ACT Past Papers with Answers

Paper 4 · ACT June 2024 · Form G20 · Math Test

Because of rising expenses, a motel manager raises the room rate of $80.00 by 20% to get the new room rate for the motel. What is the new room rate?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Which of the following matrices is equal to 53 4?

Paper 4 · ACT June 2024 · Form G20 · Math Test

A retail sales associate’s daily commission during 1 week was $30 on Monday and Tuesday and $60 on Wednesday, Thursday, and Friday. What was the associate’s average daily commission for these 5 days? 1 3 2 4 5 3 2 4 5 3 2 20 1 15 10 4 6 8 7 9 5 15 10 20 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

What value of x makes the equation below true? −x + 6 = 3x − 10

Paper 4 · ACT June 2024 · Form G20 · Math Test

Fred’s cell phone service costs $25.00 per month and includes 100 minutes. For any minutes used after the 100 minutes, he is charged $0.10 per minute. Fred has budgeted $33.00 per month for his cell phone service. What is the maximum number of minutes Fred could use in 1 month without exceeding his budget?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The function f(c) = c + 32 gives the temperature, f(c) degrees Fahrenheit, that corresponds to c degrees Celsius. To the nearest 0.1°F, what Fahrenheit temperature corresponds to 13.0°C ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

What number, when added to , gives a sum that is equal to the sum of and ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

For RT ↔ shown below, point S is on RT ___ , the length of RS ___ is 6 cm, and the length of ST ___ is 20 cm. What is the distance, in centimeters, between T and the midpoint of RS ___ ? 9 _ _ 5 1 _ _ 3 1 _ _ 6 1 _ _ 4 1 __ _ 12 1 _ _ 9 1 _ _ 7 1 _ _ 5 3 _ _ 4 R S T 6 20 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

The graph below shows the average daily consumption, in thousands of barrels, of oil for Uzbekistan,for the years 2003 through 2013. From what year to the following year did the average daily consumption decrease the most?

Paper 4 · ACT June 2024 · Form G20 · Math Test

A rectangular field that measures 300 meters by 175 meters is to be completely fenced along its perimeter. Given that fencing sells for $2.05 per meter, what will the fencing for the field cost?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Mary throws a stone from the edge of a cliff. While the stone is in flight, the equation h = 300 − 30t − 16t2 gives the height above the ground, h feet, of the stone at any given time t seconds after being thrown. What is the height, in feet, of the stone exactly 3 seconds after Mary throws the stone?

Paper 4 · ACT June 2024 · Form G20 · Math Test

What is the median of the data set below? 4, 8, 14, 4, 20 year 13 12 11 10 09 08 07 06 05 04 03 160 140 120 100 80 60 40 20 0 average daily consumption (thousands of barrels) DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

Rafael has made a scale model of City Park, shown below, in which 3 lengths are given in inches. On the model, BC ___ represents an actual length of 90 feet in the park. On the model, DE ___ represents what actual length, in feet, in the park?

Paper 4 · ACT June 2024 · Form G20 · Math Test

In the figure below, point C is on AD ___ , and 2 angle measures of nABC are given. What is the measure of ∠BCD ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The number a is positive and even. The number b is negative and odd. The number a − b is:

Paper 4 · ACT June 2024 · Form G20 · Math Test

The isosceles triangle shown below has congruent legs that are each 10 centimeters long. The perimeter of the triangle is 32 centimeters. What is the length, in centimeters, of the altitude that splits the triangle into 2 congruent right triangles?

Paper 4 · ACT June 2024 · Form G20 · Math Test

For all nonzero values of a, the expression is equal to: a2 a4 ___ _ a6 3 4 5 C A B F G E D 65° 30° ? A B C D ? 10 10 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

A 12-foot taut wire has one end attached to the ground and the other end attached to a vertical pole, as shown below. The point of contact of the wire and the pole is 8 feet above the ground. What angle does the wire make with the level ground? 1 2 1 2 1 2 1 2 1 2

Paper 4 · ACT June 2024 · Form G20 · Math Test

Marcy is making toys to sell at the local school fair. Each toy costs Marcy $2.25 to make, and she will sell them for $4.05 each. What is the minimum number of toys she can make and sell to earn a profit of at least $81.00 ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Given functions f(x) = 4x + 3 and g(x) = x2 − 2, what is the value of f_g(−3)+ ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Let z = 4 + 5i and w = 3 + 7i, where i is the imaginary unit. What is the value of 2z + w ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

If x2 − 5x − 6 = 0, what is the sum of the 2 possible values of x ? 12 ft 8 ft ? 8 __ _ 12 8 __ _ 12 8 __ _ 12 8 __ _ 12 8 __ _ 12 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

Kate is going to buy meat (beef and chicken) for a party. Beef costs $3.00 per pound, chicken costs $2.00 per pound, and Kate has a budget of $90.00 to spend on meat for the party. The shaded region in one of the following graphs represents all and only the possible combinations of beef and chicken Kate can buy while staying within her budget. Which one? (Note: Do not consider tax.)

Paper 4 · ACT June 2024 · Form G20 · Math Test

Each student in a particular classroom was given a string that was 72 inches long. Each student cut his or her string into pieces of equal length. Which of the following CANNOT be the length, in inches, of any student’s pieces? x y 80 60 40 20 0 80 60 40 20 0 chicken (pounds) beef (pounds) x y 80 60 40 20 0 80 60 40 20 0 chicken (pounds) beef (pounds) x y 80 60 40 20 0 80 60 40 20 0 chicken (pounds) beef (pounds) x y 80 60 40 20 0 80 60 40 20 0 chicken (pounds) beef (pounds) x y 80 60 40 20 0 80 60 40 20 0 chicken (pounds) beef (pounds) 1 __ _ 16 1 _ _ 2 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

The graph of the function f(x) = −9(x + 1)2 + 81 has its vertex at point (−1,81) and intersects the x-axis at points (−4,0) and (a,0). What is the value of a ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

What fraction of 4 is 2 ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

What is the least positive number that has a remainder of 4 when divided by 6 and a remainder of 5 when divided by 7 ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Joe, Tom, and Alexis are planning to participate in a 3-person relay for charity. The plan is for Joe to jog his 3 miles at 4 miles per hour (mph), Tom to jog his 3 miles at 5 mph, and then Alexis to jog her 3 miles at 6 mph. In how many hours and minutes does this 3-person team plan to complete the 9-mile relay?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Let θ be an acute angle of a right triangle. Given sin,θ = and tan,θ = , cos,θ = ? 1 _ _ 8 1 _ _ 4 1 _ _ 4 1 _ _ 2 1 _ _ 8 1 _ _ 2 a _ _ c a _ _ b b _ _ a b _ _ c c _ _ a c _ _ b 5 __ _ 81 81 __ _ 5 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

The number line shown below is marked in equal intervals. Two fractions are indicated on the number line. One of the following fractions corresponds to the point marked P. Which one?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The graph in the standard (x,y) coordinate plane below has 5 lines of symmetry that all intersect at the origin. What is the smallest positive clockwise rotation about the origin that can be applied to this graph with the result being this graph?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The following linear functions are defined either with an equation, a graph, or a table of values. Which of the following functions has the greatest slope? 6 _ _ 7 7 _ _ 8 8 _ _ 9 4 _ _ 4 9 _ _ 8 y x 1 _ _ 4 5 _ _ 4 P x h(x) 00 06 03 00 11 −16 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-G20 2 2 x j(x) 0 −6 0 04 05 14 10 O x k(x) (−1,1) (0,5) www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · 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 4 · ACT June 2024 · Form G20 · Math Test

The function y = f(x) = is graphed in the standard (x,y) coordinate plane below. One of the following statements is FALSE. Which one? y = 0.

Paper 4 · ACT June 2024 · Form G20 · Math Test

All students in a high school responded either “Yes” or “No” to the question “Are you studying enough?” The table below gives the number of students in each grade who responded. Two numbers in the table are represented by x and y. The probability that a randomly selected student from this high school is in 11th grade given that the student responded “No” is . One of the following is the value of x. Which one? y x O P(8,12) Q(10,8) R(8,2) 5 _ _ x y x 2 10 4 20 −2 −10 −4 −20 O y = 5 _ _ x 75 ___ _ 267 9th 10th 11th 12th Yes 85 92 79 102 No 65 x y 056 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com Josie has decided to make a new lampshade for her bedroom lamp. She will order materials from a website that offers 4 different print designs and 4 different color schemes that can be used with each design. The top and bottom edges of Josie’s current lampshade are parallel circles with diameters of length 6 inches and 8 inches, as pictured below. The centers of the 2 circles are directly above and below one another.

Paper 4 · ACT June 2024 · Form G20 · Math Test

What is the ratio of the area of the circle modeled by the top edge of the lampshade to the area of the circle modeled by the bottom edge of the lampshade?

Paper 4 · ACT June 2024 · Form G20 · Math Test

In order to design her lampshade, Josie must select 1 print design and 1 color scheme from the website. She will also choose 1 fabric: burlap, linen, or silk. How many different possible lampshade designs does she have to choose from?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Which of the following 2-dimensional shapes, when rotated about its vertical symmetry line, will form the shape of this lampshade?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The points K, L, M, and N are on a number line in that order such that KM = 15 units, LN = 26 units, and KN = 32 units. The coordinate of L is 0, and the coordinate of K is negative. What is the coordinate of M ? 6 8 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-G20 2 2 Use the following information to answer questions 37–39. www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

The figure below shows 3 rectangles where a, b, c, d, e, and f are side lengths measured in meters. Which of the following expressions must give the area of the shaded region, in square meters?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Rectangular pyramids A (left) and B (right) are shown below with dimensions given in feet. Let a and b be the volumes of A and B, respectively. Which of the following equations is true?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Maya’s digital music library has a total of 249 songs. Her library has 64 songs that are remixes and 85 hip-hop songs. Of the hip-hop songs in her library, 25 are remixes. How many songs in her library are NEITHER remixes NOR hip-hop songs? e f b a d c A 12 x 12 __ _ x 12 __ _ x 12 x B 1 _ _ 3 2 _ _ 3 3 _ _ 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

Which of the following expressions is equivalent to x(x − 2) + (2 − x) ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

For all a ≠ 0 and b ≠ 0, the expression simplifies to:

Paper 4 · ACT June 2024 · Form G20 · Math Test

In the ordered pairs given below, the first number is time, in hours, and the second number is distance, in miles, traveled in that time. A(0.25,1), B(0.2,0.5), C(2,7), D(0.5,8), E(0.75,9) Which of these ordered pairs represent speeds less than 4 miles per hour?

Paper 4 · ACT June 2024 · Form G20 · Math Test

A square dartboard is red and white, as shown below. Each 4-inch-long side of the red square is parallel to 2 sides of the white square and is 3 inches from the closest side of the white square. A dart will be thrown randomly and will land on the dartboard. What is the probability that the dart will land on the red square? 2 _ _ a + 2 _ _ b ______ 3 __ _ ab 4 _ _ 3 2(a + b) _______ 3 4ab _______ 3(a + b) 3 white red 4 3 3 3 1 __ _ 10 1 _ _ 7 2 _ _ 5 4 __ _ 25 16 __ _ 49 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

In nPQR shown below, the measure of ∠P is 40°, PR = 110 meters, and the measure of ∠R is 80°. Which of the following expressions gives QR, in meters? (Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, = = .)

Paper 4 · ACT June 2024 · Form G20 · Math Test

log5 25 = ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

Let A be the greatest whole number that is less than √••• • 420. Let B be the least whole number that is greater than √•• 56. What is A − B ?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The product of 2 real numbers is a nonzero rational number. Which of the following statements CANNOT be true? 80° 40° 110 R ? Q P sin ∠C ______ _ c sin ∠B ______ _ b sin ∠A ______ _ a 110 sin 40° _________ _ sin 60° 110 sin 40° _________ _ sin 80° 110 sin 60° _________ _ sin 40° 110 sin 80° _________ _ sin 40° 110 sin 80° _________ _ sin 60° 1 _ _ 5 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com A pump is used to move water in and out of a tank. The pump is turned on at t = 0 seconds when there are 20 gallons in the tank. The function V(t) represents the volume, in gallons, of water in the tank t seconds after the pump is turned on. Shown below is the graph of V(t), which is a periodic function with a period of 9 seconds. The 1st period of V(t) is shown as a solid line, and the rest is shown as dashed. The pump remains on for 1 hour.

Paper 4 · ACT June 2024 · Form G20 · Math Test

How many periods does the pump complete in 1 hour?

Paper 4 · ACT June 2024 · Form G20 · Math Test

One of the following values is the volume, in gallons, of water in the tank after 51 seconds. Which one?

Paper 4 · ACT June 2024 · Form G20 · Math Test

A 2nd tank has 30 gallons in it when its pump is turned on at t = 0 seconds. In terms of gallons of water moved over time, this pump behaves the same as the other pump. One of the following functions represents the volume, in gallons, of water in the 2nd tank t seconds after the pump is turned on. Which one? V(t) t 2 1 3 4 6 5 12 11 10 9 8 7 60 50 40 30 20 10 O volume (gallons) time (seconds) V(t) DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-G20 2 2 Use the following information to answer questions 52–54. www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

To estimate the number of bass in a small lake, a biology class caught and tagged 32 bass from the lake. The next day the class caught 60 bass from the lake and found that 9 of those bass were tagged. Assuming the 60 bass caught are representative of the entire population of bass in the lake, which of the following is closest to the number of bass in the entire population?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The graphs of y2 = x + 8 and y = 3x − 3 are shown in the standard (x,y) coordinate plane below. The 2 graphs intersect at points A and B. The solution of which of the following equations gives the x-coordinate of point A ? − 9 = x + 8

Paper 4 · ACT June 2024 · Form G20 · Math Test

The first 3 elements of a pattern are shown below. Each element is composed of small squares that are 8 mm wide and 8 mm long. Each element after the 1st element is a square that is 8 mm wider and 8 mm longer than the previous element. What is the area, in square centimeters, of the 4th element? x O y B A DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-G20 2 2 www.actexam.net www.crackab.com

Paper 4 · ACT June 2024 · Form G20 · Math Test

A shirt will be randomly selected from a display of 23 shirts. The probability that the selected shirt will be long-sleeved is . The probability that the selected shirt will be white is . The probability that the selected shirt will be long-sleeved and white is . What is the probability that the selected shirt will be long-sleeved or white or both?

Paper 4 · ACT June 2024 · Form G20 · Math Test

The ellipse in the standard (x,y) coordinate plane below is centered at the origin. The endpoints of the major and minor axes of the ellipse are labeled. Which of the following equations determines this ellipse? + (y − 5)2 = 1 + (y + 5)2 = 1

Paper 4 · ACT June 2024 · Form G20 · Math Test

Given a − b > a + b for real numbers a and b, which of the inequalities below must be true? I. a > 0 II. b < 0 III. b < a 13 __ _ 23 8 __ _ 23 3 __ _ 23 7 __ _ 23 8 __ _ 23 18 __ _ 23 22 __ _ 23 24 __ _ 23 y x O (8,0) (0,5) (0,−5) (−8,0) y2 __ _ 5 x2 __ _ 8 y2 __ _ 10 x2 __ _ 16 y2 __ _ 25 x2 __ _ 64 DO YOUR FIGURING HERE. 29 ACT-G20 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. www.actexam.net www.crackab.com