2012 December(71A) Math Question 1

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice C

$$0.75(120)+20(2)=90+40=130$$

2012 December(71A) Math Question 2

Ratios, Proportions, Percentages, Fractions

- LCM, GCF, Prime Numbers

Choice G

$$15=3\times 5$$ $$6=2\times 3$$ $$4=2\times 2$$ $$2\times 2\times 3\times 5=60$$

2012 December(71A) Math Question 3

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice D

$$(36+24)2=120$$

2012 December(71A) Math Question 4

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice J

$$180°-64°=116°$$

2012 December(71A) Math Question 5

Ratios, Proportions, Percentages, Fractions

- Proportions & Ratios

Choice B

$$\frac{1}{4}\times \frac{250}{10}=\frac{1}{4}\times 25=6\frac{1}{4}$$

2012 December(71A) Math Question 6

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice F

$$3:12=1:4$$

2012 December(71A) Math Question 7

Algebraic & Function Expressions

- Solve Algebraic Expressions

Choice C

$$-(-1)+(-3)+2$$ $$=1-3+2$$ $$=0$$

2012 December(71A) Math Question 8

Algebraic & Function Expressions

- Solve Algebraic Expressions

Choice G

$$9+3x=27$$ $$3x=27-9=18$$ $$x=6$$ $$2x=12$$

2012 December(71A) Math Question 9

Word Problems

- 1 Variable Equations

Choice A

$$100(5+0.1-0.08+0.03)$$ $$=100(5+0.05)$$ $$=505$$

2012 December(71A) Math Question 10

Word Problems

- Cost

Choice J

$$\$32000(1+0.035)$$ $$=\$32000+\$1120$$ $$=\$33120$$

2012 December(71A) Math Question 11

Ratios, Proportions, Percentages, Fractions

- Percents & Fractions

Choice E

$$\frac{1}{3}(\frac{5}{6}+\frac{1}{12}+\frac{1}{3})$$ $$=\frac{1}{3}(\frac{10}{12}+\frac{1}{12}+\frac{4}{12})$$ $$=\frac{1}{3}(\frac{15}{12})$$ $$=\frac{5}{12}$$

2012 December(71A) Math Question 12

Inequalities

- Number Line

Choice H

$$4x-2\ge 6$$ $$4x\ge 8$$ $$x\ge 2$$ $$\Rightarrow H.$$

2012 December(71A) Math Question 13

Word Problems

- 1 Variable Equations

Choice C

$$1500+900=2400$$ $$2400÷20=120$$

2012 December(71A) Math Question 14

Angles

- Collinear Points & Triangles

Choice H

$$\mathrm{\angle }A=\mathrm{\angle }B=\mathrm{\angle }C=60°$$ $$x°=180°-60°=120°$$

2012 December(71A) Math Question 15

Quadratic Equations

- Factoring

Choice E

$$16x^2=30$$ $$x^2=\frac{30}{16}$$ $$x=\sqrt{\frac{30}{16}}$$

2012 December(71A) Math Question 16

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice F

$$100(20)+30(40-20)$$ $$=2000+600$$ $$=2600$$ $$2600÷800=3\frac{1}{4}$$

2012 December(71A) Math Question 17

Statistics

- Mean, Median

Choice A

2012 December(71A) Math Question 18

Graphing Properties

- Create Graphs or Figures

Choice G

$$50100\Rightarrow 89,96$$ $$101150\Rightarrow 103,104,106,113$$ $$151200\Rightarrow 160,160,161$$

2012 December(71A) Math Question 19

Ratios, Proportions, Percentages, Fractions

- Percents & Fractions

Choice D

$$\frac{89}{x}=\frac{43}{100}$$ $$43x=8900$$ $$x=206.97$$

2012 December(71A) Math Question 20

Statistics

- Mean, Median

Choice K

$$160+1006+104+113+160+103+161+89+96=1092$$ $$\Rightarrow \frac{1092+x+y}{9+2}=\frac{1092+x+y}{11}$$

2012 December(71A) Math Question 21

Probability

- One Event

Choice B

$$\frac{3}{5}=\frac{8+r}{8+5+11+r}=\frac{8+r}{24+r}$$ $$3(24+r)=5(8+r)$$ $$72+3r=40+5r$$ $$32=2r$$ $$r=16$$

2012 December(71A) Math Question 22

Algebraic & Function Expressions

- Simplify Algebraic Expressions

Choice G

$$(5x^3-4x^2+7x-3)-(3x^3+4x^2-3x+1)$$ $$=2x^3-8x^2+10x-4$$

2012 December(71A) Math Question 23

Graphing Properties

- Create Graphs or Figures

Choice E

$$\Rightarrow (E)$$

2012 December(71A) Math Question 24

Algebraic & Function Expressions

- Solve Function Expressions

Choice J

$$f(-4)$$ $$=5(-4{)}^2-2(-4)+10$$ $$=5(16)+8+10$$ $$=80+8+10$$ $$=98$$

2012 December(71A) Math Question 25

Algebraic & Function Expressions

- Simplify Algebraic Expressions

Choice D

$$\frac{6}{12}=0.5$$ $$\Rightarrow (D)$$

2012 December(71A) Math Question 26

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice H

$$\tan \theta =\frac{3}{8}$$ $$\theta =\arctan \frac{3}{8}$$

2012 December(71A) Math Question 27

Word Problems

- Distance, Speed, Time

Choice E

$$2+3d+2=22$$ $$\Rightarrow 4+3d=22$$

2012 December(71A) Math Question 28

Equation of a Line

- Equations that Describe a Line

Choice G

$$3x+5y=6$$ $$5y=-3x+6$$ $$y=-\frac{3}{5}+6$$ $$m=-\frac{3}{5}$$

2012 December(71A) Math Question 29

Algebraic & Function Expressions

- Solve Algebraic Expressions

Choice C

$$3x-12-2x+6=-5x-15+6$$ $$x-6=-5x-9$$ $$6x=-3$$ $$x=-\frac{1}{2}$$

2012 December(71A) Math Question 30

Number Types & Properties

- Rational & Irrational Numbers and Integers

Choice H

$$Ifx=\frac{1}{2}$$ $$(\frac{1}{2}{)}^3=\frac{1}{8}$$ $$0<\frac{1}{8}<1$$ $$\Rightarrow …

2012 December(71A) Math Question 31

Exponents, Radicals, & Scientific Notation

- Exponent Expressions

Choice E

$$\frac{(2a{)}^6+3a^4-5a^4}{2a}$$ $$=\frac{8a^6-2a^4}{2a}$$ $$=4a^5-a^3$$

2012 December(71A) Math Question 32

Exponents, Radicals, & Scientific Notation

- Scientific Notation

Choice J

$$1.28\times {10}^4-3.5\times {10}^3$$ $$=12.8\times {10}^3-3.5\times {10}^3$$ $$=9.3\times {10}^3$$

2012 December(71A) Math Question 33

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice A

$${\overline{AB}}^2=3^2+4^2=5^2$$ $$\overline{AB}=5$$ $$\sin A=\frac{3}{5}$$

2012 December(71A) Math Question 34

Algebraic & Function Expressions

- Solve Algebraic Expressions

Choice H

$$\frac{1}{{12}^2}:\frac{1}{6^2}$$ $$=\frac{1}{144}:\frac{1}{36}=1:4$$ $$l=10\times 4=40$$

2012 December(71A) Math Question 35

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice C

$$3-(-2)=5$$ $$16-4=12$$ $$\sqrt{5^2+{12}^2}=\sqrt{25+144}=\sqrt{169}=13$$ $$\pi r^{2}=\pi …

2012 December(71A) Math Question 36

Trigonometry

- Pythagorean Theorem & sin cos tan

2012 December(71A) Math Question 37

Absolute Values

- Absolute Value Expressions

Choice B

$$2w+7=\mid -2\mid$$ $$\mid -2\mid =2$$ $$2w+7=2\Rightarrow w=-2.5$$

2012 December(71A) Math Question 38

Graphing Properties

- Reflection, Rotation, Symmetry, Translation

Choice K

$$\Rightarrow (K)$$

2012 December(71A) Math Question 39

Equation of a Line

- Distance & Midpoint

Choice B

$$\frac{12+(-4)}{2}=4$$ $$\frac{18+2}{2}=10$$ $$\Rightarrow (4,10)$$

2012 December(71A) Math Question 40

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice G

$$\frac{\sin 58°}{50}=\frac{\sin 68°}{\overline{AB}}$$

2012 December(71A) Math Question 41

Conics

- Circles

Choice D

$$\frac{0+8}{2}=4$$ $$\frac{6+0}{2}=3$$

2012 December(71A) Math Question 42

Angles

- Circles

Choice J

2012 December(71A) Math Question 43

Number Types & Properties

- Rational & Irrational Numbers and Integers

$$\frac{4x}{6x^2}=\frac{2}{3x}$$

A rational number is …

2012 December(71A) Math Question 44

Algebraic & Function Expressions

- Nested Functions

Choice K

$$g(-2)=2(-2)-1=-5$$ $$f(-5)=3(-5)+2=-13$$

2012 December(71A) Math Question 45

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice B

$$36=6\times 6$$ $$6\times 4=24$$

2012 December(71A) Math Question 46

Word Problems

- Distance, Speed, Time

Choice F

$$Distance=V\times Time$$ $$1 segment:2 …

2012 December(71A) Math Question 47

Similar Triangles & Types of Triangles

- Triangle Types

Choice C

$$180°-43°-32°=105°=\mathrm{\angle }B$$ $$\overline{AC}>\overline{BC}>\overline{AB}$$

2012 December(71A) Math Question 48

Absolute Values

- Graphing Absolute Values

Choice F

$$y=\mid x-1\mid -2$$ $$(1,-2)\Rightarrow -2=0-2$$

2012 December(71A) Math Question 49

Conics

- Ellipse

Choice E

$$h>0,k>0$$ $$16=4^2$$ $$4=2^2$$ …

2012 December(71A) Math Question 50

Perimeter, Area, Volume

- Other Shapes

Choice K

$$2\times 4+2\times 4$$ $$=8+8$$ $$=16$$

2012 December(71A) Math Question 51

Algebraic & Function Expressions

- Systems of Equations

Choice A

$$2x-3y=6---(1)$$ $$(1)\times 3$$ $$\Rightarrow 6x-9y=18$$ $$-9=k$$ …

2012 December(71A) Math Question 52

Exponents, Radicals, & Scientific Notation

- Exponent Expressions

Choice F

$$2^0=1$$ $$x^2+1=0$$ $$x^2=-1$$ $$x=\pm I$$ …

2012 December(71A) Math Question 53

Angles

- Circles

Choice D

$$\pi r^2$$ $$=\pi {10}^2$$ $$=100\pi$$

2012 December(71A) Math Question 54

Angles

- Circles

Choice G

$$\widehat{AB}$$ $$=2\pi r\times \frac{1}{2}$$ $$=2\pi (20)\times \frac{1}{2}$$ $$=20\pi$$

2012 December(71A) Math Question 55

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice D

$$c\Rightarrow (10,\sqrt{3})$$

2012 December(71A) Math Question 56

Angles

- Circles

Choice J

$$90°÷2=45°$$

2012 December(71A) Math Question 57

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

Choice E

$$\frac{10L}{L}=10$$ $$(L-4)10=10L-40$$

2012 December(71A) Math Question 58

Sequences and Patterns

- General Sequences

Choice K

$$T_{64}=1+2+3+...+64$$ $$=\frac{(1+64)64}{2}$$ $$=65\times 32$$ $$=2080$$

2012 December(71A) Math Question 59

Quadratic Equations

- Factoring

Choice A

$$x^2+kx+17=0$$ $$\Rightarrow (x-17)(x-1)=0$$ $$\Rightarrow x^2-x-17x+17=0$$ …

2012 December(71A) Math Question 60

Trigonometry

- Pythagorean Theorem & sin cos tan

Choice F

$$\overline{XY}=12$$ $$\tan \theta =\frac{4}{9}=\frac{\overline{XY}}{\overline{XZ}}=\frac{12}{\overline{XZ}}$$ $$4\times \overline{XZ}=9\times 12$$ $$\overline{XZ}=27$$ $$Area=\overline{XZ}\times \overline{XY}\times \frac{1}{2}$$ …