ACT Form 68A Math Answer Explanation


Choice D

$$=\mid3\mid-\mid-3\mid$$ $$=3-3$$ $$=0$$

Choice G

$$y=2x+1=3$$ $$2x+1=3$$ $$x=1$$

2009 December(68A) Math Question 3

Word Problems Practice

- 2 Variable Addition

Choice A

$$=80\times16+n\times22$$

Choice J

$$=50\times1.5=75$$

Choice E

Draw the blue one twice, …

Choice J

$$3\ pieces=x,\ y,\ z$$ $$x=2y=2(2z)=4z$$ $$y=2z$$ $$\Rightarrow x+y+z=4z+2z+z=21$$ $$\Rightarrow 7z=21$$ $$\Rightarrow z=3$$ $$x=4z=12$$

Choice C

$$(8+3)2=22$$

2009 December(68A) Math Question 8

Angles Practice

- Vertex Angles & Bisectors

Choice C

$$\triangle BCD is a 6-8-10 triangle.$$ $$\overline{BD}=10$$ $$\underline{AB}=\overline{BD}=\overline{AD}=10$$

2009 December(68A) Math Question 10

Probability Practice

- One Event

Choice F

The yellow area accounts for 1/2 of the area, so the probability is 1/2.

Choice A

$$2(3x+5)=6x+10$$ $$=6\ squares+10\ circles$$

Choice H

$$y=mx+b$$ $$5x-y-9=0$$ $$\Rightarrow -y=9-5x$$ $$\Rightarrow y=5x-9y$$

2009 December(68A) Math Question 13

Equation of a Line Practice

- Distance & Midpoint

Choice D

$$\Rightarrow\frac{S+T}{2}$$ $$=\frac{(4,10)+(6,-2)}{2}$$ $$=\frac{(10,8)}{2}$$ $$=(5,4)$$

Choice K

$$\frac{3}{5}\times\frac{1}{2}=\frac{3}{10}$$

Choice C

$$\frac{1}{a}=2$$ $$\frac{1}{b}=3$$ $$\frac{1}{2}(\frac{1}{a}+\frac{1}{b})$$ $$=\frac{1}{2}(2+3)$$ $$=\frac{5}{2}$$

2009 December(68A) Math Question 16

Word Problems Practice

- Cost

Choice J

$$30\times0.85\times0.9\times1.06=24.327\approx24.34$$

2009 December(68A) Math Question 17

Angles Practice

- Parallel Lines

Choice E

68a

$$a=c$$ $$b=d$$ $$a+b=180°$$ $$c+d=180°$$ $$a+b+c+d=360°$$

Choice G

$$5000\div50=100$$

Choice E

$$(x+2)(x-1)$$ $$=x^{2}-x+2x-2$$ $$=x^{2}+x-2$$

Choice G

$$A=1000(1+0.05)^{2}$$ $$=1000(1.1025)$$ $$=1102.5\approx 1103$$

2009 December(68A) Math Question 21

Equation of a Line Practice

- Distance & Midpoint

Choice C

$$20\ mins=\frac{1}{3}\ hr$$ $$50\times\frac{1}{3}=16.666\approx17$$

2009 December(68A) Math Question 22

Word Problems Practice

- 2 Variable Addition

Choice H

$$$1=100¢$$ $$0.40\times x+0.25\times(20-x)=6.95$$ $$0.4x+5-0.25x=6.95$$ $$0.15x=1.95$$ …

Choice B

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

Choice G

$$\sin 6°=0.1045=\frac{?}{4}$$ $$?=0.1045\times4=0.418$$

2009 December(68A) Math Question 25

Sequences and Patterns Practice

- General Sequences

Choice E

$$Level\ 1=4\times5$$ $$Level\ 2=4\times6$$ $$Level\ …

Choice J

$$F.\sqrt{-5^{2}}=5$$ $$G.\sqrt{-2^{2}}=2$$ $$H.\sqrt{\frac{1}{2}^{2}}=\frac{1}{2}$$ $$\frac{1}{2}\ is\ …

Choice B

$$16(16-6)(\frac{1}{2})=80$$

2009 December(68A) Math Question 28

Number Types & Properties Practice

- Order of Values

Choice K

$$x-y\lt0$$ $$Let\ x=1,\ y=2$$ $$F.\ …

Choice E

Move down two units, the …

2009 December(68A) Math Question 30

Inequalities Practice

- Inequality Expressions

Choice G

$$-6+7k \geq 3-8k$$ $$\Rightarrow 15k …

Choice C

68a

$$\Rightarrow \overline{AB}=4\overline{GH}$$

Choice F

$$2\frac{1}{3}\times\frac{1}{2}=1\frac{1}{6}$$

2009 December(68A) Math Question 33

Word Problems Practice

- Interesection

Choice B

$$6+1\times x=3+1\frac{1}{2}x$$ $$3=\frac{1}{2}x$$ $$x=6$$

Choice K

$$\Rightarrow x^{3}-4x^{2}-x^{2}+5x+3x+6$$ $$\Rightarrow x^{3}-5x^{2}+8x+6$$

Choice A

$$\tan \theta=\frac{0.5}{1}$$ $$\Rightarrow \tan \theta=\frac{1}{2}$$ …

Choice G

68a

2009 December(68A) Math Question 37

Perimeter, Area, Volume Practice

- Mixed Shapes

Choice C

68a

$$\pi r^{2}=16\pi $$

Choice K

68a

2009 December(68A) Math Question 39

Equation of a Line Practice

- Distance & Midpoint

Choice B

68a

2009 December(68A) Math Question 40

Perimeter, Area, Volume Practice

- Other Shapes

Choice F

68a

2009 December(68A) Math Question 41

Quadratic Equations Practice

- Factoring

Choice D

$$r=\frac{10}{2}=5$$ $$\pi r^{2}h=\pi 5^{2}h=1000$$ $$h=1000\div25\div\pi=\frac{40}{\pi}\approx\frac{40}{3.14}=12.73$$

2009 December(68A) Math Question 42

Perimeter, Area, Volume Practice

- Mixed Shapes

Choice J

$$1-\frac{1}{12}\times3=\frac{9}{12}=\frac{3}{4}$$ $$\frac{3}{4}\times\frac{1}{5}=\frac{3}{20}$$

2009 December(68A) Math Question 43

Statistics Practice

- Mean, Median

Choice A

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

Choice F

$$(9,-13)+(a,b)=2(1,-6)=(2,-12)$$ $$9+a=2\ \Rightarrow\ a=-7$$ $$-13+b=-12\ …

Choice B

Let the base of the …

2009 December(68A) Math Question 46

Probability Practice

- Combinations

Choice K

68a

$$(0,-1)\Rightarrow G,\ K$$ $$(K). m=3,\ …

Choice D

$$(10+18)\times 3\times\frac{1}{2}=42$$

Choice G

$$C=99\times h$$ $$m=0.99$$

2009 December(68A) Math Question 49

Angles Practice

- Circles

Choice D

$$4,10,25$$ $$10\div4=2.5$$ $$25\div10=2.5$$ $$25\times2.5=62.5$$

2009 December(68A) Math Question 50

Perimeter, Area, Volume Practice

- Other Shapes

Choice J

$$64=x^{3}$$ $$x=4$$ $$Total\ surface\ area=4\times4\times6=96$$

Choice C

$$2\pi r=2 \pi(4)=8\pi$$ $$\frac{7 \pi}{8\pi}=\frac{315}{360}$$ …

2009 December(68A) Math Question 52

Probability Practice

- One Event

Choice K

The equation for a circle …

Choice D

68a

$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$ $$\Rightarrow …

Choice F

68a

$$The\ side\ of\ square1:1+l$$ $$The\ …

2009 December(68A) Math Question 55

Quadratic Equations Practice

- Factoring

Choice E

$$If\ \ x\leq2\ , then\ …

2009 December(68A) Math Question 56

Word Problems Practice

- Fixed Cost + Variable Cost

Choice H

More than 6 rooms:25-10=15

6 …

Choice B

$$\Rightarrow (\cos x)^{2}=(-\frac{1}{3})^{2}=\frac{1}{9}$$ $$\frac{1}{9}=\frac{1+\cos 2x}{2}$$ …

Choice F

$$y=f(g(x))=\sqrt{10x+b}$$ $$(4,6)\Rightarrow 6=\sqrt{10\times4+b}$$ $$\Rightarrow 36=40+b$$ …

Choice A

68a

2009 December(68A) Math Question 60

Angles Practice

- Other Shapes

Choice F

$$b^{2}\gt 0;$$ $$(c^{2})^{2}\gt 0;$$ $$\Rightarrow …