ACT Past Papers with Answers

Paper 27 · ACT April 2018 · Form A09 · Math Test

What is the sum of the complex numbers 3 - 41 and 5+31? 1+81

Paper 27 · ACT April 2018 · Form A09 · Math Test

Last year at RT University, the ratio of the number of students accepted to the number of students applying for admission was 2 to 7. RT University accepted 630 students last year. How many students applied to RT University last year? 810 ACT-A09 14 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Three line segments intersect as shown in the figure below, fonning angles with measures of 150°, 40°, and x. respectively. What is the value of x ? DO YOUR FIGURING HERE. S. A carnival game is played using an open box with a rectangular bottom measuring 6 inches by 13 inches. A square with side lengths of 4 inches is painted on the bottom of the box. The game is played by dropping a small bead into the open box. If the bead comes to rest in the painted square. the player wins a prize. Assuming a bead dropped into the box comes to rest at a random spot on the bottom of the box, which of the following is closest to the probability that the bead comes to rest in the painted square?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Source question 5. Refer to the source image.

Paper 27 · ACT April 2018 · Form A09 · Math Test

25%

Paper 27 · ACT April 2018 · Form A09 · Math Test

The line below contains X, Y, and Z, in that order. The ratio of the length of XY to the length of YZ is 5.9. If it can be deterniined. what is the ratio of the length of XY to the length of XZ ? 5:14

Paper 27 · ACT April 2018 · Form A09 · Math Test

The solution set of 2x + 4 a-8 is the set of all real values of x such that: x2-2 ACT.AOg 15 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following is equivalent to (a ) 21 DO YOUR FIGURING HERE. 21

Paper 27 · ACT April 2018 · Form A09 · Math Test

If f(x) - 3x' + 7x - 8, thenf(-3) - ? 40

Paper 27 · ACT April 2018 · Form A09 · Math Test

Thvo sides of a triangle are equal in length. The third side is 3 centimeters longer than either of the other 2 sides. Given that the perimeter of the triangle is 93 centimetcrs, what is th¢ l¢ngth, in ¢¢ntimeters, of the longest side?

Paper 27 · ACT April 2018 · Form A09 · Math Test

The 220 graduating s¢nior8 of Madison High School will sit in the center section of the school auditorium at the graduation ceremony. How many rows of seats will be needed to seat all of the graduating seniors if the first row has 10 seats and each succeeding row has 2 more seats than the previous row?

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9,-11) and: AGT-AOg 16 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 14-16. A community theater group perfonned at 5 local schools. For each school. the table below shows the total number of tickets sold and the total dollar amount collected from tAcket sales. Number of tickets sold School Ticket sales 200 250 300 150 275 $1,400 $1,650 $1,800 $1,350 $1,625

Paper 27 · ACT April 2018 · Form A09 · Math Test

At School A, only 2 types of tickets were sold.. premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ? 150 IS. The theater group had to pay each school a facility charge. For use of its facility, School C charged the theater group IO% of the ticket sales and a fixed fee of $200. How much money did School C charge the theater group for use of its facility.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Source question 15. Refer to the source image.

Paper 27 · ACT April 2018 · Form A09 · Math Test

What is the difference between the median and the mean number of tickets sold at the 5 schools?

Paper 27 · ACT April 2018 · Form A09 · Math Test

What is the area, in square decimeters, of a right triangle with side lengths of 10 dm, 26 dm, and 24 dm ? ACT.A09 17 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93. 68, 93, 70, and 98. What is the 7th number on the list? DO YOUR FIGURING HERE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following is the sine of the smallest angle in a right triangle with side lengths 7, 24, and 25 inches, respectively. 25 24 24 25 25

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the figure shown below, all angles arc right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure? 10 12

Paper 27 · ACT April 2018 · Form A09 · Math Test

A triangle has a perimeter of 26 cm and sides of length x cm, (x + 3) cm, and (x + 5} cm. What is the value ofx?

Paper 27 · ACT April 2018 · Form A09 · Math Test

A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assurning the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty .

Paper 27 · ACT April 2018 · Form A09 · Math Test

An ice cream shop sells ice cream cones with exactly l of 3 ice cream flavors in the cone. The 3 flavors are vanilla, chocolate, and strawberry. Last Saturday, the shop sold 42 cones. It sold I I more with chocolate than with vanilla and 2 more with vanilla than with strawberry. How many cones with strawberry ice cream did thc shop sell that Saturday . DO YOUR FIGURING HERE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

In ￿ABc below. D is the midpoint of CB. ZABC is a right angle. AB = 8 m, and AC - 10 m. What is AD, in meters? 41 73 10 91 105

Paper 27 · ACT April 2018 · Form A09 · Math Test

Lyman has plotted 5 points in the standard (x,y) coordinate plane below. He then plots a new point as follows: the x-coordinate of the new point is the mean of the x-coordinates of the 5 points already plotted" the y-coordinate of the new point is the mean of the y-COOTdinates of the 5 points already plotted. Which of the following ordered pairs gives the coordinates of Lyman's new point? ACT-AOg 19 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

The 1st and 2nd terms of a eertain geometri¢ sequence are 10 and -5, respectively. What is the 5th term of the geometric sequence? DO YOUR FIGURING HERE. 16 16 32

Paper 27 · ACT April 2018 · Form A09 · Math Test

Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $ 1.00 per shirt that she stitches or $ l 0.00 per hour. whichever daily amount is higher. Alani stitched the following numbers of shirts.. 60 on Monday. 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani's total pay for these 5 days?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following rnost precisely describes the roots of the equation 5x + 7x + 2 - 0 ?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Paula is planning a course for a bike race. The course is in the shape of a right triangle, as shown below. Participants will begin at A, ride directly to B, then directly to C, and directly back to A. Paula wants to put a rest stop at the halfway point on the course. How many miles past B will the rest stop be? smi ACT.AOg 20 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Adams High School has 120 students. and students are taking Literature. Of the students NOT taking Literature, are taking Composition. No students are taking both Literature and Composition. How many students are taking Composition? of the DO YOUR FIGURING HERE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

For what value of x is the equation fx + ￿9 = xf36 true?

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the right triangle LSABC shown below, the length of BC is 12 feet and sin A= What is the length, in feet, of AC ? 12

Paper 27 · ACT April 2018 · Form A09 · Math Test

What integer does 3(log2 16) equal? 12

Paper 27 · ACT April 2018 · Form A09 · Math Test

A bag contaÉns several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be true about the marbles in the bag. of other colors. ACT-A09 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questlons 35-37. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip. the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour. and I ride on the roller coaster track is completed in

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following values is closest to the total distance traveled, in miles, during I compleie ride on the roller coaster track?

Paper 27 · ACT April 2018 · Form A09 · Math Test

The roller coaster is at a height of at least 235 feet for a total of 5 seconds during each complete ride. Which of the following is closest to the percent of the time during a complete ride that the roller coaster is at a height of at least 235 feet?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following values is closest to the aveIage slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds? ACT-A09 22 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

The value of £(0.5k + 2.5x + 6) is between which of the following numbers when x - l O ? DO YOUR FIGURING HERE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

For which of the following data sets is the difference between the mean and the median the gr¢at¢stg

Paper 27 · ACT April 2018 · Form A09 · Math Test

Pablo has a deck and pool in his backyard. The deck's shape is a rectangle with a semicircle removed and is shown shaded in the figure below. The lengths of the straight sides of the deck are given in feet. Pablo plans to cover the top.of the deck with stain. To decide how much stain to purchase, he needs to find the area of the lop of the deck. To the nearest square foot, what is the area of the top of the deck? 20 pool 32 20

Paper 27 · ACT April 2018 · Form A09 · Math Test

A 3-foot-wide brick sidewalk is laid around a rectangular swimming pool. The outside edge of the sidewalk measures 30 feet by 40 feet. as shown in the figure below. What is the perimeter, in feet. of the swimming pool? 30 70 116 140 816 40 ACT-AOO 23 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Given the functions f(x) = k and g(x) - g(f(x)l ? what is DO YOUR FIGURING HERE. (4-x)' 16-x

Paper 27 · ACT April 2018 · Form A09 · Math Test

A circle has a circumference of 2ffif2 feet. What is the area, in square feet. of the circle? f2

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the standard (x,y) coordinate plane, the coordinates of the y-intercept of the graph of the function y =f(x) are (0,-2). What are the coordinates of the y-intercept of the graph of the function y =flx) - 3 ?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following is an equation of a parabola that passes through the 3 points labeled in the standard (x,y) coordinate plane below? (0,3) (-3,0) (3,0) (x-3)(x+3) -(x - 3)'(x + 3) -(x- 3)(x + 3), {x-3)(x+3) (x-3)(x+3) ACT.A09 24 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

As x continually increases in value without bound, thc value of most closely approaches: DO YOUR FIGURING HERE. x+3

Paper 27 · ACT April 2018 · Form A09 · Math Test

Yulan will use a bag of 30 solid-colored marbles for a game in which each player randomly draws marbles from the bag. The number of marbles of each color is shown in the table below. Color Number Blue Rcd Black White Green 10 Yulan will randomly draw 2 marbles from the bag, one aftcr thc othcr, without replacing the first marble. What is the probability that Yulan will draw a black marble first and a green marble second? 75 145 15 39 145

Paper 27 · ACT April 2018 · Form A09 · Math Test

The expression 2b+c b-2c is undefined whenever b = ACT-AOO 25 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

What number is halfway between - and - DO YOUR FIGURING HERE. 12 26 35 27 35

Paper 27 · ACT April 2018 · Form A09 · Math Test

A function f(x) is defined as f(x) = 3, 2 real numbers satisfyf(x) = l ? -2and2 -2andO -land2 -land0 Oand2 What

Paper 27 · ACT April 2018 · Form A09 · Math Test

The ellipse shown in the standard (x,y) coordinate plane below has equation (x-3)' (y-5)' 25 l. Which of the following ordered pairs are the foci of the ellipse? (0,5) (3,0) (3,0) and (3, 9) ACT-A09 26 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

A basket contains 10 solid-colored balls 2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered l and 2 (each number is used once), the r¢d balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will be red or have a 3 printed on it? DO YOUR FIGURING HERE. 10 10 10 10 10

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the figure below, the given side lengths of LABC are in inches. What is the area, in square inches, of ABC? 12 30° 13

Paper 27 · ACT April 2018 · Form A09 · Math Test

There are 66 calories in 15 grams of grated Parn]esan cheese, and 59% of those calories are from fat. When measuring Parmesan cheese, 5 grams is equal to I tablespoon. Which of the following is cIoscst to the number of calories from fat per tablespoon of grated Parmesan cheese? ACT-A09 27 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

In the diagram below, B, F, and H are on AC, AE, and BF, respectively, and GH L BF. The area of square ABGF is the area of square ACDE. What percent of the area of ACDE does the shaded portion represent? DO YOUR FIGURING HERE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

In a data set of 10 distinct values, the single largest value is replaced with a much greater value to form a new data set. Which of the following statements is tnle about the values of ihe mean and median for the new data set as compared to the mean and median of the original data set? same. increase. IL Using the given inforrnation, the means and mcdians of the 2 data sets cannot b¢ comparcd.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Valley High School and Mountain High School have dectded that selected students will attend a daytime theatrical performance that costs $5 for each teacher and $3 for each student. One teacher and 10 students from Valley High will attend, and 2 teachers and 25 studenES from Mountain High will attend. Which of the following matrix products represents the ticket costs. in dollars. for each high school? 10 25 I 10 25 2 1 25 2 10 10 25 I 10 2 25 ACT.A09 28 GO ON TO THE NEXT PAGE.

Paper 27 · ACT April 2018 · Form A09 · Math Test

Karie is inventing a new notation in math. She has decided to use nl to denote the sum of the first n positive integers. For example, 51 means 5 + 4 + 3 + 2 + l. Kane has written 3 statements that she is investigating as possible properties of nl. I. nl+(n+l)=(n+l)I II. nl + nl= (2n)I DO YOUR FIGURING HERE. Which of these staternents, if any, is(are) true for all positive integers n ?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Rey wants to make an open box as shown below, using a square piece of cardboard. He intends to cut a 2-inch square from each corner of the cardboard and fold the cardboard along the lines shown to form the sides. The resulting box will have a volume of 72 cubic inches. What are the dimensions, in inches, of the original piece of cardboard?

Paper 27 · ACT April 2018 · Form A09 · Math Test

Which of the following quadratic equations has the complex number (i + ￿1 ) as a solution? x+l=O -Ir+2=0 END OF TEST 2 STOPI DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-AOg 29