ACT Form A09 Math Answer Explanation


2018 April(A09) Math Question 1

1. A line in the standard (x,y) coordinate plane passes through the points (-2,-6) and (5,3). The slope of the line:

Choice A

$$slope = \frac{3-(-6)}{5-(-2)}>0$$


2018 April(A09) Math Question 2

2. What is the sum of the complex numbers 3 – 4i and 5 + 3i?

Choice J

(3 - 4i) + (5 + 3i) = 8 - I


2018 April(A09) Math Question 3

3. Last year at RT University, the ratio of the number of students accepted to the number of students applying for admission was 2 to 7. RT University accepted 630 students last year. Flow many students applied to RT University last year?

Choice C

$$\frac{630}{x}=\frac{2}{7} $$ $$ x=\frac{630\times7}{2}=2205$$


2018 April(A09) Math Question 4

4. Three line segments intersect as shown in the figure below, forming angles with measures of 150°, 40°, and x°, respectively. What is the value of x ?

Choice K

4. Three line segments intersect as shown in the figure below, forming angles with measures of 150°, 40°, and x°, respectively. What is the value of x ?

x = 40 + (180-150) = 70


2018 April(A09) Math Question 5

5. A carnival game is played using an open box with a rectangular bottom measuring 6 inches by 13 inches. A square with side lengths of 4 inches is painted on the bottom of the box. The game is played by dropping a small bead into the open box. if the bead conies to rest in the painted square, the player wins a prize. Assuming a bead dropped into the box comes to rest at a random spot on the bottom of the box, which of the following is closest to the probability that the bead comes to rest in the painted square?

Choice C

5. A carnival game is played using an open box with a rectangular bottom measuring 6 inches by 13 inches. A square with side lengths of 4 inches is painted on the bottom of the box. The game is played by dropping a small bead into the open box. if the bead conies to rest in the painted square, the player wins a prize. Assuming a bead dropped into the box comes to rest at a random spot on the bottom of the box, which of the following is closest to the probability that the bead comes to rest in the painted square?

$$p=\frac{4\times4}{6\times13}\approx 0.21$$


2018 April(A09) Math Question 6

6. What is the slope-intercept form of 9x — y 5 = 0 ?

Choice H

$$9x-y-5=0 \\$$ $$\Rightarrow 9x-5=y \\$$ $$\Rightarrow y=9x-5$$


2018 April(A09) Math Question 7

Choice A

$$XY=5k\\$$ $$YZ=9k \\$$ $$\Rightarrow XZ=14k\\$$ $$\Rightarrow \frac{XY}{XZ}=\frac{5k}{9k}=\frac{5}{9}$$


2018 April(A09) Math Question 8

8. The solution set of 2x + 4 —8 is the set of all real values of .v such that:

Choice G

$$2x+4\geq -8 \\$$ $$\Rightarrow 2x\geq -8-4 \\$$ $$\Rightarrow x\geq \frac{-8-4}{2}\\$$ $$\Rightarrow x\geq -6$$


2018 April(A09) Math Question 9

9. Which of the following is equivalent to (a3)2′ ?

Choice E

$$(a^3)^{21}=a^{3\times21}=a^{63}$$


2018 April(A09) Math Question 10

10. If f(x) 3×2 + 7x — 8, then f(-3) = ?

Choice G

$$f(-3)=3(-3)^2+7(-3)-8=-2$$


2018 April(A09) Math Question 11

11. Two sides of a triangle are equal in length. The third side is 3 centimeters longer than either of the other 2 sides. Given that the perimeter of the triangle is 93 centimeters, what is the length, in centimeters, of the longest side?

Choice D

$$2a+(a+3)=93\\$$ $$a=30\\$$ $$a+3=33$$


2018 April(A09) Math Question 12

12. The 220 graduating seniors of Madison- High School will sit in the center section of the school auditorium at the graduation ceremony. How many rows of seats will be needed to seat all of the graduating seniors if the first row has 10 seats and each succeeding row has 2 more seats than the previous row?

Choice G

$$a_1=10 \\$$ $$d=2 \\$$ $$a_n=10+2(n-1)=2n+8 \\$$ $$S_n=\frac {a_1+a_n}{2}\cdot n=\frac {10+2n+8}{2}\cdot n=220 \\$$ $$n=11$$


2018 April(A09) Math Question 13

13. In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9, -11) and:

Choice B

$$\frac {9+x}{2}=3 \\$$ $$\frac {-11+y}{2}=-7 \\$$ $$\Rightarrow x=-3 ,\ y=-3$$


2018 April(A09) Math Question 14

14. A community theater group performed at 5 local schools. For each school, the table below shows the total number of tickets sold and the total dollar amount collected from ticket sales. At School A, only 2 types of tickets were sold: premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ?

Choice J

$$t+v=200\\$$ $$10t+6v=1400\\$$ $$\Rightarrow t=50,\ v=150$$


2018 April(A09) Math Question 15

15. The theater group had to pay each school a facility charge. For use of its facility, School C charged the theater group 10% of the ticket sales and a fixed fee of $200. How much money did School C charge the theater group for use of its facility?

Choice E

$$10\% \times 1800+200=380$$


2018 April(A09) Math Question 16

16. What is the difference between the median and the mean number of tickets sold at the 5 schools?

Choice K

$$median=250 \\$$ $$mean=\frac {200+250+300+150+275}{5}=235 \\$$ $$\Rightarrow median - mean = 250-235=15$$


2018 April(A09) Math Question 17

17. What is the area, in square decimeters, of a right triangle with side lengths of 10 dm, 26 dm, and 24 dm ?

Choice E

$$Area = \frac{10\times24}{2}=120 \ dm^2$$


2018 April(A09) Math Question 18

18. The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93, 68, 93, 70, and 98. What is the 7th number on the list?

Choice J

$$Mean = \frac{82+93+68+93+70+x}{7}=85 \\$$ $$\Rightarrow x=91$$


2018 April(A09) Math Question 19

19. Which of the following is the sine of the smallest angle in a right triangle with side lengths 7, 24, and 25 inches, respectively?

Choice A

$$\sin A = \frac{7}{25}$$


2018 April(A09) Math Question 20

20. In the figure shown below, all angles are right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure?

Choice G

20. In the figure shown below, all angles are right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure?

The longer length of the smaller rectangle (S2) = 12-5=7

$$Total\ area = S1+S2=10 \times 5 + 3 \times 7=71$$


2018 April(A09) Math Question 21

21. A triangle has a perimeter of 26 cm and sides of length x cm, (x + 3) cm, and (x + 5) cm. What is the value of x?

Choice A

x+(x+3)+(x+5 …


2018 April(A09) Math Question 22

22. A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty?

Choice J

$$t=\frac{480}{4}=120 …


2018 April(A09) Math Question 23

23. An ice cream shop sells ice cream cones with exactly 1 of 3 ice cream flavors in the cone. The 3 flavors are vanilla, chocolate, and strawberry. Last Saturday, the shop sold 42 cones. It sold I 1 more with chocolate than with vanilla and 2 more with vanilla than with strawberry. How many cones with strawberry ice cream did the shop sell that Saturday?

Choice A

v+c+s=42

c …


2018 April(A09) Math Question 24

24. In ABC below, D is the midpoint of CB, ZABC is a right angle, AB = 8 m, and AC = 10 m. What is AD, in meters?

Choice G

$$BC=\sqrt{AC^2-AB^2 …


2018 April(A09) Math Question 25

25. Lyman has plotted 5 points in the standard (.v,y) coordinate plane below. He then plots a new point as follows: the x-coordinate of the new point is the mean of the .v-coordinates of the 5 points already plotted; the y-coordinate of the new point is the mean of the y-coordinates of the 5 points already plotted. Which of the following ordered pairs gives the coordinates of Lyman’s new point?

Choice C

$$x=\frac{(-2)+(-1)+(-2 …


2018 April(A09) Math Question 26

26. The 1st and 2nd terms of a certain geometric sequence are 10 and —5, respectively. What is the 5th term of the geometric sequence?

Choice H

$$10, -5, \frac{5}{2 …


2018 April(A09) Math Question 27

27. Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $1.00 per shirt that she stitches or $10.00 per hour, whichever daily amount is higher. Alani stitched the following numbers of shirts: 60 on Monday, 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani’s total pay for these 5 days?

Choice C

Monday:

The daily amount for …


2018 April(A09) Math Question 28

28. Which of the following most precisely describes the roots of the equation 5×2 + 7x + 2 = 0 ?

Choice H

To find the roots of …


2018 April(A09) Math Question 29

29. Paula is planning a course for a bike race. The course is in the shape of a right triangle, as shown below. Participants will begin at A, ride directly to B, then directly to C, and directly back to A. Paula wants to put a rest stop at the halfway point on the course. How many miles past B will the rest stop be?

Choice D

29. Paula is planning a course for a bike race. The course is in the shape of a right triangle, as shown below. Participants will begin at A, ride directly to B, then directly to C, and directly back to A. Paula wants to put a rest stop at the halfway point on the course. How many miles past B will the rest stop be?

$$BC=\sqrt{AB^2+AC …


2018 April(A09) Math Question 30

30. Adams High School has 120 students, and 1/3 of thestudents are taking Literature. Of the students NOT taking Literature, I are taking Composition. No students are taking both Literature and Composition. How many students are taking Composition?

Choice G

The number of students NOT …


2018 April(A09) Math Question 31

31. For what value of x is the equation

Choice D

$$\sqrt{x}+3=6 \\$$ $$\Rightarrow …


2018 April(A09) Math Question 32

32. In the right triangle AABC shown below, the length of

Choice H

$$\sin A = \frac{3}{4 …


2018 April(A09) Math Question 33

33. What integer does 3(log2 16) equal?

Choice A

$$3(\log_2 16)=3(\log_2 …


2018 April(A09) Math Question 34

34. A bag contains several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be: true about the marbles in the bag?

Choice F

F. is apparently true, because …


2018 April(A09) Math Question 35

35. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip, the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour, and 1 ride on the roller coaster track is completed in 2.25 minutes. A graph showing the height above level ground, in feet, with respect to the time into the ride, in seconds, is given below. Which of the following values is closest to the total distance traveled, in miles, during 1. complete ride on the roller coaster track?

Choice B

Total distance travelled in 1 …


2018 April(A09) Math Question 36

36. The roller coaster is at a height of at least 235 feet for a total of 5 seconds during each complete ride. Which of the following is closest to the percent of the time during a complete ride that the roller coaster is at a height of at least 235 feet?

Choice G

$$\frac{5 \ seconds}{2.25 …


2018 April(A09) Math Question 37

37. Which of the following values is closest to the average slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds?

Choice E

37. Which of the following values is closest to the average slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds?

$$The\ slope \approx \frac{200 …


2018 April(A09) Math Question 38

38. The value of x5(0.5×2+ 2.5x + 6) is between which of the following numbers when x T 10 ?

Choice J

$$10^5(0.5\times10 …


2018 April(A09) Math Question 39

39. For which of the following data sets is the difference between the mean and the median the greatest?

Choice D

A. { 10, 10, 10, 10 …


2018 April(A09) Math Question 40

40. Pablo has a deck and pool in his backyard. The deck’s shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top of the deck?

Choice K

40. Pablo has a deck and pool in his backyard. The deck’s shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top of the deck with stain. To decide how much stain to purchase, he needs to find the area of the top of the deck. To the nearest square foot, what is the area of the top of the deck?

Diameter of the circle = 32-4-4 …


2018 April(A09) Math Question 41

41. A 3-foot-wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40 feet, as shown in the figure below. What is the perimeter, in feet, of the swimming pciol?

Choice B

41. A 3-foot-wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40 feet, as shown in the figure below. What is the perimeter, in feet, of the swimming pciol?

a=30-3-3=24 feet

b …


2018 April(A09) Math Question 42

42. Given the functions f(x) = X2anc.

Choice F

$$g(f(x))=\frac{1 …


2018 April(A09) Math Question 43

43. A circle has a circumference of 27E\ feet. What is the area, in square feet, of the circle?

Choice C

$$C=2 \pi r=2 …


2018 April(A09) Math Question 44

44. In the standard (x,v) coordinate plane, the coordinates of the y-intercept of the graph of the function v = f(x) are (0,-2). What are the coordinates of the v-intercept of the graph of the function y = f(x) — 3 ?

Choice F

44. In the standard (x,v) coordinate plane, the coordinates of the y-intercept of the graph of the function v = f(x) are (0,-2). What are the coordinates of the v-intercept of the graph of the function y = f(x) — 3 ?

The graph of the function …


2018 April(A09) Math Question 45

45. Which of the following is an equation of a parabola that passes through the 3 points labeled in the standard (x,y) coordinate plane below?

Choice A

Only Choice A satisfies that …


2018 April(A09) Math Question 46

46. As x continually increases in value without bound, the

Choice H

When x become really large …


2018 April(A09) Math Question 47

47. Yulan will use a bag of 30 solid-colored marbles for a game in which each player randomly draws marbles from the bag. The number of marbles of each color is shown in the table below.

Choice B

The probability of drawing a …


2018 April(A09) Math Question 48

48. The expression 2b + c b — 2c is undefined whenever b = ?

Choice K

The expression is undefined whenever …


2018 April(A09) Math Question 49

49. What number is halfway between and

Choice E

$$\frac{\frac{2}{5}+\frac …


2018 April(A09) Math Question 50

50. A function f(x) is defined as f(x) = 3’2-‘2. What 2 real numbers satisfy f(x) = 1 ?

Choice H

$$3^{x^2-x-2}=1=3 …


2018 April(A09) Math Question 51

51. The ellipse shown in the standard (x,y) coordinate plane below has equation 93)2 + `-Y 255,2 = 1. Which of the

Choice D

51. The ellipse shown in the standard (x,y) coordinate plane below has equation 93)2 + `-Y 255,2 = 1. Which of the

The major radius p is …


2018 April(A09) Math Question 52

52. A basket contains 10 solid-colored balls–2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will he red or have a 3 printed on it?

Choice J

52. A basket contains 10 solid-colored balls–2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will he red or have a 3 printed on it?

$$p=\frac{3+1}{10 …


2018 April(A09) Math Question 53

53. In the figure below, the given side lengths of AABC are in inches. What is the area, in square inches, of /ABC ?

Choice B

53. In the figure below, the given side lengths of AABC are in inches. What is the area, in square inches, of /ABC ?

$$Area \ of \triangle ABC = \frac …


2018 April(A09) Math Question 54

54. There are 66 calories in 15 grams of grated Parmesan cheese, and 59% of those calories are from fat. When measuring Parmesan cheese, 5 grams is equal to 1 tablespoon. Which of the following is closest to the number of calories from fat per tablespoon of grated Parmesan cheese? .

Choice J

$$\frac{59\%\times66}{15}\times3 …


2018 April(A09) Math Question 55

55. In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH I BE. The area of square ABGF is -12-t the area of square ACDE. What percent of the area of ACDE does the shaded portion represent?

Choice E

55. In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH I BE. The area of square ABGF is -12-t the area of square ACDE. What percent of the area of ACDE does the shaded portion represent?

Area of shaded portion = $$\frac …


2018 April(A09) Math Question 56

56. In a data set of 10 distinct values, the single largest value is replaced with a much greater value to form a new data set. Which of the following statements is true about the values of the mean and median for the new data set as compared to the mean and median of the original data set?

Choice F

The median will stay the …


2018 April(A09) Math Question 57

57. Valley High School and Mountain High School have decided that selected students will attend a daytime theatrical performance that costs $5 for each teacher and $3 for each student. One teacher and 10 students from Valley High will attend, and 2 teachers and 25 students from Mountain High will attend. Which of the following matrix products represents the ticket costs. in dollars, for each high school?

Choice A

The ticket cost is $$5 …


2018 April(A09) Math Question 58

58. Karie is inventing a new notation in math. She has decided to use n.L to denote the sum of the first a positive integers. For example, 51 means 5 + 4 + 3 + 2 + 1. Karie has written 3 statements that she is investigating as possible properties of

Choice F

$$I. n\downarrow+(n+1 …


2018 April(A09) Math Question 59

59. Rey wants to make an open box as shown below, using a square piece of cardboard. He intends to cut a 2-inch square from each corner of the cardboard and fold the cardboard along the lines shown to form the sides. The resulting box will have a volume of 72 cubic inches. What are the dimensions, in inches, of the original piece of cardboard?

Choice E

59. Rey wants to make an open box as shown below, using a square piece of cardboard. He intends to cut a 2-inch square from each corner of the cardboard and fold the cardboard along the lines shown to form the sides. The resulting box will have a volume of 72 cubic inches. What are the dimensions, in inches, of the original piece of cardboard?

$$(x-4)(x-4)\times2=72\\$$ $$x …


2018 April(A09) Math Question 60

60. Which of the following quadratic equations has the complex number (1 + V-1) as a solution?

Choice K

Let's start with K …