ACT Past Papers with Answers

Paper 3 · ACT September 2024 · Form H11 · Math Test

During a certain game, the probability of randomly drawing Card A is . What is the probability of randomly drawing a card that is NOT Card A ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Dawn randomly selected 6 books from the teen library, read them, and then rated them as follows: 40, 60, 10, 80, 30, and 40. Based on the sample data, what is the best estimate of Dawn’s average rating of all the books in the library? √ •• 5 _ _ 3 31 __ _ 2 5 _ _ 3 1 _ _ 8 1 _ _ 8 1 _ _ 7 1 _ _ 4 7 _ _ 8 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 3 · ACT September 2024 · Form H11 · Math Test

On a digital music player there are 153 rap songs, 72 country songs, 14 jazz songs, and 121 rock songs. Given that the player is set to randomly shuffle the song selection, what is the probability, rounded to the nearest thousandth, the 1st song played will be a country song?

Paper 3 · ACT September 2024 · Form H11 · Math Test

A city bus picks up and drops off passengers according to the table below. The bus has 0 passengers before Stop 1. After Stop 5, there are 13 passengers remaining on the bus. How many passengers did the bus pick up at Stop 1 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

What is the length, in inches, of the hypotenuse of a right triangle with a leg that is 8 inches long and a leg that is 3 inches long?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Given x = 100 and y = −20, x + y is equal to the product of −5 and what number? DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-H11 2 2 Stop Passenger pickup/drop-off 1 ? 2 Picks up 3 passengers 3 Drops off of all passengers 1 _ _ 2 4 Picks up 11 passengers 5 Drops off of all passengers 1 _ _ 2 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-H11 2 2 8. The operation ⊗ is defined by a ⊗ b = a2 a ⊗ b = 100, what is the value of b ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Source question 8. Refer to the source image.

Paper 3 · ACT September 2024 · Form H11 · Math Test

For RT ↔ shown below, point S is on RT ___ , the length of RS ___ is 6 cm, and the length of ST ___ is 16 cm. What is the distance, in centimeters, between T and the midpoint of RS ___ ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Matrices A and B are given below. A = 3 4 B = 3 4 Which of the following matrices is A − B ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

One of the lines graphed in the standard (x,y) coordinate plane below has a negative slope and a negative y-intercept. Which one?

Paper 3 · ACT September 2024 · Form H11 · Math Test

In a certain isosceles triangle, the measure of the vertex angle is 34°. What is the measure of each of the 2 base angles? R S T 6 16 −2 3 6 −8 8 1 5 −4 −10 1 2 −4 −10 2 1 −4 6 4 11 −12 6 11 4 −12 10 −2 −1 4 O r q x p n m y

Paper 3 · ACT September 2024 · Form H11 · Math Test

This month, Reed sold 40 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $4 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. How many large figurines did Reed sell this month?

Paper 3 · ACT September 2024 · Form H11 · Math Test

The 7th term and the 8th term of an arithmetic sequence are 4 and 12, respectively. What is the 2nd term of this sequence?

Paper 3 · ACT September 2024 · Form H11 · Math Test

The Cross High School girls’ softball team currently has a record of 14 wins, 11 losses, and 0 ties. What is the least number of its remaining 12 games the team must win to finish the season winning more than 50% of all the team’s games?

Paper 3 · ACT September 2024 · Form H11 · Math Test

An object is launched vertically at 49 meters per second from a 980-meter high platform. The equation for the object’s height, h, at time t seconds after launch is h(t) = −4.9t2 + 49t + 980, where h is in meters. What will be the height, in meters, of the object 6 seconds after launch?

Paper 3 · ACT September 2024 · Form H11 · Math Test

The 1st term of Pattern A is 2. The rule to find each subsequent term is to multiply the previous term by 2 and then subtract 1. The 1st term of Pattern B is 2. The rule to find each subsequent term is to subtract 1 from the previous term and then multiply by 2. What is the sum of the 4th terms of Pattern A and Pattern B ? DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-H11 2 2

Paper 3 · ACT September 2024 · Form H11 · Math Test

Which of the following binomials is a factor of x2 − x − 156 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

One of the following graphs is that of the solution set of the inequality 4x − 2 ≤ 10. Which one?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Let y be an irrational number. Which of the following statements about the value of 15y must be true?

Paper 3 · ACT September 2024 · Form H11 · Math Test

One of the following equations represents the line of best fit shown in the scatterplot below. Which one?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Points G(2,6) and H(10,14) lie in the standard (x,y) coordinate plane. What is the midpoint of GH ___ ? −1 4 x x x x 0 1 2 3 5 6 −1 4 0 1 2 3 5 6 x −1 4 0 1 2 3 5 6 −1 4 0 1 2 3 5 6 −1 4 0 1 2 3 5 6 x 2 4 6 8 O 10 y DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-H11 2 2

Paper 3 · ACT September 2024 · Form H11 · Math Test

A machine blade in the shape of a right triangle is rotated about a mechanical shaft at high speed. The mechanical shaft is along the longer leg of the triangle that represents the blade. In the diagram below, the figure on the left shows the blade at rest, and the figure on the right shows a bottom view of the blade in motion. One of the following solids is generated as the blade rotates about the shaft. Which one?

Paper 3 · ACT September 2024 · Form H11 · Math Test

The sum of 2 numbers is 22. The sum of the squares of the 2 numbers is 260. What is the product of the 2 numbers?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Trapezoid A and Trapezoid B are congruent and graphed in the standard (x,y) coordinate plane below. One of the following transformations or sequences of transformations would map Trapezoid A onto Trapezoid B. Which one? over the x-axis the left machine blade at rest bottom view of machine blade in motion A B x y O DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-H11 2 2 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-H11 2 2 26. A circle with its center at (5,4) and a radius of 3 coordinate units is graphed in the standard (x,y) coordinate plane. One point on the circle has a y-coordinate greater than that of any other point on the circle. What is the y-coordinate of that point?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Source question 26. Refer to the source image.

Paper 3 · ACT September 2024 · Form H11 · Math Test

For real constants a, b, and c, the graph in the standard (x,y) coordinate plane below is represented by an equation in one of the following forms. Which one? + bx + c

Paper 3 · ACT September 2024 · Form H11 · Math Test

Jared is driving home. He is currently 231 miles away from home. His car’s fuel tank holds 16 gallons and is full of fuel. Given that his car travels 22 miles per gallon of fuel and he doesn’t stop for fuel, how many gallons of fuel will be in his tank when he gets home?

Paper 3 · ACT September 2024 · Form H11 · Math Test

In the figure below, 5 right triangles share a common vertex, O. The legs of each of these triangles are shown dashed, and their lengths are labeled in feet. The point on each triangle that is farthest from O is labeled A, B, C, D, or E. A circle centered at O with a radius of 10 feet will be drawn. Which of the following points is outside of this circle? a _ _ x 3 _ _ 4 O x y O 1 10 8 6 7 7 6 8 9 4 A B C D E

Paper 3 · ACT September 2024 · Form H11 · Math Test

Albert won a contest for which he will be paid $1.00 on the 1st day, $2.00 on the 2nd day, $3.00 on the 3rd day, and so on for 1 year (365 days). What is the total amount of money Albert will be paid in contest winnings? (Note: For arithmetic series, Sn = , Sn is the sum of the first n terms of a sequence such that t1 is the 1st term and tn is the nth term.)

Paper 3 · ACT September 2024 · Form H11 · Math Test

Tables of values for the 2 functions f and g are shown below. What is the value of g_f(5)+ ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

In the figure below, line l is parallel to line m, and line n intersects the parallel lines. What is the value of x ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Which of the following expressions is equal to _2√• 7 + 1+_√• 7 − 1+ − _√• 7 − 1+ ? n(t1 + tn) _ _______ 2 x f(x) x g(x) −6 −4 3 5 7 −6 5 4 −4 3 4 5 5 −3 −5 −6 m l n (x + 15)° (3x + 5)° DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-H11 2 2

Paper 3 · ACT September 2024 · Form H11 · Math Test

Given i2 = −1, −2i(3 + 4i) − 3(2 + 5i) = ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

At an ice-cream shop, patrons can purchase a single scoop of 1 ice-cream flavor and 1 topping for $2.99. The owner recorded the number of different ice-cream flavors and 1-topping combinations that were purchased, as shown in the table below. To the nearest

Paper 3 · ACT September 2024 · Form H11 · Math Test

The equation y = f(x) is graphed in the standard (x,y) coordinate plane below. One of the following defines f. f(x) = ? 5 for x < −2 53 for x = −2 2 for x > −2 5 for x ≤ −2 53 for x = −2 2 for x > −2 5 for x < −2 53 for x = −2 2 for x ≥ −2 5 for x ≤ −2 53 for x = −2 2 for x ≥ −2 5 for x = −2 53 for x = −2 2 for x = −2 Sprinkles Syrup Fruit Total Vanilla 077 038 060 175 Chocolate 107 055 021 183 Swirl 118 110 059 287 Total 302 203 140 645 x y 2 4 5 1 3 2 4 1 3 −4 −1 O −2 −3 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-H11 2 2

Paper 3 · ACT September 2024 · Form H11 · Math Test

A restaurant conducted a survey to determine whether its customers like or dislike corn bread and whether they like or dislike banana bread. The table below shows the results of the survey. Given that a customer selected at random from those surveyed likes corn bread, what is the probability that the customer dislikes banana bread?

Paper 3 · ACT September 2024 · Form H11 · Math Test

For all positive values of a and b, 8 is equivalent to: √•• ba √•• a8 √•• b8 √•• •• 8b √•• 8a

Paper 3 · ACT September 2024 · Form H11 · Math Test

The positive integer 134,678 contains exactly 6 digits. Including this integer, how many 6-digit positive integers contain the digits 1, 3, 4, 6, 7, and 8 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

What is the least common denominator for + ? Like corn bread Dislike corn bread Total Like banana bread 078 57 135 Dislike banana bread 082 32 114 Total 160 89 249 82 ___ _ 249 82 ___ _ 160 114 ___ _ 249 160 ___ _ 249 192 ___ _ 249 a _ _ b x + 2 _____ _ x2 − 1 x2 − 9 _____ _ 7x − 7 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-H11 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-H11 2 2 41. Thomas wanted to test whether his coin was unfair. To do this, he flipped the coin 6 times and counted the number of heads and tails. Four of the flips resulted in heads, and two resulted in tails. One of the following statements is a correct conclusion based on Thomas’s test. Which one? the expected number of heads. the expected number of tails. heads and some resulted in tails. approximately the same number of heads and tails. predict whether the coin is unfair.

Paper 3 · ACT September 2024 · Form H11 · Math Test

Source question 41. Refer to the source image.

Paper 3 · ACT September 2024 · Form H11 · Math Test

In nABC below, BD ___ is the altitude from B to AC ___ , the measure of ∠A is 60°, AD = 10 m, and DC = 2 m. What is the area, in square meters, of nABC ? A C B 60° 10 2 D

Paper 3 · ACT September 2024 · Form H11 · Math Test

The area of any triangle is given by ab(sin,C), where a and b are the lengths of any 2 sides, and C is the interior angle formed by those 2 sides. Which of the following is closest to the area, in square feet, of a triangle with side lengths of 6.2 ft, 10.0 ft, and 14.0 ft, and with angle measures of 23°, 39°, and 118° ? (Note: sin,23° ≈ 0.39; sin,39° ≈ 0.63; sin,118° ≈ 0.88)

Paper 3 · ACT September 2024 · Form H11 · Math Test

What are the slope and y-intercept of the line that goes through (0,8) and 1 ,02 in the standard (x,y) coordinate plane? slope y-intercept

Paper 3 · ACT September 2024 · Form H11 · Math Test

What are the solutions of (x + 1)2 + 1 = 0 ? 1 _ _ 2 4 _ _ 3 4 _ _ 3 4 _ _ 3 1 _ _ 6 4 _ _ 3 −1 ± √• 3 ________ 2 −1 ± i√• 3 _________ 2 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-H11 2 2 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-H11 2 2 A small company has 12 employees and 5 job titles. The job title, number of employees with that title, and monthly salary of each employee with that title are given in the table below.

Paper 3 · ACT September 2024 · Form H11 · Math Test

What percent of employees in this company have a monthly salary greater than $5,000 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Rodrigo and Kim are both employees with the company. Rodrigo has a job title of Hardware Engineer and Kim has a different job title. The absolute value of the difference between Rodrigo’s monthly salary and Kim’s monthly salary is greater than $800. Let x represent Kim’s monthly salary, in dollars. Which of the following statements shows all and only the possible values of x ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Next year, the monthly salary of each employee with the title of Software Engineer will be increased to $6,500. No other monthly salaries will be increased or decreased, and the number of employees with each job title will remain the same. Which of the following dollar amounts is closest to the change in the mean of the 12 monthly salaries from before the increase to after the increase? Job title Number of employees Monthly salary of each employee Supervisor 1 $7,500 Software Engineer 5 $6,000 Hardware Engineer 3 $5,500 Accountant 2 $4,500 Assistant 1 $3,000 Use the following information to answer questions 46–48.

Paper 3 · ACT September 2024 · Form H11 · Math Test

In the standard (x,y) coordinate plane, the graph of y = 5x2 is reflected over the x-axis and then translated to the right 3 coordinate units. The graph of which of the following equations is the result of these 2 transformations? + 3 + 3 − 3

Paper 3 · ACT September 2024 · Form H11 · Math Test

What are the real solutions for the equation x4 − 9 = 0 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

To the nearest 0.1 second, how many seconds will it take a car to travel a distance of 100 feet given that it is traveling at 45 miles per hour? (Note: 1 mile = 5,280 feet)

Paper 3 · ACT September 2024 · Form H11 · Math Test

The interior diameter and interior height of a cylindrical container are given in inches in the figure below. Water will be poured into the empty container at a rate of 40π cubic inches per minute. At this rate, in exactly how many minutes will the container be completely filled? (Note: The volume of a cylinder with radius r and height h is πr2 1 _ _ 5 16 10 DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-H11 2 2

Paper 3 · ACT September 2024 · Form H11 · Math Test

For what real value of x is = true?

Paper 3 · ACT September 2024 · Form H11 · Math Test

Craig writes a check for $18. When he records the check in his check register, he accidentally adds $18 to his balance instead of subtracting $18, which causes a discrepancy between what Craig’s check register shows and what it should show. Because of his mistake, Craig’s check register shows:

Paper 3 · ACT September 2024 · Form H11 · Math Test

In the figure shown below, CE ___ is shared by nCDE and rectangle ABCE. The height of nCDE from D to CE ___ is 4 cm, and BC = AE = 15 cm. The area of pentagon ABCDE is 200 square centimeters. Which of the following values is closest to the length, in centimeters, of CE ___ ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

In the standard (x,y) coordinate plane below, a circle with radius 2 coordinate units is centered at the origin. Point A is on the circle and on the terminal side of a 150° angle in standard position. What are the coordinates of A ? 3x 34 ____ _34 + 7 4 A ? B C D E 15 15 1 _ _ 9 150° A O y x 1 −1 1 −1 1 _ _ 2 √• 3 ___ _ 2 1 _ _ 2 √• 3 ___ _ 2 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-H11 2 2 DO YOUR FIGURING HERE. 29 ACT-H11 2 2 Bookcases sold Probability 0 0.06 1 0.12 2 0.18 3 0.34 4 0.22 5 0.08

Paper 3 · ACT September 2024 · Form H11 · Math Test

The line plot below shows the number of miles Bob framed each day for a new sidewalk. After he finished framing, he poured concrete for mile of sidewalk each day. Which of the following is closest to the total number of days it took Bob to pour concrete for the entire sidewalk?

Paper 3 · ACT September 2024 · Form H11 · Math Test

A store that sells office furniture tracks the number of bookcases sold each day for a year and then prepares the data table below. Which of the following is closest to the number of bookcases the store can expect to sell in 100 randomly selected days?

Paper 3 · ACT September 2024 · Form H11 · Math Test

On the interval 0° ≤ x ≤ 180°, what are all the real solutions to (2 cos,x + 1)(cos,x − 1) = 0 ?

Paper 3 · ACT September 2024 · Form H11 · Math Test

The circumference of a circle is 16π feet. What is the perimeter, in feet, of a square inscribed in the circle? 1 _ _ 2 length (mi) 1 7 _ _ 8 3 _ 4 5 _ _ 8 1 _ _ 2 3 _ _ 8 1 _ 4 1 _ _ 8 0 X X X X X X X X X X X END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.