ACT Form 74C Math Answer Explanation


Choice C

$$Length = \frac{100}{5}=20 \ feet$$

2017 June(74C) Math Question 2

Probability Practice

- One Event

2. A wallet containing 2 five-dollar bills, 9 ten-dollar bills, and 5 twenty-dollar bills is found and returned to its owner. The wallet's owner will reward the finder with 1 bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty-dollar bill?

Choice J

$$p = \frac{5}{2+9+5}=\frac{5}{16}$$

2017 June(74C) Math Question 3

Probability Practice

- Combinations

3. In his costume supplies, Elmo the clown has 4 noses, 3 pairs of lips, and 2 wigs. A clown costume consists of 1 nose, 1 pair of lips, and 1 wig. How many different clown costumes can Elmo make?

Choice E

$$Number \ of \ arrangement = 4\times3\times2=24$$

Choice F

30 pens still remain, enough for 6 packages;

20 notebooks still remain, enough for 10 packages;

24 envelopes still remain, enough for 8 packages;

84 cookies still remain, enough for 7 packages;

45 candy bars still remain, enough for 9 packages;

Apparently, pens are the bottleneck.

Choice C

$$V=\frac{1}{3}\cdot \frac{22}{7}\cdot 6^2\times 28=1056$$

Choice B

$$(0.1x^2+3x+80) +(0.5x^2-2x+60)=(0.1x^2+0.5x^2)+(3x-2x)+(80+60)=0.6x^2+x+140$$

Choice H

Only d = 3t + 15 fulfils all the data in the table.

2017 June(74C) Math Question 9

Word Problems Practice

- Cost

9. Dmitry bought a pair of pants at the discounted price of $30. The original price of the pants was $40. What was the percent of the discount?

Choice C

$$$40\times(1-d)=$30 \\ $$ $$\Rightarrow d=25\%$$

Choice G

$$|-6|-|7-41|=6-34=-28$$

2017 June(74C) Math Question 11

Word Problems Practice

- 2 Variable Addition

11. Samantha, Nyla, and Jerry own shares of stock in the Triumph Hotels company. The shares of stock that they own have a combined value of $6,880. Samantha owns 70 shares, Nyla owns 50 shares, and Jerry owns 40 shares. What is the value of the shares Samantha owns?

Choice C

$$Value=$6,880\times \frac{70}{70+50+40}=$3,010$$

2017 June(74C) Math Question 12

Inequalities Practice

- Number Line

12. A new club wants to attract customers who are at least 18 but less than 30 years of age. One of the number lines below illustrates the range of ages, in years, of the customers the club wants to attract. Which number line is it?

Choice G

Only the number line in G fulfils: $$18\leq age <30$$

Choice D

$$\frac{AC}{AB}=\frac{AE}{AD} \\$$ $$ \Rightarrow \frac{AC}{6+5+4}=\frac{12}{6} \\$$ $$ \Rightarrow AC=30$$

Choice G

$$\frac{\sqrt{50}}{2}\approx 3.54 \approx 4$$

Choice D

$$9k+2k=44 \\$$ $$ \Rightarrow k=4 \\$$ $$ 9k=36$$

Choice H

$$1-\frac{1}{9}-\frac{1}{6}=\frac{13}{18}$$

Choice A

$$35\times(10+x)=42\times10 \\$$ $$ \Rightarrow 10+x=12 \\ $$ $$\Rightarrow x=2$$

Choice J

$$Area \ of \ 2 \ shaded \ regions = 8\times 10 - \frac{8\times10}{2}=40$$

2017 June(74C) Math Question 19

Inequalities Practice

- Inequality Expressions

19. Which of the following ordered pairs in the standard (x,y) coordinate plane satisfies the system of inequalities below?

Choice C

Only C fulfils all three inequations.

Choice H

The range of y = sin (x-π) is : $$-1\leq y \leq 1$$ The range of y = -5sin (x-π) is : $$-5\leq y \leq 5$$ The range of y = 3-5sin (x-π) is : $$-2\leq y \leq 8$$

Choice D

$$g(-3)=(-3)^2-4=5 \\$$ $$ \Rightarrow f(g(-3))=f(5)=2\times5+1=11$$

Choice G

$$3f+4c=$25 \\$$ $$f+2c=$11 \\$$ $$\Rightarrow …

2017 June(74C) Math Question 23

Statistics Practice

- Mean, Median

23. The scores given below were earned by 10 students on a recent biology test. What is the median score?

Choice C

$$71,\ 77,\ 78,\ 80,\ \underline{86, …

Choice H

Let the length of the …

Choice E

$$AB\times AD=1 \\$$ $$ \Rightarrow …

2017 June(74C) Math Question 26

Probability Practice

- One Event

26. A bag contains 16 red’marbles, 7 yellow marbles, and 19 green marbles. How many additional red marbles must be added to the 42 marbles already in the bag so that the probability of randomly drawing a red marble

Choice G

$$\frac{16+x}{16+x+7+19}=\frac{3}{5} \\$$ $$ \Rightarrow x= …

Choice E

$$a^{-2}=(a^{2})^{-1}=\frac{1}{a^2}$$

Choice F

If Jamie's claim is true, …

Choice D

74c

$$Area = 3 \times 5 …

Choice H

74c

$$BD=\sqrt{3^2+4^2}=5$$

Choice A

The slope of a horizontal …

Choice J

When A is reflected over …

Choice A

$$8^2\cdot 4^{0.5}=(2^3)^2\cdot (2^2)^{0.5}=2^6\cdot 2=2^7$$

Choice K

$$Number \ of \ applicants …

2017 June(74C) Math Question 35

Logarithms Practice

- Logarithm Expressions

35. What is the value of log2 1,/g ?

Choice B

$$\log_{2}{\sqrt{8}}=\log_{2}{\sqrt{2^3}}=\log_{2}{2^{\frac{3}{2}}}=\frac{3}{2}$$

2017 June(74C) Math Question 36

Angles Practice

- Circles

36. Jie asked 90 students to choose 1 favorite fruit from

Choice F

$$\frac{\frac{90-15}{3}}{90}\times 360°=100°$$

Choice E

$$\frac{4}{5}+\frac{7}{x}= \frac{4x}{5x}+\frac{7\times5}{5x}=\frac{4x+35}{5x}$$

Choice K

$$\frac{353}{85+353+47}=\frac{353}{485}$$

2017 June(74C) Math Question 39

Probability Practice

- More than One Event

39. Suppose a person will be chosen at random from these 560 residents. Which of the following values is closest to the probability that the person chosen will NOT be a high school student and will NOT have replied with no opinion?

Choice D

$$\frac{14+10+85+353}{560}\approx 0.83$$

Choice H

Of the 15 incorrectly classified …

Choice A

To simplify matters, let’s make …

Choice G

sin(-x°) = -sin x°

Choice D

Volume of box = 8 …

Choice G

Since ΔBCD is a right …

Choice D

200 days ago is equivalent …

2017 June(74C) Math Question 46

Angles Practice

- Vertex Angles & Bisectors

46. In the figure below, line m is perpendicular to line n, and both lines intersect line q at the same point. The measure of L1 is (3x — 10)°, and the measure of L2 is (2x + 10)°. What is the measure of L3 ?

Choice G

∠1 = ∠2

→3x - …

Choice E

The best way to solve …

Choice H

The Scalene Triangle has no …

2017 June(74C) Math Question 49

Probability Practice

- More than One Event

49. A professional baseball team will play 1 game Saturday • and 1 game Sunday. A sportswriter estimates the team has a 60% chance of winning on Saturday but only a 35% chance of winning on Sunday. Using the sportswriter’s estimates, what is the probability that the team will lose both games?

Choice D

A sportswriter estimates the team …

Choice J

The denominator of f(x) = …

2017 June(74C) Math Question 51

Probability Practice

- Combinations

51. Get-A-Great-Read Books is adding a new phone line. The phone company says that the first 3 digits of the phone number must be 555, but the remaining 4 digits, where each digit is a digit from 0 through 9, can be chosen by Get-A-Great-Read Books. How many phone numbers are possible?

Choice E

555_ _ _ _

Each …

2017 June(74C) Math Question 52

Conics Practice

- Circles

52. In the standard (x,y) coordinate plane, the circle centered at (1,3) that passes through (4,7) is the set of all points that are:

Choice F

74c

The circle represents all dots …

2017 June(74C) Math Question 53

Logarithms Practice

- Logarithm Expressions

53. Which of the following values is the x-coordinate of the point in the standard (x,y) coordinate plane where the graph of the line y = 7 intersects the graph of the function y = ln(x — 2) + 3 ?

Choice B

The question asks what x …

Choice F

The slope represents the copying …

Choice E

Let r be revenue, n …

2017 June(74C) Math Question 56

Inequalities Practice

- Graphing Inequalities

56. Each of the following graphs in the standard (x,5) DO YOUR FIGURING HERE.

Choice K

The quickest way would be …

Choice A

To make one banner, ¼ …

Choice F

What you need to know: …

Choice D

According to the graph, the …

2017 June(74C) Math Question 60

Matrices Practice

- Multiplication

60. The table below shows the numbers of rows and columns in each of 5 matrices.

Choice K

Requirements for Matrix Multiplication:

In …