Datasets:

---

math-eval

/

TAL-SCQ5K

like 57

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$50$$ " } ], [ { "aoVal": "B", "content": "$$60$$ " } ], [ { "aoVal": "C", "content": "$$75$$ " } ], [ { "aoVal": "D", "content": "$$90$$ " } ], [ { "aoVal": "E", "content": "$$100$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Since $x$ is the mean, $$ \\begin{aligned} x \\& =\\frac{60+100+x+40+50+200+90}{7} \\textbackslash\\textbackslash{} \\& =\\frac{540+x}{7} . \\end{aligned} $$ Therefore, $7 x=540+x$, so $x=$ (D) $90$. " ]

[]

[ [ { "aoVal": "A", "content": "$5:30$ " } ], [ { "aoVal": "B", "content": "$1:6$ " } ], [ { "aoVal": "C", "content": "$6:1$ " } ], [ { "aoVal": "D", "content": "$10:1$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio" ]

[ "We need to make units same first. $5$ minutes equal to $300$ seconds. Now we could remove the same unit, second. We get $300:30$ and simplify it to $10:1$. " ]

[]

[ [ { "aoVal": "A", "content": "$$190$$ " } ], [ { "aoVal": "B", "content": "$$200$$ " } ], [ { "aoVal": "C", "content": "$$210$$ " } ], [ { "aoVal": "D", "content": "$$220$$ " } ], [ { "aoVal": "E", "content": "Non of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns" ]

[ "$$5\\otimes 3=5\\times 6\\times 7=210$$. " ]

[]

[ [ { "aoVal": "A", "content": "$45$ " } ], [ { "aoVal": "B", "content": "$50$ " } ], [ { "aoVal": "C", "content": "$55$ " } ], [ { "aoVal": "D", "content": "$60$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences" ]

[ "$10+5\\times(9-1)=50$. " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$6$$ " } ], [ { "aoVal": "C", "content": "$$12$$ " } ], [ { "aoVal": "D", "content": "$$102$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction " ]

[ "Rearranging: $$11-9 +\\cdots + 11-9 =2+\\cdots +2 =2\\times6 = 12$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$-1010$$ " } ], [ { "aoVal": "B", "content": "$$-1009$$ " } ], [ { "aoVal": "C", "content": "$$1008$$ " } ], [ { "aoVal": "D", "content": "$$1009$$ " } ], [ { "aoVal": "E", "content": "$$1010$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers" ]

[ "$1+3+5+\\ldots+2017+2019-2 -4-6-\\ldots-2016-2018$ $=1+(3-2)+(5-4)+\\cdots +(2017-2016)+(2019-2018)$ $=1+1+1+\\cdots +1+1$ $=1010$ " ]

[]

[ [ { "aoVal": "A", "content": "$$1023\\frac{1}{1024}$$ " } ], [ { "aoVal": "B", "content": "$$1023\\frac{1023}{1024}$$ " } ], [ { "aoVal": "C", "content": "$$1024$$ " } ], [ { "aoVal": "D", "content": "$$1024\\frac{1}{1024}$$ " } ], [ { "aoVal": "E", "content": "$$1024\\frac{1023}{1024}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions" ]

[ "Nil " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "Yes " } ], [ { "aoVal": "B", "content": "No " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "NA " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$3$$ " } ], [ { "aoVal": "D", "content": "$$4$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "B " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "tens " } ], [ { "aoVal": "B", "content": "ones " } ], [ { "aoVal": "C", "content": "we don\\textquotesingle t know " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "NA " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "E " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "6ℓ " } ], [ { "aoVal": "B", "content": "18ℓ " } ], [ { "aoVal": "C", "content": "21ℓ " } ], [ { "aoVal": "D", "content": "27ℓ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity" ]

[ "$$2 \\times 3 = 6$$ $$27 - 6 = 21$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$6$$ " } ], [ { "aoVal": "C", "content": "$$17$$ " } ], [ { "aoVal": "D", "content": "$$23$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly" ]

[ "Nil " ]

[]

[ [ { "aoVal": "A", "content": "$$0$$ " } ], [ { "aoVal": "B", "content": "$$1$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$9$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction " ]

[ "$$2+4 +6 +8=1+1+3+1+5+1+7+1=1+3 +5 +7 +4$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$x=12.6$$ " } ], [ { "aoVal": "B", "content": "$$x=-12.6$$ " } ], [ { "aoVal": "C", "content": "$$x=21$$ " } ], [ { "aoVal": "D", "content": "$$x=-21$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable" ]

[ "omitted " ]

[]

[ [ { "aoVal": "A", "content": "$$81$$ " } ], [ { "aoVal": "B", "content": "$$88$$ " } ], [ { "aoVal": "C", "content": "$$90$$ " } ], [ { "aoVal": "D", "content": "$$99$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "$$8\\times9\\times10\\times11=(8\\times10)\\times (9\\times11)=80\\times99$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$115$$ " } ], [ { "aoVal": "B", "content": "$$135$$ " } ], [ { "aoVal": "C", "content": "$$250$$ " } ], [ { "aoVal": "D", "content": "$$260$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$np=10(0.8)=8$ The $80$-th percentile is $\\frac{250+260}{2} = 255$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$18$$ " } ], [ { "aoVal": "D", "content": "$$21$$ " } ], [ { "aoVal": "E", "content": "$$25$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "$$4+6+8=18$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "17, 85 " } ], [ { "aoVal": "B", "content": "18, 40 " } ], [ { "aoVal": "C", "content": "9,~ 64 " } ], [ { "aoVal": "D", "content": "17, 40 " } ], [ { "aoVal": "E", "content": "20, 50 " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction " ]

[ "13+4=17 , 57-17=40 " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$\\textbackslash$2$ " } ], [ { "aoVal": "B", "content": "$\\textbackslash$10$ " } ], [ { "aoVal": "C", "content": "$\\textbackslash$12$ " } ], [ { "aoVal": "D", "content": "$\\textbackslash$22$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "The correct answer is A. $\\textbackslash$2$, as consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the actual price they pay, which is $\\textbackslash$12 - \\textbackslash$10 = \\textbackslash$2$. " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables" ]

[ "$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$\\frac{5}{7}$$ " } ], [ { "aoVal": "B", "content": "$$\\frac{4}{7}$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{6}{7}$$ " } ], [ { "aoVal": "D", "content": "$$\\frac{3}{7}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "$$\\frac{1}{2}\\times \\frac{22}{7}\\div \\frac{11}{5}=\\frac{1}{2}\\times \\frac{22}{7}\\times \\frac{5}{11}=\\frac{5}{7}$$． " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "5 hours " } ], [ { "aoVal": "B", "content": "6 hours " } ], [ { "aoVal": "C", "content": "10 hours " } ], [ { "aoVal": "D", "content": "8 hours " } ], [ { "aoVal": "E", "content": "12 hours " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "The average amount of sleep an adult gets is 8 hours. Everyone is different, however; where some adults function off of 6 hours, others need at least 9 hours or more to feel healthy and awake. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$75$$ " } ], [ { "aoVal": "B", "content": "$$77$$ " } ], [ { "aoVal": "C", "content": "$$86$$ " } ], [ { "aoVal": "D", "content": "$$90$$ " } ], [ { "aoVal": "E", "content": "$$99$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "2016, Q 86 " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$3$$ " } ], [ { "aoVal": "D", "content": "$$4$$ " } ], [ { "aoVal": "E", "content": "Such a division is not possible " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers->Applying Distributive Law of Whole Numbers in Division" ]

[ "1+2+3+4+5+6+7+8+9+10 = 55 is not divisible by 3. " ]

[]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{1}{2}$$ " } ], [ { "aoVal": "D", "content": "$$2^{2}$$ " } ], [ { "aoVal": "E", "content": "$$2^{2008}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable->Equations with Whole Number Coefficient" ]

[ "$$2^{2007}=2^{2006}\\cdot x$$, $x=2$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "($x$,$y$)=($3$,$-1$) " } ], [ { "aoVal": "B", "content": "($x$,$y$)=($3$,$1$) " } ], [ { "aoVal": "C", "content": "($x$,$y$)=($-3$,$1$) " } ], [ { "aoVal": "D", "content": "($x$,$y$)=($-3$,$-1$) " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables" ]

[ "$3-3=0$ $3\\cdot3-2\\cdot1=9-2=7$ " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$50$$ " } ], [ { "aoVal": "C", "content": "$$60$$ " } ], [ { "aoVal": "D", "content": "$$65$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction " ]

[ "$$1+10 + 2+10 + 3+10 + 4+10 + 5+10 = 1+2+3+4+5 + 50$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$16\\times 2$$ " } ], [ { "aoVal": "B", "content": "$$12\\times 3$$ " } ], [ { "aoVal": "C", "content": "$$7\\times 5$$ " } ], [ { "aoVal": "D", "content": "$$38\\times 1$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "$$4\\times 9=36$$. $$\\text{A}$$: $$16\\times 2=32$$; $$\\text{B}$$: $$12\\times 3=36$$; $$\\text{C}$$: $$7\\times 5=35$$; $$\\text{D}$$: $$38\\times 1=38$$. " ]

[]

[ [ { "aoVal": "A", "content": "$\\dfrac{1}{3}$ " } ], [ { "aoVal": "B", "content": "$\\dfrac{2}{5}$ " } ], [ { "aoVal": "C", "content": "$\\dfrac{3}{8}$ " } ], [ { "aoVal": "D", "content": "$\\dfrac{2}{9}$ " } ], [ { "aoVal": "E", "content": "$\\dfrac{5}{12}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions" ]

[ "$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$16$$ " } ], [ { "aoVal": "B", "content": "$$24$$ " } ], [ { "aoVal": "C", "content": "$$32$$ " } ], [ { "aoVal": "D", "content": "$$64$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals" ]

[ "$4\\times4\\times4=64$ " ]

[]

[ [ { "aoVal": "A", "content": "£$$23.92$$ " } ], [ { "aoVal": "B", "content": "£$$23.98$$ " } ], [ { "aoVal": "C", "content": "£$$24.00$$ " } ], [ { "aoVal": "D", "content": "£$$24.02$$ " } ], [ { "aoVal": "E", "content": "£$$24.08$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Multiplication of Decimals" ]

[ "omitted " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$36$$ " } ], [ { "aoVal": "C", "content": "$$198$$ " } ], [ { "aoVal": "D", "content": "$$396$$ " } ], [ { "aoVal": "E", "content": "$$792$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "B " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$180$$ " } ], [ { "aoVal": "B", "content": "$$200$$ " } ], [ { "aoVal": "C", "content": "$$300$$ " } ], [ { "aoVal": "D", "content": "$$480$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$$80\\div40\\textbackslash\\%=200$$． so choose $$\\text{B}$$． " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$4a^{4}$ " } ], [ { "aoVal": "B", "content": "$4a^{8}$ " } ], [ { "aoVal": "C", "content": "$8a^{4}$ " } ], [ { "aoVal": "D", "content": "$8a^{8}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$sqrt{16a^{16}}=\\sqrt{16}\\sqrt{a^{16}}=4(a^{16\\times\\frac{1}{2}})=4a^{8}$ " ]

[]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$\\dfrac{1}{149}$ " } ], [ { "aoVal": "C", "content": "$\\dfrac{149}{150}$ " } ], [ { "aoVal": "D", "content": "$\\dfrac{1}{150}$ " } ], [ { "aoVal": "E", "content": "$$150$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions" ]

[ "Suppose $$\\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{149}\\right)$$ as $$A$$, $$\\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{150}\\right)$$ as $$B$$. $$(1+A)\\times B-(1+B)\\times A=B+AB-A-AB=B-A=\\frac 1{150}$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$253$$ " } ], [ { "aoVal": "B", "content": "$$503$$ " } ], [ { "aoVal": "C", "content": "$$1012$$ " } ], [ { "aoVal": "D", "content": "$$4048$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "E " ]

[]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$30$$ " } ], [ { "aoVal": "C", "content": "$$21$$ " } ], [ { "aoVal": "D", "content": "$$98$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Heuristics Skills-> Equivalent Substitution" ]

[ "$$6$$ pens = $$5$$ pencils, we use $\\times6$ which give us $36$ pens = $30$ pencils " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$25$$ " } ], [ { "aoVal": "B", "content": "$$50$$ " } ], [ { "aoVal": "C", "content": "$$51$$ " } ], [ { "aoVal": "D", "content": "$$49$$ " } ], [ { "aoVal": "E", "content": "$$33$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities" ]

[ "We know from the triangle inequality that the last side, $s$, fulfills $s\\textless12+13=25$. Adding $12+13$ to both sides of the inequality, we get $s+12+13\\textless25$, and because $s+12+13$ is the perimeter of our triangle, (B) 50 is our answer. " ]

[]

[ [ { "aoVal": "A", "content": "$$71$$ " } ], [ { "aoVal": "B", "content": "$$73$$ " } ], [ { "aoVal": "C", "content": "$$75$$ " } ], [ { "aoVal": "D", "content": "$$77$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "$$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times9\\times10$$ is divisible by $$3$$ and $$25$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$4^{12}$ " } ], [ { "aoVal": "B", "content": "$4^{27}$ " } ], [ { "aoVal": "C", "content": "$4^{3}$ " } ], [ { "aoVal": "D", "content": "$4^{4}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Power" ]

[ "omitted " ]

[]

[ [ { "aoVal": "A", "content": "$$79$$，$$73$$ " } ], [ { "aoVal": "B", "content": "$$80$$，$$73$$ " } ], [ { "aoVal": "C", "content": "$$79$$，$$72$$ " } ], [ { "aoVal": "D", "content": "$$80$$，$$72$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "~\\uline{~~~~~~~~~~}~$\\div 8=9$ $\\text{R}$~\\uline{~~~~~~~~~~}~ Biggest possible remainder is $7$ while smallest possible remainder is $1$. Biggest possible number of badges is $$8\\times 9+7=79$$, while the least possible number of sweets is $$8\\times 9+1=73$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "1:2 " } ], [ { "aoVal": "B", "content": "1:3 " } ], [ { "aoVal": "C", "content": "1:4 " } ], [ { "aoVal": "D", "content": "2:5 " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions" ]

[ "$90:360=1:4$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$-2$$ " } ], [ { "aoVal": "B", "content": "$$0$$ " } ], [ { "aoVal": "C", "content": "$$2$$ " } ], [ { "aoVal": "D", "content": "$$4$$ " } ], [ { "aoVal": "E", "content": "$$-4$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$2xy+\\frac{x^{4}}{y^{2}}+\\frac{y^{4}}{x^{2}} = 2xy+\\frac{x^{6}+y^{6}}{x^{2}y^{2}} = \\frac{2xyx^{2}y^{2}+x^{6}+y^{6}}{x^{2}y^{2}}= \\frac{2x^{3}y^{3}+x^{6}+y^{6}}{x^{2}y^{2}} $ $= \\frac{(x^{3}+y^{3})^{2}}{x^{2}y^{2}} =\\frac{4^{2}}{4}= 4$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$360$$ " } ], [ { "aoVal": "B", "content": "$$400$$ " } ], [ { "aoVal": "C", "content": "$$420$$ " } ], [ { "aoVal": "D", "content": "$$440$$ " } ], [ { "aoVal": "E", "content": "$$480$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$x+\\frac{x^{3}}{y^{2}}+\\frac{y^{3}}{x^{2}}+y=x+\\frac{y^{3}}{x^{2}}+y+ \\frac{x^{3}}{y^{2}}=\\frac{x^{3}}{x^{2}}+\\frac{y^{3}}{x^{2}}+\\frac{y^{3}}{y^{2}}+\\frac{x^{3}}{y^{2}}$ Continuing to combine $\\frac{x^{3}+y^{3}}{x^{2}}+\\frac{x^{3}+y^{3}}{y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)\\left(x^{3}+y^{3}\\right)}{x^{2} y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}}$ From the givens, it can be concluded that $x^{2}y^{2}=4$. Also, $(x+y)^{2}=x^{2}+2 x y+y^{2}=16$ This means that $x^{2}+y^{2}=20$. Substituting this information into $\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}}$, we have $\\frac{20\\times 4\\times22}{4}=440$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$7$$ " } ], [ { "aoVal": "D", "content": "$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition" ]

[ "Nil " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$8$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$12$$ " } ], [ { "aoVal": "D", "content": "$$14$$ " } ], [ { "aoVal": "E", "content": "$$16$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "First, note that $50+1=51$, which motivates us to factor the polynomial as $\\left(x^{2}-50\\right)\\left(x^{2}-1\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-50\\textless0\\textless x^{2}-1$. Solving this inequality, we find $1\\textless x^{2}\\textless50$. There are exactly $12$ integers $x$ that satisfy this inequality, $\\pm\\textbackslash{2,3,4,5,6,7\\textbackslash}$. Thus our answer is $(\\mathbf{C}) 12$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$0$$ " } ], [ { "aoVal": "B", "content": "$$1$$ " } ], [ { "aoVal": "C", "content": "$$2$$ " } ], [ { "aoVal": "D", "content": "$$3$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation" ]

[ "1 and 4 are equations. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$7$$ " } ], [ { "aoVal": "E", "content": "It depends on how long the piece of wood is. " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$4 + 1 = 5$ " ]

[]

[ [ { "aoVal": "A", "content": "$$3628$$ " } ], [ { "aoVal": "B", "content": "$$3668$$ " } ], [ { "aoVal": "C", "content": "$$3728$$ " } ], [ { "aoVal": "D", "content": "$$3768$$ " } ] ]

[ "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-Digit and 1-Digit (with regrouping for more than once)", "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "Stack the two numbers as shown below ,~ lining up the unit digits Remember that the 2 in 628 stands for 2 tens(20) ,the 6 in the 628 stands for 6 hundreds(600) First, multiply the ones~ $6\\times8=48$~, regroup the 4 tens to the tens column Write 8 in the ones place. Then,~ Multiply and add the tens .~$2\\times6+4=16$ Write 6 in the tens place and regroup the 1 hundred. Last, multiply and add the hundreds.~$6\\times6+1=37$ Write 7 in the hundreds place and write 3 in the thousands place. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$6$$ " } ], [ { "aoVal": "C", "content": "$$8$$ " } ], [ { "aoVal": "D", "content": "$$16$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$2^{}x \\cdot 4^{}y=2^{}x\\cdot 2^{2y}=2^{x+2y}=2^{3}=8$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$3$$ " } ], [ { "aoVal": "E", "content": "$$2$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "$$24 \\div 4 = 6$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$8$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals" ]

[ "$$\\frac{1}{7}=0.\\overline{142857}$$, it is a decimal which repeats in cycles of $6$ digits. Every $6$\\textsuperscript{th}~digit is $7$. The $1986$\\textsuperscript{th} digit is $7$, so the $1985$\\textsuperscript{th} digit is $5$. " ]

[]

[ [ { "aoVal": "A", "content": "$$6.9$$ " } ], [ { "aoVal": "B", "content": "$$7.0$$ " } ], [ { "aoVal": "C", "content": "$$7.1$$ " } ], [ { "aoVal": "D", "content": "$$7.2$$ " } ], [ { "aoVal": "E", "content": "$$7.3$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals" ]

[ "$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde6.98-4.53+10.02-5.27$$ $$=(6.98+10.02)-(4.53+5.27)$$ $$=17-9.8$$ $$=7.2$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$16$$ " } ], [ { "aoVal": "B", "content": "$$24$$ " } ], [ { "aoVal": "C", "content": "$$32$$ " } ], [ { "aoVal": "D", "content": "$$64$$ " } ], [ { "aoVal": "E", "content": "$$72$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals" ]

[ "$4\\times4\\times4=64$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$0$$ " } ], [ { "aoVal": "B", "content": "$$1$$ " } ], [ { "aoVal": "C", "content": "$$2$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "infinitely many " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "We see that the vertex of the quadratic function $y=x^{2}-4x+a^{2}$ is $\\left(2, a^{2}-4\\right)$. If $\\left(2, a^{2}-4\\right)$ will be on the line $y=x+a^{2}-6$, $a^{2} -4=2+a^{2}-6$. Solve for $a$, any value of $a$ will satisfy this equation. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$-\\frac23$$ " } ], [ { "aoVal": "B", "content": "$$-\\frac34$$ " } ], [ { "aoVal": "C", "content": "$$-1$$ " } ], [ { "aoVal": "D", "content": "$$-\\frac43$$ " } ], [ { "aoVal": "E", "content": "$$-2$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Line $l\\_1$ has the equation $y=2x-3$ when rearranged. Substituting $1$ for $y$, we find that line $l\\_2$ will meet this line at point $(2,1)$, which is point $B$. We call $\\overline{B C}$ the base and the altitude from $A$ to the line connecting $B$ and $C, y=1$, the height. The altitude has length $\\textbar-1-1\\textbar=2$. The area of $\\triangle A B C=3$. Since $A=\\frac{bh}{2}, b=3$. Points that are on the line $y= 1$ and has a distance of $3$ from $B$ are $(5,1)$ and $(-1,1)$. Since $l\\_3$ has negative slope, point $C$ is $(-1,1)$. $l\\_3$ passes through $(-1,1)$ and $(1,-1)$, and thus has slope $\\frac{1-(-1)}{-1-1}=(\\mathbf{C}) -1$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$5.5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$6.5$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "The median of the distribution is 5. The problem is easier if vou put the scores in order: 2, 3, 4, 6, 7, 9. Since the distribution has an even number of scores, there is no middle score and you must average the two middle scores, 4 and 6. " ]

[]

[ [ { "aoVal": "A", "content": "$$8$$ " } ], [ { "aoVal": "B", "content": "$$16$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$12$$ " } ], [ { "aoVal": "E", "content": "$$11$$ " } ] ]

[ "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers", "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction " ]

[ "$$26-18=8$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$32$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "$$512\\times2=1024=32\\times32$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$189$$ minutes " } ], [ { "aoVal": "B", "content": "$$172$$ minutes " } ], [ { "aoVal": "C", "content": "$$216$$ minutes " } ], [ { "aoVal": "D", "content": "$$206$$ minutes " } ], [ { "aoVal": "E", "content": "None of the above. " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion" ]

[ "3: 55pm - 1: 47om + 15 minutes = 145 minutes. " ]

[]

[ [ { "aoVal": "A", "content": "$\\dfrac{1}{2014}$ " } ], [ { "aoVal": "B", "content": "$\\dfrac{1}{2013}$ " } ], [ { "aoVal": "C", "content": "$$2014$$ " } ], [ { "aoVal": "D", "content": "$$2013$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions" ]

[ "$$3- \\frac{2}{1}=1$$ $$5- \\frac{4}{1}=1$$ $$\\cdots \\cdots$$ $$2013- \\frac{2012}{1}=1$$ $$\\frac{2014}{1}=2014$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$-50$$ " } ], [ { "aoVal": "B", "content": "$$-16$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$40$$ " } ], [ { "aoVal": "E", "content": "$$50$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations" ]

[ "$(-17)-16=-33$, so the answer is $C$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$-1$$ or $$\\frac{11}{5}$$ " } ], [ { "aoVal": "C", "content": "$$1$$ or $$\\frac{1}{5}$$ " } ], [ { "aoVal": "D", "content": "$$1$$ or $$-\\frac{11}{5}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities" ]

[ "$$5x+3=\\pm 8$$ $$x=1$$ or $$x=-\\frac{11}{5}$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$14$$ " } ], [ { "aoVal": "B", "content": "$$20$$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$$28$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition" ]

[ "The pattern of the operation is $$a \\bigtriangleup b = a\\times b\\times2$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$50$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "B " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$5$$ " } ], [ { "aoVal": "E", "content": "$$6$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Each team plays $2$ games. $1$ points: a lost and a tie. $2$ points: two ties. $3$ points: a lost and a win. $4$ points: a win and a tie. $6$ points: two wins. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$\\angle$ $\\triangle$ $\\square$ " } ], [ { "aoVal": "B", "content": "$\\square$ $\\angle$ $\\triangle$ " } ], [ { "aoVal": "C", "content": "$\\triangle$ $\\angle$ $\\square$ " } ], [ { "aoVal": "D", "content": "$\\triangle$ $\\square$ $\\angle$ " } ], [ { "aoVal": "E", "content": "$\\square$ $\\triangle$ $\\angle$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations" ]

[ "$\\square=27$ $\\angle=28$ $\\triangle=40$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$17$$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$$27$$ " } ], [ { "aoVal": "E", "content": "$$36$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions" ]

[ "Let~$b$~be the number of boys and~$g$~be the number of girls. $\\dfrac{2}{3}b=\\dfrac{3}{4}g\\textbackslash{} \\Rightarrow\\textbackslash{} b=\\dfrac{9}{8}g$ For~$g$~and~$b$~to be integers,~~must cancel out with the denominator, and the smallest possible value is . This yields~~boys. The minimum number of students is~$8+9=\\boxed{\\left( B\\right)17}$ Solution 2 We know that~$\\dfrac{2}{3}B=\\dfrac{3}{4}G\\textbackslash{} or\\textbackslash{} \\dfrac{6}{9}B=\\dfrac{6}{8}G.$~So, the ratio of the number of boys to girls is~$9:8$. The So, the ratio of the number of boys to girls is~$8+9=\\boxed{\\left( B\\right)17}$. " ]

[]

[ [ { "aoVal": "A", "content": "$$7$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers" ]

[ "NA " ]

[]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers" ]

[ "The ones digit of the product is the same as the ones digit of $$0^{4}$$, $$1^{4}$$, $$2^{4}$$, $$3^{4}$$, $$4^{4}$$, $$5^{4}$$, $$6^{4}$$, $$7^{4}$$, $$8^{4}$$, or $$9^{4}$$. The ones digit can be $$0$$, $$1$$, $$5$$, or $$6$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$285$$ " } ], [ { "aoVal": "B", "content": "$$305$$ " } ], [ { "aoVal": "C", "content": "$$405$$ " } ], [ { "aoVal": "D", "content": "$$425$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences" ]

[ "Each whole number in the second sequence is $$5$$ more than the corresponding number in the first sequence. We have $$280 +5 \\times5 = 305$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$0-5$$ " } ], [ { "aoVal": "B", "content": "$$1-5$$ " } ], [ { "aoVal": "C", "content": "$$0-9$$ " } ], [ { "aoVal": "D", "content": "$$1-9$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "NA " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$25$$ " } ], [ { "aoVal": "B", "content": "$$18$$ " } ], [ { "aoVal": "C", "content": "$$52$$ " } ], [ { "aoVal": "D", "content": "$$51$$ " } ], [ { "aoVal": "E", "content": "$$50$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities" ]

[ "We know from the triangle inequality that the last side, $s$, fulfills $s+18\\textgreater25$. Therefore, $P\\textgreater25+25$. The least integer value of $P$ is $51$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$24$$ " } ], [ { "aoVal": "B", "content": "$$\\frac{1}{24}$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{b}{6a}$$ " } ], [ { "aoVal": "D", "content": "$$\\frac{a}{6b}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering Fraction by Comparing Its Reciprocal" ]

[ "$$\\frac{2}{a}\\div \\frac{b}{12}= \\frac{2}{a}\\times \\frac{12}{b}= \\frac{24}{ab}=24 $$， " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$100$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$36$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions" ]

[ "$$\\frac{x^{2}}{12^{2}}=\\left(\\frac{x}{12}\\right)^{2}=\\left(\\frac{120}{12}\\right)^{2}=\\left(10\\right)^{2}=100$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$20$$ " } ], [ { "aoVal": "C", "content": "$$1001$$ " } ], [ { "aoVal": "D", "content": "$$111$$ " } ], [ { "aoVal": "E", "content": "$$1111$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division" ]

[ "chair number " ]

[]

[ [ { "aoVal": "A", "content": "$$15$$ " } ], [ { "aoVal": "B", "content": "$$-23$$ " } ], [ { "aoVal": "C", "content": "$$0$$ " } ], [ { "aoVal": "D", "content": "$$-1$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Knowing the Number Lines" ]

[ "$$\\text{A}$$ is a positive number, $$\\text{B}$$ and $$\\text{D}$$ are two negative numbers, $$\\text{C}$$ is zero, which is neither positive nor negative. We choose $$\\text{C}$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$5.5$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$6.5$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions" ]

[ "$$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left ( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{10009}{39}+ \\frac{1009}{51}\\right )$$ $$=2018\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right ) \\div \\frac{1000}{3}\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right )$$ $=6$. " ]

[]

[ [ { "aoVal": "A", "content": "$$-3$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$3x+3$$ " } ], [ { "aoVal": "D", "content": "$$6x+3$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions" ]

[ "We can observe that when we remove the parentheses, all the $$x$$s are offset. $$5-4+3-2+1-0= 3$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$a-b$$ " } ], [ { "aoVal": "B", "content": "$$a+b$$ " } ], [ { "aoVal": "C", "content": "$$a+3b$$ " } ], [ { "aoVal": "D", "content": "$$a-3b$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number" ]

[ "omitted " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$5$$ " } ], [ { "aoVal": "E", "content": "$$6$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations" ]

[ "$15-9\\times1=6$ $6\\div(3-1)=3$ pieces of paper were cut. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$0$$ " } ], [ { "aoVal": "B", "content": "$$1$$ " } ], [ { "aoVal": "C", "content": "$$2$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "infinitely many " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "We see that the vertex of the quadratic function $y=x^{2}+a^{2}$ is $\\left(0, a^{2}\\right)$. The $y$-intercept of the line $y=x+a$ is $(0, a)$. We want to find the values (if any) such that $a=a^{2}$. Solving for $a$, the only values that satisfy this are 0 and 1, so the answer is $(\\text{C}) 2$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$30$$ " } ], [ { "aoVal": "B", "content": "$$60$$ " } ], [ { "aoVal": "C", "content": "$$90$$ " } ], [ { "aoVal": "D", "content": "$$180$$ " } ], [ { "aoVal": "E", "content": "$$360$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Setting $y=A x^{2}+B=C x^{2}+D$, we find that $A x^{2}-C x^{2}=x^{2}(A-C)=D-B$, so $x^{2}=\\frac{D-B}{A-C} \\geq 0$ by the trivial inequality. This implies that $D-B$ and $A-C$ must both be positive or negative. If two distinct values are chosen for $(A, C)$ and $(B, D)$ respectively, there are 2 ways to order them so that both the numerator and denominator are positive/negative (increasing and decreasing). We must divide by 2 at the end, however, since the 2 curves aren\\textquotesingle t considered distinct. Calculating, we get $$ \\frac{1}{2} \\cdot\\left(\\begin{array}{l} 6 \\textbackslash\\textbackslash{} 2 \\end{array}\\right)\\left(\\begin{array}{l} 4 \\textbackslash\\textbackslash{} 2 \\end{array}\\right) \\cdot 2=(\\text { C) } 90 $$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$0$$ " } ], [ { "aoVal": "D", "content": "$$3$$ " } ], [ { "aoVal": "E", "content": "$$1$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Factor the polynomial as $\\left(x^{2}-4\\right)\\left(x^{2}-3\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-4\\textless0\\textless x^{2}-3$. Solving this inequality, we find $3\\textless x^{2}\\textless4$. There is no integer $x$ that satisfies this inequality. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$\\frac5{49}$ " } ], [ { "aoVal": "B", "content": "$\\frac5{89}$ " } ], [ { "aoVal": "C", "content": "$\\frac5{17}$ " } ], [ { "aoVal": "D", "content": "$\\frac1{31}$ " } ], [ { "aoVal": "E", "content": "$\\frac5{81}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Fractions" ]

[ "The last fraction should be $\\frac{85}{89}$, so the answer is $\\frac5{89}.$ " ]

[]

[ [ { "aoVal": "A", "content": "$$11$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$13$$ " } ], [ { "aoVal": "D", "content": "$$14$$ " } ], [ { "aoVal": "E", "content": "$$20$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction" ]

[ "To calculate the total number of cups, do not need to consider the color of the cup. At the beginning, there were three cups. The number at last is $3+5+3+1=12$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$3$ lbs " } ], [ { "aoVal": "B", "content": "$4$ lbs " } ], [ { "aoVal": "C", "content": "$5$ lbs " } ], [ { "aoVal": "D", "content": "$6$ lbs " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution" ]

[ "We can write their relationships as the equations below: $A+B+P+P=12$ $A+P=5$ $B+P+P=A+P+5$ So, $B+P+P=5+5=10$, $A=12-10=2$, $P=5-2=3$, $B=12-2-3-3=4$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$\\frac{1}{3}$$ " } ], [ { "aoVal": "B", "content": "$$-1$$ " } ], [ { "aoVal": "C", "content": "$$1$$ " } ], [ { "aoVal": "D", "content": "$$3$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Rearranging, we find $x+y=2x, -x=y, \\frac xy = -1$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$33.3$ " } ], [ { "aoVal": "B", "content": "$$30$$ " } ], [ { "aoVal": "C", "content": "$$25$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation" ]

[ "$1\\div 4=25\\textbackslash\\%$ " ]

[]

[ [ { "aoVal": "A", "content": "$$13$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$11$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$9$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions" ]

[ "$y = 728 \\div 56 = 13$ " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$3$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions" ]

[ "$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$260$$ " } ], [ { "aoVal": "B", "content": "$$208$$ " } ], [ { "aoVal": "C", "content": "$$182$$ " } ], [ { "aoVal": "D", "content": "$$200$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation" ]

[ "$100\\times (1+30\\textbackslash\\%)=130$ $130+130\\times (1-40\\textbackslash\\%)=130+78=208$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$0.7$$ " } ], [ { "aoVal": "B", "content": "$\\dfrac{777}{1000}$ " } ], [ { "aoVal": "C", "content": "$$1$$ " } ], [ { "aoVal": "D", "content": "$\\dfrac{7}{9}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals" ]

[ "$0.163163163\\cdots+0.614614614\\cdots=0.777777777\\cdots=\\dfrac{7}{9}$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$24$$ " } ], [ { "aoVal": "B", "content": "$$25$$ " } ], [ { "aoVal": "C", "content": "$$26$$ " } ], [ { "aoVal": "D", "content": "$$27$$ " } ], [ { "aoVal": "E", "content": "$$28$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "Note that the sum of the first two numbers is $21 \\cdot 2=42$, the sum of the middle two numbers is $26 \\cdot 2=52$, and the sum of the last two numbers is $30 \\cdot 2=60$. It follows that the sum of the four numbers is $42+60=102$, so the sum of the first and last numbers is $102-52=50$. Therefore, the average of the first and last numbers is $50 \\div 2=$ (B) $25$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$(1+2+3+4)\\times 6$ " } ], [ { "aoVal": "B", "content": "$(1+2+3+4)$\\textsuperscript{2} " } ], [ { "aoVal": "C", "content": "$(16+1)\\times16\\div2$ " } ], [ { "aoVal": "D", "content": "$1\\times1+2\\times2+3\\times2+4\\times3+6+8\\times2+12\\times2+16$ " } ], [ { "aoVal": "E", "content": "$4\\times20$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers" ]

[ "$(1+2+3+4)\\times 1+(1+2+3+4)\\times 2+(1+2+3+4)\\times 3+(1+2+3+4)\\times 4=(1+2+3+4)\\times (1+2+3+4)$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$24$$ " } ], [ { "aoVal": "C", "content": "$$72$$ " } ], [ { "aoVal": "D", "content": "$$80$$ " } ], [ { "aoVal": "E", "content": "$$144$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules" ]

[ "$\\_3C\\_1\\times \\_4C\\_2\\times \\_4C\\_1=72$. " ]

[]

[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{1}{2}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions" ]

[ "$$\\frac{1}{2}x+y-1=\\frac{1}{2}(x+2y)-1=\\frac{3}{2}-1=\\frac{1}{2}$$． " ]

[]

[ [ { "aoVal": "A", "content": "$$3567$$ " } ], [ { "aoVal": "B", "content": "$$35$$ " } ], [ { "aoVal": "C", "content": "$$22$$ " } ], [ { "aoVal": "D", "content": "$$21$$ " } ], [ { "aoVal": "E", "content": "$356$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form" ]

[ "$3+5+6+7=21$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$\\dfrac{3}{5}$$ " } ], [ { "aoVal": "B", "content": "$$\\dfrac{3}{6}$$ " } ], [ { "aoVal": "C", "content": "$$\\dfrac{3}{7}$$ " } ], [ { "aoVal": "D", "content": "$$\\dfrac{3}{8}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering" ]

[ "Same numerator, so smaller denominator means larger fraction. " ]