ACT Past Papers with Answers

Paper 15 · ACT June 2021 · Form D06 · Math Test

For what value of a is the equation a + 10 = 6 true?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the least common denominator of the fractions , , and ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

⎪5 − 3⎪ − ⎪1 − 6⎪ = ? A B C D 40° 110° ? 1 _ _ 2 3 _ _ 8 1 __ _ 20 4 __ _ 15 DO YOUR FIGURING HERE. 14 GO ON TO THE NEXT PAGE.

Paper 15 · ACT June 2021 · Form D06 · Math Test

In the trapezoid below, AB ___ is parallel to DC ___ _ . What is the measure of ∠C ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Gao earns his regular pay of $12 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Gao is paid 1 times his regular pay. How much does Gao earn in a week in which he works 56 hours?

Paper 15 · ACT June 2021 · Form D06 · Math Test

On the first day of school, Ms. Dubacek gave her third-grade students 6 new spelling words to learn. On each day of school after that, she gave the students 3 new spelling words. How many new spelling words had she given the students by the end of the 21st day of school?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the value of the expression ? (Note: 3! = 3(2)(1) and 6! = 6(5)(4)(3)(2)(1)) 1 _ _ 2 8! ____ _ (4!)2 1 _ _ 2 45° 85° A B C D DO YOUR FIGURING HERE. 15 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

Right triangle nABC and its side lengths given in inches are shown below. What is sin,B ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

(6a3 − 5ac2 + 12c) − (4c − 3a3 − 2ac2 ) is equivalent to: − 2ac2 + 14c − 7ac2 + 16c − 3ac2 + 08c − 7a2 c4 + 16c2 − 3a2 c4 + 08c2

Paper 15 · ACT June 2021 · Form D06 · Math Test

Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 2 and −x + y = 7 ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Tim’s flight was originally scheduled to depart at 4:51 p.m., but it was delayed 563 minutes. What time did Tim’s flight eventually depart?

Paper 15 · ACT June 2021 · Form D06 · Math Test

A circle with the equation x2 + y2 = 144 is graphed in the standard (x,y) coordinate plane. At what points does the circle intersect the x-axis?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Given that x2 − 5x − 36 factors into 2 binomial factors with integer coefficients, which of the following binomials is 1 of those factors? A B C b c a a _ _ b a _ _ c b _ _ a b _ _ c c _ _ a DO YOUR FIGURING HERE. 16 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

Two vectors are shown in the standard (x,y) coordinate plane below. One of the following vectors in the standard (x,y) coordinate plane is the sum of these 2 vectors. Which one?

Paper 15 · ACT June 2021 · Form D06 · Math Test

A square and a rectangle have the same area. The length of the rectangle is 196 centimeters, and the width of the rectangle is 4 centimeters. What is the length, in centimeters, of a side of the square? y x 2 4 −2 6 4 2 −2 O y x 2 4 −2 6 4 2 −2 O x 2 4 −2 6 4 2 −2 O y x 2 4 −2 6 4 2 −2 O x 2 4 −2 6 4 2 −2 O y x 2 4 −2 6 4 2 −2 O DO YOUR FIGURING HERE. 17 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

T-shirts are on sale for D dollars each, including tax. Valentina has N dollars with which to purchase T-shirts. After she purchases the maximum number she can, Q T-shirts, she has R dollars left. For all possible choices of D and N, which of the following equations models a correct relationship between D, N, Q, and R, as defined?

Paper 15 · ACT June 2021 · Form D06 · Math Test

At a sandwich shop, customers can order either a meat or a vegetarian sandwich on either white or wheat bread. Out of a total of 50 customers, 20 ordered a sandwich on white bread, 28 ordered a meat sandwich, and 12 ordered a meat sandwich on white bread. The given information is summarized in the table below. How many customers ordered a vegetarian sandwich on wheat bread?

Paper 15 · ACT June 2021 · Form D06 · Math Test

A team of biologists tagged and released 90 deer in a forest. From the same forest 2 weeks later, the biologists collected a random sample of 30 deer, 5 of which were tagged. Let p be the proportion of deer in this forest that are tagged. What is p̂, the sample proportion, for this sample?

Paper 15 · ACT June 2021 · Form D06 · Math Test

√• 2 + √• 8 + √•• 18 = ? Type of bread Meat Vegetarian Total White 12 ? 20 Wheat ? ? ? Total 28 ? 50 1 __ _ 24 1 __ _ 18 1 _ _ 6 1 _ _ 5 1 _ _ 3 DO YOUR FIGURING HERE. 18 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

Which of the following inequalities is equivalent to 3 − 2x > 7 − x ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Let a be positive and b be negative. If it can be determined, in which quadrant of the standard (x,y) coordinate plane is the point (−a,b2 ) located?

Paper 15 · ACT June 2021 · Form D06 · Math Test

The mass of a certain type of bacteria grows exponentially, doubling every 20 minutes. What was the mass, in milligrams, of the bacteria exactly 2 hours after the mass first reached 10 milligrams?

Paper 15 · ACT June 2021 · Form D06 · Math Test

One day will be randomly selected from the 7 days in a week. Then 1 month will be randomly selected from the 12 months in a year. What is the probability that the selected day will be Tuesday and the selected month will be January? quadrants of the standard (x,y) coordinate plane I II III IV x y O 1 __ _ 84 1 __ _ 42 1 __ _ 19 2 __ _ 19 4 _ _ 3 4 _ _ 3 19 __ _ 84 DO YOUR FIGURING HERE. 19 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

The average weight of Juan, Jim, and Malik is exactly 160 pounds. The average weight of Juan, Jim, Malik, and Harry is exactly 150 pounds. How many pounds does Harry weigh?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the value of the expression _log6(36)+_log3(9)+ ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Each of 2 identical number cubes, shown below, has a different integer, 1 through 6, on each face. Consider the sample space determined by rolling these number cubes and adding the 2 integers on the faces that land on top. What is the positive difference between the greatest sum and the least sum in this sample space?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What angle measure, in radians, is equal to 30° ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

For one school week, Hannah recorded the following temperatures, in degrees Fahrenheit, so she could investigate the difference between the high and low temperature each day. Day Low High Monday −3° 26° Tuesday −5° 32° Wednesday −7° 22° Thursday 03° 40° Friday 02° 40° To the nearest degree, what was the mean of the differences in daily high and low temperatures for these 5 days? π _ _ 6 π _ _ 5 π _ _ 3 π _ _ 2 5π __ _ 6 DO YOUR FIGURING HERE. 20 GO ON TO THE NEXT PAGE. ACT-D06 2 2

Paper 15 · ACT June 2021 · Form D06 · Math Test

0% of their final semester grades will come from their homework averages, and the remaining 70.0% will come from their test averages. She also said that the final exam will count for 20.0% of the test average. What percent of the science final semester grade is the final exam grade?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the 322nd digit after the decimal point in the repeating decimal 0.1357 ____ _ ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

You and a friend each have a can full of water. You start pouring the water from your can into an empty bucket at a constant rate of 4 ounces per second. While you are still pouring water, 3 seconds after you started, your friend starts pouring the water from her can into the same bucket at a constant rate of 2 ounces per second. How many seconds after you first started pouring the water into the bucket will it contain 24 ounces of water? Expense Fraction of income fixed 3 _ _ 8 food 1 _ _ 4 utilities 1 _ _ 8 transportation 1 __ _ 12 personal 1 __ _ 16 entertainment 1 __ _ 24 5 __ _ 48 1 __ _ 48 1 __ _ 24 1 __ _ 16 1 _ _ 8 DO YOUR FIGURING HERE. 21 GO ON TO THE NEXT PAGE. ACT-D06 2 2 DO YOUR FIGURING HERE. 22 GO ON TO THE NEXT PAGE. ACT-D06 2 2 33. A package of candy contains pieces each of which is 1 of 6 possible colors: brown, red, green, yellow, orange, and blue. In each package, of the pieces are brown and the remaining pieces have an even distribution of the other 5 colors. What is the probability that a piece drawn randomly from the package is red?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Source question 33. Refer to the source image.

Paper 15 · ACT June 2021 · Form D06 · Math Test

Which of the following intervals is the range of the function f(x) = −(x − 3)2 + 4 ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Anoki made a scale drawing of his rectangular classroom. The classroom is 7.5 meters by 9.0 meters. In his scale drawing, Anoki made the length of the shorter side of the classroom 9.0 centimeters. What is the length, in centimeters, of the longer side of the classroom in Anoki’s scale drawing?

Paper 15 · ACT June 2021 · Form D06 · Math Test

In rhombus ABCD shown below, AC = 5 feet and BD = 6 feet. What is the area of ABCD, in square feet? 1 _ _ 3 1 __ _ 15 2 __ _ 15 1 _ _ 6 1 _ _ 5 2 _ _ 3 A B C D

Paper 15 · ACT June 2021 · Form D06 · Math Test

One number is 25% of a second number, and the second number is 70% of a third number. The first number is what percent of the third number?

Paper 15 · ACT June 2021 · Form D06 · Math Test

The monthly rent charged for a store at Center Street Mall is $2 per square foot of floor area. The floor plan of a store at Center Street Mall is shown in the figure below, with right angles as indicated and all distances given in feet. How much monthly rent is charged for this store?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Mrs. Neeson, a science teacher, told her students that

Paper 15 · ACT June 2021 · Form D06 · Math Test

A rectangle with an area of 30 square inches has length and width, in inches, that are both integers. Which of the following CANNOT be the perimeter, in inches, of the rectangle? 60 30 33 27 18 36 45 39 DO YOUR FIGURING HERE. 23 GO ON TO THE NEXT PAGE. ACT-D06 2 2 DO YOUR FIGURING HERE. 24 GO ON TO THE NEXT PAGE. ACT-D06 2 2 A couple is deciding between 2 condos to purchase. Some information about each condo is given below. The couple assumes that the market value of either condo will increase exponentially at a rate of 4% per year.

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the positive difference, in dollars, of the 2 list prices?

Paper 15 · ACT June 2021 · Form D06 · Math Test

The couple will consider the price per square foot of each condo. Let x and y be the price per square foot, rounded to the nearest $1, of Condo X and Condo Y, respectively. One of the following comparisons is true. Which one?

Paper 15 · ACT June 2021 · Form D06 · Math Test

The annual property tax for Condo X is 2% of its assessed value. What is the assessed value of Condo X ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

In the complex plane, consider the segment whose endpoints are the points corresponding to −6 + 3i and 2 − 7i. The midpoint of this segment corresponds to which of the following complex numbers? Property details List price Area in ft2 Price per ft2 Annual property tax Condo X $210,000 2,274 $92 $3,824 Condo Y $189,900 1,726 ? $3,524 Use the following information to answer questions 41–43.

Paper 15 · ACT June 2021 · Form D06 · Math Test

In the standard (x,y) coordinate plane, the 3 lines with equations y = x − 3, y = − x + 2, and x = 0 bound a triangular region. What is the area, in square coordinate units, of that triangular region? (A blank grid has been provided for your use.)

Paper 15 · ACT June 2021 · Form D06 · Math Test

In square ABCD shown below, AC ___ is a diagonal and the length of BC ___ is 75 feet. Which of the following quantities is NOT a rational number? ___ , in feet ___ , in feet

Paper 15 · ACT June 2021 · Form D06 · Math Test

The volume of a solid object is equal to the volume of water it displaces when completely submerged in water. A solid object will be placed in a rectangular tank that has a base of 35 cm by 30 cm and is filled with water to a uniform depth of 13 cm. When the object is completely submerged, the new depth of the water in the tank is 15 cm. What is the volume, in cubic centimeters, of the object? y O x B C 75 A D 2 _ _ 5 3 _ _ 5 DO YOUR FIGURING HERE. 25 GO ON TO THE NEXT PAGE. ACT-D06 2 2 DO YOUR FIGURING HERE. 26 GO ON TO THE NEXT PAGE. ACT-D06 2 2 The 2 circles graphed in the standard (x,y) coordinate plane below are centered at the origin, O. In coordinate units, the radius of the smaller circle is 2, and the radius of the larger circle is 4. Points A(−4,0), B, and C(4,0) are on the larger circle. The measure of ∠BOC is 45°. (Note: Both axes have the same scale.)

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the x-coordinate of B ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

A 3rd circle, not shown, is the image resulting from applying the 1st transformation listed below to the smaller circle and then applying the 2nd transformation listed below to the result of the 1st transformation. 1st: A dilation with center O and scale factor 2 2nd: A translation of 8 coordinate units to the right The 3rd circle has how many points in common with the larger circle?

Paper 15 · ACT June 2021 · Form D06 · Math Test

What is the area, in square coordinate units, of the region that is outside the smaller circle and inside the larger circle? B y x O C(4,0) A(−4,0) 4 ___ _ √• 3 4 ___ _ √• 2 Use the following information to answer questions 48–51. DO YOUR FIGURING HERE. 27 GO ON TO THE NEXT PAGE. ACT-D06 2 2 51. Which of the following is an equation of OB ↔ ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Source question 51. Refer to the source image.

Paper 15 · ACT June 2021 · Form D06 · Math Test

A sequence is given by s1 = 4 and sn + 1 = 2sn − 3 for n ≥ 1. What is s5 ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

In the figure below, the distances between 2 pairs of cities are shown, as well as the angle formed at Ewing, which has a measure of 127°. Which of the following values is closest to the distance, in miles, from Deerborn to Fergus? (Note: cos,127° ≈ −0.6; sin,127° ≈ 0.8)

Paper 15 · ACT June 2021 · Form D06 · Math Test

Which of the following expressions is equivalent to − ? Ewing Deerborn Fergus 127° 1 _____ x + a 1 _____ x − a 2a _____ _ _ x2 − a2 a2 _____ _ _ x2 − a2 2x _____ _ _ x2 − a2 1 _____ _ _ x2 − a2 1 __ _ 2a DO YOUR FIGURING HERE. 28 GO ON TO THE NEXT PAGE. ACT-D06 2 2 55. One of the following equations represents the ellipse shown below in the standard (x,y) coordinate plane. Which one?

Paper 15 · ACT June 2021 · Form D06 · Math Test

Source question 55. Refer to the source image.

Paper 15 · ACT June 2021 · Form D06 · Math Test

One of the following equations is that of a parabola with x-intercepts −5 and in the standard (x,y) coordinate plane. Which equation? − 11x − 20 + 11x − 20 − 17x − 15 + 17x − 15 − 17x − 04

Paper 15 · ACT June 2021 · Form D06 · Math Test

There are 100 fractions in the following set. 5 , , , , … , , , 6 Each fraction after the first is found by adding 3 to the preceding fraction’s numerator and denominator. What is the product of these 100 fractions? (2,2) (5,−3) (−1,−3) (2,−8) y x O (y + 3)2 ___ ____ 5 (x − 2)2 ___ ____ 3 (y − 3)2 ___ ____ 5 (x + 2)2 ___ ____ 3 (y − 3)2 ___ ____ 3 (x + 2)2 ___ ____ 5 (y + 3)2 ___ ____ 25 (x − 2)2 ___ ____ 9 (y − 3)2 ___ ____ 25 (x + 2)2 ___ ____ 9 3 _ _ 4 298 ___ _ 301 295 ___ _ 298 292 ___ _ 295 10 __ _ 13 7 __ _ 10 4 _ _ 7 1 _ _ 4 1 _ _ 3 1 _ _ 4 1 ___ _ 100 1 ___ _ 301

Paper 15 · ACT June 2021 · Form D06 · Math Test

If 2x = 7 and 2y = 14, then x − y = ?

Paper 15 · ACT June 2021 · Form D06 · Math Test

The table indicates the grade (10 or 11) and high school (North or South) of the 270 students enrolled in Algebra II in the Green City School District. Suppose 2 of these students will be chosen at random to represent the Algebra II classes at a local STEM (Science, Technology, Engineering, and Mathematics) event. Which of the following expressions gives the probability that both chosen students will be from the same grade and the same high school?

Paper 15 · ACT June 2021 · Form D06 · Math Test

A certain company has 120 employees, 85 of whom have business degrees. Of the employees with business degrees, 75 are certified public accountants (CPAs). There are 14 employees who are not CPAs and also do not hold a business degree. One employee of the company will be selected at random to be interviewed for a television news program. What is the probability that the selected employee will be a CPA ? (Note: A business degree is NOT required to be a CPA.) North South Grade 10 47 93 Grade 11 73 57 57(56) ________ 270(269) 73(72) ________ 270(269) 93(92) ________ 270(269) 47(46) ________ 270(269) 56 ___ _ 270 73 ___ _ 270 93 ___ _ 270 47 ___ _ 270 1 _ _ 4 93(57) ________ 270(269) 47(73) ________ 270(269) 73(57) ________ 270(269) 47(93) ________ 270(269) 1 _ _ 4 1 _ _ 4 75 ___ _ 120 85 ___ _ 120 89 ___ _ 120 96 ___ _ 120 99 ___ _ 120 DO YOUR FIGURING HERE. 29 ACT-D06 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.