ACT Form 71G Math Answer Explanation



2013 April(71G) Math Question 1

Word Problems

- 1 Variable Equations


Choice C

$$40\times$12.5+6\times$12.5\times2$$ $$=500+150$$ $$=650$$


Choice K

$$\frac{4(x-6)}{3}=16$$ $$\Rightarrow 4(x-6)=16\times3=48$$ $$\Rightarrow 4x-24=48$$ $$\Rightarrow 4x=72$$ $$\Rightarrow x=18$$


Choice A

$$2x+8=30$$ $$x=11$$


Choice J

$$\Rightarrow 6x-3=3x+1$$ $$\Rightarrow 3x=4$$ $$\Rightarrow x=\frac{4}{3}$$


2013 April(71G) Math Question 6

Probability

- Combinations


Choice K

$$5\times6\times5=150$$


2013 April(71G) Math Question 7

Word Problems

- Temperature


Choice E

$$120-(-29)=149$$


Choice G

$$=\frac{3\times4+1\times5}{3\times1-4\times5}$$ $$=\frac{12+5}{3-20}$$ $$=\frac{17}{-17}$$ $$=-1$$


2013 April(71G) Math Question 9

Absolute Values

- Graphing Absolute Values


Choice E

$$x=3,y=0\Rightarrow (3,0)$$ $$x=0,y=6\Rightarrow (0,6)$$ $$(3,0+4)=(3,4)$$ $$(0,6+4)=(0,10)$$


Choice G

$$21=3\times7$$ $$6=2\times3$$ $$4=2\times2$$ $$\Rightarrow 2\times2\times3\times7=84$$


2013 April(71G) Math Question 11

Statistics

- Mean, Median


Choice A

$$89\times5=445$$ $$445-78-92-96-94=85$$


Choice H

$$\frac{2520}{12\times14}=15$$


2013 April(71G) Math Question 13

Word Problems

- 1 Variable Equations


Choice D

$$15-(x\times f+x\times h)$$ $$=15-x(f+h)$$


2013 April(71G) Math Question 14

Absolute Values

- Absolute Value Expressions


Choice H

$$=\mid-48+6\mid=\mid-42\mid=42$$


Choice E

$$The\ area\ of\ a\ circle=\pi r^{2}$$ $$\Rightarrow \pi R^{2}-3\pi r^{2}$$


2013 April(71G) Math Question 16

Angles

- Parallel Lines


Choice H

$$y=50$$ $$x+y=180$$ $$\Rightarrow x=130$$ $$x-y=130-50=80$$


2013 April(71G) Math Question 17

Inequalities

- Number Line


Choice B

$$3x-5\geq 7$$ $$\Rightarrow 3x\geq7+5$$ $$\Rightarrow x\geq \frac{7+5}{3}$$ $$\Rightarrow x\geq \frac{12}{3}$$ $$\Rightarrow x\geq 4$$


Choice K

$$s(-3)=3(-3)^{2}-5$$ $$=3(9)-5$$ $$=27-5$$ $$=22$$


2013 April(71G) Math Question 19

Angles

- Circles


Choice C

71g

$$\angle WCZ-\angle WCY$$ $$150°-100°=50°=\angle YCZ$$ $$\angle XCY=\angle XCZ-\angle YCZ$$ $$ =80°-50°=30°$$


Choice G

$$500\div200=2.5$$ $$6\div2.5=2.4$$


Choice A

$$\frac{27}{5}=5.4$$ $$\frac{24}{6}=4$$ $$\frac{20}{4}=5$$ $$4\times500=2000$$


Choice H

$$(7+6)s+(8+6.5)f+(5.5+5)b$$ $$=13s+14.5f+10.5b$$


Choice B

$$5a=3---(1)$$ $$2a+3b=5---(2)$$ $$(2)\times5-(1)\times2$$ $$\Rightarrow (10a+15b)-(10a)=5\times5-3\times2$$ …


Choice H

$$24\times150=3600$$ $$4\times60=240$$ $$3600\div240=15$$


Choice E

$$7-(-4)x^{2}-6x+(5-3)$$ $$=11x^{2}-6x+2$$


2013 April(71G) Math Question 26

Graphing Properties

- Interpret Graphs or Figures


Choice J

$$(x^{2})^{3}(x^{4})^{5}=x^{a}$$ $$=x^{2\times3+4\times5}=x^{a}$$ $$6+20=a$$ $$a=26$$


Choice D

$$\frac{0.003}{100}=0.0003$$


2013 April(71G) Math Question 28

Probability

- One Event


Choice H

$$2500\times0.15=375$$


2013 April(71G) Math Question 29

Probability

- One Event


Choice D

$$45+5+15+5=70$$


2013 April(71G) Math Question 30

Probability

- One Event


Choice F

$$200\times0.45=90$$ $$\Rightarrow \frac{90}{200}=0.45$$ $$\Rightarrow \frac{90+15}{200+25}=\frac{105}{225}$$


2013 April(71G) Math Question 31

Angles

- Collinear Points & Triangles


Choice C

$$4y+11y=15y$$ $$y=\frac{180}{15}=12$$ $$4y=48$$ $$\angle B=180°-43°-48°=89°$$


2013 April(71G) Math Question 32

Conics

- Circles


Choice F

$$x-\sqrt{5}=0$$ $$x=\sqrt{5}$$ $$y-1=0$$ $$y=1$$


2013 April(71G) Math Question 33

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice E

$$\tan 31°=\frac{?}{103}$$ $$?=\tan 31°103$$


Choice J

y=4 is a line parallel …


Choice B

$$2x+3y=12---(line\ l)$$ $$\Rightarrow y=-\frac{2}{3}x+4$$ $$y=(-\frac{2}{3}\times2)x+(4-3)$$ …


2013 April(71G) Math Question 36

Trigonometry

- Graphing Trig Functions


Choice H

71g


Choice C

$$5r\times2r=90$$ $$10r^{2}=90$$ $$r^{2}=9$$ $$r=3$$ $$3\times5=15$$


2013 April(71G) Math Question 38

Graphing Properties

- Interpret Graphs or Figures


Choice G

As time elapses, the distance …


Choice B

$$2\times2\times(1\frac{1}{4})+(1\frac{1}{4})(1\frac{1}{4})$$ $$5+\frac{25}{16}$$ $$=6+\frac{9}{16}$$


Choice K

71g


2013 April(71G) Math Question 41

Inequalities

- Graphing Inequalities


Choice D

71g


Choice K

$$\frac{2x-y}{x+y}=\frac{3}{4}$$ $$4(2x-y)=3(x+y)$$ $$8x-4y=3x+3y$$ $$5x=7y$$ $$\frac{x}{y}=\frac{7}{5}$$


Choice C

$$8:7=5:? $$ $$\frac{8}{7}=\frac{5}{?}$$ $$8\times?=5\times7$$ $$?=\frac{35}{8}=4\frac{3}{8}$$


Choice H

The formula is BMI = …


2013 April(71G) Math Question 45

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice E

71g

$$15^{2}-5^{2}=\overline{AD}^{2}$$ $$225-25=200=\overline{AD}^{2}$$ $$\overline{AD}=\sqrt{200}=10\sqrt{2}$$


2013 April(71G) Math Question 46

Perimeter, Area, Volume

- Other Shapes


Choice G

71g

$$\triangle\times4+\Box$$ $$\Rightarrow\triangle=10\times12\times\frac{1}{2}=60$$ $$\Rightarrow\Box =10\times10=100$$ $$\triangle\times4+\Box=60\times4+100=340$$


2013 April(71G) Math Question 47

Perimeter, Area, Volume

- Other Shapes


Choice D

$$(12+24)\times16\times\frac{1}{2}$$ $$=36\times16\times\frac{1}{2}$$ $$=288$$ $$\frac{288}{90}=3...18$$

Marie …


2013 April(71G) Math Question 48

Angles

- Other Shapes


Choice F

$$3a°\lt90°$$ $$a\lt30$$


2013 April(71G) Math Question 49

Word Problems

- 1 Variable Equations


Choice C

$$Correct\rightarrow 2x$$ $$Incorrect\rightarrow x$$ $$30+10(2x)-5(x)=150$$ …


Choice F

$$f(x)=\frac{2x+b}{x+a}$$ $$=\frac{2x}{x+a}+\frac{b}{x+a}$$ $$=\frac{2}{1+\frac{a}{x}}+\frac{\frac{b}{x}}{1+\frac{a}{x}}$$ $$\lim_{\frac{a}{x}\rightarrow0}\frac{2}{1+\frac{a}{x}}=2$$ $$\lim_{\frac{b}{x}\rightarrow0}\frac{\frac{b}{x}}{1+\frac{a}{x}}=0$$


2013 April(71G) Math Question 51

Number Types & Properties

- Order of Values


Choice B

$$-0.43\lt-0.423\lt-0.42$$ $$\Rightarrow -\frac{43}{100}\lt-0.423\lt-\frac{42}{100}$$ $$n=-43$$


2013 April(71G) Math Question 52

Statistics

- Mean, Median


Choice F

71g

$$\frac{51+53}{2}=52$$


2013 April(71G) Math Question 53

Angles

- Circles


Choice D

$$\frac{25}{3}\pi=\frac{25\times180°}{3}=1500°$$ $$1500°=360°\times4+60°$$


2013 April(71G) Math Question 54

Number Types & Properties

- Complex Number


Choice J

$$(6-7i)(\pi+6i)$$ $$=6\pi+36i-7i\pi+42$$ $$=(J)$$


2013 April(71G) Math Question 55

Quadratic Equations

- Factoring


Choice A

$$x=4,$$ $$4^{2}-4a-12=0$$ $$\Rightarrow 16-4a-12=0$$ $$\Rightarrow …


2013 April(71G) Math Question 56

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice J

$$=\frac{\frac{1}{(\cos x)^{2}}\cdot\sin x}{\frac{\sin x}{\cos x}}$$ …


2013 April(71G) Math Question 57

Perimeter, Area, Volume

- Other Shapes


Choice E

71g


2013 April(71G) Math Question 58

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice F

71g

$$30°:60°:90°$$ $$=1:\sqrt{3}:2$$


2013 April(71G) Math Question 59

Sequences and Patterns

- Arithmetic Sequences


Choice E

$$n\gt 0,$$ $$x,x+n,x+2n=120$$ $$\Rightarrow 3x+3n=120$$ …


Choice F

71g

$$f(x)=\sqrt[3]{x+2}$$ $$=(x+2)^{-3}$$ $$f^{-1}(x)=x^{3}-2$$