ACT Form 68C Math Answer Explanation


2010 June(68C) Math Question 1

Probability Practice

- One Event

1. The face of a fair spinner is divided into 24 sectors, each of which is I of 5 colors:Blue, Purple, Green Orange, or Red. The table below gives each color and the probability that the spinner, when spun, will stop on that color On which color shown in the table is the spinner LEAST likely to stop?

Choice C

$$Blue=\frac{1}{4}=\frac{6}{24}$$ $$Purple=\frac{1}{8}=\frac{3}{24}$$ $$Green=\frac{1}{12}=\frac{2}{24}$$ $$Orange=\frac{3}{8}=\frac{9}{24}$$ $$Red=\frac{1}{6}=\frac{4}{24}$$

The chance of stopping in green is the lowest.

2010 June(68C) Math Question 2

Word Problems Practice

- Cost

2. Saul goes shopping and decides to buy 4 shirts at a price of $20.08 cach. Which of the following expressions gives the total price, in dollars, of the
4 shirts?

Choice K

$$4\times$20.08=4($20)+4($0.08)$$

2010 June(68C) Math Question 3

Quadratic Equations Practice

- Factoring

3. Which of the following expressions is equivalent to x2-9?

Choice C

$$(x-3)(x+3)=x^{2}+3x-3x+3^{2}=x^{2}+9$$

Choice H

$$\angle BAE=180°-90°-38°=52°$$

Choice D

$$70\ beats \times 60\ minutes\times24\ …

Choice K

$$\frac{(-7)^{2}-1}{(-7)+1}$$ $$=\frac{49-1}{-6}$$ $$=\frac{48}{-6}$$ $$=-8$$

Choice C

$$(-6,11)+(+11,-6)=(5,5)$$

Choice G

$$7+4x=31$$ $$4x=24$$ $$x=6$$ $$3x=18$$

Choice E

$$Weeks=0,\ height=4$$ $$Slope=1\frac{1}{2}$$ $$h=4+1\frac{1}{2}w$$

Choice H

$$h(a,b)=a^{b}-b^{a}$$ $$h(3,2)=3^{2}-2^{3}=9-8=1$$

2010 June(68C) Math Question 11

Angles Practice

- Collinear Points & Triangles

11. In the figure below, ∠ BAC measures35°, ∠ABC measures 115, and points B, C, and D are collinear What is the measure of ∠ACD?

Choice E

$$\angle ACD=180°-\angle ACB$$ $$\angle ACD=35°+115°=150°$$

2010 June(68C) Math Question 12

Inequalities Practice

- Inequality Expressions

12. Koji had $50.00 to spend on school supplies. He bought a schoolbag for $18.50, a box of pencils for
$2.50, and a package of pens for $4.00. Koji still must buy b binders at $3.50 each and n spiral notebooks at s0.75 each. Which of the following inequalities represents how many binders and spiral notebooks he can buy with the remaining money?
(Note: No tax is charged on school supplies.)

Choice K

$$$50-$18.5-$2.5-$4=$25$$ $$3.5b+0.75n\leq25$$

2010 June(68C) Math Question 13

Angles Practice

- Collinear Points & Triangles

13. In the figure below, ZAEB is congruent to ZDEC and BE is congruent to CE. One of the following angle congruences completes what is needed to prove as directly as possible that AABE is congruent to ADCE by applying the Angle-Side-Angle(ASA) property.
Which one?

Choice B

68c

Angel-Side-Angel(ASA)

2010 June(68C) Math Question 14

Probability Practice

- One Event

14. Of the 40 marbles in Dakarai's bag, all are solid in color and 16 are blue. The probability that he will randomly choose a yellow marble from the bag How many yellow marbles are in Dakarai's bag?

Choice H

$$40\times\frac{1}{8}=5$$

Choice B

$$36\times4=144$$ $$144=x^{2}$$ $$x=12$$

2010 June(68C) Math Question 16

Statistics Practice

- Mean, Median

16. Arita played in 7 softball games. In the first 4 games she had 2, 3, 1, and 3 hits, respectively. In the last
3 games, she had a total of 6 hits. What was her average number of hits per game in the 7 games?

Choice G

$$\frac{2+3+1+3+6}{7}=\frac{15}{7}$$

2010 June(68C) Math Question 17

Word Problems Practice

- 2 Variable Addition

17. A test has 50 questions and is worth 130 points. It consists of x 5-point questions and y 2-point questions Which of the following systems of equations, when solved, gives the number of each type of question that is on the test?

Choice C

$$x+y=50---50\ questions$$ $$x\cdot5+y\times2=130---130\ points$$ $$\Rightarrow 5x+2y=130$$

Choice F

$$4.5=\frac{1}{t}$$ $$t=\frac{1}{4.5}=\frac{2}{9}$$

Choice A

$$=(4a-6a)+(7b-6b)+(6c+3c)$$ $$=-2a+b+9c$$

Choice J

$$50=2\times5\times5$$ $$30=2\times3\times5$$ $$70=2\times5\times7$$ $$[50,30,70]=2\times3\times5\times5\times7=1050$$

Choice C

$$B=7LH$$ $$420=7\times30\times H$$ $$H=2$$

Choice G

$$y=mx+b$$ $$5x+7y=7$$ $$\Rightarrow 7y=-5x+7$$ $$\Rightarrow …

Choice E

$$\triangle A=\frac{1}{2}bh$$ $$h=\overline{AB}$$ $$20=\frac{1}{2}\times5\times \overline{AB}$$ …

Choice J

68c

$$3-4-5\ triangle$$ $$\Rightarrow 300:400:500$$ $$x=500$$

Choice D

$$=\mid (-54)+20\mid$$ $$=\mid -34 \mid$$ …

Choice G

$$6x-y=x+5y$$ $$\Rightarrow 5x=6y$$ $$\Rightarrow y=\frac{5x}{6}$$

Choice E

$$2:7=10:x$$ $$x=\frac{7\times10}{2}=35$$

Choice G

$$=x^{5+-(3^{2})}$$ $$=x^{5+(-9)}$$ $$=x^{-4}$$

2010 June(68C) Math Question 29

Word Problems Practice

- Cost

Use the following information to answer questions 29-31
Kyla purchased 25 pieces of candy from Laszko's Candy Shop. Her purchase consists of 7 lollipops, 4 candy bars,
10 licorice sticks, and 4 gumballs. The unit price of each candy item is shown in the table below. Kyla's purchase without sales tax, totaled $10.30. Laszko's charges an
8% sales tax on each purchase, which is calculated by multiplying the purchase total by 0.08 and rounding to the nearest $0. 01

29. Kyla gave the shop clerk $15.00. How much change should Kyla have received?

Choice A

$$10.3(1.08)=11.124$$ $$15-11.124=-3.876\approx-3.88$$

2010 June(68C) Math Question 30

Statistics Practice

- Mean, Median

30. Without sales tax, what was the average price Kyla paid per piece of candy, to the nearest $0.01?

Choice J

$$10.3\div25$$ $$=0.412\approx0.41$$

2010 June(68C) Math Question 31

Probability Practice

- Combinations

31. Kyla offers to sell 2 of the 25 pieces of candy to her brother Virgil. She lets Virgil have a choice of 2 pieces of the same candy item or l piece each of 2 different candy items. Kyla will have Virgil pay the same total cost for the 2 pieces that he would pay for the 2 pieces at Laszko's. How many different total costs(in dollars)
are possible for Virgil's choice of 2 pieces?

Choice B

Lollipop: L

Candy bar: C …

Choice G

$$2r=36$$ $$\Rightarrow 2\pi r=36\pi$$

2010 June(68C) Math Question 33

Quadratic Equations Practice

- FOIL

33. For all real x, ?

Choice D

$$\frac{[3(x-2)]^{2}}{3}$$ $$=\frac{3^{2}(x-2)^{2}}{3}$$ $$=3(x-2)^{2}$$ $$=3(x^{2}-4x+4)$$ $$=3x^{2}-12x+12$$

2010 June(68C) Math Question 34

Inequalities Practice

- Inequality Expressions

34. Which of the following is a solution statement for the inequality 6x-6 < 7+10x?

Choice F

$$6x-6 \lt 7+10x$$ $$\Rightarrow -6-7 …

Choice C

The two sets of opposite …

Choice J

$$Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ $$\Rightarrow m=\frac{4-2}{9-5}=\frac{2}{4}=\frac{1}{2}$$

2010 June(68C) Math Question 37

Angles Practice

- Circles

37. The hour and minute hands of the clock shown below move at constant speeds. What is the measure of the angle formed by the hour and minute hands at exactly 1:30?

Choice E

68c

At 1:30, the hour hand …

Choice F

$$\sin 55°\approx 0.82=\frac{20}{Support\ rope}$$ $$\Rightarrow …

Choice C

$$\pi r^{2}\times20$$ $$=3.14\times 6^{2}\times20$$ $$=2260.8$$ …

Choice G

$$20:35=12:x$$ $$x=21$$

Choice C

$$x(2x)=162$$ $$2x^{2}=162$$ $$x^{2}=81$$ $$x=9$$ $$2(x+2x)=6x=54$$

2010 June(68C) Math Question 42

Word Problems Practice

- Cost

Choice K

$$$10\times0.6\times0.9=5.4$$

Choice C

$$(C)\ y=\frac{4x+3}{x-2}$$

Since I can't …

2010 June(68C) Math Question 44

Matrices Practice

- Addition & Subtraction

Choice J

$$3+x=y$$ $$\frac{x}{2}+5=y$$ $$\Rightarrow \frac{x}{2}+5=3+x$$ $$\Rightarrow …

2010 June(68C) Math Question 45

Statistics Practice

- General Statistics

Choice D

$$100+15=115$$

2010 June(68C) Math Question 46

Angles Practice

- Circles

Choice K

$$405°=360°+45°$$ $$360°+30°=390°$$

Choice D

$$(a,b)+(3,-11)=(5,-7)$$ $$\frac{a+3}{2}=5 \Rightarrow a=7$$ $$\frac{b+(-11)}{2}=-7 …

Choice F

68c

$$\sin25°=0.423,\ \cos25°=sin(90-25)°=\sin65°=0.906$$ $$\frac{200}{\sin 90°}=\frac{x}{\sin25°}=\frac{y}{\sin65°}$$ $$\Rightarrow …

Choice B

68c

A graph is said to …

Choice K

68c

$$\Rightarrow 8\times8=64$$ $$64-\pi (4)^{2}=64-3.14(16)=13.76\approx14$$

Choice B

$$(width+length)2=perimeter$$ $$width=w$$ $$length=w+x$$ $$\Rightarrow (w+w+x)2=P$$ …

Choice F

68c

$$13^{2}=5^{2}+x^{2}$$ $$\Rightarrow x=12$$ $$\cos \theta=\frac{-12}{13}$$

2010 June(68C) Math Question 53

Quadratic Equations Practice

- FOIL

Choice A

$$(a+b)^{2}=a^{2}+b^{2}$$ $$\Rightarrow a^{2}+2ab+b^{2}=a^{2}+b^{2}$$ $$\Rightarrow 2ab=0$$ …

Choice J

$$ $1\times3+$3\times0=$3 $$ $$ $1\times4+$3\times1=$7 …

2010 June(68C) Math Question 55

Angles Practice

- Collinear Points & Triangles

Choice A

$$\angle 1=\angle 2$$ $$\angle 1+\angle …

Choice H

68c

Choice C

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

Choice F

$$\mid x-1 \mid \lt B$$ …

Choice A

68c

$$Area\ of\ a\ circle:\pi r^{2}$$ …

2010 June(68C) Math Question 60

Quadratic Equations Practice

- Factoring

Choice J

68c