ACT Form 70G Math Answer Explanation



Choice B

$$\frac{3x}{2}+16=10$$ $$\frac{3x}{2}=-6$$ $$3x=-12$$ $$x=-4$$


2012 April(70G) Math Question 2

Probability

- One Event


Choice J

$$P=\frac{36+22}{100}=\frac{58}{100}=\frac{29}{50}$$


Choice C

$$3.6x+2.4x=1.03-7.99$$ $$\Rightarrow 6x=-6.96$$ $$x=-1.16$$


2012 April(70G) Math Question 4

Angles

- Collinear Points & Triangles


Choice B

$$\angle BCA=180°-81°=99°$$ $$\angle BAC=180°-150°=30°$$ $$\angle B=180°-99°-30°=51°$$


2012 April(70G) Math Question 5

Quadratic Equations

- Factoring


Choice E

$$x^{2}-6x-16=0$$ $$(x-8)(x+2)=0$$ $$x=8,-2$$


2012 April(70G) Math Question 6

Absolute Values

- Absolute Value Expressions


Choice G

$$\Rightarrow\mid2\mid-\mid-4\mid$$ $$=2-4$$ $$=-2$$


2012 April(70G) Math Question 7

Word Problems

- Cost


Choice C

$$$70\times0.8=$56$$ $$$56\times(1+0.06)=56+3.36=59.36$$


Choice K

$$(-3)^{2}(2)^{3}-(-3)(2)^{2}+(-3)$$ $$=9\times8+3\times4-3$$ $$=72+12-3$$ $$=81$$


2012 April(70G) Math Question 9

Word Problems

- Distance, Speed, Time


Choice C

$$2\times60=120$$ $$120\div5=24$$ $$24\times11=264$$ $$\because 1\ ft= 12\ inches$$ $$264\div12=22$$


Choice H

$$\frac{1}{2}\times24=12$$ $$\frac{2}{3}\times24=16$$ $$\frac{5}{6}\times24\times2=20\times2=40$$ $$12+16+40=68$$


2012 April(70G) Math Question 11

Graphing Properties

- Interpret Graphs or Figures


Choice A

Any point that is 3 units from (6, 4) could be an adjacent vertex to the vertex at (6, 4).

The most obvious points that are 3 units from (6, 4) will share either the x or the y coordinate with (6, 4) and have the other coordinate 3 units greater than or less than that of (6, 4).

A is the correct answer


Choice K

$$\frac{1}{8}+\frac{3}{4}=\frac{7}{8}$$ $$\frac{7}{8}\times2=\frac{7}{4}=1\frac{3}{4}$$


2012 April(70G) Math Question 13

Equation of a Line

- Distance & Midpoint


Choice C

$$\frac{1+7}{2}=4$$ $$\frac{9+-3}{2}=3$$


2012 April(70G) Math Question 14

Angles

- Parallel Lines


Choice H

(G) would not prove the two lines are parallel.

$$\angle 1\neq\angle 7$$


Choice C

$$\frac{(x+4)(2x+2)}{2}$$ $$=\frac{2x^{2}+2x+8x+8}{2}$$ $$x^{2}+5x+4$$


Choice K

$$f(-3)=(-3)^{2}-(-3)+1=9+3+1=13$$


Choice D

$$25\times16=x^{2}$$ $$400=x^{2}$$ $$x=20$$


2012 April(70G) Math Question 18

Graphing Properties

- Interpret Graphs or Figures


2012 April(70G) Math Question 19

Statistics

- Mean, Median


Choice D

$$(6+15+20+30)\div4$$ $$=71\div4$$ $$=17\frac{3}{4}$$


2012 April(70G) Math Question 20

Word Problems

- Cost


Choice F

$$33\times30000=990000$$ $$990000\times0.06=59400$$ $$30\times30000=900000$$ $$900000\times0.07=63000$$ $$63000-59400=3600$$


Choice A

$$=\frac{1}{5}\times\frac{a^{5}}{a^{2}}\times\frac{b^{3}}{b^{7}}\times\frac{c^{4}}{c}$$ $$=\frac{1}{5}\times a^{3}\times \frac{1}{b^{4}}\times c^{3}$$ $$=\frac{a^{3}c^{3}}{5b^{4}}$$


Choice K

$$24\ hrs=24\times60=1440\ mins$$ $$70\times1440=100800=1.008\times10^{5}$$


Choice D

$$5x+6x+9x=20x=100$$ $$x=5$$ $$9x=9\times5=45$$


2012 April(70G) Math Question 24

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice H

70g

$$25^{2}=20^{2}+x^{2}$$ $$x=15$$ $$\tan A=\frac{20}{15}$$


2012 April(70G) Math Question 25

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice E

Using the Pythagorean Theorem until …


$$2x+3y-1=0$$ $$\because y=mx+b$$ $$\Rightarrow 3y=-2x+1$$ …


Choice C

$$=(2x^{2})+(x+2x+3x-2x-2x-2x)+(3+1-1)$$ $$=2x^{2}+3$$


Choice K

$$1 feet = 12 inches$$ …


2012 April(70G) Math Question 29

Word Problems

- Fixed Cost + Variable Cost


Choice C

$$C=3.5A+120$$ $$C=3.5(270)+120$$ $$=1065$$


Choice J

70g

$$270=18\times x$$ $$x=15$$ $$18+18+15=51$$


2012 April(70G) Math Question 31

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice C

$$\sin\theta=\frac{10000}{8\times5280}$$ $$\theta=\arcsin\frac{10000}{8\times5280}$$


2012 April(70G) Math Question 32

Number Types & Properties

- Order of Values


Choice F

$$\sqrt{3}\approx1.732$$ $$1\frac{5}{6}=1.83$$ $$\frac{5}{3}=1.67$$

Therefore, F …


2012 April(70G) Math Question 33

Sequences and Patterns

- Geometric Sequences


Choice E

$$\frac{-2}{1}=-2$$ $$\frac{4}{-2}=-2$$ $$\Rightarrow 1,-2,4,-8,16,-32,64$$


2012 April(70G) Math Question 34

Angles

- Collinear Points & Triangles


Choice F

70g

(F) could be true because …


Choice C

$$\frac{\triangle ABC}{\triangle DEF}$$ $$=\frac{2}{3}$$ $$=\frac{20}{x}$$ …


2012 April(70G) Math Question 36

Word Problems

- Fixed Cost + Variable Cost


Choice G

(G) 40% of net sales …


2012 April(70G) Math Question 37

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice B

$$\tan35°=\frac{?}{450}$$ $$\Rightarrow ?=450\tan35°$$


2012 April(70G) Math Question 38

Inequalities

- Inequality Expressions


Choice G

$$\frac{5+3x}{2}-3\gt0$$ $$\Rightarrow \frac{5+3x}{2}\gt 3$$ $$\Rightarrow …


2012 April(70G) Math Question 39

Word Problems

- 1 Variable Equations


Choice E

$$\frac{1.5}{1.5+1}=\frac{1.5}{2.5}$$ $$\frac{1.5}{2.5}=\frac{x}{2500}$$ $$\Rightarrow x = …


Choice J

$$x^{2}-4=x^{2}-2^{2}=(x+2)\times(x-2)$$ $$4x-8=4\times(x-2)$$ $$\Rightarrow\frac{1}{(x+2)(x-2)}+\frac{1}{4\times(x-2)}$$ $$\Rightarrow (x+2)\times(x-2)\times4$$


Choice C

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


Choice F

$$Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ $$=\frac{-2-(-5)}{10-(-2)}=\frac{1}{4}$$

Plug this slope …


2012 April(70G) Math Question 43

Probability

- One Event


Choice E

The 53 people who used …


Choice H

$$3\times7=21$$ $$21\times4=84$$


Choice A

$$\frac{1}{4}\times-4=-1$$


2012 April(70G) Math Question 46

Equation of a Line

- Distance & Midpoint


Choice J

The helicopter is 2 + …


Choice D

2 is the only even …


2012 April(70G) Math Question 48

Inequalities

- Intersection of Lines


Choice G

70g

(G) The shaded region involves …


Choice A

$$x+y=-a---(1)$$ $$x-y=b---(2)$$ $$(1)-(2)$$ $$\Rightarrow (x+y)-(x-y)=-a-b$$ …


2012 April(70G) Math Question 50

Angles

- Circles


Choice G

$$2\pi r\times\frac{45}{360}$$ $$=2\pi r\times\times\frac{1}{8}$$ $$=\frac{1}{4}\pi …


Choice A

$$3a=b---(1)$$ $$8a-2=b---(2)$$ $$(2)-(1)$$ $$5a-2=0$$ $$a=\frac{2}{5}$$


2012 April(70G) Math Question 52

Quadratic Equations

- Factoring


Choice J

$$x^{2}+2ax+a^{2}$$ $$\Rightarrow 2a=-6$$ $$\Rightarrow a=-3$$ …


Choice D

A complete revolution is equivalent …


Choice K

The denominator of any fraction …


2012 April(70G) Math Question 55

Perimeter, Area, Volume

- Mixed Shapes


Choice A

The area of a rectangle …


2012 April(70G) Math Question 56

Perimeter, Area, Volume

- Other Shapes


Choice K

These triangles are equilateral.

Each …


2012 April(70G) Math Question 57

Conics

- Circles


Choice D

$$I.$$ $$ -3-(-7)=4,\ -3-(0)=3$$ $$\sqrt{4^{2}+3^{2}}=5$$ …


Choice J

There are 25 even numbers …


2012 April(70G) Math Question 59

Absolute Values

- Graphing Absolute Values


Choice A

f(x)– 4 represents a shift …


2012 April(70G) Math Question 60

Sequences and Patterns

- Logical Expressions


Choice K

Those statements are equivalent:

If …