ACT Form 70C Math Answer Explanation


2012 June(70C) Math Question 1

Statistics Practice

- Mean, Median

Choice C

$$\frac{1260}{8}=157.5$$

Choice H

$$4\times L=144$$ $$L=36$$

2012 June(70C) Math Question 3

Word Problems Practice

- Cost

Choice D

$$\frac{50-40}{50}\times100=\frac{10}{50}\times100=20$$

Choice J

$$\frac{8}{50}=\frac{x}{500}$$ $$\Rightarrow x=80$$

Choice C

$$(8+12)2=20(2)=40$$

Choice H

$$300+$10\times n$$

2012 June(70C) Math Question 7

Probability Practice

- Combinations

Choice B

$$2\times5=10$$

Choice J

$$\Rightarrow 2x-12+x=36$$ $$\Rightarrow 3x-12=36$$ $$\Rightarrow 3x=48$$ $$\Rightarrow x=16$$

Choice D

$$3(4+a)=2(9+a)$$ $$12+3a=18+2a$$ $$a=6$$

Choice F

$$12\div(-6)=-2$$ $$(-96)\times(-2)=192$$

Choice D

$$(-4,-9)\rightarrow(-4+4,-9+9)=(0,0)$$

Choice F

$$510\div(5\times12)=510\div60=8.5$$

Choice C

$$\frac{150}{0.75}=112.5$$

2012 June(70C) Math Question 14

Word Problems Practice

- 1 Variable Equations

Choice G

$$3.9\div3=1.3$$ $$1.49-1.3=0.19$$

Choice E

$$=(4\times3)(a^{1+4})(b^{2+3})$$ $$=12a^{5}b^{5}$$

Choice G

$$\frac{3+15}{2}=9$$

Choice E

She stopped.

2012 June(70C) Math Question 18

Angles Practice

- Parallel Lines

Choice G

$$\angle 1\cong\angle3$$ $$\angle 2\cong\angle4$$ $$\angle 8\cong\angle6$$ $$\angle 5\cong\angle7$$

Choice C

$$=5-6x+3$$ $$=8-6x$$

Choice J

An obtuse angle is a type of angle that is always larger than 90° but less than 180°.

Choice C

$$f(-5)=\frac{-3[(-5)^{2}+3(-5)+2]}{15(-5)+15}$$ $$=\frac{-3(25-15+2)}{-75+15}$$ $$=\frac{-3(12)}{-60}$$ $$=\frac{36}{60}$$ $$=\frac{3}{5}$$

Choice G

$$y=mx+b$$ $$2y=-3x+6$$ $$y=\frac{-3}{2}x+6$$ $$m=\frac{-3}{2}$$

Choice A

$$\sqrt{20}-\sqrt{45}$$ $$=\sqrt{5}\sqrt{4}-\sqrt{5}\sqrt{9}$$ $$=\sqrt{5}(\sqrt{4}-\sqrt{9})$$ $$=\sqrt{5}(2-3)$$ $$=-\sqrt{5}$$

2012 June(70C) Math Question 24

Word Problems Practice

- % Interest

Choice F

$$l=Prt$$ $$t=\frac{l}{Pr}=\frac{l}{P\times0.05}$$

Choice A

$$f(2005)=2f(1998)+100$$

Choice K

$$4^{2}+6^{2}=x^{2}$$ $$16+36=52=x^{2}$$ $$x=\sqrt{52}$$

2012 June(70C) Math Question 27

Angles Practice

- Collinear Points & Triangles

Choice C

$$\angle A+\angle B+\angle C=180°$$ $$\angle …

Choice G

$$\cos B=\frac{\overline{AB}}{\overline{BC}}$$

Choice B

$$g(1)=1^{2}+1=1+1=2$$ $$f(g(1))=f(2)=2+3=5$$

Choice K

$$=3^{3}\times x^{2\times3}=27x^{6}$$

Choice B

$$15^{2}-9^{2}=\overline{AE}^{2}$$ $$225-81=144=12^{2}$$ $$\overline{AE}=12$$ $$12+4=16$$

Choice K

$$3\frac{3}{7}=3\frac{30}{70}$$ $$-(-3.5)=3.5=3\frac{35}{70}$$ $$3\frac{2}{5}=3\frac{28}{70}$$ $$\Rightarrow 3\frac{2}{5}\lt3\frac{3}{7}\lt-(-3.5)$$

2012 June(70C) Math Question 33

Word Problems Practice

- 2 Variable Addition

Choice D

$$S:x$$ $$L:10-x$$ $$x(20)+(10-x)35=260$$ $$20x+350-35x=260$$ $$350-260=15x$$ …

2012 June(70C) Math Question 34

Word Problems Practice

- Cost

Choice H

$$55+55+55(0.85)=137.5$$

Choice B

$$12=20a+b---(1)$$ $$(20+5)(12-2)$$ $$\Rightarrow 10=25a+b---(2)$$ $$(2)-(1)$$ …

Choice K

$$\frac{1}{1+\frac{1}{1+\frac{1}{2}}}$$ $$=\frac{1}{1+\frac{1}{\frac{3}{2}}}$$ $$=\frac{1}{1+\frac{2}{3}}$$ $$=\frac{1}{\frac{3}{5}}$$ $$=\frac{5}{3}$$

Choice D

$$y=0=-2x+8$$ $$x=4$$

2012 June(70C) Math Question 38

Quadratic Equations Practice

- Factoring

Choice H

$$h=-16t^{2}+48t$$ $$32=-16t^{2}+48t$$ $$\Rightarrow -16t^{2}+48t-32=0$$ $$\Rightarrow …

2012 June(70C) Math Question 39

Inequalities Practice

- Number Line

Choice D

$$3x-2\gt9$$ $$\Rightarrow 3x\gt11$$ $$\Rightarrow x\gt\frac{11}{3}$$ …

Choice J

$$(7,-3)\Rightarrow(7-7,-3+3)=(0,0)=headquarters$$ $$(7,-3)\Rightarrow(7+5-2,-3+4)=(10,1)$$ $$(0,0)\rightarrow(10,1)$$ $$\sqrt{(10-1)^{2}+(1-0)^{2}}=\sqrt{81+1}=\sqrt{82}\approx 9.05$$

Choice F

$$\tan40°=\frac{\overline{XY}}{100}$$ $$\overline{XY}=100\tan 40°$$

Choice F

$$\sin 56°=\frac{125}{?}$$ $$?=\frac{125}{\sin 56°}$$

Choice C

70c

$$\pi r^{2}=\pi\times3^{2}=9\pi$$

2012 June(70C) Math Question 44

Conics Practice

- Circles

Choice G

70c

$$r=1-(-1)=2$$

2012 June(70C) Math Question 45

Inequalities Practice

- Graphing Inequalities

Choice B

$$m=-\frac{a-0}{b-0}=-\frac{a}{b}$$ $$\Rightarrow y\leq-\frac{a}{b}x+a$$

Choice F

$$r_{B}=\frac{2x}{2}=x$$ $$x:x=1:1$$

Choice E

$$1:1:\sqrt{2}$$ $$\Rightarrow 5\sqrt{2}:5\sqrt{2}:10$$ $$18\times5\sqrt{2}+5\sqrt{2}\times5\sqrt{2}\times\frac{1}{2}$$ $$=90\sqrt{2}+25$$ …

Choice J

There are 8 pauses between …

2012 June(70C) Math Question 49

Inequalities Practice

- Inequality Expressions

Choice A

$$2a=3b$$ $$\frac{1}{4}b\times4=\frac{1}{2}c\times4$$ $$\Rightarrow b=2c$$ $$2a=3b=6c$$ …

Choice F

Because the amount he is …

Choice C

$$\because i^{2}= -1$$

The correct …

Choice G

70c

$$\frac{100}{4}=2r$$ $$r=12.5$$ $$2\pi r\times\frac{1}{2}=\pi r=\pi\times12.5$$ …

2012 June(70C) Math Question 53

Inequalities Practice

- Graphing Inequalities

Choice C

Simply graph y = a-x …

Choice J

$$12^{2}f=2fd^{2}$$ $$144f=2fd^{2}$$ $$72=d^{2}$$ $$d=6\sqrt{2}$$

Choice A

70c

$$30°:60°:90°=1:\sqrt{3}:2$$ $$\Rightarrow 2:2\sqrt{3}:4$$ $$Area=2\times2\sqrt{3}\times\frac{1}{2}\times4$$ $$=8\sqrt{3}$$

Choice J

$$\because 13^{2}=5^{2}+12^{2}$$

The unknown leg …

Choice D

$$\frac{1}{11^{20}}-\frac{1}{11^{21}}$$ $$=\frac{1\times11}{11^{20}\times11}-\frac{1}{11^{21}}$$ $$=\frac{11}{11^{21}}-\frac{1}{11^{21}}$$ $$=\frac{10}{11^{21}}$$

Choice F

70c

$$\tan\theta\times\cos\theta$$ $$=\frac{2}{\sqrt{5}}\times\frac{\sqrt{5}}{3}$$ $$=\frac{2}{3}$$

Choice E

70c

The side length of each …

Choice F

For example, if x=-1 then …