ACT Past Papers with Answers

Paper 18

ACT December 2020

Form D03 · Math Test · 60 questions

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Which of the following expressions is equivalent to the expression below? −7(5a − b) + 3(−8b + a)

A−38a − 31bB−34a − 25bC−34a − 17bD−32a − 25bE−32a − 17b

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For Bill’s birthday party, his parents will pay $35 for the cake plus $15 per person for catering expenses. They will spend at most a total of $300 for his party. The greatest integer in the solution set of one of the following inequalities gives the maximum number of people, p, who can attend the party. Which one?

Ap + 50 ≥ 300Bp(15p + 35) ≥ 300C(35 + 15)p ≤ 300D15p ≤ 300E15p + 35 ≤ 300

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The number 312.8 is 34% of x. What is the value of x rounded to the nearest whole number?

A00,009B00,011C00,106D00,920E10,635

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For RT ↔ shown below, point S is on RT ___ , the length of RS ___ is 8 cm, and the length of ST ___ is 18 cm. What is the distance, in centimeters, between T and the midpoint of RS ___ ? R S T 8 18 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

A13B17C18D22E26

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Paper 18 · ACT December 2020 · Form D03 · Math Test

A certain committee is composed of 9 juniors and 11 seniors. Two different members of the committee will be randomly selected for 2 different leadership roles. Given that the 1st member who will be selected is a senior, what is the probability that the 2nd member who will be selected is a junior?

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

What is the least common multiple of 60, 70, and 90 ?

A0000,60B000,220C000,630D001,260E378,000

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The Newton High School girls’ softball team currently has a record of 8 wins, 5 losses, and 0 ties. What is the least number of its remaining 10 games the team must win to finish the season winning more than 50% of all the team’s games?

A3B4C5D6E7

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For what value of x is 2(x − 12) + x = 24 true?

A00B04C12D16E24

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The principal of Lowe High School (LHS) authorized a study to estimate the percent of the LHS student population that will attend a 4-year college after graduation. LHS students in honors courses were asked about their postgraduation plans, and their responses were recorded. Students in other courses were NOT included in the study. Which of the following phrases best describes the principal’s study? 10 __ _ 20 11 __ _ 20 9 __ _ 19 9 __ _ 20 10 __ _ 19 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-D03 2 2

ARandomized censusBRandomized experimentCNonrandomized experimentDRandomized sample surveyENonrandomized sample survey

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Triangles nABC and nA′B′C′ are graphed in the standard (x,y) coordinate plane below. Triangle nA′B′C′ is the image of nABC under one of the following transformations. Which one?

A90° clockwise rotation about the originB90° counterclockwise rotation about the originCHorizontal translationDReflection across the x-axisEReflection across the y-axis

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Banu will build a fence around a rectangular 30-foot-by-25-foot play area. Given that fencing costs $4.05 per foot, how much will the fencing cost for Banu to completely surround the play area?

A$445.50B$344.25C$324.00D$268.00E$222.75

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The diagonal of a rectangular flat television screen is

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For all a ≠ 0, is equivalent to: y x 2 4 6 8 −8 −6 −4 −2 8 6 4 2 O A A′ B C B′ C′ a8 __ _ a4 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-D03 2 2

A1Ba2Ca4Da12Ea32

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Paper 18 · ACT December 2020 · Form D03 · Math Test

An ellipse with a major axis of length 6 inches and a minor axis of length 4 inches is inscribed in a rectangle, as shown below. The region inside the rectangle but outside the ellipse is shaded. What is the area, in square inches, of the shaded region? (Note: The area, A, of any ellipse can be found by the formula A = πab where a is the length of the major axis and b is the length of the minor axis.)

A24 − 24πB24 − 12πC24 − 06πD6πE24 + 06π

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Given 2x − 3 = 6, what is the value of x ?

A3 −B3 − 3C3 +D3 + 3E4 + 3

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Paper 18 · ACT December 2020 · Form D03 · Math Test

What is the largest possible product for 2 even integers whose sum is 18 ?

A11B19C77D80E81

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Juanita walked from her home to the bakery, first walking 0.3 miles due east and then 0.4 miles due north. What is the straight-line distance, in miles, from the bakery to Juanita’s home? 6 4 1 _ _ 2 1 _ _ 2 3 ___ _ 2 3 ___ _ 2 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-D03 2 2

A0.1B0.2C0.3D0.5E0.7

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Paper 18 · ACT December 2020 · Form D03 · Math Test

3 4− 3 4= ?

A3 4B3 4C3 4D3 4E3 4

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The line with equation 2x + 5y = 9 is graphed in the standard (x,y) coordinate plane. What is the slope of the line?

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A−B−CChoice C — see source imageDChoice D — see source imageE2

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Yolanda is calculating the weekly payroll for her small business. One employee earns $7.20 per hour and has worked 4 days this week: 9 hours the first day, 8 hours the second day, 6 hours the third day, and 7 hours the fourth day. Which of the following is the employee’s pay for this week, before any deductions are made?

A$226.80B$225.00C$219.60D$131.40E$038.70

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Paper 18 · ACT December 2020 · Form D03 · Math Test

What is the (x,y) solution, if one exists, to the system of equations y = 2x + 6 and 6x + 12 = 3y ? −17 14 −9 −8 −13 11 10 −8 26 −6 −3 3 −30 −3 1 −16 −30 25 1 −16 −2 3 2 17 4 −3 19 0 5 _ _ 2 2 _ _ 5 2 _ _ 5 5 _ _ 2 1 _ _ 4 1 _ _ 2 3 _ _ 4 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-D03 2 2 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-D03 2 2 22. Sets A, B, and C are defined below. A = {1, 2, 3, 4, 5, 6, 7, 8, 9} B = {2, 4, 6, 8} C = {4, 8} A number will be randomly selected from A. What is the probability that the selected number will be an element of C and an element of B ?

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A(−3,0)B(−2,0)C( 0,4)D( 0,6)EThere is no solution to this system.6Choice F — see source image7Choice G — see source image8Choice H — see source image9Choice J — see source image101

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Source question 22. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Maranda is going to a leadership conference and was given the map below to guide her to the Conference Center. The map has no scale, but she knows that the distance between Exits 77 and 79 on Interstate 29 is 2 miles. On the map, this distance is of an inch. She plans to exit Interstate 29 at Exit 77, travel on 41st Street to Cliff Avenue, and then proceed on Cliff Avenue to the Conference Center. The distance on the map from Exit 77 to the Conference Center over this route is 3 inches. What is this distance, in miles? 1 _ _ 9 2 _ _ 9 4 _ _ 9 6 _ _ 9 3 _ _ 4 3 _ _ 8 41st St. Minnesota Cliff Ave. Exit 77 Exit 79 Exit 81 Exit 399 12th St. Conference Center Russell 229 229 29 29 90

A04B05C09D12E18

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The histogram below shows the results of a survey of 100 people. Each person identified the number of hours per week that they watch TV. How many people surveyed watch TV at least 4 hours per week?

A57B38C28D21E19

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Each side of a square is 4 cm long. One vertex of the square is at (6,2) on a square coordinate grid marked in centimeter units. Which of the following points on the grid could be another vertex of the square?

A(10, 2)B( 7, 3)C( 2, 5)D( 1,−5)E(−4, 2)

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Paper 18 · ACT December 2020 · Form D03 · Math Test

0 inches. The width of the screen is 22.7 inches, and the height of the screen is 10.0 inches less than the width of the screen. Which of the following is closest to the area, in square inches, of the television screen?

A144B165C288D330E590

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Given that ∠R is the included angle between the 2 congruent sides of the isosceles triangle nRST, and the measure of ∠R is 50°, what is the measure of ∠S ? number of hours 0 2 4 6 8 10 [0, 2) [2, 4) [4, 6) [6, 8) [8, 10) 30 25 20 15 10 5 0 number of people 28 15 21 17 19 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-D03 2 2

A020°B050°C065°D080°E130°

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Paper 18 · ACT December 2020 · Form D03 · Math Test

In the standard (x,y) coordinate plane, what is the distance, in coordinate units, from A15 ,−32 to B1−1 ,−32?

A00B02C03D06E12

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Hikers’ World Foods sells raisin-nut mix in bulk to stores. The dollar amount per pound, P(x), for a store to purchase x pounds of raisin-nut mix from Hikers’ World is given by the function below. P(x) = 3.50 + 0.90x To the nearest $0.01, which of the following dollar values is equal to the total price for a store to purchase 100 pounds of raisin-nut mix in a single order from Hikers’ World?

A$350.00B$359.00C$440.00D$616.00E$903.50

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Paper 18 · ACT December 2020 · Form D03 · Math Test

In right triangle nABC shown below, sin,C = and the length of AB ___ is 14 inches. What is the length, in inches, of AC ___ ?

A24B74C10D19.6E24

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The 1st term of a geometric sequence is 27, and the 4th term is 64. In terms of n, what is the nth term of the sequence? n − 1 n n − 1 n 8 _ _ 9 1 _ _ 3 5 _ _ 9 8 _ _ 9 2 _ _ 9 7 _ _ 9 8 _ _ 9 5 _ _ 7 14 A B C 3 _ _ 4 3 _ _ 4 4 _ _ 3 4 _ _ 3 4 _ _ 3 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-D03 2 2

A271 2B271 2C271 2D271 2E271 2n

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Paper 18 · ACT December 2020 · Form D03 · Math Test

A series of transformations are applied to the graph in the standard (x,y) coordinate plane below. The graph below is reflected across the x-axis. The new graph is reflected across the y-axis. This new graph is rotated 90° clockwise ( ) about the origin. The resulting graph is one of the following graphs. Which one?

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

What is the least positive number that has a remainder of 3 when divided by 6 and a remainder of 6 when divided by 9 ? y x x y x x y x O O O O O y x O DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-D03 2 2

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A15B18C24D42E726y7Choice J — see source image8y9Choice K — see source image10Choice H — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

What rational number is exactly halfway between and on the real number line?

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

On a certain day in Katie’s yard, the average rate of change in temperature per hour between 1 p.m. and 11 p.m. was −2°F per hour. The temperature in Katie’s yard at 11 p.m. that day was 42°F. Which of the following was the temperature in Katie’s yard at 1 p.m. that day?

A14°FB22°FC62°FD64°FE84°F

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Given that i is the imaginary unit, which of the following complex numbers is equal to (7 + 6i)2 ?

A13B85C13 + 84iD14 + 12iE85 + 84i

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Two motorcycles, starting at the same point at the same time, travel away from each other at a 90° angle. One travels at 40 miles per hour and the other at 60 miles per hour. If they continue traveling at these constant rates, after about how many hours will they be 200 miles apart? 2 _ _ 8 6 __ _ 14 2 __ _ 11 19 __ _ 14 19 __ _ 28 5 __ _ 56 19 __ _ 56 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-D03 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-D03 2 2 A website about birds made the 4 claims below about American robins.

A1.4B2.8C3.2D7.7E8.7

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Suppose the population of American robins increased each year from 2005 to 2015. The conservation organization will consider American robins threatened provided that their population in 2025 is no greater than what number?

A000,960,000B009,600,000C022,400,000D096,000,000E224,000,000

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The population of American robins in 2015 is equal to

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

A certain robin flew for 15 seconds at the maximum reported flight speed cited by the website. Which of the following values is closest to the number of meters the robin flew during that time? (Note: 1 meter ≈ 3.3 feet) Use the following information to answer questions 38–40.

A064B240C697D792E960

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Let x be a real number. Which of the following statements is true for all possible values of x ?

A−x < xB−x < ⎪x⎪Cx = ⎪x⎪D⎪x⎪ = ⎪−x⎪E−⎪x⎪ = ⎪−x⎪

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Paper 18 · ACT December 2020 · Form D03 · Math Test

In the standard (x,y) coordinate plane, the 3 distinct points A(3,5), B(6,8), and C are collinear, and B is equidistant from A and C. What are the coordinates of C ?

A(4,7)B(9,11)C(1.5,1.5)D(4.5,6.5)E(7.5,10.5)

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Paper 18 · ACT December 2020 · Form D03 · Math Test

If 90° < θ < 180° and sin,θ = , then cos,θ = ?

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AChoice A — see source imageBChoice B — see source imageC−D−E−

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The mean of 10 numbers entered into a computer statistics program was 75.0. One number was incorrectly entered as 73 instead of 78. When the 73 is replaced by 78, by how much will the mean increase?

A0.1B0.5C1.5D3.0E5.0

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Paper 18 · ACT December 2020 · Form D03 · Math Test

At Mort’s Sporting Goods Store, the sale price of a pair of athletic shoes is 30% off the regular price of the shoes. The sale price of the shoes is $84.00. What is the regular price of the shoes? 8 __ _ 17 8 __ _ 15 17 __ _ 8 17 __ _ 8 15 __ _ 17 17 __ _ 15 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-D03 2 2 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-D03 2 2 Data from a random sample of 335 car owners in a certain city are listed below. The table indicates the number of owners in 3 age brackets (16−25, 26−45, 46−60) who own cars from 3 car companies (A, B, C) in this city. Each owner in the sample owns only 1 car.

A$054.00B$064.62C$109.20D$114.00E$120.00

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Two car owners from this sample will be chosen at random. Given that no owner is chosen twice, which of the following expressions gives the probability that both owners chosen will be from the same age bracket?

A+ +B+ +C+ +D1 21 2E1 21 2

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For those in the sample who are 26 to 45 years old, which of the following values is closest to the average number of car owners per company?

A037B045C052D112E155

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Paper 18 · ACT December 2020 · Form D03 · Math Test

A circle graph will be drawn with 3 sectors each representing the proportion of owners from Company A, B, and C who are 16 to 25 years old. What is the measure of the central angle for the Company A sector of the graph? Age (in years) Car companies A B C Total 16−25 26–45 46–60 016 24 040 080 054 48 053 155 065 23 012 100 Total 135 95 105 335 100(99) ______ __ _ 335(334) 155(154) ______ __ _ 335(334) 80(79) ______ __ _ 335(334) 105(104) ______ __ _ 335(334) 95(94) ______ __ _ 335(334) 135(134) ______ __ _ 335(334) 100 ___ _ 335 155 ___ _ 335 80 ___ _ 335 100 ___ _ 333 155 ___ _ 334 80 ___ _ 335 1 _ _ 3 1 _ _ 3 1 _ _ 3 Use the following information to answer questions 46–48. DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-D03 2 2 49. The vertices of nPQR are given in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of nPQR ?

A05°B17°C20°D43°E72°6247258309481050

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Source question 49. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The table below gives values of the functions f and g at different values of x. What is f_g(1)+ ?

A−6B1C2D3E7

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Joe, Carmen, and Dave each receive an allowance. The ratio of Joe’s allowance to Dave’s allowance is 3:2, and the ratio of Dave’s allowance to Carmen’s allowance is 3:4. What is the ratio of Joe’s allowance to Carmen’s allowance?

A1:2B1:6C2:5D3:4E9:8

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The figure below shows a flower bed consisting of 3 regions each bordered by garden edging. The edging forms 3 concentric circles with the distance between successive borders equal to the radius, r meters, of the smallest circle. The length of edging needed for the border of the smallest region is 10 meters. What is the total length, in meters, of edging needed for the borders of all 3 regions?

A030B060C090D110E140

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Paper 18 · ACT December 2020 · Form D03 · Math Test

If ln x = 2, then x = ? y x O P(5,10) R(−3,6) Q(5,4) edging r r r x 1 2 3 f(x) 3 −6 2 g(x) 2 7 1 2 _ _ e DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-D03 2 2 54. The first 4 elements of a pattern are shown below. Each element is composed of small squares that are 18 inches wide and 18 inches long. Each element is a square with both dimensions 18 inches less than the dimensions of the next element. What is the perimeter, in feet, of the 5th element?

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A1BChoice B — see source imageC2eD0eE0e2606707.58209251030

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Source question 54. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

For all positive x, which of the following is equal to 2 + − ?

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

In nABC shown below, the given side lengths are in meters. Which of the following expressions gives the area, in square meters, of nABC ? + 112 + 112 − 2(10)(11)(cos 30°)

A(11)(10)B√102C(11)(10)(cos,30°)D(11)(10)(sin,30°)E√102

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Paper 18 · ACT December 2020 · Form D03 · Math Test

The simple interest for 1 year for an investment was $372. If the interest rate had been 1% higher for this investment, the simple interest for 1 year would have been $434. How much money was invested? 6 _____ _ 2x + 4 3x _____ x + 2 5x + 1 _____ _ x + 2 6x − 6 _____ _ 2x + 4 7x + 2 _____ _ 2x + 4 3x − 4 _____ _ 3x + 6 3x − 4 _____ _ 3x + 7 C A B 30° 10 11 1 _ _ 2 1 _ _ 2 1 _ _ 2 DO YOUR FIGURING HERE. 29 ACT-D03 2 2 58. For what values of b does the equation x2 + bx + 1 = 0 have no real solutions?

A$ , 62B$ ,520C$ ,620D$5,200E$6,2006All b < 07All b < 18All b < 290 < b < 410−2 < b < 2

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Paper 18 · ACT December 2020 · Form D03 · Math Test

Source question 58. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 18 · ACT December 2020 · Form D03 · Math Test

In the standard (x,y) coordinate plane below, the endpoints of the major and minor axes of the ellipse are labeled. Which of the following equations determines the ellipse? + (y − 7)2 = 1 + (y + 7)2 = 1

A+ = 1B+ = 1C+ = 1D(x − 4)2E(x + 4)2

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Paper 18 · ACT December 2020 · Form D03 · Math Test

One root of the quadratic polynomial ax2 + 13x − 6 is equal to −3. Which of the following binomials is a factor of ax2 + 13x − 6 ? y x O (0,7) (4,0) (−4,0) (0,−7) x2 __ _ 4 y2 __ _ 7 x2 __ _ 8 y2 __ _ _ 14 x2 __ _ _ 16 y2 __ _ _ 49 2 _ _ 5 2 _ _ 5 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

Ax −Bx +Cx − 3Dx − 5Ex + 5

Form D03 · Math Test · 60 questions

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