ACT Past Papers with Answers

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A function, f, is defined by f(x,y) = 3x2 − 2y. What is the value of f(2,3) ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

What is the value of x when 9 − 11x = 13 − 9x is true?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A company reimburses its employees for use of a personal vehicle for company travel at the rate of $10.00 per day plus $0.445 per mile. Jorge, an employee of the company, traveled exactly 120 miles on Monday and exactly 100 miles on Tuesday using his personal vehicle for company travel. For these 2 days, what was the amount of Jorge’s reimbursement?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Given that a n b = a2 + b − , what is the value of a n b when a = 5 and b = ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Before opening her lemonade stand, Haley purchased lemonade mix for $2.30 and a package of cups for $1.50. Haley sells each cup of lemonade for $0.50. Which of the following expressions gives Haley’s total profit, in dollars, from selling x cups of lemonade?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

In nABC, the measure of ∠B is 90°, and the measure of ∠A is 4 times the measure of ∠C. What is the measure of ∠C ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The Sheffield High School girls’ softball team currently has a record of 11 wins, 8 losses, and 0 ties. What is the least number of its remaining 14 games the team must win to finish the season winning more than 50% of all the team’s games?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A line in the standard (x,y) coordinate plane passes through the point (3,4). The slope of the line: a _ _ b 1 _ _ 2 1 _ _ 2 1 _ _ 4 1 _ _ 2 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 10. The probability that a certain basketball player will make any given free throw is 0.8. Based on this probability, how many free throws should this player expect to have to attempt in order to make 20 free throws?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Source question 10. Refer to the source image.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Jerrica drives to and from school once per day in a car that travels 20 miles on 1 gallon of gas. A trip from Jerrica’s house to school and back is 6 miles. Gas costs $5 per gallon. Suppose Jerrica rides her bike to and from school for 10 school days. How much money will Jerrica save on gas by not driving to and from school those days?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

If x > 0 and 2x2 + 5x = 3, what is the value of x ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A 5-foot awning extends 2 feet horizontally over the entrance to the vertical building shown below. Which of the following expressions has a value equal to the measure of the angle θ between the building and the awning? 1 2 1 2 1 2 1 2 1 2 1 _ _ 2 3 _ _ 2 5 _ _ 2 5 θ 2 2 _ _ 5 2 ____ _ √•• 21 2 _ _ 5 √•• 21 ____ _ 2 2 _ _ 5 The results for the 200-meter dash at the Shamrock High School (SHS) track meet are shown in the table below. The SHS track is unique in that it is circular and has an outer diameter of 240 meters. The stadium has a capacity of 5,000 people.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

What is the mean, in seconds, of the times listed in the table for the 200-meter dash?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Each ticket for the track meet had a price of $8. Tickets were sold for exactly 85% of the stadium’s capacity. How many dollars did SHS collect through ticket sales for this meet?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The circular region containing the track and the infield (the grassy region enclosed by the track) is divided into sectors that each have a central angle of 60°. Each sector is a different color. What is the area, in square meters, of each sector? 200-meter dash Name Time (seconds) Anthony 21.20 Burke 22.01 Cory 21.33 Kate 22.13 Lindsey 21.20 Nathan 21.50 Rebecca 21.48 Sam 22.19 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 Use the following information to answer questions 14–16.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The solution set of the system of inequalities below includes which of the following (x,y) pairs? x > y x + y > 3

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The area of the trapezoid shown below is 20 square feet, the height is 5 feet, and the length of one base is 2 feet. What is b, the length of the other base, in feet?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Let (3x − 1)(2x − 5) = ax2 + bx + c. What is the value of a + b + c ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

For a ≠ 0 and any real number n, the expression is equivalent to which of the following? b 5 2 a2n + 1 _____ an DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

For what positive value of a is it true that _√•• 8a+_√•• 2a+ = 16 ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A basket contains 3 red apples, 4 green apples, and 2 yellow apples. An apple is drawn at random, eaten, and then another apple is randomly drawn. If the first apple is red, what is the probability the second apple is yellow?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Which of the following numbers is irrational?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The expression 7[3 − 2(x − 4)] is equivalent to: 1 _ _ 2 1 __ _ 12 1 _ _ 8 1 _ _ 4 2 _ _ 9 5 __ _ 81 1 _ _ 3 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Rate of change is defined to be the vertical change between any 2 points divided by the horizontal change between the same 2 points. A function containing the point (0,1) has a constant rate of change equal to . The function is shown in one of the standard (x,y) coordinate plane graphs below. Which one?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

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

Paper 1 · ACT February 2025 · Form Z14 · Math Test

One neon sign flashes every 4 seconds, and another neon sign flashes every 6 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time? 3 _ _ 2 x O (0,1) y x O (0,1) y x O (0,1) (0,1) y x O y x O (0,1) 3 _ _ 8 7 __ _ 16 13 __ _ 8 13 __ _ 16 5 __ _ 24 1 __ _ 32 13 __ _ 32 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 Jerry is building a rectangular patio against one side of his house. The top surface of the patio, along with its width and diagonal, is shown in the figure below. To build the patio, he will first dig a rectangular hole to a uniform depth of 8 inches. He will then fill the hole with gravel to a uniform depth of 3 inches. He will purchase gravel from his local rock quarry for $54 per cubic yard (1 cubic yard = 27 cubic feet). Next, he will pour concrete on top of the gravel to obtain a smooth surface for the patio. Finally, he will frame and build a rectangular concrete step with the dimensions shown below.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Jerry will purchase 42 cubic feet of gravel for his patio. The local rock quarry will sell gravel in the exact volume needed by the customer. What is the cost, in dollars, to purchase the gravel from the local rock quarry?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

What is the area, in square feet, of the top surface of Jerry’s patio?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Jerry will use bags of concrete mix to make the step. Each bag makes 0.4 cubic feet of concrete. To the nearest 0.1 bag, how many bags of concrete mix will he need for the step? 25 ft 7 ft patio step 3 ft 1 ft

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A carpenter needs a board 35 inches long and another board 27 inches long. Both pieces are to be cut from a single board 72 inches long. Together, the 2 cuts subtract a total of inch. What length of board is left over, in inches?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Given matrices A and B such that A = 3 4 and B − A = 3 4, what is matrix B ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A Chinese language proficiency test was given to 60 university students. The students’ scores were recorded as integers. The table below shows the frequency and cumulative frequency of test scores in certain ranges. To be classified as proficient, a student must score 70 or higher on the test. What is the ratio of the number of students who were classified as proficient to the number who were NOT classified as proficient? 5 _ _ 8 1 _ _ 2 1 _ _ 8 1 _ _ 4 3 _ _ 4 13 __ _ 16 27 __ _ 80 3 _ _ 4 4 −3 2 0 −7 −1 4 −4 7 −1 6 1 0 1 −5 1 −13 −2 −8 −7 9 1 −1 0 8 −7 −1 0 0 −7 5 −1 13 2 9 1 13 2 Range of scores Frequency Cumulative frequency 50−59 60−69 70−79 80−89 90−100 06 16 16 12 10 06 22 38 50 60 9 −1 8 7 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A group of 4 friends decide to go to a movie. After buying their tickets, they find 5 empty chairs in the theater. How many different seating arrangements are possible if the 4 friends sit, at most 1 person per chair, in these 5 chairs?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Carina rolls 2 cubes. Each has the whole numbers from 1 through 6 on its faces, 1 per face. The faces of each cube are equally likely to land up. What is the probability that the sum of the numbers on the faces landing up is 3 or more?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

In the figure shown below, AB ___ i DE ___ , C is the intersection of AE ___ and BD ___ , ∠D is a right angle, and the given side lengths are in inches. What is the length of AC ___ , in inches?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The domain of the real-valued function f(x) = is the set of all x-values that satisfy: 1 __ _ 36 1 __ _ 18 1 __ _ 11 10 __ _ 11 35 __ _ 36 C D 3 4 ? 5 A B E 15 __ _ 4 25 __ _ 4 25 __ _ 3 2 _______ √•••• x − 3 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-Z14 2 2 39. For f(x) = 2x + 3 and g(x) = x2 − 4, which of the following expressions represents f_g(x)+ ? − 1 − 5 − 8 + 5 + 12x + 5

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Source question 39. Refer to the source image.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

For all y > 0, which of the following is a simplified form of − ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A wheel with a radius of 1 centimeter rolls without slipping along the ground. After exactly 2 revolutions, how many centimeters has the wheel traveled along the ground?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

For Cameron’s birthday party, his mom bought 4 pizzas, each the same size but with a different topping. She cut those pizzas into 6, 7, 8, and 9 equal pieces, respectively, as shown below, giving 5 slices to each of the 6 boys attending. If each boy ate all 5 of his slices and had at least 3 different kinds of pizza, which of the following expressions gives the largest amount of pizza that 1 boy could have eaten (expressed in fractions of a pizza)? 2(y − 1) _______ 4y + 4 y − 1 _____ y + 1 1 _ _ 2 1 _ _ 2 y − 1 _______ 3(y + 1) y − 1 _______ 2(y + 1) 3 _ _ 9 1 _ _ 8 1 _ _ 7 2 _ _ 9 1 _ _ 8 1 _ _ 7 1 _ _ 6 1 _ _ 9 1 _ _ 8 1 _ _ 7 2 _ _ 6 1 _ _ 8 2 _ _ 7 2 _ _ 6 1 _ _ 8 1 _ _ 7 3 _ _ 6

Paper 1 · ACT February 2025 · Form Z14 · Math Test

When x, y, and z are positive integers, which of the following relationships will assure that the product x0 y1 z−1 will have a value greater than 1 ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Sumiko, who works at a restaurant, recorded the amounts of her customers’ checks and the corresponding amounts of her tips, both in dollars, for 25 consecutive customers she served. She plotted the data in the standard (x,y) coordinate plane below with the amount of the check on the x-axis and the amount of the tip on the y-axis. Sumiko then performed a linear regression on the data, finding the regression equation to be y = 0.16x − 0.44 with a correlation coefficient, r, of 0.81. She also graphed the regression line. From her statistical analysis, Sumiko can correctly conclude that every $1 increase in the total amount of the check will result in approximately:

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The cost of a certain type of carpet is $10 per square yard. What would be the cost of carpet of this type to cover a rectangular floor 12 feet by 18 feet ? y x O 10 20 30 40 50 5 10 amount of check (in dollars) amount of tip (in dollars) DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The function f(x) = x5 is defined for all real numbers x. Which of the following expressions represents f −1 (x) ? −

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A car accelerates at a constant rate from 0 miles per hour to 60 miles per hour in 15 seconds and averages 30 miles per hour over the 15-second period. The car maintains the constant speed of 60 miles per hour for the next 15 seconds. What fraction of a mile has the car traveled in these 30 seconds?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

If a − b = 5 and c = 7a − 9 − 7b, then c = ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

If sin,θ = and tan,θ = − , then cos,θ = ? 1 _ _ 5 1 _ _ 5 x _ _ 5 x _ _ 5 1 _ _ 8 1 _ _ 4 3 _ _ 8 1 _ _ 2 3 _ _ 4 √• 3 ___ _ 3 1 _ _ 2 2√• 3 ____ _ 3 √• 3 ___ _ 2 √• 3 ___ _ 6 1 _ _ 2 √• 3 ___ _ 2 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The graph in the standard (x,y) coordinate plane of y = a(x − b)2 , where ⎪a⎪ ≠ ⎪b⎪, is reflected across the x-axis. Which of the following is an equation of the reflection?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

For i2 = −1, = ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

All 30 of Mr. Gray’s algebra students took the midterm test, and Mr. Gray computed the average test score for the class. Then, one of Mr. Gray’s students, Mandy, found that her test should have been scored 5 points higher than it was originally scored. All other students’ scores were correct. After correcting the scoring error on Mandy’s test, the average test score for the class increased by how many points?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

What is the value of z in the solution to the system of equations below? 2x + 0y − z = 00 0x − 3y + z = 18 0x + 0y 000= 01 2 + 3i _____ _ i 1 __ _ 30 1 _ _ 6 1 _ _ 5 1 _ _ 2 DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

What is the maximum possible value of for x in the set 51, , 06and y in the set 5 , , 6?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

In the figure below, ABEH is a square. Points C and D are on BE ___ such that BC ___ , CD ___ , and DE ___ all have the same length. Points F and G are on EH ___ such that EF ___ , FG ___ , and GH ___ _ all have the same length. How many of the triangles numbered 1−5 (nABC, nACD, nADE, nAEF, and nAFG, respectively) have the same area as nAGH ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The midpoints of the sides of square ABCD are the vertices of square KLMN, shown below. The side length of square ABCD is 14 meters. What is the area, in square meters, of the shaded portion?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

Given sin,30° = , what is the area, in square meters, of the triangle shown below? 5 4 3 2 1 H G F E D C B A A L K N D B M C 1 _ _ 2 30° 6 m 4 m 1 _ _ 2 1 _ _ 4 1 _ _ 8 1 _ _ 2 x __ _ y2 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-Z14 2 2

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The graph of which of the equations below is a hyperbola with the same asymptotes as the graph of − = 1 ?

Paper 1 · ACT February 2025 · Form Z14 · Math Test

The graph below shows the distribution of a data set. The variables a−h represent 8 consecutive positive integers in order from least to greatest. The frequencies of a, f, g, and h are equal; the frequency of e is 2 times the frequency of a; the frequency of b and of d is 3 times the frequency of a; and the frequency of c is 4 times the frequency of a. Which of the following statements about the mean, median, and mode of the data set is true? is less than the mean. is less than the mode. less than the median. equal to the median. is equal to the mode.

Paper 1 · ACT February 2025 · Form Z14 · Math Test

A solid rectangular block of steel weighs w pounds. Which of the following expressions gives the weight, in pounds, of a larger solid rectangular block that is made of the same kind of steel and has length, width, and height 4 times those of the smaller block? (Note: Assume that weight is proportional to volume.) y2 __ _ 4 y2 __ _ 9 y2 __ _ 9 y2 __ _ 9 x2 __ _ 9 x2 __ _ 4 x2 __ _ 4 x2 __ _ 4 x2 __ _ 9 y2 __ _ 4 variable frequency a b c d e f g h x2 __ _ 9 y2 __ _ 4 DO YOUR FIGURING HERE. 29 ACT-Z14 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.