maths experts Graham Cumming and his team..  
+
+# Sign up to get Emporium emails  
+
+Get updates on the latest news, support resources, training and alerts for entry deadlines and key dates direct to your inbox. Just email [email protected] to sign up..  
+
+# Emporium website  
+
+Over 12 000 documents relating to past and present Edexcel mathematics qualifications available free. Visit www.edexcelmaths.com to register for an account.  
+
+# Qualification at a glance  
+
+# Content and assessment overview  
+
+The Pearson Edexcel Level 3 Advanced GCE in Mathematics consists of three externally-examined papers.  
+
+Students must complete all assessment in May/June in any single year.  
+
+![The image describes the structure of the Pure Mathematics papers, including content overview. It does not contain a specific question number or part.](images/img_4.png)  
+
+# Assessment overview  
+
+Paper 1 and Paper 2 may contain questions on any topics from the Pure Mathematics content.   
+Students must answer all questions.   
+Calculators can be used in the assessment..  
+
+![Paper 3: Statistics and Mechanics (*Paper code: 9MA0/03)](images/img_5.png)  
+
+\*See Appendix 8: Codes for a description of this code and all other codes relevant to this qualification.  
+
+# 2 Subject content and assessment information  
+
+# Qualification aims and objectives  
+
+The aims and objectives of this qualification are to enable students to:  
+
+understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study   
+extend their range of mathematical skills and techniques   
+understand coherence and progression in mathematics and how different areas of mathematics are connected   
+apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general   
+use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the. mathematical rationale for these decisions clearly   
+reason logically and recognise incorrect reasoning   
+generalise mathematically   
+construct mathematical proofs   
+use their mathematical skills and techniques to solve challenging problems that require them to decide on the solution strategy   
+recognise when mathematics can be used to analyse and solve a problem in context   
+represent situations mathematically and understand the relationship between problems in context and mathematical models that may be applied to solve them   
+draw diagrams and sketch graphs to help explore mathematical situations and interpret. solutions   
+make deductions and inferences and draw conclusions by using mathematical reasoning   
+interpret solutions and communicate their interpretation effectively in the context of the problem   
+read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding read and comprehend articles concerning applications of mathematics and communicate their understanding   
+. use technology such as calculators and computers effectively and recognise when their. use may be inappropriate   
+. take increasing responsibility for their own learning and the evaluation of their own mathematical development.  
+
+# Overarching themes  
+
+The overarching themes should be applied along with associated mathematical thinking and understanding, across the whole of the detailed content in this specification..  
+
+These overarching themes are inherent throughout the content and students are required to develop skills in working scientifically over the course of this qualification. The skills show. teachers which skills need to be included as part of the learning and assessment of the. students.  
+
+# Overarching theme 1: Mathematical argument, Ianguage and proof  
+
+A Level Mathematics students must use the mathematical notation set out in the booklet Mathematical Formulae and Statistical Tables and be able to recall the mathematical formulae and identities set out in Appendix 1.  
+
+![HAS TO BE PROCESSED - two column table](images/img_6.png)  
+
+Overarching theme 2: Mathematical problem solving   
+
+![HAS TO BE PROCESSED - two column table](images/img_8.png)  
+
+Overarching theme 3: Mathematical modelling   
+
+![HAS TO BE PROCESSED - two column table](images/img_7.png)  
+
+# Use of data in statistics  
+
+Pearson has provided a large data set, which will support the assessment of Statistics in Paper 3: Statistics and Mechanics. Students are required to become familiar with the data set in advance of the final assessment..  
+
+Assessments will be designed in such a way that questions assume knowledge and understanding of the data set. The expectation is that these questions should be likely to give a material advantage to students who have studied and are familiar with the data set. They might include questions/tasks that:  
+
+assume familiarity with the terminology and contexts of the data, and do not explain them in a way that gives students who have not studied the data set the same opportunities to access marks as students who have studied them   
+use summary statistics or selected data from, or statistical diagrams based on, the data set - these might be provided in the question or task, or as stimulus materials   
+are based on samples related to the contexts in the data set, where students' work with the data set will help them understand the background context and/or require students to interpret data in ways that would be too demanding in an unfamiliar context.  
+
+Students will not be required to have copies of the data set in the examination, nor will they be required to have detailed knowledge of the actual data within the data set.  
+
+The data set can be downloaded from our website, qualifications.pearson.com. This data set should be appropriate for the lifetime of the qualification. However we will review the data set on an annual basis to ensure it is appropriate. If we need to make changes to the data set, we will notify centres before the beginning of the two-year course before students complete their examination.  
+
+# Paper 1 and Paper 2: Pure Mathematics  
+
+To support the co-teaching of this qualification with the AS Mathematics qualification, common content has been highlighted in bold..  
 
 ![HAS TO BE PROCESSED - three column table](images/img_9.png)  
 
@@ -28,25 +187,19 @@
 
 ![HAS TO BE PROCESSED - three column table](images/img_14.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_15.png)  
+![Topics 3.3, 3.4 and 4.1 Mark Scheme](images/img_15.png)  
 
 ![HAS TO BE PROCESSED - three column table](images/img_16.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_17.png)  
+![Content and Guidance for Trigonometry, sections 5.1, 5.2, 5.3, and 5.4.](images/img_17.png)  
 
 ![HAS TO BE PROCESSED - three column table](images/img_18.png)  
 
-#  
-
-#  
-
-#  
-
-![HAS TO BE PROCESSED - three column table](images/img_19.png)  
+![HAS TO BE PROCESSED - two column table](images/img_19.png)  
 
 ![HAS TO BE PROCESSED - three column table](images/img_20.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_21.png)  
+![Topics 7.1, 7.2, 7.3 Content](images/img_21.png)  
 
 ![HAS TO BE PROCESSED - three column table](images/img_22.png)  
 
@@ -58,242 +211,577 @@
 
 ![HAS TO BE PROCESSED - three column table](images/img_26.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_27.png)  
+# Assessment information  
+
+First assessment: May/June 2018.   
+The assessments are 2 hours each.   
+The assessments are out of 100 marks.   
+Students must answer all questions..   
+Calculators can be used in the assessments.   
+The booklet Mathematical Formulae and Statistical Tables will be provided for use in the assessments..  
+
+# Synoptic assessment  
+
+Synoptic assessment requires students to work across different parts of a qualification and to show their accumulated knowledge and understanding of a topic or subject area.  
 
-#  
+Synoptic assessment enables students to show their ability to combine their skills, knowledge and understanding with breadth and depth of the subject..  
 
-#  
+These papers assess synopticity.  
 
-#  
+# Sample assessment materials  
+
+A sample paper and mark scheme for these papers can be found in the Pearson Edexcel Level 3 Advanced GCE in Mathematics Sample Assessment Materials (SAMs) document.  
+
+# Paper 3: Statistics and Mechanics  
+
+All the Pure Mathematics content is assumed knowledge for Paper 3 and may be tested in parts of questions.  
+
+To support the co-teaching of this qualification with the AS Mathematics qualification, common content has been highlighted in bold..  
+
+![Topics 1 and 2, Content 1.1 and 2.1](images/img_27.png)  
 
 ![HAS TO BE PROCESSED - three column table](images/img_28.png)  
 
-![Assessment Objectives for GCE A Level.](images/img_29.png)  
+![HAS TO BE PROCESSED - three column table](images/img_29.png)  
+
+![HAS TO BE PROCESSED - three column table](images/img_30.png)  
+
+![HAS TO BE PROCESSED - three column table](images/img_31.png)  
+
+![HAS TO BE PROCESSED - three column table](images/img_32.png)  
+
+![HAS TO BE PROCESSED - two column table](images/img_33.png)  
+
+![HAS TO BE PROCESSED - three column table](images/img_34.png)  
+
+![HAS TO BE PROCESSED - three column table](images/img_35.png)  
+
+# Assessment information  
+
+First assessment: May/June 2018.   
+.The assessment is 2 hours..   
+.The assessment is out of 100 marks..   
+Students must answer all questions..   
+Calculators can be used in the assessment. The booklet 'Mathematical Formulae and Statistical Tables' will be provided for use in the assessment.  
+
+# Synoptic assessment  
+
+Synoptic assessment requires students to work across different parts of a qualification and to show their accumulated knowledge and understanding of a topic or subject area.  
+
+Synoptic assessment enables students to show their ability to combine their skills, knowledge and understanding with breadth and depth of the subject..  
+
+This paper assesses synopticity.  
+
+# Sample assessment materials  
+
+A sample paper and mark scheme for this paper can be found in the Pearson Edexcel Level 3 Advanced GCE in Mathematics Sample Assessment Materials (SAMs) document.  
+
+# Assessment Objectives  
+
+![HAS TO BE PROCESSED - two column table](images/img_36.png)  
+Further guidance on the interpretation of these assessment objectives is given in Appendix 4.  
+
+# Breakdown of Assessment Objectives  
+
+![The image shows a table with assessment objectives for GCE A Level papers. It includes percentages for AO1, AO2, and AO3.](images/img_37.png)  
+NB: Totals have been rounded either up or down.  
+
+# 3 Administration and general information  
+
+# Entries  
+
+Details of how to enter students for the examinations for this qualification can be found in our UK Information Manual. A copy is made available to all examinations officers and is available on our website: qualifications.pearson.com  
+
+# Discount code and performance tables  
+
+Centres should be aware that students who enter for more than one GCE qualification with the same discount code will have only one of the grades they achieve counted for the.   
+purpose of the school and college performance tables. This will be the grade for the larger.   
+qualification (i.e. the A Level grade rather than the AS grade). If the qualifications are the.   
+same size, then the better grade will be counted (please see Appendix 8: Codes)..  
+
+Students should be advised that if they take two GCE qualifications with the same discount code, colleges, universities and employers which they wish to progress to are likely to take the view that this achievement is equivalent to only one GCE. The same view may be taken if students take two GCE qualifications that have different discount codes but have significant overlap of content. Students or their advisers who have any doubts about their subject combinations should check with the institution they wish to progress to before embarking on their programmes.  
+
+# Access arrangements, reasonable adjustments, special consideration and malpractice.  
+
+Equality and fairness are central to our work. Our equality policy requires all students to. have equal opportunity to access our qualifications and assessments, and our qualifications to be awarded in a way that is fair to every student..  
+
+We are committed to making sure that:  
+
+students with a protected characteristic (as defined by the Equality Act 2010) are not,. when they are undertaking one of our qualifications, disadvantaged in comparison to students who do not share that characteristic all students achieve the recognition they deserve for undertaking a qualification and that this achievement can be compared fairly to the achievement of their peers..  
+
+# Language of assessment  
+
+Assessment of this qualification will be available in English. All student work must be in English.  
+
+# Access arrangements  
+
+Access arrangements are agreed before an assessment. They allow students with special educational needs, disabilities or temporary injuries to:.  
+
+access the assessment show what they know and can do without changing the demands of the assessment.  
+
+The intention behind an access arrangement is to meet the particular needs of an individual. student with a disability, without affecting the integrity of the assessment. Access. arrangements are the principal way in which awarding bodies comply with the duty under the Equality Act 2010 to make 'reasonable adjustments'..  
+
+Access arrangements should always be processed at the start of the course. Students will.   
+then know what is available and have the access arrangement(s) in place for assessment.  
+
+# Reasonable adjustments  
+
+The Equality Act 2010 requires an awarding organisation to make reasonable adjustments. where a person with a disability would be at a substantial disadvantage in undertaking an assessment. The awarding organisation is required to take reasonable steps to overcome. that disadvantage.  
+
+A reasonable adjustment for a particular person may be unique to that individual and therefore might not be in the list of available access arrangements..  
+
+Whether an adjustment will be considered reasonable will depend on a number of factors, including:  
+
+. the needs of the student with the disability.   
+.the effectiveness of the adjustment   
+.the cost of the adjustment; and.   
+. the likely impact of the adjustment on the student with the disability and other students.  
 
-#  
+An adjustment will not be approved if it involves unreasonable costs to the awarding. organisation, or affects timeframes or the security or integrity of the assessment. This is because the adjustment is not 'reasonable'..  
 
-#  
+# Special consideration  
 
-#  
+Special consideration is a post-examination adjustment to a student's mark or grade to reflect temporary injury, illness or other indisposition at the time of the examination/ assessment, which has had, or is reasonably likely to have had, a material effect on a candidate's ability to take an assessment or demonstrate their level of attainment in an assessment.  
 
-#  
+# Further information  
 
-#  
+Please see our website for further information about how to apply for access arrangements and special consideration.  
 
-#  
+For further information about access arrangements, reasonable adjustments and special consideration, please refer to the JcQ website: www.jcq.org.uk.  
 
-#  
+# Malpractice  
 
-#  
+# Candidate malpractice  
 
-#  
+Candidate malpractice refers to any act by a candidate that compromises or seeks to compromise the process of assessment or which undermines the integrity of the qualifications or the validity of results/certificates.  
 
-#  
+Candidate malpractice in examinations must be reported to Pearson using a JCQ Form M1 (available at www.jcq.org.uk/exams-office/malpractice). The form should be emailed to [email protected]. Please provide as much information and supporting. documentation as possible. Note that the final decision regarding appropriate sanctions lies with Pearson.  
 
-#  
+Failure to report malpractice constitutes staff or centre malpractice.  
 
-#  
+# Staff/centre malpractice  
 
-#  
+Staff and centre malpractice includes both deliberate malpractice and maladministration of. our qualifications. As with candidate malpractice, staff and centre malpractice is any act that. compromises or seeks to compromise the process of assessment or which undermines the integrity of the qualifications or the validity of results/certificates..  
 
-$\mathsf{A}^{*}$  
+All cases of suspected staff malpractice and maladministration must be reported immediately, before any investigation is undertaken by the centre, to Pearson on a JCQ Form M2(a) (available at www.jcq.org.uk/exams-office/malpractice). The form, supporting documentation and as much information as possible should be emailed to [email protected]. Note that the final decision regarding appropriate sanctions lies with Pearson.  
 
-#  
+Failure to report malpractice itself constitutes malpractice.  
 
-#  
+More detailed guidance on malpractice can be found in the latest version of the document General and Vocational Qualifications Suspected Malpractice in Examinations and Assessments Policies and Procedures, available at www.jcq.org.uk/exams-office/malpractice.  
 
-#  
+# Awarding and reporting  
 
-#  
+This qualification will be graded, awarded and certificated to comply with the requirements of Ofqual's General Conditions of Recognition.  
 
-#  
+This A Level qualification will be graded and certificated on a six-grade scale from $\mathsf{A}^{*}$ to E using the total combined marks (out of 3o0) for the three compulsory papers. Individual papers are not graded.  
 
-#  
+Students whose level of achievement is below the minimum judged by Pearson to be of sufficient standard to be recorded on a certificate will receive an unclassified U result.  
 
-#  
+The first certification opportunity for this qualification will be 2018.  
 
-$a x^{2}+b x+c=0$ $\frac{-b\pm{\sqrt{b^{2}-4a c}}}{2a}$  
+# Student recruitment and progression  
 
-#  
+Pearson follows the JCQ policy concerning recruitment to our qualifications in that:  
+
+they must be available to anyone who is capable of reaching the required standard . they must be free from barriers that restrict access and progression equal opportunities exist for all students.  
+
+# Prior learning and other requirements  
+
+There are no prior learning or other requirements for this qualification.  
+
+Students who would benefit most from studying this qualification are likely to have a Level 2 qualification such as a GCsE in Mathematics.  
+
+# Progression  
+
+Students can progress from this qualification to:  
+
+. a range of different, relevant academics or vocational higher education qualifications employment in a relevant sector   
+further training.  
+
+# Appendices  
+
+Appendix 1: Formulae 49   
+Appendix 2: Notation 53   
+Appendix 3: Use of calculators 59   
+Appendix 4: Assessment Objectives. 60   
+Appendix 5: The context for the development of this qualification 62   
+Appendix 6: Transferable skills 64   
+Appendix 7: Level 3 Extended Project qualification 65   
+Appendix 8: Codes 67  
+
+# Appendix 1: Formulae  
+
+Formulae that students are expected to know for A Level Mathematics are given below and will not appear in the booklet Mathematical Formulae and Statistical Tables, which will be provided for use with the paper.  
+
+# Pure Mathematics  
+
+# Quadratic Equations  
+
+$a x^{2}+b x+c=0$ has roots $\frac{-b\pm{\sqrt{b^{2}-4a c}}}{2a}$  
+
+# Laws of Indices  
 
 $$
 \begin{array}{l}{{a^{x}a^{y}\equiv a^{x+y}}}\ {{}}\ {{a^{x}\div a^{y}\equiv a^{x-y}}}\ {{}}\ {{(a^{x})^{y}\equiv a^{x y}}}\end{array}
 $$  
 
-#  
+# Laws of Logarithms  
+
+$$
+\begin{array}{l}{{\log_{a}x+\log_{a}y\equiv\log_{a}\left(x y\right)}}\ {{{}}}\ {{\log_{a}x-\log_{a}y\equiv\log_{a}\left(\displaystyle\frac{x}{y}\right)}}\ {{{}}}\ {{k\log_{a}x\equiv\log_{a}\left(x^{k}\right)}}\end{array}
+$$  
 
-$x=a^{n}\Leftrightarrow n=\log_{a}x$ $a>0$ $x>0$ $\begin{array}{l}{{\log_{a}x+\log_{a}y\equiv\log_{a}\left(x y\right)}}\ {{{}}}\ {{\log_{a}x-\log_{a}y\equiv\log_{a}\left(\displaystyle\frac{x}{y}\right)}}\ {{{}}}\ {{k\log_{a}x\equiv\log_{a}\left(x^{k}\right)}}\end{array}$  
+# Coordinate Geometry  
 
-#  
+A straight line graph, gradient $m$ passing through $\left(x_{1},y_{1}\right)$ has equation $y-y_{1}=m{\bigl(}x-x_{1}{\bigr)}$ Straight lines with gradients $m_{1}$ and $m_{2}$ are perpendicular when $m_{1}m_{2}=-1$  
 
-$m$ $\left(x_{1},y_{1}\right)$ $y-y_{1}=m{\bigl(}x-x_{1}{\bigr)}$  
+# Sequences  
+
+General term of an arithmetic progression:  
+
+$$
+u_{n}=a+\left(n-1\right)d
+$$  
 
-$m_{1}$ $m_{2}$ $m_{1}m_{2}=-1$  
+General term of a geometric progression:  
 
-#  
+$$
+u_{n}=a r^{n-1}
+$$  
 
-$u_{n}=a+\left(n-1\right)d$   
-$u_{n}=a r^{n-1}$  
+# Trigonometry  
 
-#  
+In the triangle ABC  
 
-$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ $a^{2}=b^{2}+c^{2}-2b c\cos A$ $ {\mathsf{A r e a}}={\frac{1}{2}}a b\sin C$   
+Sine rule: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$   
+Cosine rule: $a^{2}=b^{2}+c^{2}-2b c\cos A$   
+$ {\mathsf{A r e a}}={\frac{1}{2}}a b\sin C$   
 $\mathrm{cos}^{2}A+\mathrm{sin}^{2}A\equiv1$   
 $\sec^{2}A\equiv1+\tan^{2}A$   
 $\mathrm{cosec}^{2}A\equiv1+\mathrm{cot}^{2}A$   
-$\mathrm{sin}2A\equiv2$ $A$ $A$   
+$\mathrm{sin}2A\equiv2$ sin $A$ cos $A$   
 $\mathrm{cos}2A\equiv\mathrm{cos}^{2}A-\mathrm{sin}^{2}A$   
-$12A\equiv{\frac{2\tan A}{1-\tan^{2}A}}$  
+tan $12A\equiv{\frac{2\tan A}{1-\tan^{2}A}}$  
 
-#  
+# Mensuration  
 
-$r$ $d$  
+Circumference and area of circle, radius $r$ and diameter $d$  
 
 $$
 C=2\pi r=\pi d\quad\quad A=\pi r^{2}
 $$  
 
-$b$ $c$ $c$ $c^{2}=a^{2}+b^{2}$  
+Pythagoras' theorem:  
+
+In any right-angled triangle where a, $b$ and $c$ are the lengths of the sides and. $c$ is the hypotenuse, c2= a2 + b2  
 
-$={\frac{1}{2}}(a+b)h$ $a$ $b$ $h$  
+Area of a trapezium $={\frac{1}{2}}(a+b)h$ , where $a$ and $b$ are the lengths of the parallel sides and $h$ is their perpendicular separation.  
 
-$=$ $\times$  
+Volume of a prism $=$ area of cross section $\times$ length.  
 
-$r,$ $\theta$ $s$ $A$  
+For a circle of radius. $r,$ where an angle at the centre of. $\theta$ radians subtends an arc of length. $s$ and encloses an associated sector of area $A$  
 
 $$
 s=r\theta A={\frac{1}{2}}r^{2}\theta
 $$  
 
-#  
+# Calculus and Differential Equations  
+
+Differentiation   
+Function Derivative   
+$x^{n}$ nxn-1   
+sin kx k cos kx   
+cos kx -k sin kx   
+ekr kelox   
+ln x 1 x   
+f(x) +g(x) f'(x)+g'(x)   
+f(x)g(x) f'(x)g(x)+f(x)g'(x)   
+f(g(x) f(g(x)g(x)   
+Integration   
+Function Integral   
+$x^{n}$ ${\frac{1}{n+1}}x^{n+1}+c,n\neq-1$   
+cos kx ${\frac{1}{k}}\sin k x+c$   
+sin kx $-{\frac{1}{k}}\cos k x+c$   
+ehr $\frac{1}{k}\mathtt{e}^{k x}+c$   
+1 $\ln\left|x\right|+c,x\neq0$   
+x   
+f'(x)+g'(x) f(x) +g(x)+c   
+f'(g(x))g'(x) f(g(x))+c   
+Area under a curve $=\intop_{a}^{b}y\mathrm{d}x(y\geqslant0)$  
+
+# Vectors  
+
+$$
+\left|x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\right|={\sqrt{\left(x^{2}+y^{2}+z^{2}\right)}}
+$$  
+
+# Statistics  
+
+The mean of a set of data: ${\overline{{x}}}={\frac{\sum x}{n}}={\frac{\sum\mathrm{f}x}{\sum\mathrm{f}}}$  
+
+The standard Normal variable: $Z={\frac{X-\mu}{\sigma}}$ where $X\sim\mathrm{N}{\left(\mu,\sigma^{2}\right)}$  
 
-#  
+# Mechanics  
 
-#  
+# Forces and Equilibrium  
 
-$x^{n}$   
-  
-  
-  
-  
-  
-  
-  
-  
-${\frac{1}{n+1}}x^{n+1}+c,n\neq-1$   
-${\frac{1}{k}}\sin k x+c$   
-$-{\frac{1}{k}}\cos k x+c$   
-$\frac{1}{k}\mathtt{e}^{k x}+c$   
-$\ln\left|x\right|+c,x\neq0$  
+Weight $={\mathsf{m a s s}}\times g$  
 
-$=\intop_{a}^{b}y\mathrm{d}x(y\geqslant0)$  
+Friction: $F\leqslant\mu R$  
 
-#  
+Newton's second law in the form: $F=m a$  
+
+# Kinematics  
+
+For motion in a straight line with variable acceleration:  
 
 $$
-\left|x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\right|={\sqrt{\left(x^{2}+y^{2}+z^{2}\right)}}
+\begin{array}{l l}{{\displaystyle\nu=\frac{\mathrm{d}\boldsymbol{r}}{\mathrm{d}t}}}&{{\qquada=\frac{\mathrm{d}\boldsymbol{\nu}}{\mathrm{d}t}=\frac{\mathrm{d}^{2}\boldsymbol{r}}{\mathrm{d}t^{2}}}}\ {{}}&{{}}\ {{\displaystyle r=\int\nu\mathrm{d}t}}&{{\qquad\nu=\int a\mathrm{d}t}}\end{array}
 $$  
 
-#  
+# Appendix 2: Notation  
 
-${\overline{{x}}}={\frac{\sum x}{n}}={\frac{\sum\mathrm{f}x}{\sum\mathrm{f}}}$  
+The tables below set out the notation that must be used in A Level Mathematics examinations. Students will be expected to understand this notation without need for. further explanation.  
 
-$Z={\frac{X-\mu}{\sigma}}$ $X\sim\mathrm{N}{\left(\mu,\sigma^{2}\right)}$  
+![HAS TO BE PROCESSED - two column table](images/img_38.png)  
 
-#  
+![HAS TO BE PROCESSED - two column table](images/img_39.png)  
 
-#  
+![HAS TO BE PROCESSED - two column table](images/img_40.png)  
 
-$={\mathsf{m a s s}}\times g$   
-$F\leqslant\mu R$   
-$F=m a$  
+![HAS TO BE PROCESSED - two column table](images/img_41.png)  
 
-#  
+![HAS TO BE PROCESSED - two column table](images/img_45.png)  
 
-$$
-\begin{array}{l l}{{\displaystyle\nu=\frac{\mathrm{d}\boldsymbol{r}}{\mathrm{d}t}}}&{{\qquada=\frac{\mathrm{d}\boldsymbol{\nu}}{\mathrm{d}t}=\frac{\mathrm{d}^{2}\boldsymbol{r}}{\mathrm{d}t^{2}}}}\ {{}}&{{}}\ {{\displaystyle r=\int\nu\mathrm{d}t}}&{{\qquad\nu=\int a\mathrm{d}t}}\end{array}
-$$  
+![Image description unavailable](images/img_44.png)  
 
-#  
+![Q6 Part 6.1, 6.2, 6.3, 6.4](images/img_43.png)  
 
-![HAS TO BE PROCESSED - two column table](images/img_30.png)  
+![HAS TO BE PROCESSED - two column table](images/img_42.png)  
 
-![HAS TO BE PROCESSED - two column table](images/img_31.png)  
+![HAS TO BE PROCESSED - two column table](images/img_47.png)  
 
-![HAS TO BE PROCESSED - two column table](images/img_33.png)  
+![HAS TO BE PROCESSED - two column table](images/img_46.png)  
 
-![HAS TO BE PROCESSED - two column table](images/img_32.png)  
+![HAS TO BE PROCESSED - two column table](images/img_49.png)  
 
-![HAS TO BE PROCESSED - three column table](images/img_34.png)  
+![HAS TO BE PROCESSED - two column table](images/img_48.png)  
 
-![HAS TO BE PROCESSED - two column table](images/img_35.png)  
+# Appendix 3: Use of calculators  
 
-![HAS TO BE PROCESSED - two column table](images/img_37.png)  
+Students may use a calculator in all A Level Mathematics examinations. Students are responsible for making sure that their calculators meet the guidelines set out in this appendix.  
 
-![HAS TO BE PROCESSED - two column table](images/img_36.png)  
+The use of technology permeates the study of A Level Mathematics. Calculators used must include the following features:  
 
-![HAS TO BE PROCESSED - two column table](images/img_38.png)  
+.an iterative function   
+. the ability to compute summary statistics and access probabilities from standard statistical distributions.  
 
-#  
+In addition, students must be told these regulations before sitting an examination:  
 
-![HAS TO BE PROCESSED - two column table](images/img_39.png)  
+![HAS TO BE PROCESSED - two column table](images/img_50.png)  
 
-$\ast_{\mathsf{a n}}$  
+Advice: $\ast_{\mathsf{a n}}$ invigilator may give a student a replacement calculator.  
 
-#  
+# Appendix 4: Assessment Objectives  
 
-![HAS TO BE PROCESSED - two column table](images/img_40.png)  
+The following tables outline in detail the strands and elements of each Assessment Objective for A Level Mathematics, as provided by Ofqual in the document GCE Subject Level Guidance for Mathematics.  
 
-![HAS TO BE PROCESSED - two column table](images/img_41.png)  
+.A 'strand' is a discrete bullet point that is formally part of an assessment objective . An 'element' is an ability that the assessment objective does not formally separate, but that could be discretely targeted or credited.  
+
+![HAS TO BE PROCESSED - two column table](images/img_51.png)  
+
+![HAS TO BE PROCESSED - two column table](images/img_52.png)  
+
+AO3: Solve problems within mathematics and in other contexts  
+
+![HAS TO BE PROCESSED - two column table](images/img_53.png)  
+
+# Assessment Objectives coverage  
+
+There will be full coverage of all elements of the Assessment Objectives, with the exception of AO3.2b and AO3.5c, in each set of A Level Mathematics assessments offered by Pearson. Elements AO3.2b and AO3.5c will be covered in each route through the qualification within three years.  
+
+# Appendix 5: The context for the development of this qualification  
+
+All our qualifications are designed to meet our World Class Qualification Principles[1] and our ambition to put the student at the heart of everything we do..  
+
+We have developed and designed this qualification by:  
+
+reviewing other curricula and qualifications to ensure that it is comparable with those taken in high-performing jurisdictions overseas   
+consulting with key stakeholders on content and assessment, including learned bodies, subject associations, higher-education academics, teachers and employers to ensure this qualification is suitable for a UK context   
+reviewing the legacy qualification and building on its positive attributes.  
+
+This qualification has also been developed to meet criteria stipulated by Ofqual in their documents GCE Qualification Level Conditions and Requirements and GCE Subject Level Conditions and Requirements for Mathematics, published in April 2016.  
+
+[1] Pearson's World Class Qualification Principles ensure that our qualifications are:  
+
+demanding, through internationally benchmarked standards, encouraging deep learning and measuring higher-order skills. rigorous, through setting and maintaining standards over time, developing reliable and valid assessment tasks and processes, and generating confidence in end users of the knowledge, skills and competencies of certified students   
+inclusive, through conceptualising learning as continuous, recognising that students develop at. different rates and have different learning needs, and focusing on progression   
+empowering, through promoting the development of transferable skills, see Appendix 6..  
+
+# From Pearson's Expert Panel for World Class Qualifications  
+
+# May 2014  
+
+" The reform of the qualifications system in England is a profoundly important change to the education system. Teachers need to know that the new qualifications will assist them in helping their learners make progress in their lives..  
+
+When these changes were first proposed we were approached by Pearson to join an 'Expert Panel' that would advise them on the development of the new qualifications.  
+
+We were chosen, either because of our expertise in the UK education system, or because of our experience in reforming qualifications in other systems around the world as diverse as Singapore, Hong Kong, Australia and a number of countries across Europe.  
+
+We have guided Pearson through what we judge to be a rigorous qualification development process that has included:  
+
+extensive international comparability of subject content against the highest-performing jurisdictions in the world   
+benchmarking assessments against UK and overseas providers to ensure that they are at the right level of demand   
+establishing External Subject Advisory Groups, drawing on independent subject-specific expertise to challenge and validate our qualifications   
+subjecting the final qualifications to scrutiny against the DfE content and Ofqual   
+accreditation criteria in advance of submission.  
+
+Importantly, we have worked to ensure that the content and learning is future oriented. The design has been guided by what is called an 'Efficacy Framework', meaning learner outcomes have been at the heart of this development throughout.  
+
+We understand that ultimately it is excellent teaching that is the key factor to a learner's. success in education. As a result of our work as a panel we are confident that we have supported the development of qualifications that are outstanding for their coherence,. thoroughness and attention to detail and can be regarded as representing world-class best. practice. "  
+
+# Sir Michael Barber (Chair)  
+
+# Professor Lee Sing Kong  
+
+Chief Education Advisor, Pearson plc  
+
+Director, National Institute of Education, Singapore  
+
+# Bahram Bekhradnia  
+
+President, Higher Education Policy Institute  
+
+Professor Jonathan Osborne Stanford University  
+
+# Dame Sally Coates  
+
+# Professor Dr Ursula Renold  
+
+Principal, Burlington Danes Academy  
+
+Federal Institute of Technology, Switzerland  
+
+# Professor Robin Coningham  
+
+# Professor Bob Schwartz  
+
+Pro-Vice Chancellor, University of Durham  
+
+Harvard Graduate School of Education  
+
+# Dr Peter Hill  
+
+Former Chief Executive ACARA  
+
+All titles correct as at May 2014  
+
+# Appendix 6: Transferable skills  
+
+# The need for transferable skills  
+
+In recent years, higher education institutions and employers have consistently flagged the. need for students to develop a range of transferable skills to enable them to respond with confidence to the demands of undergraduate study and the world of work..  
+
+The Organisation for Economic Co-operation and Development (OECD) defines skills, or competencies, as 'the bundle of knowledge, attributes and capacities that can be learned and that enable individuals to successfully and consistently perform an activity or task and can be built upon and extended through learning.' [1]  
+
+To support the design of our qualifications, the Pearson Research Team selected and. evaluated seven global 21st-century skills frameworks. Following on from this process, we identified the National Research Council's (NRc) framework as the most evidence-based and robust skills framework. We adapted the framework slightly to include the Program for. International Student Assessment (PISA) ICT Literacy and Collaborative Problem Solvinge (CPS) Skills.  
+
+The adapted National Research Council's framework of skills involves: [2]  
+
+# Cognitive skills  
+
+Non-routine problem solving - expert thinking, metacognition, creativity. .  Systems thinking - decision making and reasoning. : Critical thinking - definitions of critical thinking are broad and usually involve general cognitive skills such as analysing, synthesising and reasoning skills. .Icr literacy - access, manage, integrate, evaluate, construct and communicate. [3]  
+
+# Interpersonal skills  
+
+.Communication - active listening, oral communication, written communication, assertive communication and non-verbal communication.  
+
+Relationship-building skills - teamwork, trust, intercultural sensitivity, service.   
+orientation, self-presentation, social influence, conflict resolution and negotiation.  
+
+. Collaborative problem solving - establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.  
+
+# Intrapersonal skills  
+
+. Adaptability - ability and willingness to cope with the uncertain, handling work stress, adapting to different personalities, communication styles and cultures, and physical adaptability to various indoor and outdoor work environments.   
+Self-management and self-development - ability to work remotely in virtual teams, work autonomously, be self-motivating and self-monitoring, willing and able to acquire new information and skills related to work..  
+
+Transferable skills enable young people to face the demands of further and higher education,. as well as the demands of the workplace, and are important in the teaching and learning of this qualification. We will provide teaching and learning materials, developed with stakeholders, to support our qualifications..  
+
+# Appendix 7: Level 3 Extended Project qualification  
+
+# What is the Extended Project?  
+
+The Extended Project is a standalone qualification that can be taken alongside GCEs. It supports the development of independent learning skills and helps to prepare students for. their next step - whether that be higher education or employment. The qualification:  
+
+is recognised by higher education for the skills it develops is worth half of an Advanced GCE qualification at grades A\*-E carries UCAS points for university entry.  
+
+The Extended Project encourages students to develop skills in the following areas: research, critical thinking, extended writing and project management. Students identify and agree a topic area of their choice for in-depth study (which may or may not be related to a GCE subject they are already studying), guided by their teacher..  
+
+Students can choose from one of four approaches to produce:  
 
-#  
+. a dissertation (for example an investigation based on predominately secondary research)   
+: an investigation/field study (for example a practical experiment)   
+.  a performance (for example in music, drama or sport)   
+an artefact (for example creating a sculpture in response to a client brief or solving an engineering problem). The qualification is coursework based and students are assessed on the skills of managing,.   
+planning and evaluating their project. Students will research their topic, develop skills to.   
+review and evaluate the information, and then present the final outcome of their project.  
 
-#  
+The Extended Project has 120 guided learning hours (GLH) consisting of a 40-GLH taught. element that includes teaching the technical skills (for example research skills) and an 80-GLH guided element that includes mentoring students through the project work.. The qualification is. $100\%$ internally assessed and externally moderated..  
 
-#  
+# How to link the Extended Project with mathematics  
 
-#  
+The Extended Project creates the opportunity to develop transferable skills for progression to higher education and to the workplace, through the exploration of either an area of personal interest or a topic of interest from within the mathematics qualification content.  
 
-#  
+Through the Extended Project, students can develop skills that support their study of mathematics, including:  
 
-#  
+conducting, organising and using research   
+independent reading in the subject area   
+planning, project management and time management   
+defining a hypothesis to be tested in investigations or developing a design brief collecting, handling and interpreting data and evidence   
+evaluating arguments and processes, including arguments in favour of alternative interpretations of data and evaluation of experimental methodology   
+critical thinking.  
 
-#  
+In the context of the Extended Project, critical thinking refers to the ability to identify and develop arguments for a point of view or hypothesis, and to consider and respond to. alternative arguments.  
 
-#  
+# Types of Extended Project related to mathematics  
 
-#  
+Students may produce a dissertation on any topic that can be researched and argued. In mathematics this might involve working on a substantial statistical project or a project that requires the use of mathematical modelling.  
 
-#  
+Projects can give students the opportunity to develop mathematical skills that cannot be adequately assessed in examination questions.  
 
-#  
+Statistics - students can have the opportunity to plan a statistical enquiry project, use. different methods of sampling and data collection, use statistical software packages to process and investigate large quantities of data and review results to decide if more data is needed.   
+. Mathematical modelling - students can have the opportunity to choose modelling. assumptions, compare with experimental data to assess the appropriateness of their. assumptions and refine their modelling assumptions until they get the required accuracy of results.  
 
-#  
+# Using the Extended Project to support breadth and depth  
 
-#  
+In the Extended Project, students are assessed on the quality of the work they produce and. the skills they develop and demonstrate through completing this work. Students should. demonstrate that they have extended themselves in some significant way beyond what they. have been studying in mathematics. Students can demonstrate extension in one or more dimensions:  
 
-#  
+. deepening understanding - where a student explores a topic in greater depth than in. the specification content. This could be an in-depth exploration of one of the topics in the specification   
+. broadening skills - where a student learns a new skill. This might involve learning the skills in statistics or mathematical modelling mentioned above or learning a new. mathematical process and its practical uses widening perspectives - where the student's project spans different subjects.. Projects in a variety of subjects need to be supported by data and statistical analysis. Students studying mathematics with design and technology can carry out design projects. involving the need to model a situation mathematically in planning their design..  
 
-#  
+A wide range of information to support the delivery and assessment of the Extended Project, including the specification, teacher guidance for all aspects, an editable scheme of work and exemplars for all four approaches, can be found on our website.  
 
-#  
+# Appendix 8: Codes  
 
-#  
+![The image contains information about different types of codes and their uses. It includes discount codes, regulated qualifications framework codes, subject codes, and paper codes. It does not contain question numbers or parts.
+Description of the image.](images/img_54.png)  
+\*https://www.gov.uk/government/publications/key-stage-4-qualifications-discount-codesand-point-scores  
 
-#  
+# Edexcel, BTEC and LCCI qualifications  
 
-#  
+Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK's largest awarding body offering academic and vocational qualifications that are globally recognised and benchmarked. For further information, please visit our qualifications website at qualifications.pearson.com. Alternatively, you can get in touch with us using the details on our contact us page at qualifications.pearson.com/contactus  
 
-$100\%$  
+# About Pearson  
 
-#  
+Pearson is the world's leading learning company, with 35,000 employees in more than. 70 countries working to help people of all ages to make measurable progress in their lives. through learning. We put the learner at the centre of everything we do, because wherever Iearning flourishes, so do people. Find out more about how we can help you and your learners at qualifications.pearson.com.  
 
-#  
+References to third party material made in this specification are made in good faith. Pearson does not endorse, approve or accept responsibility for the content of materials, which may. be subject to change, or any opinions expressed therein. (Material may include textbooks,. journals, magazines and other publications and websites.).  
 
-#  
+All information in this specification is correct at time of publication.  
 
-![HAS TO BE PROCESSED - three column table](images/img_42.png)  
+Original Origami Artwork designed by Beth Johnson and folded by Mark Bolitho Origami photography: Pearson Education Ltd/Naki Kouyioumtzis.  
 
-#  
+ISBN 978 1 446 95709 7  
 
-#  
+All the material in this publication is copyright $\circleddash$ Pearson Education Limited 2020