ACT Past Papers with Answers

Paper 12 · ACT April 2022 · Form E25 · Math Test

What is the value of x in the equation = x + ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

(3a6 b9 ) is equivalent to: b10 b9 b9 b10 b9 Color of marble Probability Red 0.2 Blue 0.3 Yellow 0.2 Green 0.1 Orange 0.1 Purple 0.1 3 _ _ 4 1 _ _ 3 1 _ _ 4 4 _ _ 7 5 __ _ 12 1 __ _ 12 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 12 · ACT April 2022 · Form E25 · Math Test

During the month of July, Garth’s Video tracked the number of videos rented for each transaction. A total of 600 transactions were made during the month of July. The results are shown in the table below. How many transactions of exactly 3 video rentals were made during the month of July?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The total price for the pizza Jana and her friends bought was $15.60. The pizza was cut into 8 equal slices, and Jana ate 3 of the slices. Jana paid a portion of the total price that was the same as the portion of the pizza she ate. What portion of the total price did Jana pay?

Paper 12 · ACT April 2022 · Form E25 · Math Test

If f(x) = (5x + 3)2 , then f(1) = ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The mean of 4 numbers is 6. Given that 3 of the numbers are 3, 6, and 7, what is the remaining number? Number of videos rented Percent of transactions 1 20% 2 36% 3 26% 4 08% 5 or more 10% 8 _ _ 3 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

The midpoint of NQ ___ is located at M(3,5) in the standard (x,y) coordinate plane. Given that the coordinates of Q are (1,2), what are the coordinates of N ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

What is the value of ⎪−3⎪ − ⎪7 − 49⎪ ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Australia’s Sydney Opera House covers a rectangular region that has a length of 605 feet and a width of 388 feet. Which of the following values is closest to the area, in acres, of the rectangular region? (Note: 1 acre = 43,560 square feet)

Paper 12 · ACT April 2022 · Form E25 · Math Test

52 x−2 y4 7−1 is equivalent to: y4 y4

Paper 12 · ACT April 2022 · Form E25 · Math Test

The lengths of the 2 shorter sides of a right triangle are 2 cm and 3 cm, respectively. Which of the following values is closest to the length, in centimeters, of the longest side of the triangle? 3 _ _ 2 7 _ _ 2 10y4 ____ _ 7x2 25y4 ____ _ 7x2 70y4 ____ _ x2 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

When y = x and x + y = 10 are graphed in the standard (x,y) coordinate plane, at what point do they intersect?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The first 4 terms of a geometric sequence are listed in order below. What is the seventh term of the sequence? 24, 12, 6, 3, …

Paper 12 · ACT April 2022 · Form E25 · Math Test

Let s be any real number such that 4 < å s < 9. Which of the following is a possible value of s ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

In the standard (x,y) coordinate plane, which of the following lines goes through (0,2) and is parallel to y = −5x + 7 ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

What is the slope of the line in the standard (x,y) coordinate plane that contains the points (6,−1) and (4,3) ? 1 _ _ 5 1 _ _ 5 1 _ _ 2 1 _ _ 5 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

If 8y = 3x − 5, then x = ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

A tank has a capacity of 30 gallons and is full of water. Jamal then removes of the water in the tank. How many gallons of water are left in the tank?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Which of the following expressions is equivalent to 3(a + b) − 5(a − 2b) ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

An English teacher decided to give a second test over the same material as a first test. To reward those students who did well and to provide an incentive to students to improve their score, he announced that he would calculate the combined test score by starting with the first test score and adding of the increase in test score from their first test to their second test. Trish scored 57 points on her first test and 72 points on her second test. What is her combined test score? 8 _ _ 3 8 _ _ 3 8y − 5 _____ _ 3 8y + 5 _____ _ 3 5 _ _ 6 1 _ _ 8 1 _ _ 8 1 _ _ 7 7 _ _ 8 7 _ _ 8 2 _ _ 3 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

Which of the following expressions is equal to 3 √•• • 24 ? √• 3 √• 6

Paper 12 · ACT April 2022 · Form E25 · Math Test

On a rectangular sheet of paper, Aiko drew a triangle whose base length is the same as the length of the sheet and whose height is the same as the width of the sheet. What is the ratio of the area of the triangle to the area of the rectangular sheet of paper?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Norah invited 4 friends to a table tennis party. Each of the 5 people at the party played every other person exactly 1 time. The table below shows the number of games won by each player except Norah. There were no ties. How many games did Norah win?

Paper 12 · ACT April 2022 · Form E25 · Math Test

A parallelogram has a perimeter of 80 inches, and 1 of its sides measures 18 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides? 1 _ _ 4 1 _ _ 3 1 _ _ 2 Player Games won Collier 2 Evangeline 1 Gabe 1 Norah ? Maria 3 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-E25 2 2 The 2010 ADA Standards for Accessible Design require that elevator cars with centered doors, like the one shown below, have a minimum door clear width of 42 inches. They also require a minimum number of wheelchair spaces in 1 assembly area, such as a classroom, based on the number of seats in the assembly area, as the table below indicates.

Paper 12 · ACT April 2022 · Form E25 · Math Test

Door clear widths, in feet, of 5 elevator cars with centered doors built before 2010 are listed below.

Paper 12 · ACT April 2022 · Form E25 · Math Test

An elevator car with centered doors has a door clear width that is 8% wider than the minimum distance required by the 2010 ADA standard. Which of the following distances, in inches, is closest to the door clear width of the elevator car? door clear width L 2 3 4 5 6 Number of seats in 1 assembly area Minimum number of wheelchair spaces 004 to 025 1 026 to 050 2 051 to 150 4 151 to 300 5 301 to 500 6 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-E25 2 2 Use the following information to answer questions 26–28.

Paper 12 · ACT April 2022 · Form E25 · Math Test

A local college will construct a 2-floor building next year. Each of the 5 classrooms on the 1st floor will have 20 seats, and each of the 8 classrooms on the 2nd floor will have 35 seats. To comply with the 2010 ADA standard, what is the fewest total number of wheelchair spaces needed in the 13 classrooms?

Paper 12 · ACT April 2022 · Form E25 · Math Test

A paint researcher collected the following data about the relationship between the paint level in a paint can and the surface area painted from this can. Assume there is a linear relationship between x and y. Which of the following is an equation showing this relationship?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Which of the following sentences is true about the 2 nonright angles of any right triangle?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The temperature in Chicago was −4°F at noon and rose 24°F by 3:00 p.m. The temperature in New Orleans was 42°F at noon and dropped 24°F by 3:00 p.m. How did the temperatures in Chicago and New Orleans compare at 3:00 p.m. ? distance from top of can (x inches) surface area painted (y square feet) 03 096 07 224 11 352 352 ___ _ 11 96 __ _ 3 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-E25 2 2 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-E25 2 2 32. In the figure below, AB ↔ and CE ↔ intersect at O, OC → bisects ∠BOD, and the measure of ∠AOD is 40°. What is the measure of ∠AOE ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Source question 32. Refer to the source image.

Paper 12 · ACT April 2022 · Form E25 · Math Test

The entire length of a rope is coiled into 6 circular loops, each with a diameter of 10 inches, as shown below. Which of the following is closest to the length, in inches, of the rope?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Given the matrix equation below, what is the value of ab ? 3 4+ 3 4= 3 4

Paper 12 · ACT April 2022 · Form E25 · Math Test

In right triangle nABC, the right angle is at B, and sin,A = . What is the value of tan,C ? 40° D C B E A O ? 10 −4 4 10 3 2 b a 0 −6 12 5 3 1 _ _ 3 2 _ _ 3 12 __ _ 13 5 __ _ 12 5 __ _ 13 12 __ _ 5 12 __ _ 13 13 __ _ 5 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-E25 2 2 36. During rehearsal for the Founders’ Day choir program, the director, Mrs. Mazurek, tried 3 different configurations, each using all the choir members at the rehearsal. One configuration was to have only rows of 12, one was to have only rows of 15, and one was to have only rows of 20. None of these configurations worked because for each, the last row had 1 person less than the other rows. What was the least of the possible numbers of choir members at the rehearsal?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Source question 36. Refer to the source image.

Paper 12 · ACT April 2022 · Form E25 · Math Test

The equation x2 + P = 0, where P is an integer, has 2 integer solutions for x. Which of the following is a possible value of P ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Of the 17 members of Xavier High School’s honor society, 1 member will be chosen at random to attend a conference. The table below shows the number of honor society members according to class and whether they are in their first or second year in the honor society. What is the probability that the member chosen will NOT be a senior who is in his or her second year in the honor society?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Given x = 4y and y = 2z, which of the following expressions is equivalent to x + 4y − 8z in terms of z ? First year Second year Junior 2 0 Senior 8 7 2 __ _ 17 7 __ _ 17 8 __ _ 17 10 __ _ 17 17 __ _ 17

Paper 12 · ACT April 2022 · Form E25 · Math Test

Using the street map shown below, you are directed to take a 4-block-long route to walk from First and Main Streets to Third and Market Streets. If each of the different 4-block-long routes consists of a unique sequence of streets, how many such routes could you take?

Paper 12 · ACT April 2022 · Form E25 · Math Test

For i = √•• −1, (3 + i)2 = ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Define the functions f(x) and g(x) such that f(x) = 2x and g(x) = √•••• • x + 3. For all x such that x ≥ −3, which of the following expressions is equal to f_g(x)+ ? + 3 + 6x

Paper 12 · ACT April 2022 · Form E25 · Math Test

In a small high school with 20 seniors, 8 of the seniors are in soccer, 9 of the seniors are in band, and 5 of the seniors are in both. How many seniors are in neither soccer nor band? First and Main Streets Third and Market Streets DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

For any real number x such that x < −5 in the equation below, which of the following statements must be true of the number represented by y ? y = −√•••• • x + 5

Paper 12 · ACT April 2022 · Form E25 · Math Test

The population of Northtown on January 1 for the years 2001 through 2007 is shown in the table below. What is the average yearly change in population from January 1, 2003, to January 1, 2005 ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The bottom of the empty rectangular storage bin shown below is a square. If 175 cubic feet of salt are poured into the bin and leveled, how many feet of the bin will be filled? Year Population 2001 1,506 2002 1,612 2003 1,726 2004 1,844 2005 1,972 2006 2,098 2007 2,224 50 feet 5 feet 5 feet DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-E25 2 2

Paper 12 · ACT April 2022 · Form E25 · Math Test

One of the following graphs is the graph of y ≤ ax + b for some positive a and positive b. Which graph?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The ratings from a survey taken by 90 students are summarized in the frequency bar graph below. The possible ratings on the survey are 0, 1, 2, 3, and 4. What is the mean of the 90 ratings? O x y A. D. O x y B. O x y O x y E. O x y C. 40 30 20 10 0 rating number of students 0 1 2 3 4 40 10 25 10 5 4 _ _ 9 1 _ _ 2 10 __ _ 17 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-E25 2 2 DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-E25 2 2 49. A vote revealed that chocolate ice cream was favored by more students in Hillhouse High School than any other flavor of ice cream. Which of the following statistical measures was most likely used to determine this result? Harold is planning a garden as shown in the scale drawing below. The line segments represent the fence surrounding the garden, with an opening in the fence to access the garden. Each small square in the scale drawing represents a square with a side length of 2 feet. Each marked point is at the vertex of a small square in the drawing.

Paper 12 · ACT April 2022 · Form E25 · Math Test

Source question 49. Refer to the source image.

Paper 12 · ACT April 2022 · Form E25 · Math Test

What will be the length, in feet, of the fence surrounding Harold’s garden?

Paper 12 · ACT April 2022 · Form E25 · Math Test

What will be the area, in square feet, of Harold’s garden?

Paper 12 · ACT April 2022 · Form E25 · Math Test

What is the measure of the angle labeled θ in the scale drawing of the garden? 1 2 1 2 1 2 1 2 1 2 θ 6 _ _ 8 6 _ _ 8 6 _ _ 8 8 _ _ 8 8 _ _ 6 Use the following information to answer questions 50–52.

Paper 12 · ACT April 2022 · Form E25 · Math Test

What is the solution of the equation log2 = 1 ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

For the functions f(x) = 4x + 12 and g(x) = , what is the set of real numbers x on which g_f(x)+ is defined?

Paper 12 · ACT April 2022 · Form E25 · Math Test

One alarm beeps 4 seconds after it is activated and at the end of every 6 seconds after that. Another alarm beeps 29 seconds after it is activated and at the end of every 30 seconds after that. The 2 alarms are activated at the same time and are left on for t minutes, where t is a whole number. What is the total number of times the 2 alarms beep in those t minutes?

Paper 12 · ACT April 2022 · Form E25 · Math Test

The inequality 3x4 y < 0 is true for real numbers x and y. If it can be determined, which of the following inequalities must be true?

Paper 12 · ACT April 2022 · Form E25 · Math Test

In the figure shown below, square MNPT is inscribed in square ABCD. The length of DC ___ _ is x inches, and the length of BN ___ is y inches. In terms of x and y, which of the following expressions gives the area, in square inches, of MNPT ? − y2 + y2 − 2xy + 0y2 − 2xy + 2y2 1 _ _ x 1 _ _ 3 √••••• • 3x + 4 ________ x − 2 3 _ _ 4 x in y in D C A B N T M P DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-E25 2 2 DO YOUR FIGURING HERE. 29 ACT-E25 2 2 58. For all distinct nonzero values of x and y, which of the following expressions is equivalent to ?

Paper 12 · ACT April 2022 · Form E25 · Math Test

Source question 58. Refer to the source image.

Paper 12 · ACT April 2022 · Form E25 · Math Test

For 0° < a° < 90° and 0 < b < 1, when cos,a° = b, which of the following expressions is equivalent to cos(2a°) ? (Note: cos,2θ = (cos,θ)2 − (sin,θ)2 ) − a2 − 1

Paper 12 · ACT April 2022 · Form E25 · Math Test

In the figure shown below, each of the points labeled P through X is a point of tangency between 2 circles. Each vertex of nABC is the center of a circle. Each circle has a radius of r cm. Which of the following expressions represents the area, in square centimeters, of nABC ? √• 3 √• 3 x _ _ y − 1 _____ _ 1 _ _ y − 1 _ _ x 1 _ _ x 1 _ _ y x2 − 1 _____ _ x − y 8r2 √• 3 _______ 3 U X V P A W Q R B C S T END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.