ACT Past Papers with Answers

Paper 14 · ACT December 2021 · Form E23 · Math Test

The degree measures of the 3 angles of the triangle below are expressed in terms of x. What is the value of x ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

A 48.5-ounce batch of cologne will be used to fill empty bottles. Each full bottle will contain 0.35 ounces of cologne. This batch of cologne will fill at most how many bottles full of cologne?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Of the 200 parking spaces in a parking lot, 6% of the spaces are reserved for handicapped parking. Of those parking spaces NOT reserved for handicapped parking, 20 are suitable for compact cars only. How many spaces that are NOT reserved for handicapped parking are suitable for noncompact cars? 35x5 y4 _____ _ 5xy (6x)° (5x)° (4x)° DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 14 · ACT December 2021 · Form E23 · Math Test

What is the value of 2⎪2 − 9⎪ − 3(5 + 2) ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Ricardo started a savings account for his daughter Ruth by depositing $500 into the account for her 1st birthday. For each successive birthday, Ricardo deposits $200 more than the amount deposited for the previous birthday. This is the only money deposited into the account. What is the total amount of money Ricardo will have deposited into the account for Ruth up to and including her 6th birthday?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Tawanna bought a used car. She made an initial payment of $700.00. She then made 36 equal monthly payments. The total amount Tawanna paid for the car was $7,000.00. What was the amount of each of her monthly payments?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Which of the following matrices is equal to 3 4+ 3 4? 9 −4 2 1 −6 7 8 6 −40 31 84 −26 3 11 10 7 3 3 10 7 15 11 10 7 11 −3 2 13 DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-E23 2 2

Paper 14 · ACT December 2021 · Form E23 · Math Test

Lyle and Ming are painting an art room. They started with 4 gallons of paint. On the first day, Lyle used gallon of paint and Ming used 1 gallons of paint. How many gallons of paint were left when they completed their first day of painting?

Paper 14 · ACT December 2021 · Form E23 · Math Test

In the standard (x,y) coordinate plane, what is the slope of the line through (−3,1) and (5,6) ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The lengths of corresponding sides of 2 similar right triangles are in the ratio 4:5. The hypotenuse of the smaller triangle is 24 inches long. How many inches long is the hypotenuse of the larger triangle?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The lengths of the 3 sides of right triangle nABC shown below are given in meters. What is sin,A ? 1 _ _ 2 1 _ _ 4 3 _ _ 4 1 _ _ 4 3 _ _ 4 1 _ _ 4 1 _ _ 2 5 _ _ 2 5 _ _ 8 5 _ _ 8 5 _ _ 2 7 _ _ 2 15 8 17 A B C 8 __ _ 17 8 __ _ 15 15 __ _ 17 17 __ _ 15 17 __ _ 8 DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-E23 2 2 DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-E23 2 2 13. In the figure shown below, C is on the segment with endpoints A and D. The distance between A and B is 2,000 km, between A and C is 1,600 km, between A and D is 2,500 km, and between B and C is 1,200 km. What is the distance, in kilometers, between B and D ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Source question 13. Refer to the source image.

Paper 14 · ACT December 2021 · Form E23 · Math Test

What is the sum of the 2 solutions of the equation x2 − 4x − 45 = 0 ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

In the figure shown below, all angles are right angles, and the side lengths given are in inches. What is the area, in square inches, of the figure?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Quadrant I of the standard (x,y) coordinate plane is shown on a large computer screen. A blinking dot is positioned at (2,3). The dot makes exactly 2 moves: first, horizontally in the positive x direction for 4 seconds at a speed of 0.5 coordinate units per second; then, vertically in the positive y direction for 2 seconds at the same speed. At what point is the dot located after these 2 moves? C B D A 2 11 5 9 A weeklong summer camp is held in June for children in Grades 3−6. Parents and guardians who enrolled their children for camp by May 15 received a 20% discount off the regular enrollment fee for each child enrolled. For each grade, the table below gives the number of children enrolled by May 15 as well as the regular enrollment fee per child. The grade of any child is that child’s grade in school as of May 15.

Paper 14 · ACT December 2021 · Form E23 · Math Test

By May 15, Mr. Ramirez had enrolled his 2 children for camp. One child was in Grade 4, and the other was in Grade 6. What was the total amount Mr. Ramirez paid to enroll his 2 children?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Which of the following equations gives a true relationship between the regular enrollment fee, f, and the grade, g, of any child enrolled in the camp?

Paper 14 · ACT December 2021 · Form E23 · Math Test

By May 15, Ms. Chen had enrolled her 2 children for camp. One child was in Grade 3, and the other was in Grade 4. For each grade, the names of all the children enrolled by May 15 will be entered into a drawing for a free T-shirt. For each grade, 1 name will be randomly drawn. What is the probability that the names of both of Ms. Chen’s children will be drawn? Grade Enrollment by May 15 Regular enrollment fee 3 20 $350 4 15 $400 5 28 $450 6 18 $500 7 __ _ 60 2 __ _ 81 1 ___ _ 300 100 _____ 2,187 1 _____ 3,240 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-E23 2 2 Use the following information to answer questions 17–19.

Paper 14 · ACT December 2021 · Form E23 · Math Test

You drove 18 miles in 20 minutes at a constant speed and did NOT exceed the speed limit, given in miles per hour. Among the following, which is the lowest that the speed limit could have been?

Paper 14 · ACT December 2021 · Form E23 · Math Test

What value of x makes the equation − = −3x true?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The equation R = gives the resistance, R, in terms of the power, P, and the current, I, of an electrical system. Which of the following expressions gives I in terms of P and R ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

One welcome sign flashes every 8 seconds, and another welcome sign flashes every 12 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time? 1 _ _ 4 1 ___ _ 243 1 __ _ 81 P __ _ I2 √ •• R __ P √ •• P __ R P __ R R __ P DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-E23 2 2 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-E23 2 2 24. The area of a certain square is 900 square inches. What is the perimeter of this square, in inches?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Source question 24. Refer to the source image.

Paper 14 · ACT December 2021 · Form E23 · Math Test

The Department of Natural Resources (DNR) is estimating the deer population in Twin Pines County. Several months ago, DNR rangers captured, tagged, and then released 108 deer. Recently, DNR rangers captured 54 deer in the county and found that 36 of them had been tagged in the earlier capture. The DNR estimates the deer population in the county using the proportion below. What is the DNR estimate of the deer population in the county? =

Paper 14 · ACT December 2021 · Form E23 · Math Test

In an arithmetic sequence, the 10th term (a10) is 30 and the common difference is 2. What is the 1st term (a1) ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

A pedometer records the number of steps a person takes as he or she walks. When a pedometer records 3,898 steps taken by a person who covers a distance of

Paper 14 · ACT December 2021 · Form E23 · Math Test

Among a group of 20 students, 13 students are members of the Math Club, 11 students are members of the Drama Club, and 9 students are members of both clubs. How many of the 20 students are NOT members of either club? tagged deer in capture 1 ____________________ deer population tagged deer in capture 2 ____ ________________ deer in capture 2 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-E23 2 2 29. To increase the mean of 7 numbers by 4, by how much would the sum of the 7 numbers have to increase?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Source question 29. Refer to the source image.

Paper 14 · ACT December 2021 · Form E23 · Math Test

Which of the following is an equation of the circle in the standard (x,y) coordinate plane whose center is at (4,−3) and whose radius is 5 coordinate units long? + (y + 3)2 = 05 + (y + 3)2 = 25 + (y + 4)2 = 25 + (y − 4)2 = 05 + (y − 3)2 = 25

Paper 14 · ACT December 2021 · Form E23 · Math Test

All 25 students in a chemistry class took a test. Each student earned a test score that was an integer number of points, and no 2 students earned the same test score. The median test score was 80 points. How many students earned a test score that was greater than 80 points?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Shefali goes to a farmers’ market every Saturday. Two Saturdays ago, Shefali purchased 3 apples and 4 oranges for a total of $3.47. Last Saturday, she purchased 12 oranges, but no apples, and spent $6.36. Today, she only has one $10 bill. Given that none of the prices have changed over the last 3 weeks, what is the maximum number of apples she can purchase today? (Note: No sales tax is charged at this farmers’ market.) Fletcher purchased 5 items at Hippity-Bippity Toy Store for a total of $18.55, which included sales tax. When he arrived home, he discovered that his receipt was torn and did not show the price of the bag of balloons or the 6% sales tax applied to the sum of the 5 prices. The partial receipt is shown below.

Paper 14 · ACT December 2021 · Form E23 · Math Test

Fletcher left his home 1 hour 15 minutes before he entered the store. He spent 25 minutes in the store before he made his purchase. What time did Fletcher leave his home?

Paper 14 · ACT December 2021 · Form E23 · Math Test

To the nearest $0.10, what was the price of the bag of balloons?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The price of the doll was how much greater than the mean of the 4 prices shown on the partial receipt? Date: 12-20-2014 Time: 2:30 p.m. Hippity-Bippity Toy Store Item Price Bag of marbles $2.00 Doll $6.00 Car $3.00 Jump rope $4.00 Bag of balloon DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-E23 2 2 Use the following information to answer questions 33–36.

Paper 14 · ACT December 2021 · Form E23 · Math Test

Malik will spend a total of $30.00 before sales tax on x bags of marbles and y cars purchased at the prices shown on the partial receipt. One of the following line segments graphed in the standard (x,y) coordinate plane contains points for all possible combinations of x and y. Which one?

Paper 14 · ACT December 2021 · Form E23 · Math Test

In nDEF, shown in the figure below, EG ___ is an altitude, ∠DEF is a right angle, EF = 20 centimeters, and the measure of ∠EDF is 30°. What is EG, in centimeters? O x y 15 6 5 O x y 5 10 O x y 15 10 O x y 10 15 O x y 12 E D 30° G F 20 cm ? DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-E23 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-E23 2 2 38. Let the polynomial functions f and g be defined as f(x) = x2 + 7x − 3 and g(x) = x2 − 4x + 5. Let h(x) = f(x) − g(x). What is h(2) ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Source question 38. Refer to the source image.

Paper 14 · ACT December 2021 · Form E23 · Math Test

A student is using a protractor, as shown below, to find the measures of the interior angles of nABC. Which of the following is closest to the degree measure of ∠C ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

For real numbers x and y such that 0 ≤ x ≤ 5 and y ≥ 9, the expression can have which of the following values?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Given the functions f(x) = x2 + 1 and g(x) = x − 3, which of the following expressions is f_g(x)+ ? − 8 − 6x + 10 + 0x − 02 + 0x − 03 − 3x2 + x − 3 0 180 90 1 0 1 7 0 2 0 1 6 0 3 0 1 5 0 4 0 1 4 0 50 130 60 120 70 110 80 100 100 80 110 70 120 60 130 50 1 4 0 4 0 1 5 0 3 0 1 6 0 2 0 1 7 0 1 0 180 0 B C A x + y ____ _ y 10 __ _ 9 14 __ _ 5 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-E23 2 2 42. Given that the equation = is true, what is the value of ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Source question 42. Refer to the source image.

Paper 14 · ACT December 2021 · Form E23 · Math Test

Juro traveled to 3 locations during a workday. Juro 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 kilometers, traveled. Which of the following values is closest to Juro’s average speed, in kilometers per hour, for the parts of the workday when he was traveling?

Paper 14 · ACT December 2021 · Form E23 · Math Test

What is the amplitude of the function y = 3 sin,x ? 5 _ _ 2 4x − y ____ _ _ x + y x _ _ y 2 _ _ 3 5 _ _ 2 7 _ _ 3 7 _ _ 5 7 __ _ 18 450 300 150 0 2 4 6 0 8 1012 total distance (km) time (hours) 1 _ _ 3 3 _ _ 2

Paper 14 · ACT December 2021 · Form E23 · Math Test

For all nonzero values of w, which of the following expressions is equivalent to + ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Let A, B, and C represent the digits in the hundreds, tens, and ones places, respectively, of a certain 3-digit whole number. Let D, E, and F represent the digits in the hundreds, tens, and ones places, respectively, of a different 3-digit whole number. The positive difference between the 2 numbers is greater than 100. Which of the following inequalities must be true?

Paper 14 · ACT December 2021 · Form E23 · Math Test

A number line graph includes the points at real numbers a and b, as shown below. Which of the following inequalities expresses an interval that must include the product ab ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Sani’s course grade in his chemistry class is based on 3 tests and 1 final exam. Each of the 3 test scores is weighted as 20% of the course grade, and the final exam score is weighted as 40% of the course grade. Sani’s 3 test scores are 78, 86, and 82, respectively. What is the minimum score that Sani will have to earn on the final exam in order to receive a course grade of at least 86 ? 2 __ _ w2 4 __ w 2w + 1 ___ ___ _ w2 4w + 2 ___ ___ _ w2 6 ___ ___ _ w + w2 6 __ _ w2 6 __ _ w3 a b 0 1 −1 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-E23 2 2

Paper 14 · ACT December 2021 · Form E23 · Math Test

The triangle below has vertices A(−1,−2), B(2,2), and C(−1,4). What is the area of nABC, in square coordinate units?

Paper 14 · ACT December 2021 · Form E23 · Math Test

For some real number x, √•• x2 ≠ x. Therefore x is:

Paper 14 · ACT December 2021 · Form E23 · Math Test

In the standard (x,y) coordinate plane below, point A has coordinates (2,−4), and point B(8,−1) divides AC ___ so that the ratio AB:BC is 1:3. What are the coordinates of point C ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

A wire binds 4 identical posts together as shown below. Each post has a 3-inch radius. What is the length, to the nearest inch, of the shortest wire that will go around the 4 posts without overlap? O A(−1,−2) B(2,2) C(−1,4) x y 5 _ _ 2 x y O A(2,−4) B(8,−1) r = 3 in DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-E23 2 2

Paper 14 · ACT December 2021 · Form E23 · Math Test

Given that b is rational and i = √•• −1, the product of the expression (3 + bi) and which of the following expressions must be a rational number?

Paper 14 · ACT December 2021 · Form E23 · Math Test

For positive integers x and y where x < 8, logx,8 = y. What is the value of y ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The right triangle shown below is 8 squares high and 10 squares long. One of the following values is the ratio of the shaded area to the unshaded area. Which one?

Paper 14 · ACT December 2021 · Form E23 · Math Test

For all positive integers x, which of the following expressions is equivalent to x · x ? √• x √• •• x12 12 √• • • x5 24 √• x 8 10 3 _ _ 7 3 __ _ 10 7 __ _ 13 7 __ _ 20 15 __ _ 28 1 _ _ 6 1 _ _ 4 DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-E23 2 2

Paper 14 · ACT December 2021 · Form E23 · Math Test

One day on the New York Currency Exchange, 1 British pound (£1) could be exchanged for $2.75 in U.S. currency, and 1 Canadian dollar ($1) could be exchanged for $0.92 in U.S. currency. On that day, how much Canadian currency, rounded to the nearest Canadian cent, could be exchanged for £2 ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

The sides of an acute triangle measure 17 cm, 16 cm, and 15 cm, respectively. The measure of the smallest angle of the triangle is a solution for A to which of the following equations? = 152 + 162 − 2(15)(16)sin,A = 152 + 162 − 2(15)(16)cos,A = 152 + 172 − 2(15)(17)cos,A = 162 + 172 − 2(16)(17)sin,A = 162 + 172 − 2(16)(17)cos,A

Paper 14 · ACT December 2021 · Form E23 · Math Test

Set A and Set B each consist of 5 distinct numbers. The 2 sets contain identical numbers with the exception of the number with the least value in each set. The number with the least value in Set B is greater than the number with the least value in Set A. The value of which of the following measures must be greater for Set B than for Set A ?

Paper 14 · ACT December 2021 · Form E23 · Math Test

Of the 16 cars on a rental-car lot, 6 are minivans, 7 are sedans, and 3 are hatchbacks. Thalia will rent 3 of these cars, chosen at random, for business associates. What is the probability that Thalia will rent 1 of each of the 3 types of cars? 1 _ _ 3 1 __ _ 16 3 __ _ 16 9 __ _ 40 9 __ _ 80 DO YOUR FIGURING HERE. 29 ACT-E23 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.