ACT Form 66F Math Answer Explanation


Choice E

$$12:4=x:12$$ $$4x=144$$ $$x=36$$

Choice H

$$500-140=360$$ $$360\div40=9$$

Choice A

$$\frac{x^{2}-1}{x+1}$$ $$=\frac{(-5)^{2}-1}{(-5)+1}$$ $$=\frac{24}{-4}$$ $$=-6$$

2009 April(66F) Math Question 4

Word Problems Practice

- 1 Variable Equations

Choice J

$$9.25-8.5=0.75$$ $$0.75\times27=20.25$$

2009 April(66F) Math Question 5

Probability Practice

- One Event

Choice C

$$P=\frac{1}{13-3}=\frac{1}{10}$$

Choice H

$$(15+6)\times2=42$$

2009 April(66F) Math Question 7

Word Problems Practice

- 2 Variable Addition

Choice B

$$6\times142=852$$ $$2000-852=1148$$ $$1184\div8=143.5$$

Choice J

$$\frac{8}{12}=\frac{10}{r}$$ $$8r=120$$ $$r=15$$

Choice E

$$12(x-11)=-15$$ $$\Rightarrow 12x-132=-15$$ $$\Rightarrow 12x=117$$ $$\Rightarrow 4x=39$$ $$\Rightarrow x=\frac{39}{4}$$

2009 April(66F) Math Question 10

Angles Practice

- Collinear Points & Triangles

Choice C

$$f(-2)=9(-2)^{2}+5(-2)-8$$ $$=9(4)-10-8$$ $$=36-18$$ $$=18$$

Choice J

$$30=3\times10$$ $$20=2\times10$$ $$70=7\times10$$ $$[30,20,70]=2\times3\times7\times10=420$$

Choice E

$$Originally\ wanted=\frac{x}{2}$$ $$(x\times2)\div\frac{x}{2}=4$$ $$\Rightarrow (x\times2)\div4=\frac{x}{2}$$

Choice G

66f

$$125\div5=25$$ $$25=5\times5$$ $$5\times12=60$$

Choice E

$$\angle B=90°$$ $$\angle A+\angle B+\angle C=180°$$ $$\Rightarrow \angle A+\angle C=90°$$ $$\because \angle A\gt 43°$$ $$90-43=47$$ $$\therefore \angle C \lt 47°$$

Choice G

$$I. $$ $$(2+1)^{4}+(6+3)^{2}\neq10$$ $$II. $$ $$(2-1)^{4}+(6-3)^{2}$$ $$=(1)^{4}+(3)^{2}$$ $$=1+9$$ $$=10$$ $$III.$$ $$(2\div1)^{4}+(6\div3)^{2}$$ $$=(1)^{4}+(2)^{2}$$ $$=1+4$$ $$=5$$ $$\neq 10$$

Choice E

66f

$$(0,5)\Rightarrow 5=2(0)+5$$ $$Only\ (E)\ is\ correct.$$

Choice F

$$\Rightarrow (n+4)8=2n-10$$

Choice A

Assuming that x years have passed...

$$\Rightarrow 20,000+800x=15,200+2,000x$$

Choice J

66f

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

Choice E

$$=7x+21-6x+6$$ $$=x+27$$

Choice G

$$x+y=32---(1)$$ $$x-y=12---(2)$$ $$(1)+(2)$$ $$\Rightarrow 2x=44$$ …

2009 April(66F) Math Question 23

Quadratic Equations Practice

- FOIL

Choice C

$$(2x-3)^{2}$$ $$=4x^{2}-12x+9$$ $$\Rightarrow a=4,b=-12,c=9$$ $$a+b+c=4-12+9=1$$

Choice H

66f

$$\Rightarrow 15\times15+5\times10$$ $$=225+50$$ $$=275$$

Choice A

66f

It can be seen from the table that f(x) moves in increments of 0.2, meaning f(x) is a linear function. It follows that f(4) = 0.2.

Choice H

$$y=mx+b$$ $$6y=14x+5$$ $$y=\frac{14}{6}+\frac{5}{6}$$ $$m=\frac{14}{6}=\frac{7}{3}$$

2009 April(66F) Math Question 27

Quadratic Equations Practice

- Factoring

Choice C

$$x^{2}+x-12$$ $$=(x-3)(x+4)$$ $$\Rightarrow x=3,-4$$ $$3+(-4)=-1$$

Choice J

$$3+5+7=15$$ $$\Rightarrow 15\times\frac{5}{3}=25$$

2009 April(66F) Math Question 29

Statistics Practice

- Mean, Median

Choice A

$$\Rightarrow -6,-5,-3,-2,1,2,4$$ $$The\ median:\ -2$$

2009 April(66F) Math Question 30

Quadratic Equations Practice

- Factoring

Choice G

$$x^{2}-23(x)=50$$ $$\Rightarrow x^{2}-23(x)-50=0$$ $$\Rightarrow (x-25)(x+2)=0$$ …

2009 April(66F) Math Question 31

Word Problems Practice

- Distance, Speed, Time

Choice B

$$d=\frac{1}{2}at^{2}$$ $$80=\frac{1}{2}(20)t^{2}$$ $$80=10t^{2}$$ $$8=t^{2}$$ $$t\approx2.82$$

Choice F

$$\frac{abc^{2}d}{bcd}=ac$$ $$\frac{a^{2}bc^{3}d}{abc^{2}d}=ac$$ $$\Rightarrow a^{2}bc^{3}d(ac)=a^{3}bc^{4}d$$

2009 April(66F) Math Question 33

Probability Practice

- One Event

Choice D

66f

$$\Rightarrow \frac{2+5+6}{20}$$ $$=\frac{13}{20}$$

2009 April(66F) Math Question 34

Angles Practice

- Circles

Choice J

66f

$$\Rightarrow \frac{4}{20}=\frac{2}{10}$$ $$\frac{2}{10}\times360°=72°$$

2009 April(66F) Math Question 35

Statistics Practice

- Mean, Median

Choice B

$$=\frac{0(2)+1(5)+2(6)+3(4)+4(2)+5(1)}{20}$$ $$=\frac{0+5+12+12+8+5}{20}$$ $$=\frac{42}{20}$$ $$=2.1$$

2009 April(66F) Math Question 36

Quadratic Equations Practice

- Factoring

Choice F

$$\Rightarrow\frac{(x+7)(x+1)}{(x+7)(x-3)}\times\frac{x-3}{x+1}$$ $$\Rightarrow 1$$

Choice E

66f

$$\sin 72°=\frac{x}{144}$$ $$x=144\sin 72°$$

Choice G

$$\Rightarrow(\frac{-8+2}{2},\frac{-3+3}{2})$$ $$=(\frac{-6}{2},\frac{0}{2})$$ $$=(-3,0)$$ $$\Rightarrow x=-3$$

Choice B

$$\Rightarrow\sqrt{(-6-(-2))^{2}+(-7-(-3))^{2}}$$ $$=\sqrt{16+16}$$ $$=\sqrt{32}$$ $$\approx 5.65$$ …

Choice K

"The sum of two rational …

Choice B

$$i=\sqrt{-1}$$ $$i^{2}=-1$$ $$\Rightarrow (i^{2})^{2}=1$$ $$\Rightarrow …

Choice H

$$x=3$$ $$y=(3-3)^{2}+2=2$$

2009 April(66F) Math Question 43

Perimeter, Area, Volume Practice

- Other Shapes

Choice C

$$\pi r^{2}=25\pi$$ $$25\pi\times6=150$$

Choice F

66f

$$The\ perimeter\ of\ \triangle ABC:\triangle …

Choice E

66f

$$\triangle 45°-45°-90°=1:1:\sqrt{2}$$ $$\triangle 30°-60°-90°=1:\sqrt{3}:2$$ $$H=\frac{100}{\sqrt{2}}+20\sqrt{3}+30$$ …

2009 April(66F) Math Question 46

Conics Practice

- Circles

Choice H

The equation of a circle …

2009 April(66F) Math Question 47

Perimeter, Area, Volume Practice

- Mixed Shapes

Choice A

$$2a\times(6-2a^{2})$$ $$=12a-4a^{3}$$

Choice F

$$Let n be 2 or …

2009 April(66F) Math Question 49

Logarithms Practice

- Logarithm Expressions

Choice D

Logarithm base 5 of 5 …

Choice J

$$\frac{156-144}{144}=\frac{12}{144}\approx0.083$$

2009 April(66F) Math Question 51

Statistics Practice

- Mean, Median

Choice D

$$\frac{156+145+140+x}{4}=150$$ $$441+x=600$$ $$x=159$$

Choice G

$$Week\ 1=30$$ $$Week\ 2=30(1.1)=33$$ $$Week\ …

2009 April(66F) Math Question 53

Trigonometry Practice

- Graphing Trig Functions

Choice B

66f

Choice K

66f

$$3:4:5$$ $$=24:32:40$$ $$The\ height=32$$

Choice C

$$\mid x^{2}-12 \mid -4=0$$ $$\Rightarrow\ …

Choice K

66f

$$10\rightarrow2=Walk\ toward$$ $$Speed=\frac{8}{4}=2$$ $$2\rightarrow6=Walk\ away$$ …

2009 April(66F) Math Question 57

Angles Practice

- Circles

Choice D

$$2:10\rightarrow 5:30$$ $$=3\ hours\ 20mins=3\frac{1}{3}\ …

Choice K

66f

$$24^{2}+7^{2}=25^{2}$$ $$\Rightarrow \sin \phi=\frac{7}{25}$$

Choice B

$$w+z=5$$ $$(w,z)=(1,4),(2,3),(3,2),(4,1)$$ $$2^{w}=x$$ $$x^{z}=64$$ $$(1,4)\Rightarrow2^{1}=2,\ …

2009 April(66F) Math Question 60

Perimeter, Area, Volume Practice

- Mixed Shapes

Choice F

66f

$$\sqrt{(4\sqrt{2})^{2}+4^{2}}=\sqrt{48}=4\sqrt{3}$$ $$4\sqrt{3}=2r$$ $$r=2\sqrt{3}$$