ACT Past Papers with Answers

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given p = 40 and q = −12, p + q is equal to the product of −4 and what number?

Paper 7 · ACT June 2023 · Form F12 · Math Test

In nABC, ∠A and ∠C are congruent, and the measure of ∠B is 93.5°. What is the measure of ∠A ? 1 _ _ 2 2 _ _ 7 7 __ _ 12 8 __ _ 49 16 __ _ 49 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 7 · ACT June 2023 · Form F12 · Math Test

Ken is paid a regular hourly wage of $15 per hour, before taxes and benefits are deducted, for working up to and including 40 hours in 1 week. For each additional hour he works in a week, Ken is paid 2 times his regular hourly wage. Ken worked 44 hours this week. What was his pay for this week before taxes and benefits were deducted?

Paper 7 · ACT June 2023 · Form F12 · Math Test

What is the length, in inches, of the hypotenuse of a right triangle with a leg that is 7 inches long and a leg that is 4 inches long?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given 3x − 7 = 8x − 16 is true, x = ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

As shown in the figure below, points A, B, and D lie on a line. The measure of angle ABC (m∠ABC) is x°, and m∠CBD is (5x + 4)°. Which of the following equations is true? 23 __ _ 5 23 __ _ 11 23 __ _ 11 9 _ _ 5 9 _ _ 5 A B C D DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-F12 2 2 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-F12 2 2 8. A restaurant currently has an outdoor rectangular dining section measuring 30 feet by 40 feet. The shorter sides will be increased by 10 feet each, resulting in a larger rectangular dining section. What is the positive difference, in square feet, between the areas of the resulting and current dining sections?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Source question 8. Refer to the source image.

Paper 7 · ACT June 2023 · Form F12 · Math Test

What is the value of ⎪−4⎪ − ⎪6 − 29⎪ ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Christopher works in a clothing store. He earns $7.50 per hour, plus 6% of his sales. Which of the following expressions gives Christopher’s earnings, in dollars, when he works x hours and has y dollars in sales?

Paper 7 · ACT June 2023 · Form F12 · Math Test

For RT ↔ shown below, point S is on RT ___ , the length of RS ___ is 8 cm, and the length of ST ___ is 20 cm. What is the distance, in centimeters, between T and the midpoint of RS ___ ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

A conference presenter earned $48.50 for attending a conference and $15.35 per hour for the hours she spent preparing for her presentation. Let y be the amount of money, in dollars, earned by the presenter when she spent x hours preparing for her presentation. Which of the following equations gives the relationship between x and y ? R S T 8 20

Paper 7 · ACT June 2023 · Form F12 · Math Test

Ben and Shawnee are painting a room in the library. They started with 7 gallons of paint. On the first day, Ben used gallon of paint and Shawnee used 3 gallons of paint. How many gallons of paint were left when they completed their first day of painting?

Paper 7 · ACT June 2023 · Form F12 · Math Test

If x = −4, then = ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

In the standard (x,y) coordinate plane, what is the slope of the line represented by the equation y = 4x + 2 ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

The trinomial x2 + 11x + 24 can be factored into 2 binomials with positive integer coefficients. Which of the following binomials is 1 of the factors? 1 _ _ 2 3 _ _ 4 3 _ _ 4 1 _ _ 2 3 _ _ 4 1 _ _ 4 1 _ _ 4 41 __ _ 20 41 __ _ 52 5 __ _ 16 31 __ _ 52 41 __ _ 20 −5 + 9x ______ _ x2 − 9x 1 _ _ 2 1 _ _ 2 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

Which of the following matrices is equal to 43 4? 3 4

Paper 7 · ACT June 2023 · Form F12 · Math Test

Point P(5,−1), which is graphed in the standard (x,y) coordinate plane below, will be reflected across the x-axis. What will be the coordinates of the image of P ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given that x ≤ 2 and x + y ≥ 6, what is the LEAST value that y can have?

Paper 7 · ACT June 2023 · Form F12 · Math Test

A square vegetable garden is built in a rectangular 50-meter-by-40-meter lawn. The lengths of the sides of the garden are 5 meters. What area of the lawn, in square meters, is outside of the vegetable garden? 16 −12 2 4 10 1 −1 _ _ 2 0 −3 _ _ 2 −3 _ _ 4 −8 0 24 −12 y x P(5,−1) O 6 −3 −2 0 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

The distance of the longest jump of each of the participants in a long jump competition is given in the stem-and-leaf plot below. What is the probability that a long jump participant chosen at random from the competition will have jumped at least 75 inches?

Paper 7 · ACT June 2023 · Form F12 · Math Test

In the figure below, DE ↔ i GF ↔ , point A lies on DE ___ , points C and B lie on GF ___ , m∠GCA = 120°, and m∠GBA = 50°. What is m∠CAB ? (Note: The figure is NOT drawn to scale. The degree measure of ∠STU is denoted m∠STU.)

Paper 7 · ACT June 2023 · Form F12 · Math Test

Gabe will use 1 fluid ounce of fertilizer for every 30 square feet of soil. At this rate, how much fertilizer, to the nearest 0.01 gallon, will Gabe use for 0.8 acres of soil? (Note: 1 acre = 43,560 square feet; 1 gallon = 128 fluid ounces) 3 __ _ 13 7 __ _ 13 3 __ _ 10 4 __ _ 10 6 __ _ 10 A B F D E G C Stem Leaf 6 8 9 7 1 4 7 8 9 8 0 1 2 Key: 7 3 = 73 inches DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-F12 2 2 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-F12 2 2 24. On each of 10 tests, Andreas scored 2 points higher than Mischa. When their average test scores on these 10 tests are compared, how many points higher is Andreas’s average than Mischa’s average?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Source question 24. Refer to the source image.

Paper 7 · ACT June 2023 · Form F12 · Math Test

For a certain basketball player, the probability of success on any given free throw attempt is 0.7. What is the least number of free throw attempts for which the result is expected to be at least 18 successes?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Some consecutive terms of a geometric sequence are below. …, 64, 48, 36, 27, … What is the common ratio of this sequence?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Sets A, B, and C are defined below. A = {1, 2, 3, 4, 5, 6, 7, 8, 9} B = {3, 6, 9} C = {2, 4, 6, 8} A number will be randomly selected from set A. What is the probability that the selected number will be an element of set B and an element of set C ? 3 _ _ 4 4 _ _ 3 1 _ _ 9 2 _ _ 9 6 _ _ 9 7 _ _ 9 In a science class, students measured the weights, in pounds, of 23 pumpkins and counted the seeds in each pumpkin. A scatterplot of the data is shown below. To the nearest pound, the average weight of these pumpkins was 10 pounds, and the average number of seeds per pumpkin was 444 seeds. An equation of the regression line of best fit is y = 15x + 294, where x is the weight, in pounds, and y is the number of seeds.

Paper 7 · ACT June 2023 · Form F12 · Math Test

According to the regression line of best fit, what is the predicted number of seeds for a pumpkin weighing 27 pounds?

Paper 7 · ACT June 2023 · Form F12 · Math Test

When one of the pumpkins is removed from the group of 23 pumpkins, the average number of seeds per pumpkin for the remaining 22 pumpkins is 10 fewer than it was for all 23 pumpkins. How many seeds are in the removed pumpkin?

Paper 7 · ACT June 2023 · Form F12 · Math Test

An object that weighs 1 pound on Earth has a mass of

Paper 7 · ACT June 2023 · Form F12 · Math Test

Source question 31. Refer to the source image.

Paper 7 · ACT June 2023 · Form F12 · Math Test

A vertical radio tower stands on level ground. From a point 200 feet along level ground from the base of the tower, the angle of elevation to the top of the tower is 50°. Which of the following values is closest to the height, in feet, of the radio tower? (Note: sin,50° ≈ 0.77, cos,50° ≈ 0.64, tan,50° ≈ 1.20)

Paper 7 · ACT June 2023 · Form F12 · Math Test

In the figure below, the measure of ∠ABC is 87°, the measure of ∠ABE is 68°, and the measure of ∠DBC is 52°. What is the measure of ∠DBE ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Consider the number 630.6 × 10a , where a is an integer. What is scientific notation for this number? n _ _ 2 n _ _ 2 n _ _ 2 A B C D E RunOnline sells shoes and accessories to members and nonmembers of their club. Members are charged a onetime fee of $40 in order to pay the member price. The nonmember and member prices of certain items are given below. All given prices include tax and shipping. Last year, RunOnline had a total of 1,000 customers. Of those customers, 25% were members.

Paper 7 · ACT June 2023 · Form F12 · Math Test

Ed and Sarah both bought p pairs of shoes from RunOnline. Ed is a member and Sarah is a nonmember. Ed’s total cost, including the onetime fee, was equal to Sarah’s total cost. What is p ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

From RunOnline, a nonmember purchased a total of 5 items: 2 hats, 2 water bottles, and 1 workout bag. Which of the following dollar amounts is closest to the mean cost per item purchased by this nonmember?

Paper 7 · ACT June 2023 · Form F12 · Math Test

RunOnline is currently selling 100 water bottles to members each year. It was predicted that for every $0.50 decrease in the member price, RunOnline will sell 10 more water bottles to members each year. RunOnline decides to lower the member price to $10 per water bottle. Based on the prediction and excluding the onetime fee, what will be the total revenue from water bottles sold to members the year following the price reduction? Item Nonmember price Member price Pair of shoes $100 $90 Hat $012 $10 Water bottle $015 $14 Workout bag $027 $20 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-F12 2 2 Use the following information to answer questions 35–37.

Paper 7 · ACT June 2023 · Form F12 · Math Test

Which of the following expressions is equivalent to (2x)6 (10y2 ) ? y2 y2 y2 y2 y2

Paper 7 · ACT June 2023 · Form F12 · Math Test

The vertices of nPQR are given in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of nPQR ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Which of the following expressions is undefined?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given that i is the imaginary unit, which of the following numbers is equal to (4 + 3i)2 ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given that f(x) = x2 − 5x + 6 and g(x) = x2 − 7x − 10, what is g_f(−1)+ ? y x O P(8,10) R(1,2) Q(8,4) 1 _______ _ sin1− π _ _ 22 1 _____ _ cos(0) 1 _____ _ sin(0) DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

For all nonzero values of x and y, which of the following expressions is equal to · ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

In a 73-member choir of only altos and sopranos, there are 19 more altos than sopranos. What is the ratio of altos to sopranos?

Paper 7 · ACT June 2023 · Form F12 · Math Test

A drum contains 40 liters of a 6% potassium bromide solution. This solution is mixed with 80 liters of pure water to produce a new potassium bromide solution. What percent of the new solution is potassium bromide?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Given that sin,θ = , which of the following values is a possible value of cos,θ ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

A certain rectangle in the standard (x,y) coordinate plane has a length of 7 coordinate units and a width of 5 coordinate units. The point (0,0) is in the interior of this rectangle. Two vertices of this rectangle are at (3,2) and (3,−3). What is the x-coordinate of the other 2 vertices? xy2 __ __ 2x4 9x3 y2 _____ 3y 3y3 __ _ _ 2 3y3 __ _ _ 2x 9y3 __ _ _ 5 6x6 __ _ _ y 2 _ _ 3 1 _ _ 9 1 _ _ 3 5 _ _ 9 √• 5 ___ _ 9 √• 5 ___ _ 3 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

Two nonvertical parallel lines in the standard (x,y) coordinate plane have the equations y = m1x + b1 and y = m2x + b2. The 2 lines are not coincident. Which of the following assertions must be true? I. b1 = b2 II. b1 ≠ b2 III. m1 = m2 IV. m1 ≠ m2

Paper 7 · ACT June 2023 · Form F12 · Math Test

The function f(x) when graphed in the standard (x,y) coordinate plane has the features below: I. One of its intercepts is located at (−3,0). II. f(x) increases for all x > 3. III. f(x) is not defined for x = −2. One of the following is the graph of f(x). Which one? x 3 3 6 6 −3 −3 −6 −6 O x 2 2 4 4 −2 −2 −4 −4 O x 2 10 4 20 −2 −10 −4 −20 O y x 4 4 8 8 −8 −4 −4 −8 O x 1 1 2 2 3 4 −2 −3 −1 O DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

In nPQR shown below, r = 8 meters, p = 10 meters, and the measure of ∠Q is 120°. The solution of which of the following equations gives the length q in meters? (Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, = = and c2 = a2 + b2 − 2ab cos,∠C.) = 82 + 102 − 2(8)(10) cos,q = 82 + 102 − 2(8)(10) cos,120°

Paper 7 · ACT June 2023 · Form F12 · Math Test

Consider the 4 expressions below, where m and n are distinct integers greater than 2. , , , If it can be determined, which of the 4 expressions must have the greatest value?

Paper 7 · ACT June 2023 · Form F12 · Math Test

The original price of an item was decreased by 20%. The 1st reduced price was decreased by 20% and then that 2nd reduced price was decreased by 50%. The price that resulted from these 3 decreases was what percent less than the original price? sin ∠C ______ _ c sin ∠B ______ _ b sin ∠A ______ _ a 8 __ _ 10 sin q _____ 120 8 __ _ 10 sin 120° _______ q sin 8° ____ __ 120 sin 10° ____ ___ q m − 1 _____ n m ____ _ n + 1 m __ n m ____ _ n − 1 m _____ n − 1 m _____ n + 1 120° r = 8 P q R p = 10 Q m __ n m − 1 _____ n DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

A particular company produces 500 computers a day. For 20 days the number of defective computers produced each day was recorded, and the results were placed in the table below. Based on this data, on average over a long period of time, what is the expected number of defective computers produced on any given day?

Paper 7 · ACT June 2023 · Form F12 · Math Test

One of the following equations is an equation of the circle graphed in the standard (x,y) coordinate plane below. Which one is it? + y2 = 1 + y2 − 2x = 1 + y2 − 2y = 1 + y2 + 2x = 1 + y2 + 2y = 1

Paper 7 · ACT June 2023 · Form F12 · Math Test

Aman left his bicycle at his friend’s house last night. Today, he decided to walk from home to his friend’s house, visit, and then ride the bicycle back home along the same route he walked. Aman walked at 3 mph, visited for 1.5 hours, and then rode the bicycle at 8 mph. Aman arrived home 3 hours after he started walking. Which of the following values is closest to the number of miles Aman walked?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Points A(8,5) and C(−4,11) lie in the standard (x,y) coordinate plane. Point B lies on AC ___ such that AB:BC = 1:2. What are the coordinates of B ? O x y Number of defective computers Number of days 0 14 1 04 2 01 3 01 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-F12 2 2

Paper 7 · ACT June 2023 · Form F12 · Math Test

The ratio of a to b is 3 to 1, and the ratio of b to c is 6 to 1. What is the value of ?

Paper 7 · ACT June 2023 · Form F12 · Math Test

In the 3 equations below, A, B, and C are positive real numbers. Each equation will be graphed in the standard (x,y) coordinate plane. Which of the following equations will result in lines that have a negative slope? I. Ax + By = C II. Ax − By = C III. −Ax − By = C

Paper 7 · ACT June 2023 · Form F12 · Math Test

The function f(x) = 5 has an inverse function, f −1 (x), defined for all x > 0 by which of the following expressions?

Paper 7 · ACT June 2023 · Form F12 · Math Test

Rectangle P has an area of 24 square inches. Rectangle Q has a perimeter of 24 inches. The ratio of the area of Rectangle P to the area of Rectangle Q is 2:3. Which of the quantities below can be determined from just the given information? I. The perimeter of Rectangle P II. The area of Rectangle Q III. The ratio of the perimeter of Rectangle P to the perimeter of Rectangle Q 2a + 3b _____ _ _ _ 4b + 3c 1 _ _ 3 8 _ _ 9 9 __ _ 22 24 __ _ 7 2 ____ __ log5 x x _ _ 2 1 _____ ___ (log5 x)2 1 _ _ 2 DO YOUR FIGURING HERE. 29 ACT-F12 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.