ACT Past Papers with Answers

Paper 16 · ACT April 2021 · Form D05 · Math Test

In the standard (x,y) coordinate plane, point A has coordinates (−7,−5). Point A is translated 7 units to the left and 5 units down, and that image is labeled A′. What are the coordinates of A′ ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Olga worked on a project for 4 hours on each of 6 workdays. On the 7th day of working on the project, Olga worked of the time she had worked each of the previous workdays to complete the project. How many hours did it take Olga to complete the project? 1 _ _ 2 1 _ _ 3 1 _ _ 6 1 _ _ 2 1 _ _ 2 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 16 · ACT April 2021 · Form D05 · Math Test

Given that 5 pounds of coffee makes exactly 210 servings, how many pounds of coffee makes exactly 70 servings?

Paper 16 · ACT April 2021 · Form D05 · Math Test

For RT ↔ shown below, point S is on RT ___ , the length of RS ___ is 10 cm, and the length of ST ___ is 18 cm. What is the distance, in centimeters, between T and the midpoint of RS ___ ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

For all real values of p and r, which of the following expressions is equivalent to p(2 − r) + 8(p − r) ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Fifty shoppers at a pet store were asked if they owned at least 1 cat or at least 1 dog. Data from their answers were recorded below. How many of these shoppers said that they owned NEITHER a cat NOR a dog? 2 _ _ 3 2 _ _ 3 1 _ _ 3 R S T 10 18 Ownership Number of shoppers Cat(s) only 13 Dog(s) only 24 Both cat(s) and dog(s) 07 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-D05 2 2 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-D05 2 2 8. Yvette has 6 pairs of leggings, 2 pairs of shoes, and 6 T-shirts, which all go together well. How many different groupings consisting of 1 of her 6 pairs of leggings, 1 of her 2 pairs of shoes, and 1 of her 6 T-shirts are available for Yvette to wear?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Source question 8. Refer to the source image.

Paper 16 · ACT April 2021 · Form D05 · Math Test

According to the United States Department of Commerce, the approximate area of Rhode Island is

Paper 16 · ACT April 2021 · Form D05 · Math Test

Rectangle A has a length of 64 inches and a width of 48 inches. Rectangle B has a length and a width that are both times the length and the width of Rectangle A. Rectangle C has a length and a width that are both times the length and the width of Rectangle B. What is the perimeter, in inches, of Rectangle C ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The expression _x6 + 3 is equivalent to: 3 _ _ 4 3 _ _ 4 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-D05 2 2 12. A king-sized inflatable rectangular bed when fully inflated will have inside dimensions, in inches, of 78 by 75 by 5. An air pump can pump air into the bed at a rate of 100 cubic inches per second. At that rate, which of the following is closest to the number of seconds it will take to fully inflate the bed?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Source question 12. Refer to the source image.

Paper 16 · ACT April 2021 · Form D05 · Math Test

Jake wants to build a scale model of his house. The house is 48 feet long and 32 feet wide, and it is 30 feet tall at the highest point. Jake wants the model to be 8 inches long. How wide, in inches, should his model be?

Paper 16 · ACT April 2021 · Form D05 · Math Test

You see a circle graph in a newspaper article about student employment, but no percentages are given for the sectors. You want to use the information contained in the graph in a report for your sociology class. You measure the central angle of the sector titled “work during the week” with your protractor, and it measures 144°. According to the circle graph and your measurement, the “work during the week” sector is what percent, to the nearest percent, of the circle graph?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Josiah stands on level ground 15 ft from the base of a cliff. The angle of elevation from where Josiah is standing to the top of the cliff is 50°, as shown below. Which of the following values is closest to the height, in feet, of the cliff? (Note: sin,50° ≈ 0.8; cos,50° ≈ 0.6; tan,50° ≈ 1.2) 1 _ _ 3 1 _ _ 2 4 _ _ 5 50° 15 ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Consider the line 3x − 4y = 6 in the standard (x,y) coordinate plane. For the point on this line with x-coordinate equal to 3, what is the y-coordinate?

Paper 16 · ACT April 2021 · Form D05 · Math Test

What is the solution set to the equation x2 − x = 12 ?

Paper 16 · ACT April 2021 · Form D05 · 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 16 · ACT April 2021 · Form D05 · Math Test

In the standard (x,y) coordinate plane, a line intersects the y-axis at (0,2) and contains the point (8,5). What is the slope of the line? 15 __ _ 4 3 _ _ 4 3 _ _ 4 6 _ _ 5 15 __ _ 4 y x O P(5,11) Q(8,7) R(5,3) 3 _ _ 8 2 _ _ 3 5 _ _ 6 6 _ _ 5 8 _ _ 3 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-D05 2 2

Paper 16 · ACT April 2021 · Form D05 · Math Test

One of the following values for a makes the expression undefined. Which one?

Paper 16 · ACT April 2021 · Form D05 · Math Test

What is the least positive number that has a remainder of 3 when divided by 5 and a remainder of 7 when divided by 9 ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Two warning signs begin flashing at the same time. One sign flashes every 3 seconds, and the other sign flashes every 8 seconds. How many seconds elapse from the moment the 2 signs flash at the same time until they next flash at the same time?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Sets A, B, and C are defined below. A = {1, 2, 3, 4, 5, 6} B = {2, 4, 6} C = {1, 2} 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 ? 1 _ _ 6 2 _ _ 6 4 _ _ 6 2a + 5 _____ _ a2 + 1 5 _ _ 2 5 _ _ 6 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-D05 2 2

Paper 16 · ACT April 2021 · Form D05 · Math Test

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

Paper 16 · ACT April 2021 · Form D05 · Math Test

The circle that has a center of (−3,4) and is tangent to the y-axis is graphed in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of this circle?

Paper 16 · ACT April 2021 · Form D05 · Math Test

An 8-sided game piece with faces numbered from 1 to 8 is rolled twice. What is the probability that an 8 is rolled both times? (Note: Assume that each side has an equally likely chance of being rolled.)

Paper 16 · ACT April 2021 · Form D05 · Math Test

When (3x − 2)4 is expanded and the like terms are combined, what is the coefficient of the x4 term? 5 __ _ 48 1 __ _ 64 13 __ _ 64 y x O (−3,4) 1 __ _ 64 1 __ _ 32 1 _ _ 8 1 _ _ 4 1 _ _ 2 3 __ _ 16 7 __ _ 32 13 __ _ 16 13 __ _ 32 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-D05 2 2

Paper 16 · ACT April 2021 · Form D05 · Math Test

Bo and Tia will balance perfectly on the seesaw shown below if w1 × d1 = w2 × d2, where w1 and d1 are the weight of Bo and his distance from the fulcrum, respectively, and w2 and d2 are similarly defined for Tia. Bo weighs 60 pounds and is sitting 3 feet from the fulcrum. Tia weighs Bo’s weight. What distance, in feet, from the fulcrum must Tia sit in order for Bo and Tia to balance perfectly on the seesaw?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Given that 3(x − 2) = 6x − 3, what is the value of 9x − 2 ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Ally is planting flowers around her square patio. The region she is planting is a 1-foot-wide strip that runs along 3 sides of her 5-foot-by-5-foot patio, as shown below. What is the area, in square feet, of the shaded region where Ally is planting flowers?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Consider 3 circles: A, B, and C. The sum of the radii of Circle A and Circle B is 5 m. The sum of the radii of Circle A and Circle C is 8 m. The sum of the radii of Circle B and Circle C is 7 m. What is the length, in meters, of the radius of Circle C ? 1 _ _ 2 2 _ _ 3 fulcrum Bo Tia 1 _ _ 6 1 _ _ 3 1 _ _ 4 5 __ _ 12 1 _ _ 2 1 1 1 5 5 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-D05 2 2 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-D05 2 2 32. What is the complex conjugate of the number below? 2 + 3i

Paper 16 · ACT April 2021 · Form D05 · Math Test

Source question 32. Refer to the source image.

Paper 16 · ACT April 2021 · Form D05 · Math Test

The function P(x) = x3 − 10x2 + 9x − 90, where x is the number of items sold, models the profit P(x), in dollars, for Company A. The company breaks even when the profit is $0. How many items must Company A sell to break even?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Which of the following statements shows that any subtraction can be written instead as an addition?

Paper 16 · ACT April 2021 · Form D05 · Math Test

What is the value of − 3 − ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Given f(x) = −x − 4 and h(x) = 2x + 3, what is h_f(x)+ ? − 11x − 12 + 11x + 12 1 _ _ 4 5 _ _ 4 7 _ _ 6 √ •• 9 _ _ 4 √ ••• 1 _ _ 8

Paper 16 · ACT April 2021 · Form D05 · Math Test

Rectangle JKLM is shown below. The given side lengths are in feet. What is the cosine of ∠KJL ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The first 3 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 after the 1st element is a square that is 18 inches wider and 18 inches longer than the previous element. What is the area, in square feet, of the 4th element?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The operation ⊗ is defined on the set of positive integers by the rule a ⊗ b = a + b2 . What is the value of (4 ⊗ 3) ⊗ 5 ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The number a is a positive integer greater than 1. The number b is a negative integer. The number ab is: 9 J K M L 7 7 _ _ 9 7 __ _ 16 9 __ _ 16 7 ______ √••• 130 9 ______ √••• 130 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-D05 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-D05 2 2 The table below is part of a delivery truck log used in Aaron’s trucking business. “Mileage out” and “Mileage in” represent the truck’s mileage readings when it leaves the office and when it returns to the office, respectively, giving only the last 3 digits of the cumulative mileage reading. The “Hours away” column gives the amount of time from when the truck leaves the office until it returns to the office. When moving, the truck travels at an average speed of 50 miles per hour and does not travel more than 1,000 miles in any given day. Driver Ben forgot to complete the log for June 18.

Paper 16 · ACT April 2021 · Form D05 · Math Test

According to the mileage reading, what distance, in miles, did the truck travel on June 20 ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The figure shown below represents the route traveled on July 16. Aaron started at the office, drove 75 miles due north to the 1st stop, then 40 miles due east to the 2nd stop, and then 105 miles due south to the last stop. On his return trip, Aaron drove a straight road from the last stop to the office without stopping. Given that Aaron drove at the truck’s average speed, which of the following values is closest to the time, in hours, Aaron drove on the return trip? 40 1st stop 2nd stop last stop office 75 105 3 _ _ 5 5 _ _ 7 7 _ _ 5 5 _ _ 3 Date Mileage out Mileage in Driver Hours away June 17 274 499 Aaron 5.00 June 18 Ben June 19 736 989 Lenny 5.50 June 20 989 245 Aaron 6.00 June 21 245 495 Lenny 5.75 Use the following information to answer questions 41–43.

Paper 16 · ACT April 2021 · Form D05 · Math Test

From June 17 through June 21, the average of the “Hours away” was 5.50 hours. To the nearest 0.01, what is the value of “Hours away” when Ben was driving the truck?

Paper 16 · ACT April 2021 · Form D05 · Math Test

In nABC shown below, the given side lengths are in meters. What is the area, in square meters, of nABC ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The value of log(x), to the nearest 0.1, is given in the table below for 4 different values of x. To the nearest 0.1, what is the value of log(3 × 105,000 ) ? A C B 60° 6 8 x log(x) 0,003 0.5 0,030 1.5 0,300 2.5 3,000 3.5 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-D05 2 2

Paper 16 · ACT April 2021 · Form D05 · Math Test

Susan completed 20 courses in college and her grade point average was 3.15 (A = 4.0 and B = 3.0). If all of her grades were A’s or B’s, and each course grade carried equal weight, what is the number of A’s that Susan received?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The right semicircular cylinder shown below has a height of 5 centimeters and a semicircular base of radius 3 centimeters. What is the volume, in cubic centimeters, of the right semicircular cylinder?

Paper 16 · ACT April 2021 · Form D05 · Math Test

For positive real numbers M and N, log = ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

For what real number b, if any, will the equation a − 2b + ab = 2 be true for both a = 1 and a = −1 ? 3 5 45 __ _ 4 45 __ _ 2 75 __ _ 2 M __ _ N log M ______ log N DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-D05 2 2 DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-D05 2 2 Terri is a dress designer and owns a retail store. She designs, produces, and sells 5 dress styles. These styles and the production cost of 1 dress of each style are shown in the table below.

Paper 16 · ACT April 2021 · Form D05 · Math Test

Terri will hang 1 dress of each style along a rod in the window of her store. How many total possible orders (permutations) of these dresses are there for Terri to consider?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Terri will offer a coupon in the local newspaper for 20% off the regular price of a dress. What is the regular price Terri must set for a Style B dress so that the sale price using the coupon is exactly $15.00 more than the cost of producing 1 Style B dress?

Paper 16 · ACT April 2021 · Form D05 · Math Test

The labor cost of each dress is 40% of the production cost. What is the average labor cost per dress for 1 dress of each of the 5 styles?

Paper 16 · ACT April 2021 · Form D05 · Math Test

It took 0.5 second for an object to travel 60.5 feet. To the nearest 0.01 mile per hour, what was the speed of the object? (Note: 1 mile = 5,280 feet) Style Production cost of 1 dress A $15.00 B $25.00 C $45.00 D $60.00 E $65.00 Use the following information to answer questions 50–52.

Paper 16 · ACT April 2021 · Form D05 · Math Test

Representatives of vectors u, v, p, q, and r are shown in the standard (x,y) coordinate plane below. One of the following vectors is equal to the vector u + v. Which one?

Paper 16 · ACT April 2021 · Form D05 · Math Test

In the standard (x,y) coordinate plane below, a shaded square is shown with vertices at (2,3), (2,4), (3,3), and (3,4). Two lines, y = rx and y = sx, each intersect the shaded square at exactly 1 point. Given that r ≠ s, what is the positive difference of r and s ?

Paper 16 · ACT April 2021 · Form D05 · Math Test

A random number generator that generates an integer 1 through 6 will be used 15,000 times. Each time an integer is generated, the number will be recorded. Which of the following descriptors will most likely characterize the distribution of the 15,000 recorded numbers? x 4 3 2 1 −1 −2 −3 −4 O 4 3 2 1 −1 −2 −3 −4 y v r q u p y x 2 1 4 3 4 1 2 3 O 1 _ _ 6 1 _ _ 3 1 _ _ 2 2 _ _ 3 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-D05 2 2

Paper 16 · ACT April 2021 · Form D05 · Math Test

In the standard (x,y) coordinate plane, define the h−v distance between 2 points to be the length, in coordinate units, of the shortest path between the 2 points using only horizontal and vertical segments. The expression ⎪5 − 2⎪ + ⎪3 − (−4)⎪ gives the h−v distance between which of the following pairs of points?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Let m and s be the mean and standard deviation, respectively, of the ages of children in a certain daycare center. Which of the following gives the mean and standard deviation of the ages of the same children 5 years later? Mean Standard deviation

Paper 16 · ACT April 2021 · Form D05 · Math Test

The ellipse in the standard (x,y) coordinate plane below is the graph of + = 1. Which of the following points are the foci of the ellipse?

Paper 16 · ACT April 2021 · Form D05 · Math Test

Lucinda ran a 3-mile cross-country course in