ACT Form 68G Math Answer Explanation


2010 April(68G) Math Question 1

Angles Practice

- Parallel Lines

Choice H

$$=8+20x+9-2x$$ $$=18x+17$$

Choice C

$$(-2,8)+(8,-2)=(6,6)$$

2010 April(68G) Math Question 4

Word Problems Practice

- 2 Variable Addition

Choice K

$$=17\times70+20\times n$$

2010 April(68G) Math Question 5

Word Problems Practice

- Cost

Choice C

$$\frac{60}{80}=0.75$$

2010 April(68G) Math Question 6

Angles Practice

- Collinear Points & Triangles

Choice F

$$180-114=66$$ $$66\div2=33$$

2010 April(68G) Math Question 7

Probability Practice

- One Event

Choice E

$$P=\frac{blue+yellow}{28}$$ $$=\frac{8+4}{28}$$ $$=\frac{12}{28}$$ $$=\frac{3}{7}$$

2010 April(68G) Math Question 8

Word Problems Practice

- Distance, Speed, Time

Choice G

$$\frac{60}{1\frac{1}{2}}$$ $$=\frac{60}{\frac{3}{2}}$$ $$=60\times\frac{2}{3}$$ $$=40$$

2010 April(68G) Math Question 9

Statistics Practice

- Mean, Median

Choice D

$$62\ is\ the\ lowest\ score.$$ $$(78+83+86+93)\div4=85$$

Choice F

$$5y=m-n$$ $$y=\frac{m-n}{5}$$

Choice D

$$5+2x=19$$ $$2x=19-5=14$$ $$x=7$$ $$3x=21$$

Choice H

$$\frac{24}{4}=6$$ $$6\times6=36$$

Choice C

$$7\times10^{-2}\times4.58\times 10^{6}$$ $$=32.06\times10^{4}$$ $$=320600$$

2010 April(68G) Math Question 14

Quadratic Equations Practice

- Factoring

Choice G

$$=(x-4)(x-2)$$

Choice D

$$c\lt d,\ e\lt c,\ e\gt b,\ b\gt a$$ $$\Rightarrow a\lt b \lt e\lt c \lt d$$

Choice F

$$=\frac{2\times4+1\times6}{2\times1-4\times6}$$ $$=\frac{8+6}{2-24}$$ $$=\frac{14}{-22}$$ $$=\frac{7}{-11}$$

2010 April(68G) Math Question 17

Word Problems Practice

- 1 Variable Equations

Choice B

$$red:\ r,\ blue:\ b$$ $$Lance=3\ medium+3\ large$$ $$medium=5r+3b$$ $$large=10r+5b$$ $$Lance=3(5r+3b)+3(10r+5b)$$ $$=15r+9b+30r+15b$$ $$=45r+24b$$ $$\Rightarrow 24\ blue$$

Choice J

$$80=2^{4}\times5$$ $$70=2\times5\times7$$ $$30=2\times3\times5$$ $$[L.C.M]=2^{4}\times3\times5\times7=1680$$

Choice B

$$It's\ a\ 5-12-13\ triangle.$$ $$(5+12)-13=4$$

Choice K

$$(a^{8})^{24}$$ $$=a^{8\times24}$$ $$=a^{192}$$

Choice D

$$h(-3)$$ $$=4(-3)^{2}-3(-3)$$ $$=36+9$$ $$=45$$

2010 April(68G) Math Question 22

Word Problems Practice

- Cost

Choice K

$$\Rightarrow p-0.3p$$

Choice B

$$1.29\times\frac{2}{5}=0.516$$

Choice K

Its cost is $5, so …

2010 April(68G) Math Question 25

Probability Practice

- Factorials

Choice D

$$6!=1\times2\times3\times4\times5\times6$$ $$3!=1\times2\times3$$ $$2!=1\times2$$ $$\Rightarrow \frac{1\times2\times3\times4\times5\times6}{1\times2\times3\times1\times2}$$ …

2010 April(68G) Math Question 26

Word Problems Practice

- 2 Variable Addition

Choice K

$$x+y=1000---(1)$$ $$0.05x+0.25y=90---(2)$$ $$(2)\times20$$ $$\Rightarrow x+5y=1800---(3)$$ …

2010 April(68G) Math Question 27

Perimeter, Area, Volume Practice

- Mixed Shapes

Choice C

68g

$$\Box= 2\times2=4$$ $$4-1\times1\times\pi$$ $$=4-\pi$$

Choice K

$$4:7=20:x$$ $$4x=140$$ $$x=35 $$

Choice C

68g

$$\frac{20}{x}=\tan 50°$$ $$x=\frac{20}{\tan 50°}$$

2010 April(68G) Math Question 30

Perimeter, Area, Volume Practice

- Other Shapes

Choice H

It's the definition of a …

2010 April(68G) Math Question 31

Inequalities Practice

- Inequality Expressions

Choice A

$$3x-7 \lt 5+9x $$ $$\Rightarrow …

Choice H

$$2\pi r$$ $$=2\times3.14\times4$$ $$=25.12$$ $$\approx …

Choice B

$$-5\mid-8+9\mid$$ $$=-5(1)$$ $$=-5$$

Choice H

68g

$$x=(at\ least\ 1\ class\ of\ …

Choice D

$$Marigolds:\ 60\times1+40\times4+?\times6$$ $$=60+160+6?$$ $$Petunias:\ 25\times4+100\times6$$ …

Choice K

$$1\times60\times\frac{1}{10}=6$$ $$6\times x=15$$ $$x=2.5$$

Choice B

$$1\times30=30$$ $$30=4\times7...2$$

Choice K

68g

$$Y=(c+a,b)$$

2010 April(68G) Math Question 39

Angles Practice

- Other Shapes

Choice B

68g

$$x=90°-50°=40°$$

Choice F

68g

2010 April(68G) Math Question 41

Perimeter, Area, Volume Practice

- Other Shapes

Choice D

$$r=\frac{10}{2}=5$$ $$V=\pi r^{2}h$$ $$1000= 3.14\times5^{2}\times …

Choice J

$$1-\frac{1}{12}\times3=\frac{9}{12}$$ $$\frac{9}{12}\times\frac{1}{5}=\frac{3}{20}$$

2010 April(68G) Math Question 43

Quadratic Equations Practice

- Factoring

Choice A

$$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$ $$\Rightarrow x=\frac{5\pm\sqrt{25-4(1)(3)}}{2(1)}$$

Choice F

$$\frac{(9,-13)+(a,b)}{2}=(1,-6)$$ $$9+a=1\times2$$ $$\Rightarrow a=-7$$ $$-13+b=-6\times2$$ …

Choice B

68g

$$\cos 75°=\frac{x}{10}$$ $$x=10\cos 75°$$

Choice K

68g

The intercept with the Y …

2010 April(68G) Math Question 47

Perimeter, Area, Volume Practice

- Other Shapes

Choice D

68g

$$(18+10)\times3\times\frac{1}{2}=42$$

Choice G

$$y=mx+b$$ $$C=0.99\times H+0$$ $$m=0.99$$ $$0.99\ …

Choice D

$$\frac{10}{4}=2.5$$ $$\frac{25}{10}=2.5$$ $$25\times2.5=62.5$$

Choice J

$$64=4\times4\times4$$ $$4\times4\times6=96$$

2010 April(68G) Math Question 51

Angles Practice

- Circles

Choice C

$$2\pi r=2\pi(4)=8\pi$$ $$8\pi-7\pi=\pi$$ $$\frac{\pi}{8\pi}\times360°=45°$$

2010 April(68G) Math Question 52

Conics Practice

- Circles

Choice K

The general equation for a …

Choice D

68g

$$\frac{18}{\sin 47°}=\frac{x}{\sin 76°}$$ $$x=\frac{18\sin 76°}{\sin …

Choice F

68g

$$\sqrt{2}(l+x)-\sqrt{2}x$$ $$=\sqrt{2}l$$

Choice E

$$If\ x\leq2...$$ $$Let\ x=1$$ $$\mid …

Choice H

68g

$$More\ or\ equal\ to\ 6=25-(fewer\ …

Choice B

$$\cos x=-\frac{1}{3}$$ $$(\cos x)^{2}=\frac{1+\cos 2x}{2}$$ …

Choice F

$$y=f(g(x))$$ $$\Rightarrow 6=f(g(4))$$ $$g(4)=10(4)+b=40+b$$ $$f(40+b)=\sqrt{40+b}=6=\sqrt{36}$$ …

Choice A

68g

$$\Rightarrow10\times10=100$$

2010 April(68G) Math Question 60

Inequalities Practice

- Inequality Expressions

Choice F

$$a\gt 0$$ $$b^{2}\gt 0$$ $$c^{4}\gt …