ACT Past Papers with Answers

4n' • 3n" is equivalent to: 7nl2

Devon bought running shoes at a price that was off the original price of $88. He paid a sales tax of 7% on the discounted price and gave the clerk four $20 bills. How much change should he receive? $ 7.84

Brandon is having a bake sale at school to raise $140.00 to donate to the local animal shelter. He sells brownies for $1.00 each and cookies for $0.50 each. Jiven that Brandon sells 82 brownies, and all sales go to the donation, how many cookies does he need to sell to reach his goal? 58 116 DO YOUR FIGURING HERE. ACT-C02 14 GO ON TO THE NEXT PAGE. 2

In the figure below, AB is congruent to BC, and AE intersects BF at C. What is the measure of ZB? A A DO YOUR FIGURING HERE. A 2 → E 38° 14° 38° 76° 142°

Patty, Carla, Shada, and Ling ran a race. The bar graph below gives each girl's running time, in seconds. many of the girls ran the race in less time than the average of the 4 running times? Patty Carla Shada Ling 181 84 162 0 20 40 60 2394 80 100

Between 9:00 a.m. and 10:20 a.m., 18,000 visitors entered the Family Fun Amusement Park. Between 9:00 a.m. and 10:20 a.m., an average of how many visitors per minute entered the park?

The point (4,r) lies on the graph of y=-3x + 2 in the standard (x)) coordinate plane. What is the value of r? -4 -18 К. -24

Sebastian programs his calculator to evaluate a linear function, but he doesn't say what the function is. When 8 is entered, the calculator displays the value 6. When 12 is entered, the calculator displays the value 9. Which of the following expressions explains what the calculator will display when any number, n, is entered?

A function f(x) is defined as f(x) = -4x?. What is 5(-5) ? -400 80 100 400

When x = -1, what is the value of 4x - 2x?? -6 2 6 ACT-C02 16 GO ON TO THE NEXT PAGE. 2AAAAA 4AAA2

In the figure shown below, all angles are right angles, and the side lengths given are in yards. What is the DO YOUR FIGURING HERE. area, in square yards, of the figure? 12 74 98 110 134 10

A certain fraternity had its freshmen members keep a log of their hours spent playing video games. When midterm grades were known, the fraternity president plotted the data in the standard (x,y) coordinate plane with average hours per week spent playing video games on the x-axis and midterm grade point average (GPA) on the y-axis as shown in the figure below. He then performed a linear regression on the data. Which of the following statements is true of the regression

Given 4x + 2 = -10, then |5 - 2| = ? 4 9 11 ACT-C02 17 GO ON TO THE NEXT PAGE. 2

The graph of y = 3 sin(x + 2) is shown in the standard (x,y) coordinate plane below. What is the maximum value of this function? DO YOUR FIGURING HERE. 2 27 x awN

For AABC shown below, what is the value of tan B ? DO YOUR FIGURING HERE. V2 in C V3 in

Given the true statement "If I live in Chicago, then I live in Illinois," which of the following statements must be true? •. If 1 live in Illinois, then I live in Chicago Illinois. Chicago.

Shown below, a board 3 feet 8 inches long is cut into 2 equal parts. What is the length, to the nearest inch, of each part? 3 feet 8 inches 1 foot 10 inches 5 inches

What is the minimum number of square floor tiles, each 9 inches on a side, that could be used to cover the floor of a rectangular hallway 15 feet long and 6 feel 28 56 81 90 ACT-C02 19 GO ON TO THE NEXT PAGE. 2ДДДДДДДAД2

Graphed in the standard (ry) coordinate plane below is DO YOUR FIGURING HERE. line 1 and the circle with equation (x- 2) + y*=1. Line / passes through O(0,0) and is tangent to the circle at A, and B is the center of the circle. What is the measure of ZAOB ? 5°

One square has a side whose length is x centimeters, and a second square has a side whose length is (x - 2) centimeters. What expression below represents the sum of the areas of the 2 squares, in square centimeters? 2-4

When graphed in the standard (x,y) coordinate plane, the line with equation x+ y = - has a slope of: ₽. -30 н. -10

Lucie sold a jacket on Kojo's site. The starling price of the jacket was $6.25, and its selling price was S34.20. What is the sum of the listing fee and selling fee Lucie paid to sell the jacket? $1.71 $2.21

For the items his classmates listed on his site last Friday, Kojo was paid listing fees that totaled $5.75. What is the maximum number of the items listed last Friday whose starting prices could have been in the range of $5.00-$19.99? 11 39

Erick sold 2 items on Kojo's site. The sum of the the 2 items given that the starting price was equal to the selling price for each of the 2 items? y = 116.00

Admission to a carnival is $4 for children and $6 for adults. A group of 21 people pays $90 for admission to the carnival. What is the ratio of the number of children to the number of adults in this group? 4:1

For all nonzero x, y, and z, which of the following is 22y2 equal to ? 16x',2 *'° 162* 16y" 70,10

The functions f and g are defined as f(x) = 2x + 3 and 8(x) =x - 1. What is f(8(-1)) ?

In a window display at a flower shop, there are 3 spots DO YOUR FIGURING HERE. for 1 plant each. To fill these 3 spots, Adam has 7 plants to select from, each of a different type. Selecting from the / plants, Adam can make how many possible display arrangements with l plant in each (Note: The positions of the unselected plants do not matter.) 3 7 18 210

In quadrilateral ABCD shown below, BC | AD, BC = 20 inches, AD = 28 inches, and the distance between BC and AD is 7 inches. What is the area, in square inches, of quadrilateral ABCD? -20 C B 140 168 196 336 560 7 -28

The figure below shows a solid concrete ramp for skateboarding. The length is 10 feet, the width is 6 feet, and the height is 3 feet. Which of the following values is closest to the volume, in cubic feet, of the concrete used to construct the ramp? 32 76 90 115 180 -10

A rectangle that is c inches by d inches is in the interior of a rectangle that is a inches by b inches, as shown below. The area of the shaded region is what fraction of the area of the large rectangle, in terms of a, b, c, and d? ab cd cd (a- c)b- d) ab ACT-C02 23 GO ON TO THE NEXT PAGE. 2ДАДДДДДДД2

A company prints contest codes on its fun-size bags of DO YOUR FIGURING HERE. candy, Each 6-character code consists of the letter A followed by the letter H followed by 4 of the digits O through 9. The digits may repeat. Which of the following expressions gives the number of different 6-character codes that are possible? I(I)(10)(10)(10)(10) 2(2)(10)(9)(8)(7)

A box contains 6 objects. Of those, 3 are disks (2 blue and 1 red) and 3 are triangles (1 blue, 1 red, and 1 yellow). If the probability of drawing each object is the same, what is the probability that an object drawn from the box is a blue object or a triangle? 1

When l0g4 x = -3, what is x ? 64 12 ACT-C02 24 GO ON TO THE NEXT PAGE. 2 2 DO YOUR FIGURING HERE. Use the following information to answer questions 42-44. The whole number test scores of all 30 students Ms. Smith's science class are represented in the cumulative frequency bar graph below. Ms. Smith's Science Test Scores 32- 28- 24 20 4 0 41-50 41-60 41-70 41-80 41-90 41-100 student test scores

How many students in Ms. Smith's science class had a score greater than 70 on the test? 13 18 20 72

Which of the following intervals must contain the median score of the students' test scores Ms. Smith's science class? 61-70 66-75 71-80

The students in Mr. Cho's class took the same test as those in Ms. Smith's class. The number of students in Mr. Cho's class with a score in the range 41-50 was 3 less than 4 times the number of students in Ms. Smith's class with a score in the range 41-50. How many students in Mr. Cho's class had a score in the range 41-50 on this test? 4 3 1 ACT-C02 25 GO ON TO THE NEXT PAGE. 2

A surveyor needs to find the length from point A to point C across a lake as shown in the figure below. The measurements of which of the following angles and side lengths are sufficient for the surveyor to determine the length of AC using only the law of sines? A A A A 2 DO YOUR FIGURING HERE. (Note: The law of sines says sin A angle side length A, B a a, C C a sin B sin C.)

Given that x = -2 is a solution to x? + bx - 6 = 0, which of the following polynomials is a factor of x? + bx - 6? x-3 x+1 ACT-C02 26 GO ON TO THE NEXT PAGE. 2

Square ABCE, shown below, has a side length of 10 inches. Point D is the midpoint of CE, and F is the midpoint of AE. What is the ratio of the area of ADEF, shown shaded, to the area of pentagon ABCDF? A F E ^ 2 DO YOUR FIGURING HERE. 1:3 1:4 1:7 C

For some positive integer k, the sum of the absolute values of all the integers from -k through k is 12. What is the value of k? 2 3 4

Two real-valued functions are defined by f(x) = Vx+1 and g(x) = (x- 3)". What is the domain of /(g(x)) ? B [0,00) [1,00 [3 00 D 4,00 -00.

Source question 52. Refer to the source image.

The solution to the equation 3d + 17 = 13 is which of the types of numbers listed below? I. Rational II. Irrational III. Positive IV. Negative V. Integer ACT-C02 27 GO ON TO THE NEXT PAGE. 2

A highway engineer is using a road map to lay out a detour for the westbound lane of a section of highway that, on the map, is a straight line going east and west. On the map, the detour goes 4 miles straight north, 1 mile straight west, 2 miles straight north, 6 miles straight west, 3 miles straight south, 1 mile straight east, and finally 3 miles straight south, back to the highway. According to the map, how many more miles will a westbound driver travel by taking the detour than he would if he could stay on the highway? 6

In the complex numbers, where i =-1, =3+=? F 3- i

The degree measures of the interior angles of a certain pentagon are in the ratio 2:3:4:4:5 What is the measure of the largest interior angle of this pentagon? 30° 60° 90° 120° 150°

The function y =/(x) is graphed in the standard (x) coordinate plane below. The domain of f is the set of all positive real numbers. One of the following graphs is the graph of y = - |f(x)|. Which one is it? DO YOUR FIGURING HERE. ins.

The sale price of a jacket is 10% off the original price. The clearance price of the jacket is 30% off the sale price. The clearance price is what percent off the original price? 27% • 33%

How long, in centimeters, is 1 side of a square whose perimeter is equal to the circumference of a circle with a radius of 2 centimeters? 4TT К. 4 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-C02 29