ACT Past Papers with Answers

A retail sales associate's daily commission during 1 week was $30 on Monday and Tuesday and $70 on Wednesday, Thursday, and Friday. What was the associate's average daily commission for these 5 days? $50 $51 $54 $55 $56

What is the greatest common factor of 45, 50, and 84?

For what value of x is the equation 2(x - 12) + x = 36 true? 4 8 20 ACT-C01 14 GO ON TO THE NEXT PAGE. 2 A A

A bag contains exactly 22 solid-colored buttons: 4 red, 6 blue, and 12 white. What is the probability of randomly selecting 1 button that is NOT white? n= 2 DO YOUR FIGURING HERE. 22 10

On a map, _ inch represents 12 actual miles. Two towns that are 5 inches apart on this map are how many actual miles apart? 60 30 24 12

Caden had exactly 45 plants to sell. After Day 1 of his sale, he had exactly 42 plants left. After Day 2, Caden had exactly 39 plants left. After Day 3, he has exactly 36 plants left. Assuming Caden will continue to sell plants at that daily rate, how many of these plants will he have left at the end of Day 6 ? 27 6 3

An on-demand movie service charges $5 per month, plus $2 for each movie rented. Which of the following equations models the relationship between M, the number of movies rented per month, and T. the total monthly cost, in dollars, for the service? M = 5 + 2T T = 2 + 5M

What are the solutions to the quadratic equation (2x+5)(3x- 4) =0? в. -5 and - 2 3 and 2 5 and - 2 § and +|m +/m tim ACT-C01 15 GO ON TO THE NEXT PAGE. 2

An 8-inch-by-6-inch rectangle is cut along a diagonal to form 2 triangles. What is the area, in square inches, of each triangle? 7 G 12 14 24 48 DO YOUR FIGURING HERE. 2

In a class of tenth graders, no student participated in more than 1 of the following extracurricular activities: 2 the class played in the band; sang in the chorus; I played football; and 60 played basketball. What fraction of the class did not participate in any 1 of these 4 activities? 5,400 L 20 74 79 57 60

What is the smallest integer greater than V6l? 4 7 10

In AABC shown below, sin C = and the length of AB is 6 inches. What is the length, in inches, of AC ? V5 4 5 9 ACT-C01 16 GO ON TO THE NEXT PAGE. 2

The table below shows the first 5 terms of an arithmetic sequence. Which of the following is a general expression for the ath term? Term position (n) 1 nth term don- LAWN 17 2 DO YOUR FIGURING HERE. 2n - - 3n - 2 4п - 3 5n - 4 К. бл - 5

What is the perimeter, in feet, of the figure shown below? 8 ft 60 62 70 80 84 20 fl 14 f 20 f

Manuel estimates that § of a pizza is left. Stephen estimates that is left. They are going to compromise for a joint estimate by using the number halfway between their 2 estimates. What is their joint estimate? 17 24 = - 2

So far this basketball season, Sherita made 46 of her first 60 free throws, giving her a free-throw average of about 76.7%. What is the minimum number of free throws she would need to make from now on in order to have a free-throw average of at least 80% ? 0 4 20 ACT-CO1 17 GO ON TO THE NEXT PAGE. 2

Data Set A consists of the 8 numbers listed below. Data Set B consists of the 8 numbers in A and a 9th number, which is greater than 90. How will the mean and the median of B compare to the mean and the median of A ?

A truck traveling at 35 mph has a leaky radiator that is losing 4 fluid ounces per minute. How many miles will the truck travel before the radiator, which held 480 fluid ounces when it began to leak, is empty? К. 120.0

In the standard (x.y) coordinate plane. what 15 the midpoint of the line segment that has endpoints (-5.8) and (3.-1) ? в. (-і. 3) с. (}. 1) ACT-COF 18 GO ON TO THE NEXT PAGE. 2

The ordered pairs (x,y) in one of the following tables belong to a linear function. Which one? ^ 2 DO YOUR FIGURING HERE. O - N 0 3 0 -Nm -Nm 0 1 0 - ON- -N 3 0

In AABC shown below, mZA = x°, mLB = (2x)°. mLC = (3x)°, AB = c inches, AC = b inches, and BC = a inches. Which of the following inequalities correctly relates the side lengths of ABC? (Note: mLA denotes the measure of LA. and AB denotes the length of AB. The triangle is NOT drawn to scale.) a<bee с<а<ь

Source question 24. Refer to the source image.

The perimeter of a particular rectangle is 36 centimeters. The longer sides of the rectangle are each 2 centimeters longer than each of the shorter sides of the rectangle. What is the length, in centimeters, of one of the longer sides of this rectangle? 8 9 18 32 2 DO YOUR FIGURING HERE. Use the following information to answer questions 26-28. Winter Fun Ski Resort sells only 2 types of tickets-adult and student. On Monday, the resort sold 200 tickets, 1 ticket to each skier. Of those tickets, 25 were sold to first-time skiers. When Alyssa skis the resort's main.run, her elevation, E feet, at any point on the run is modeled by the equation E = 300,000 - where t is the number of seconds 1 + 100 after she begins skiing at the start of the main run.

The resort collected a total of $6,000 in ticket sales on Monday. The price of an adult ticket is $50 and the price of a student ticket is $25. How many adult and student tickets were sold on Monday? adult student 40 160 80 120 100 100 120 80 160 40

On Monday, the resort sold 1 ticket to each of the & members of the Herzog family. Assume this family is a representative sample of all of the skiers at the resort on Monday. How many of the 8 members of the Herzog family are NOT first-time skiers?

What is Alyssa's elevation, in feet, at the start of the main run? 30 300 3,000 ACT-C01 20 GO ON TO THE NEXT PAGE. 2

One side of square ABCD has a length of 18 meters. A certain rectangle whose area is equal to the area of ABCD has a width of 6 meters. What is the length, in meters, of the certain rectangle? 24 27 30 54 ^ 2 DO YOUR FIGURING HERE.

The 2 × 2 matrices A and B below are related to matrix C by the equation C= 2A - 3B. What is matrix C? 1- 131] B=|21]

Jen is doing an experiment to determine whether a high-protein food affects the ability of white mice to find their way through a maze. The mice in the experimental group were given the high-protein food; the mice in the control group were given regular food. Jen then timed the mice as they found their way through the maze. The table below shows the results. Mouse number 5 Experimental group 1 min 46 sec 2 min 2 sec 2 min 20 sec 1 min 51 sec 1 min 41 sec Control group 2 min 13 sec 1 min 49 sec 2 min 28 sec 2 min 7 sec 1 min 58 sec The average time the mice in the experimental group took to find their way through the maze was how many seconds less than the average time taken by the mice in the control group? 8 11 13 16 19 ACT-C01 21 GO ON TO THE NEXT PAGE. 2^АДДАДА

In the United States, phone numbers begin with a DO YOUR FIGURING HERE. 3-digit area code. Now, there are restrictions on some of the digits, but in the future, as more and more area codes are needed, the restrictions may need to be lifted. It, and when, there are no restrictions and each of the 3 digits can be any integer from 0 through 9, how many area codes will be possible? 27 30 729

The function y = 2 sin(8xcx) is graphed in the standard (r.y) coordinate plane below. How many x-intercepts does the graph of this function have on the interval

If both x and (5 + + %) are positive integers, what is the least possible value of x? 21 27 36 63 189 ACT-C01 22 GO ON TO THE NEXT PAGE. 2 2 DO YOUR FIGURING HERE. Use the following information to answer questions 35-38. In parallelogram ABCD shown below, the diagonals intersect at E, mBDC = 42°, mLBDA = 71°, and AB = (}n - 5) inches. (Note: The figure is NOT drawn to scale; mPQR denotes the measure of ZPQR.) 2 A 3 n- 5 - 42°

What is mBAD? В. 42° . 67°

Given that DC = ("+ 7) inches, what is the value of n? 4 6 12 К. 36

Suppose A and Care located at (2,10) and (30,3), respectively, in the standard (x,y) coordinate plane. What are the coordinates of E?

Which of the following triangles is congruent to ДАВЕ ? Н. ДВСЕ ABCD ACDE ACT-C01 23 GO ON TO THE NEXT PAGE. 2

The track for a model railroad display is set up as 2 circles that are tangent to one another and have diameters of 30 feet and 50 feet, respectively, as shown below. The engine of the train travels at a constant rate of 75 feet per minute. To the nearest minute, how many minutes does the engine take to go in a figure 8 pattern around the entire track exactly I time? 30 feet DO YOUR FIGURING HERE. - MAN 50 feet

( =?

What is the value of the positive real number x such that log, 25) = -2? 50 ACT-C01 24 GO ON TO THE NEXT PAGE. - 2

The points (-4,-5), (0,-3), and (6,0) lie on a line in the standard (x,y) coordinate plane. Which of the following points also lies on that line? (-1,-4) (4,-1)

Rya and Sampath start running laps from the same starting line at the same time and in the same direction on a certain indoor track. Rya completes one lap in 16 seconds, and Sampath completes the same lap in 28 seconds. Both continue running at their same respective rates and in the same direction for 10 minutes. What is the fewest number of seconds after starting that Rya and Sampath will again be at their starting line at the same time? 88 120 220 К. 448

The CFO of Math King Enterprises estimates that if the company sets a price of c cents for each unit of their new product, then the weekly profit from selling the product will be modeled by p(c) = 1,600c - 4c* where 0 ≤ c ≤ 400. According to this model, for which of the following values of c will the weekly profit for this product be the largest? 20 В. 40 100 200 400

Given consecutive positive integers a, b, c, and d such that a <b<c< d, which of the following expressions has the greatest value? 2 DO YOUR FIGURING HERE. н. д a+b b + c c+ d

The ratio of the perimeters of two squares is 2:3. If the area of the larger square is 324 square feet, what is the length, in feet, of the side of the smaller square? 18 24 27 36 ACT-C01 25 GO ON TO THE NEXT PAGE. 24 AAA

Wind blowing against a flat surface exerts a maximum force equal to kS? where S is the area of the surface, v is the wind's velocity, and k is a constant. If a 40 mile-per-hour (mph) wind can exert a maximum force of 50 pounds on a 1-square-foot flat surface, what is the maximum force, in pounds, that an 80 mph wind can exert on a 2-square-foot flat surface? 100 128 200 400

Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk? 2 DO YOUR FIGURING HERE. 16 44 50 58 10 20

Radius OA of the circle shown below is perpendicular to AP. The circle intersects OP at B. The length of AP is 12 centimeters, and the measure of ZAPO is 20°. Which of the following values is closest to the length, in centimeters, of BP? 12 P 20° (Note: sin 20° - 0.342, cos 20° = 0.940, and tan 20° = 0.364)

The average of 10 test scores is x. When the highest DO YOUR FIGURING HERE. score and lowest score are removed from the 10 scores, the average is y. Which of the following is an expression for the average of the highest score and lowest score? 2 10x - 8y 10x + 8y 4 2

Which of the following is the solution set of 271 = 95n - 4 ?

Each face of 2 cubes with faces numbered from 1 through 6 has a 5 chance of landing up when the 2 cubes are tossed. What is the probability that the sum of the numbers on the faces landing up will be less than 6 ? 36 18 5 13 12 13 36 ACТ-C01 27 GO ON TO THE NEXT PAGE. 2АААДДДДА2 2 DO YOUR FIGURING HERE. traveling east on I-70 toward St. Louis at an average leaves St. Louis in his car traveling west on 1-70 toward Kansas City at an average speed of 57 mph. The driving distance from St. Louis to Kansas City is 240 miles. At what time, to the nearest minute, will they drive past each other on I-70 ? 3:50 p.m. 3:53 p.m. 3:55 p.m. 4:06 p.m.

Source question 55. Refer to the source image.

There are 10 points in a plane, and no 3 of the points are collinear. These 10 points, taken 2 points at a time, determine how many distinct lines? 10 20 Н. 35 45 К. 90

The expression n! (read as n factorial) is defined as the product of all positive integers up to and including n, whenever n is a positive integer. For example, 4! = 1 • 2 • 3 • 4. Whenever n is a positive integer, which of the following is equivalent to (I+ 1)!6!? п!3! В. 120 (6n + 6)! (3n)!

Which of the following must be true for each set of 4 consecutive positive integers? I. At least 1 of the 4 integers is prime. II. At least 2 of the 4 integers have a common prime factor. Ill. At least 1 of the 4 integers is a factor of at least 1 of the 3 other integers. I only Il and Ill only ACT-C01 28 GO ON TO THE NEXT PAGE. 2

When (x + 1)* is expanded and like terms are combined, what is the coefficient of i'? 4

A hill makes an angle of 20° with the horizontal, AD, as shown below. A taut guy wire, AB, extends from the base of the hill, point A, to point B on a vertical pole. Point B is 25 ft directly above where the pole is inserted into the ground at point C. Given that the length of AC is 60 ft, which of the following expressions represents the length, in feet, of the guy wire? (Note: For a triangle with sides of length a, b, and c that are opposite angles LA, LB, and LC. respectively. sin LA = sin <B = sin <C and ở = a + b - 2ab cos LC.) ^ A DO YOUR FIGURING HERE. 2 25 pole guy wire 60' 20° 25 sin 60° sin 20° 25 sin 70° sin 20° 25 sin 110° sin 20° END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-COT 29