ACT Past Papers with Answers

Paper 31 · ACT April 2017 · Form 74F · Math Test

The 35-member History Club is meeting to choose a student government representative. The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Hiroko, who is a member of the club but NOT an officer, will be chosen?

Paper 31 · ACT April 2017 · Form 74F · Math Test

For what value of x is the equation 22x + 7 = 215 true?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Let the function f be defined as f(x) = 5x2 − 7(4x + 3). What is the value of f(3) ? 4 __ _ 35 1 __ _ 35 1 __ _ 32 1 _ _ 3

Paper 31 · ACT April 2017 · Form 74F · Math Test

A wallet containing 5 five-dollar bills, 7 ten-dollar bills, and 8 twenty-dollar bills is found and returned to its owner. The wallet’s owner will reward the finder with 1 bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty- dollar bill?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The ABC Book Club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?

Paper 31 · ACT April 2017 · Form 74F · Math Test

In parallelogram ABCD below, AC ___ is a diagonal, the measure of ∠ABC is 40°, and the measure of ∠ACD is 57°. What is the measure of ∠CAD ? 1 __ _ 20 4 __ _ 51 1 _ _ 8 2 _ _ 5 2 _ _ 3 40° 57° ? C B A D GO ON TO THE NEXT PAGE.

Paper 31 · ACT April 2017 · Form 74F · Math Test

When x = , what is the value of ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1,−4) ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The fluctuation of water depth at a pier is shown in the figure below. One of the following values gives the positive difference, in feet, between the greatest water depth and the least water depth shown in this graph. Which value is it?

Paper 31 · ACT April 2017 · Form 74F · Math Test

What is the slope of the line through (−2,1) and (2,−5) in the standard (x,y) coordinate plane? 8x − 3 _____ _ x 1 _ _ 2 1 _ _ 2 5 _ _ 2 3 _ _ 2 11 __ _ 2 0 2 4 6 8 10 12 14 16 18 20 12 10 8 6 4 2 0 number of hours after 6 a.m. depth (feet) 3 _ _ 2 3 _ _ 2

Paper 31 · ACT April 2017 · Form 74F · Math Test

In Cherokee County, the fine for speeding is $17 for each mile per hour the driver is traveling over the posted speed limit. In Cherokee County, Kirk was fined $221 for speeding on a road with a posted speed limit of 30 mph. Kirk was fined for traveling at what speed, in miles per hour?

Paper 31 · ACT April 2017 · Form 74F · Math Test

What is the sum of the solutions of the 2 equations below? 00008x = 12 2y + 10 = 22

Paper 31 · ACT April 2017 · Form 74F · Math Test

The average of 5 distinct scores has the same value as the median of the 5 scores. The sum of the 5 scores is

Paper 31 · ACT April 2017 · Form 74F · Math Test

What is the value of the expression below? ⎪⎪−8 + 4⎪ − ⎪3 − 9⎪⎪

Paper 31 · ACT April 2017 · Form 74F · Math Test

Which of the following expressions is equivalent to x ? √" x √"" x2 2 _ _ 5 1 _ _ 2 1 _ _ 2 2 _ _ 3 x2 __ _ 3 x(2) ____ 3 GO ON TO THE NEXT PAGE. ACT-1874FPRE 2 2 27

Paper 31 · ACT April 2017 · Form 74F · Math Test

In the standard (x,y) coordinate plane, what is the slope of the line given by the equation 4x = 7y + 5 ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

For which of the following conditions will the sum of integers m and n always be an odd integer?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The lengths of the 2 legs of right triangle nABC shown below are given in inches. The midpoint of AB ___ is how many inches from A ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

In nDEF, the length of DE ___ is √"" 30 inches, and the length of EF ___ is 3 inches. If it can be determined, what is the length, in inches, of DF ___ ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Laura plans to paint the 8-foot-high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. Two walls are 10 feet wide, and the other 2 walls are 15 feet wide. The combined area of the 1 window and the 1 door in her room is 60 square feet. What is the area, in square feet, of the wall surface Laura plans to paint? 4 _ _ 7 4 _ _ 7 7 _ _ 4 24 B C A 32

Paper 31 · ACT April 2017 · Form 74F · Math Test

The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle, in inches?

Paper 31 · ACT April 2017 · Form 74F · Math Test

8% of 60 is of what number?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Armin is trying to decide whether to buy a season pass to his college basketball team’s 20 home games this season. The cost of an individual ticket is $14, and the cost of a season pass is $175. The season pass will admit Armin to any home basketball game at no additional cost. What is the minimum number of home basketball games Armin must attend this season in order for the cost of a season pass to be less than the total cost of buying an individual ticket for each game he attends?

Paper 31 · ACT April 2017 · Form 74F · Math Test

= ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

A circle in the standard (x,y) coordinate plane has center C(−1,2) and passes through A(2,6). Line segment AB ___ is a diameter of this circle. What are the coordinates of point B ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Which of the following expressions is a factor of x3 − 64 ? + 16 − 04x + 16 1 _ _ 5

Paper 31 · ACT April 2017 · Form 74F · Math Test

The average of a list of 4 numbers is 90.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 80, and the fourth number in the new list is 96. What is the average of this new list of numbers?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The number a is located at −2.5 on the number line below. One of the following number lines shows the location of a2 . Which number line is it?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Maria ordered a pizza. She ate only of it and gave the remaining pizza to her 3 brothers. What fraction of the whole pizza will each of Maria’s brothers receive, if they share the remaining pizza equally? −6 −8 −4 −2 8 4 2 0 6 a −6 −8 −4 −2 8 4 2 0 6 a2 −6 −8 −4 −2 8 4 2 0 6 a2 −6 −8 −4 −2 8 4 2 0 6 a2 −6 −8 −4 −2 8 4 2 0 6 a2 −6 −8 −4 −2 8 4 2 0 6 a2 2 _ _ 9 7 _ _ 9 3 _ _ 7 1 _ _ 3 7 __ _ 27 2 __ _ 27

Paper 31 · ACT April 2017 · Form 74F · Math Test

The number 1,001 is the product of the prime numbers 7, 11, and 13. Knowing this, what is the prime factorization of 30,030 ? Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea’s scale drawing, 1 inch represents 1.5 feet.

Paper 31 · ACT April 2017 · Form 74F · Math Test

What is the area, in square inches, of the scale drawing of the park?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Mikea’s proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The length of the south side of the park is what percent of the length of the north side? merry-go-round 4 16 inches slide sandbox climber 28 inches 40 inches 6 _ _ 7 GO ON TO THE NEXT PAGE. ACT-1874FPRE 2 2 Use the following information to answer questions 32–34. 29 The Smith family is planning to build a 3-room cabin which consists of 2 bedrooms (BR) and 1 living room (LR). Shown below are the rectangular floor plan (left figure) and a side view of the cabin (right figure). In the side view, the roof forms an isosceles triangle (nABC), the walls are perpendicular to the level floor _ED ___ +, AC ___ i ED ___ , F is the midpoint of AC ___ , and BF ___ ⊥ AC ___ . During the week the Smiths plan to roof the cabin, there is a 20% chance of rain each day.

Paper 31 · ACT April 2017 · Form 74F · Math Test

Mr. Smith plans to build a 3-foot-wide walkway around the outside of the cabin, as shown in the floor plan. What will be the area, in square feet, of the top surface of the walkway?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Mrs. Smith will install a ceiling fan in each room of the cabin and will place curtains over the 4 windows. Each of the ceiling fans has a price of $52.00. The price of curtains for each small window (S) is $39.50, and the price of curtains for the large window (L) is twice that for the small window. Based on this information, which of the following values is closest to the total price Mrs. Smith will pay for curtains and ceiling fans? walkway 24′ B F A 36′ 30′ 30′ 30° 30° 24′

Paper 31 · ACT April 2017 · Form 74F · Math Test

Mr. and Mrs. Smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Which of the following expressions, when evaluated, equals an irrational number? 2

Paper 31 · ACT April 2017 · Form 74F · Math Test

A line through the origin and (10,4) is shown in the standard (x,y) coordinate plane below. The acute angle between the line and the positive x-axis has measure θ. What is the value of tan,θ ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The equation ⎪2x − 8⎪ + 3 = 5 has 2 solutions. Those solutions are equal to the solutions to which of the following pairs of equations? −2x − 5 = −5 −2x − 8 = 2 −(2x − 8) = 8 −(2x − 8) = 8 −(2x − 8) = 2 √" 2 ____ √" 8 √" 8 ____ √" 2 y x O (10,4) θ √"" 29 ____ _ 2 2 ____ _ √"" 29 5 ____ _ √"" 29 2 _ _ 5 5 _ _ 2 GO ON TO THE NEXT PAGE. ACT-1874FPRE 2 2 Use the following information to answer questions 35–37. 30

Paper 31 · ACT April 2017 · Form 74F · Math Test

The frequency chart below shows the cumulative number of Ms. Hernandez’s science students whose test scores fell within certain score ranges. All test scores are whole numbers. How many students have a test score in the interval 71−80 ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The number of decibels, d, produced by an audio source can be modeled by the equation d = 10 log1 2, where I is the sound intensity of the audio source and K is a constant. How many decibels are produced by an audio source whose sound intensity is 1,000 times the value of K ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Mario plays basketball on a town league team. The table below gives Mario’s scoring statistics for last season. How many points did Mario score playing basketball last season? Score range Cumulative number of students 65−70 65−80 65−90 065−100 12 13 19 21 I __ K Type of shot Number attempted Percent successful 1-point free throw 80 75% 2-point field goal 60 90% 3-point field goal 60 25%

Paper 31 · ACT April 2017 · Form 74F · Math Test

The graph of y = ⎪x − 6⎪ is in the standard (x,y) coordinate plane. Which of the following transforma- tions, when applied to the graph of y = ⎪x⎪, results in the graph of y = ⎪x − 6⎪ ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Toby wants to find the volume of a solid toy soldier. He fills a rectangular container 8 cm long, 6 cm wide, and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is

Paper 31 · ACT April 2017 · Form 74F · Math Test

A box in the shape of a cube has an interior side length of 18 inches and is used to ship a right circular cylinder with a radius of 6 inches and a height of 12 inches. The interior of the box not occupied by the cylinder is filled with packing material. Which of the following numerical expressions gives the number of cubic inches of the box filled with packing material? − 2π(6)(12) − 2π(6)2 − 2π(6)(12) − π(6)(12)2 − π(6)2 (12) − π(12)3

Paper 31 · ACT April 2017 · Form 74F · Math Test

A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards ? GO ON TO THE NEXT PAGE. ACT-1874FPRE 2 2 31

Paper 31 · ACT April 2017 · Form 74F · Math Test

Source question 48. Refer to the source image.

Paper 31 · ACT April 2017 · Form 74F · Math Test

The graph of a function y = f(x) consists of 3 line segments. The graph and the coordinates of the endpoints of the 3 line segments are shown in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of the region bounded by the graph of y = f(x), the positive y-axis, and the positive x-axis?

Paper 31 · ACT April 2017 · Form 74F · Math Test

The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the value of the greater number minus the lesser number? ABC Cabs fare ($) miles 0 2 4 6 14 12 10 08 06 04 02 00 Tary Taxicabs fare ($) miles 0 2 4 6 14 12 10 08 06 04 02 00 y x O (0,4) (5,0) (2,3) (3,3) 32

Paper 31 · ACT April 2017 · Form 74F · Math Test

The list of numbers 41, 35, 30, X, Y, 15 has a median of 25. The mode of the list of numbers is 15. To the nearest whole number, what is the mean of the list?

Paper 31 · ACT April 2017 · Form 74F · Math Test

You are given the following system of equations: y = x2 rx + sy = t where r, s, and t are integers. For which of the following will there be more than one (x,y) solution, with real-number coordinates, for the system? + 4st > 0 − 4rt > 0 − 4st < 0 − 4rt < 0 + 4rt < 0

Paper 31 · ACT April 2017 · Form 74F · Math Test

The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term of the sequence?

Paper 31 · ACT April 2017 · Form 74F · Math Test

One of the following graphs in the standard (x,y) coordinate plane is the graph of y = sin2 x + cos2 x over the domain − ≤ x ≤ . Which one? π _ _ 2 π _ _ 2 y x O x O x O O y x O y x π _ _ 2 π _ _ 2 −π _ _ 2 −π _ _ 2 π _ _ 2 −π _ _ 2 −π _ _ 2 π _ _ 2 π _ _ 2 −π _ _ 2 GO ON TO THE NEXT PAGE. ACT-1874FPRE 2 2 48. ABC Cabs and Tary Taxicabs both have an initial fare of a whole number of dollars for 1 passenger. The fare increases a whole number of dollars at each whole number of miles traveled. The graphs below show the 1-passenger fares, in dollars, for both cab companies for trips up to 6 miles. When the fares of the 2 cab companies are compared, what is the cheaper fare for a 5-mile trip?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Source question 55. Refer to the source image.

Paper 31 · ACT April 2017 · Form 74F · Math Test

At the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads faceup. Let the random variable x represent the total number of points awarded on any toss of the coins. What is the expected value of x ?

Paper 31 · ACT April 2017 · Form 74F · Math Test

For what positive real value of k, if any, is the determinant of the matrix 3 4equal to k ? (Note: The determinant of matrix 3 4equals ad − bc.) π _ _ 4 π _ _ 2 3 _ _ 2 9 _ _ 2 4 k k 3 b d a c END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

Paper 31 · ACT April 2017 · Form 74F · Math Test

Given a positive integer n such that in = 1, which of the following statements about n must be true? (Note: i2 = −1)

Paper 31 · ACT April 2017 · Form 74F · Math Test

For − ≤ θ ≤ , ⎪sin,θ⎪ ≥ 1 is true for all and only the values of θ in which of the following sets?

Paper 31 · ACT April 2017 · Form 74F · Math Test

Ray PK → bisects ∠LPM, the measure of ∠LPM is 11x°, and the measure of ∠LPK is (4x + 18)°. What is the measure of ∠KPM ? π _ _ 2 π _ _ 2 2 _ _ 7 1 _ _ 5 π _ _ 2 π _ _ 2 π _ _ 2 π _ _ 2 π _ _ 2 π _ _ 2 π _ _ 2 ACT-1874FPRE 2 2 55. What is the period of the function f(x) = csc(4x) ?