ACT Past Papers with Answers

Paper 8 · ACT April 2023 · Form F11 · Math Test

In the figure below, parallel lines m and n are cut by transversal line t, and 2 angle measures are given. What is the value of x ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

The 1st term in the geometric sequence below is −9. If it can be determined, what is the 6th term? −9, 18, −36, 72, −144, … 12 __ _ 5 12 __ _ 5 (2x + 5)° m n t 135° DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 8 · ACT April 2023 · Form F11 · Math Test

The word average indicates arithmetic mean.

Paper 8 · ACT April 2023 · Form F11 · Math Test

How many minutes would it take a ship to travel 100 miles at a constant speed of 40 miles per hour?

Paper 8 · ACT April 2023 · Form F11 · Math Test

A fan has 3 evenly spaced blades of negligible thickness, as shown below. What is the measure of an angle between 2 blades?

Paper 8 · ACT April 2023 · Form F11 · Math Test

⎪6 − 5⎪ − ⎪3 − 7⎪ = ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Which of the following values is the solution to the equation below? x + = 8 1 __ _ 30 1 __ _ 11 1 _ _ 6 1 _ _ 5 1 _ _ 4 ? 1 _ _ 4 1 _ _ 4 2 _ _ 3 3 _ _ 8 3 _ _ 4 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-F11 2 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

What is the volume, in cubic inches, of a sphere with a diameter of 10 inches? (Note: The volume of a sphere, V, with radius r is given by the formula V = πr3 .)

Paper 8 · ACT April 2023 · Form F11 · Math Test

A rhombus is a quadrilateral with all 4 sides of equal length. Three vertices of a rhombus are graphed in the standard (x,y) coordinate plane below. One of the following points is the location of the 4th vertex of this rhombus. Which one?

Paper 8 · ACT April 2023 · Form F11 · Math Test

For an architecture class project, Lizette is making a scale drawing of Mr. Patel’s classroom, which is rectangular with a width of 25 feet and a length of 30 feet. Lizette draws a 3-inch line segment to represent the width of the rectangle. How long a line segment, in inches, should Lizette draw to represent the length of the rectangle? 4 _ _ 3 60π ___ _ 3 100π _____ 3 400π _____ 3 500π _____ 3 4,000π _____ __ 3 y O x 2 4 6 −6 −4 −2 6 4 2 −2 −4 −6 1 _ _ 2 3 _ _ 5 7 __ _ 12 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-F11 2 2 www.actexam.net

Paper 8 · ACT April 2023 · Form F11 · Math Test

In the standard (x,y) coordinate plane, a line intersects the y-axis at (0,3) and contains the point (9,4). What is the slope of the line?

Paper 8 · ACT April 2023 · Form F11 · Math Test

The equations of four (x,y) relations are given below. I. 5y = (x − 1)(x − 3)(x + 3) II. (x − 1)2 + (y − 1)2 = 9 III. = √"""" " x + 4 − 1 IV. y + 5 = 1 2 x The graph in the standard (x,y) coordinate plane of each of these relations is shown below. Of these relations, which are functions?

Paper 8 · ACT April 2023 · Form F11 · Math Test

If (x + k)2 = x2 + 88x + k2 , then k = ? 1 _ _ 9 3 _ _ 5 2 _ _ 3 3 _ _ 2 y _ _ 4 2 _ _ 5 y x O y x O I II IV III y x O y x O DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-F11 2 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

Which of the following equations represents the axis of symmetry of this parabola?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Each side of square ABCD has a length of 20 ft. A certain rectangle whose area is equal to the area of ABCD has a width of 10 ft. What is the length, in feet, of the rectangle?

Paper 8 · ACT April 2023 · Form F11 · Math Test

In Amul’s yard, there was no snow on the ground at 10:15 a.m. From 10:15 a.m. until 3:30 p.m., it snowed at an average rate of inch per hour. How many inches of snow were on the ground at 3:30 p.m. ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

On each of 8 tests, Gustav scored 2 points higher than Russ. When their average test scores on these 8 tests are compared, how many points higher is Gustav’s average than Russ’s average? 2 _ _ 9 1 _ _ 3 1 __ _ 10 1 + 2 + 1 _____ ____ 3 + 9 + 10 30 + 20 + 9 _____ _____ 90 1 + 2 + 1 ________ 90 1 × 2 × 1 ___ __ ____ 3 × 9 × 10 1 × 2 × 1 ___ ___ __ 90 1 _ _ 2 23 __ _ 40 5 _ _ 8 3 _ _ 4 23 __ _ 40 5 _ _ 8 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-F11 2 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

Each of 5 different data sets is summarized with its own boxplot below. Which of these data sets has the greatest interquartile range?

Paper 8 · ACT April 2023 · Form F11 · Math Test

A surveyor is standing on ground that is level with the base of the cell phone tower shown below. From the point on the ground where the surveyor is standing, the angle of elevation to the top of the tower is 40°. The distance from the surveyor to the tower is 200 feet. Which of the following values is closest to the height, in feet, of the tower? (Note: sin,40° ≈ 0.64, cos,40° ≈ 0.77, and tan,40° ≈ 0.84)

Paper 8 · ACT April 2023 · Form F11 · Math Test

Given x + y = 30 and x − y = 18, what is the value of y ? 30 25 60 85 90 50 10 65 90 145 Data Set A Data Set B 105 60 120 135 145 Data Set C 35 25 40 55 150 Data Set D 85 20 105 125 135 Data Set E 10 30 50 70 90 110 130 150 cell phone tower 40° 200 ft ? DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-F11 2 2 www.crackab.com

Paper 8 · ACT April 2023 · Form F11 · Math Test

Let m and n be positive numbers such that m < n. Which of the following expressions has the greatest value?

Paper 8 · ACT April 2023 · Form F11 · Math Test

The mean of 3 consecutive whole numbers is 30. What are the 3 numbers?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Given that sin,A = , which of the following values could tan,A equal?

Paper 8 · ACT April 2023 · Form F11 · Math Test

On the local car dealer’s lot, there are only 25 cars with power windows and only 17 cars with heated seats. The number of cars on the lot with both power windows and heated seats must be:

Paper 8 · ACT April 2023 · Form F11 · Math Test

To determine the number of fish in a pond, a biologist catches a random sample of 200 fish, tags them, and releases them back into the pond. A week later, the biologist catches a random sample of 120 fish from this pond, and 32 of them have tags. Which of the following is the best estimate of the number of fish in the pond? m + n _____ m m + n _____ n m + n _____ m + n m _____ m + n n _____ m + n 24 __ _ 25 1 __ _ 24 7 __ _ 24 24 __ _ 7 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-F11 2 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

Isabelle divided a sum of money among 4 types of investments as shown in the pie chart below. Given that $100 was invested into a savings account, what amount, to the nearest $10, did she invest in equities?

Paper 8 · ACT April 2023 · Form F11 · Math Test

A jar of solid-colored marbles contains some yellow marbles, 21 blue marbles, 40 red marbles, and 14 green marbles. The probability of randomly drawing a green marble is . How many yellow marbles are in the jar?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Dai traveled to 3 locations during a workday. Dai remained at each location a whole number of hours. The graph below shows the relationship between time, in hours, into his workday and total distance, in miles, traveled. Which of the following values is closest to Dai’s average speed, in miles per hour, for the parts of the workday when he was traveling? mutual funds 50% equities (2x + 4)% savings account 4% certificates of deposit x% 2 __ _ 15 300 200 100 0 2 4 6 0 8 1012 total distance (miles) time (hours) DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-F11 2 2 The chart below provides some facts about 4 planets in our solar system. *The strength of surface gravity refers to the gravitational acceleration of an object near the surface of the planet. The values given are percents of 32.2 ft/sec2 (feet per second per second), which is the gravitational acceleration of an object near the surface of Earth.

Paper 8 · ACT April 2023 · Form F11 · Math Test

What is the positive difference between the given values of average distance from the Sun for Mars and for Mercury?

Paper 8 · ACT April 2023 · Form F11 · Math Test

According to the table, which of the following expressions is equal to the difference, in feet per second per second, between the gravitational acceleration of an object near the surface of Venus and the gravitational acceleration of an object near the surface of Mercury? Mercury Venus Earth Mars Average distance from the Sun (millions of miles)

Paper 8 · ACT April 2023 · Form F11 · Math Test

For all the planets in the solar system, the equation T = 0.4D1.5 models the relationship between T, the orbital period in Earth days, and D, the average distance in millions of miles from the Sun, given in the table. According to this model, which of the following expressions is equal to Mercury’s orbital period in Earth days? ) ) √"" 36+ 2 √""""""" 0.4 · 36+ 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

The formula C = (F − 32) gives the conversion from F degrees Fahrenheit to C degrees Celsius. The formula K = C + 273 gives the conversion from C degrees Celsius to K kelvins. To the nearest integer, what is the average surface temperature, in kelvins, of Mars?

Paper 8 · ACT April 2023 · Form F11 · Math Test

At 12 midnight the center of a hurricane is 360 miles from the coast of Miami, as shown in the figure below. The hurricane has an approximate radius of 120 miles and is currently approaching the Miami area at 30 miles per hour. If the hurricane keeps its current conditions, what time, to the nearest hour, will the leading edge of the hurricane first reach Miami? 5 _ _ 9 120-mile radius Miami Florida 360 miles leading edge DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-F11 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-F11 2 2 35. The figure below is a section of a college basketball court. The square has sides that are 12 feet long, and 1 side of the square is a diameter of the circle. The shaded region is to be refinished at a cost of $6.25 per square foot. The cost of the refinishing is closest to which of the following?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Source question 35. Refer to the source image.

Paper 8 · ACT April 2023 · Form F11 · Math Test

Given that the equation = is true, what is the value of ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Julia will serve grape juice from 12-ounce cans at her graduation party. She already has 3 boxes that each contain 12 such cans. How many more 12-ounce cans of grape juice does Julia need to have exactly enough juice to serve 60 guests 8 ounces each?

Paper 8 · ACT April 2023 · Form F11 · Math Test

On a typical day at Limestone College, of all students ride a bicycle to class. Among the rest of the students, ride the bus and walk. On a typical day, what fraction of the students ride the bus to class? 3x − y ____ _ _ x + y x _ _ y 1 _ _ 5 1 _ _ 2 3 _ _ 5 3 _ _ 2 3 _ _ 5 1 _ _ 6 1 _ _ 3 1 _ _ 5 2 __ _ 15 1 __ _ 10 1 __ _ 15 1 __ _ 18 2 _ _ 4 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-F11 2 2 39. Vectors u and v are shown in standard position in the standard (x,y) coordinate plane below. Which of the following vectors in standard position in the standard (x,y) coordinate plane is v − u ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Source question 39. Refer to the source image.

Paper 8 · ACT April 2023 · Form F11 · Math Test

Suzi ran 3 laps on a circular path with a radius of 49 meters. Which of the following values is closest to the distance, in meters, that Suzi ran? y x O (1,−3) (3,4) v u y x O x O y x O x O y x O (4,−7) (−2,−7) (−4,−1) (2,7) (4,1) DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-F11 2 2 One thousand people registered to run a 5-mile road race. Each of the 1,000 people who registered paid either the early, regular, or late registration fee given in the table below. Ninety percent of all the registered people started the race, and 95% of the people who started the race also finished the race.

Paper 8 · ACT April 2023 · Form F11 · Math Test

There were 300 people who paid the early registration fee, 400 people who paid the regular fee, and 300 people who paid the late fee. What is the total revenue from entry fees, in dollars, written in scientific notation?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Kirk ran the 1st x miles of the race at a rate of 7 minutes per mile and the rest of the race at a rate of 8 minutes per mile. One of the following expressions gives the total amount of minutes that it took Kirk to run the race. Which one?

Paper 8 · ACT April 2023 · Form F11 · Math Test

One registered person will be randomly selected to win a raffle prize. Which of the following expressions is equal to the probability that the selected person did NOT finish the race? Type of registration Registration fee Early $25.00 Regular $35.00 Late $45.00 x − 5 _____ 8 x _ _ 7 5 − x _____ 8 x _ _ 7 Use the following information to answer questions 41–43. www.actexam.net DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-F11 2 2 44. For the real number x, which of the following statements is true about the solutions of the equations below? I. = II. =

Paper 8 · ACT April 2023 · Form F11 · Math Test

Source question 44. Refer to the source image.

Paper 8 · ACT April 2023 · Form F11 · Math Test

The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. What is the total number of white cubes that were used to build the prism?

Paper 8 · ACT April 2023 · Form F11 · Math Test

In the standard (x,y) coordinate plane, only 1 parabola of the form y = (x − h)2 + k has x-intercepts of 3 and

Paper 8 · ACT April 2023 · Form F11 · Math Test

What is the 330th digit after the decimal point in the repeating decimal 4.6238 ____ _ ? 12 3 _ _ 8 _____ _ ⎪x⎪ ___ 5 123 _ _ 8 ______ _ x _ _ 5 www.crackab.com DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-F11 2 2 48. + + = ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Source question 48. Refer to the source image.

Paper 8 · ACT April 2023 · Form F11 · Math Test

Counting repetition, how many prime factors appear in any prime factorization of the integer (63)5 ? (Note: For example, counting repetition, 5 prime factors appear in the prime factorization of 588 as 2 · 2 · 3 · 7 · 7.)

Paper 8 · ACT April 2023 · Form F11 · Math Test

For whole numbers x and y, the list below has 4 as its mean, median, and mode. What is the value of xy ? 2, 6, 4, 1, x, y

Paper 8 · ACT April 2023 · Form F11 · Math Test

Consider the graphs of the functions f(x) = (x + 2)(x − 8) and g(x) = x2 + 5x − 12 in the standard (x,y) coordinate plane. What is the sum of the y-intercepts of the functions? a − b ____ _ a + b b _____ a − b a _____ a + b 2(a − b) _______ _ a + b 2(a2 + b2 ) ______ ___ a2 − b2 2(a2 − ab + b2 ) __________ ___ a2 − b2 2a ___________ _ (a + b)(a − b) 2a _____ _ 3a + b DO YOUR FIGURING HERE. 29 ACT-F11 2 2 GO ON TO THE NEXT PAGE.

Paper 8 · ACT April 2023 · Form F11 · Math Test

The tablecloth shown below is white except for a pattern formed by 4 red rectangular strips, each 2 inches wide and 36 inches long, arranged as shown. If all of the angles formed by the strips are right angles, how many square inches of the tablecloth are red?

Paper 8 · ACT April 2023 · Form F11 · Math Test

For all real numbers x and y, the 2 operations ★ and e are defined below. x ★ y = xy + y x e y = x + xy For all real numbers a and b, what is (a e b) ★ b ? + b + b + b + b2

Paper 8 · ACT April 2023 · Form F11 · Math Test

If (xy )(xk ) = 1, what relationship must exist between y and k ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

Which of the following numbers is a solution to the equation 3x2 + x + 5 = 0 ? √"" 15 ____ _ 3 i√"" 15 ______ 3 −1 + √"" 61 _________ 6 −1 + i√"" 59 _________ _ 6 −1 + 2i√"" 15 __________ _ 6

Paper 8 · ACT April 2023 · Form F11 · Math Test

In the standard (x,y) coordinate plane, one of the following is an equation of the circle that can be inscribed in the ellipse 4x2 + 9y2 = 36. Which equation is that? + y2 = 36 + y2 = 9 + y2 = 4 + (y − 9)2 = 36 + (y − 4)2 = 36

Paper 8 · ACT April 2023 · Form F11 · Math Test

In the figure below, points A, B, and D lie on the circle with center C. The measure of ∠BCD is 60°. Chords AB ___ and AD ___ have the same length. What is the measure of ∠ABC ?

Paper 8 · ACT April 2023 · Form F11 · Math Test

The 3 statements given below are all true about certain positive integers a, b, and c. a is an even prime number b is an odd integer such that 6 < b < 11 c is a perfect square such that 10 < c < 30 How many ordered triples (a,b,c) satisfy the 3 statements? 60° C A B D DO YOUR FIGURING HERE. 30 GO ON TO THE NEXT PAGE. ACT-F11 2 2 www.actexam.net

Paper 8 · ACT April 2023 · Form F11 · Math Test

The side lengths of nABC shown below are 10 m, 18 m, and 21 m. Which of the following expressions represents the measure of ∠B ? (Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, c2 = a2 + b2 − 2ab cos,∠C.) _212 − 102 − 182 − 2(10)(18)+ _212 − 102 − 182 + 2(10)(18)+ _212 − 102 + 182 − 2(10)(18)+ 1 2 1 2

Paper 8 · ACT April 2023 · Form F11 · Math Test

The graph of f(x) is shown in the standard (x,y) coordinate plane below. The graph of f(x) has horizontal asymptotes at y = −2 and y = 2. One of the following intervals represents the domain of f −1 (x). Which one? y x 1 2 2 3 4 −1 −2 −2 −3 −4 1 −1 O 212 − 102 + 182 _____________ −2(10)(18) A 21 C B 10 18 ? 212 − 102 − 182 _____________ −2(10)(18) DO YOUR FIGURING HERE. 31 ACT-F11 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.