ACT Form 74C Math Answer Explanation

2017 June(74C) Math Question 1

1. The top surface of a rectangular table has an area of 100 square feet and a width of 5 feet. What is the length, in feet, of the surface?

Choice C

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

2017 June(74C) Math Question 2

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

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

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

2017 June(74C) Math Question 4

4. Esteban and his family are making care packages to send to children at summer camp. Each complete care package contains 5 pens, 2 notebooks, 3 envelopes, 12 cookies, and 5 candy bars. Esteban and his family have already made 7 complete care packages and the following materials remain:

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.

2017 June(74C) Math Question 5

5. A formula for the volume of a right circular cone is

Choice C

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

2017 June(74C) Math Question 6

6. In AACD below, B is on AC, E is on AD, the measure of LCAD is 28°, and AD is perpendicular to both BE and CD. What is the measure of ZCBE ?

2017 June(74C) Math Question 7

7. What is the sum of 0.1×2 + 3x + 80 and 0.5×2 — 2x + 60 for all x ?

Choice B

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

2017 June(74C) Math Question 8

8. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.

Choice H

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

2017 June(74C) Math Question 9

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

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

2017 June(74C) Math Question 10

10. What is the value of |-6| — |7 — 41|?

Choice G


2017 June(74C) Math Question 11

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

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: $$18\leq age <30$$

2017 June(74C) Math Question 13

13. In the figure shown below, E and G lie on AC, D and F lie on AB, DE and FG are parallel to BC, and the given lengths are in feet. What is the length of AC, in feet?

Choice D

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

2017 June(74C) Math Question 14

14. Which of the following integers is closest to

Choice G

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

2017 June(74C) Math Question 15

15. The ratio of Jane’s age to her daughter’s age is 9:2. The sum of their ages is 44. How old is Jane?

Choice D

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

2017 June(74C) Math Question 16

16. For the next school year, a college will use of the

Choice H


2017 June(74C) Math Question 17

17. What value of x makes the proportion below true?

Choice A

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

2017 June(74C) Math Question 18

18. The rectangle shown• in the figure below is partitioned into 3 triangles, 2 of which are shaded. What is the total area, in square inches, of the 2 shaded regions?

Choice J

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

2017 June(74C) Math Question 19

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.

2017 June(74C) Math Question 20

20. The graph • of y = 3 — 5 sin(x — n) is shown in the standard (x ,y) coordinate plane below. What is the range of y ?

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 : $$-2\leq y \leq 8$$

2017 June(74C) Math Question 21

21. Given functions f (x) = 2x + 1 and g(x) = x2 — 4, what is

Choice D

$$g(-3)=(-3)^2-4=5 …

2017 June(74C) Math Question 22

22. A fabric store sells flannel and calico fabrics. Joan pays $25 for 3 yards of flannel and 4 yards of calico. Chris pays $11 for 1 yard of flannel and 2 yards of calico. What is the price of 1 yard of calico?

Choice G

$$3f+4c=$25 \\$$ $$f+2c …

2017 June(74C) Math Question 23

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 …

2017 June(74C) Math Question 24

24. A parallelogram has a perimeter of 84 inches, and 1 of its sides measures 16 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

Choice H

Let the length of the …

2017 June(74C) Math Question 25

25. In the figure below, all of the small squares are equal DO YOUR FIGURING HERE.

Choice E

$$AB\times AD=1 \\$$ $$ \Rightarrow …

2017 June(74C) Math Question 26

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 …

2017 June(74C) Math Question 27

27. For all a > 0, which of the following expressions is equal to a-2 ?

Choice E

$$a^{-2}=(a^{2})^{-1 …

2017 June(74C) Math Question 28

28. Jamie claims, "If a triangle is in Set A, then it is not isosceles." Later, Jamie discovers that AMNP is a counterexample proving this claim false. Which of the following statements must be true about AMNP ?

Choice F

If Jamie's claim is …

2017 June(74C) Math Question 29

29. What is the area, in square coordinate units, of ABCD ?

Choice D

29. What is the area, in square coordinate units, of ABCD ?

$$Area = 3 \times 5 =15$$

2017 June(74C) Math Question 30

30. What is the distance, in coordinate units, from B to D ?

Choice H

30. What is the distance, in coordinate units, from B to D ?

$$BD=\sqrt{3^2+4 …

2017 June(74C) Math Question 31

1. What is the slope of BC ?

Choice A

The slope of a horizontal …

2017 June(74C) Math Question 32

32. Parallelogram ABCD will be reflected over the y-axis. What will be the coordinates of the image of A ?

Choice J

When A is reflected over …

2017 June(74C) Math Question 33

33. Which of the following is equivalent to 82 – 40.5 ?

Choice A

$$8^2\cdot 4^{0 …

2017 June(74C) Math Question 34

34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted?

Choice K

$$Number \ of \ applicants \ not \ accepted …

2017 June(74C) Math Question 35

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

Choice B

$$\log_{2}{\sqrt{8}}=\log_ …

2017 June(74C) Math Question 36

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

Choice F

$$\frac{\frac{90-15}{3}}{90 …

2017 June(74C) Math Question 37

37. For all real numbers x such that x # 0, 4 7.; + 7 — = ?

Choice E

$$\frac{4}{5}+\frac{7 …

2017 June(74C) Math Question 38

38. What fraction of these nonstudent residents replied that they disapproved of the change in hours?

Choice K

$$\frac{353}{85+353+47 …

2017 June(74C) Math Question 39

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 …

2017 June(74C) Math Question 40

40. After constructing the table, it was discovered that the student status of 15 residents who replied that they approved had been incorrectly classified as nonstudents. After correcting the errors, exactly 60% of the college students had replied that they approved. To the nearest 1%, what percent of high school students replied that they approved?

Choice H

Of the 15 incorrectly classified …

2017 June(74C) Math Question 41

41. Set A and Set B each consist of 5 distinct numbers. The 2 sets contain identical numbers with the exception of the number with the least value in each set. The number with the least value in Set B is greater than the number with the least value in Set A. The value of which of the following measures must be greater for Set B than- for Set A?

Choice A

To simplify matters, let’s …

2017 June(74C) Math Question 42

42. For all x such that 0 x < 90, which of the following . expressions is NOT equal to sin x° ?

Choice G

sin(-x°) = -sin x°

2017 June(74C) Math Question 43

43. A 3-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of

Choice D

Volume of box = 8 × 8 …

2017 June(74C) Math Question 44

44. Quadrilateral ABCD is shown in the figure below with the lengths of the 4 sides given in meters. The measure of ZC is 90°. What is tan A ?

Choice G

Since ΔBCD is a right …

2017 June(74C) Math Question 45

45. Given today is Tuesday, what day of the week was it 200 days ago?

Choice D

200 days ago is equivalent …

2017 June(74C) Math Question 46

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 - 10 = 2x …

2017 June(74C) Math Question 47

47. The greatest common factor of 2 whole numbers is 10. The least common multiple of these same 2 numbers is 120. What are the 2 numbers?

Choice E

The best way to solve …

2017 June(74C) Math Question 48

48. The side lengths of a certain triangle are 4, 5, and 7 centimeters. Which of the following descriptions best classifies this triangle?

Choice H

The Scalene Triangle has no …

2017 June(74C) Math Question 49

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 …

2017 June(74C) Math Question 50

50. The graph of f(x) 2 X- 3 is shown below. What is

Choice J

The denominator of f(x …

2017 June(74C) Math Question 51

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

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

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:

The circle represents all dots …

2017 June(74C) Math Question 53

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 …

2017 June(74C) Math Question 54

54. Three copy machines—A, B, and C—copy at the same rate and will all be used to make copies of a report. At 8:00 a.m., all 3 machines begin copying. Machine A breaks down at 10:00 a.m. and is back in service at 1:00 p.m. Machine B breaks down at 12:00 p.m. (noon) and begins copying again at 3:00 p.m. All 3 machines finish copying at 5:00 p.m. when the copying of the report is complete. One of the following graphs shows n, the number of copies made, as a function of t, the time at any given point during the copying. Which graph is it? DO YOUR FIGURING HERE.

Choice F

The slope represents the copying …

2017 June(74C) Math Question 55

55. A sporting-goods store sells baseball caps for $22 each. At this price, 40 caps are sold per week. For every $1 decrease in price, the store will sell 4 more caps per week. The store will adjust the price to maximize revenue. What will be the maximum possible revenue for 1 week?

Choice E

Let r be revenue, n …

2017 June(74C) Math Question 56

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

Choice K

The quickest way would be …

2017 June(74C) Math Question 57

57. The art club designed and made banners of the school colors, blue and white, for their fund-raiser. Each

Choice A

To make one banner, ¼ …

2017 June(74C) Math Question 58

58. For all real numbers x and the imaginary number i, which of the following expressions is equivalent to

Choice F

What you need to know …

2017 June(74C) Math Question 59

59. The graph in the standard (x,y) coordinate plane below is the graph of one of the following functions. Which one?

Choice D

According to the graph, the …

2017 June(74C) Math Question 60

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

Choice K

Requirements for Matrix Multiplication:

In …