ACT Past Papers with Answers

Paper 37 · ACT September 2015 · Form 72C · Math Test

The monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310, respectively. What is the mean of these monthly fees? 62 ___ _ 150 66 ___ _ 150 68 ___ _ 150 73 ___ _ 150 84 ___ _ 150 O B AB number of people blood type 70 60 50 40 30 20 10 0 62 67 15 6 A

Paper 37 · ACT September 2015 · Form 72C · Math Test

On a particular road map, inch represents 18 miles. About how many miles apart are 2 towns that are 2 inches apart on this map?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Given f = cd3 , f = 450, and d = 10, what is c ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

If f(x) = (3x + 7)2 , then f(1) = ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Jorge’s current hourly wage for working at Denti Smiles is $12.00. Jorge was told that at the beginning of next month, his new hourly wage will be an increase of 6% of his current hourly wage. What will be Jorge’s new hourly wage? 1 _ _ 2 1 _ _ 2 1 _ _ 2 GO ON TO THE NEXT PAGE.

Paper 37 · ACT September 2015 · Form 72C · Math Test

The first term is 1 in the geometric sequence 1, −3, 9, −27, …. What is the SEVENTH term of the geometric sequence?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The shipping rate for customers of Ship Quick consists of a fee per box and a price per pound for each box. The table below gives the fee and the price per pound for customers shipping boxes of various weights. Gregg wants Ship Quick to ship 1 box that weighs 15 pounds. What is the shipping rate for this box?

Paper 37 · ACT September 2015 · Form 72C · Math Test

A computer chip 0.32 cm thick is made up of layers of silicon. If the top and bottom layers are each 0.03 cm thick and the inner layers are each 0.02 cm thick, how many inner layers are there?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The table below shows the number of cars Jing sold each month last year. What is the median of the data in the table? Weight of box (pounds) Fee Price per pound Less than 10 10−25 More than 25 $05.00 $10.00 $20.00 $1.00 $0.65 $0.30

Paper 37 · ACT September 2015 · Form 72C · Math Test

Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds. Which of the following equations represents this relationship between d and t ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The length of a rectangle with area 54 square centimeters is 9 centimeters. What is the perimeter of the rectangle, in centimeters?

Paper 37 · ACT September 2015 · Form 72C · Math Test

In the figure below, C is the intersection of AD ___ and BE ___ . If it can be determined, what is the measure of ∠BAC ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Antwan drew the circle graph below describing his time spent at school in 1 day. His teacher said that the numbers of hours listed were correct, but that the central angle measures for the sectors were not correct. What should be the central angle measure for the Core subjects sector? t 00 01 02 03 04 05 d 14 20 26 32 38 44 35° 35° 45° B C D E A Core subjects 4 hours Electives 3 hours Lunch and passing time 1 hour Choir 1 hour GO ON TO THE NEXT PAGE. 2 2

Paper 37 · ACT September 2015 · Form 72C · Math Test

Source question 15. Refer to the source image.

Paper 37 · ACT September 2015 · Form 72C · Math Test

A car accelerated from 88 feet per second (fps) to 220 fps in exactly 3 seconds. Assuming the acceleration was constant, what was the car’s acceleration, in feet per second per second, from 88 fps to 220 fps ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

In a plane, the distinct lines AB ↔ and CD ↔ intersect at A, where A is between C and D. The measure of ∠BAC is 47°. What is the measure of ∠BAD ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

In which of the following are , , and arranged in ascending order?

Paper 37 · ACT September 2015 · Form 72C · Math Test

In scientific notation, 670,000,000 + 700,000,000 = ? 1 __ _ 44 2 _ _ 3 1 _ _ 3 1 _ _ 3 5 _ _ 8 5 _ _ 6 1 _ _ 2 5 _ _ 6 5 _ _ 8 1 _ _ 2 5 _ _ 8 1 _ _ 2 5 _ _ 6 1 _ _ 2 5 _ _ 8 5 _ _ 6 5 _ _ 6 1 _ _ 2 5 _ _ 8 1 _ _ 2 5 _ _ 6 5 _ _ 8

Paper 37 · ACT September 2015 · Form 72C · Math Test

For trapezoid ABCD shown below, AB ___ i DC ___ _ , the measures of the interior angles are distinct, and the measure of ∠D is x°. What is the degree measure of ∠A in terms of x ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

To get a driver’s license, an applicant must pass a written test and a driving test. Past records show that 80% of the applicants pass the written test and 60% of those who have passed the written test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants would you expect to get driver’s licenses?

Paper 37 · ACT September 2015 · Form 72C · Math Test

If a, b, and c are positive integers such that ab = x and cb = y, then xy = ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following expressions is equivalent to y2 (6x + 2y + 12x − 2y) ? + 12x − 2y3 + 12x − y3 − 2y

Paper 37 · ACT September 2015 · Form 72C · Math Test

An artist makes a profit of (500p − p2 ) dollars from selling p paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $60,000 ? x° A B C D 1 _ _ 2 GO ON TO THE NEXT PAGE. 2 2 15. This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. How many large figurines did Kami sell this month?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Source question 25. Refer to the source image.

Paper 37 · ACT September 2015 · Form 72C · Math Test

In the figure shown below, the measure of ∠BAC is (x + 20)° and the measure of ∠BAD is 90°. What is the measure of ∠CAD ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

What is the perimeter, in inches, of the isosceles right triangle shown below, whose hypotenuse is 8√" 2 inches long?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The equation y = ax2 + bx + c is graphed in the standard (x,y) coordinate plane below for real values of a, b, and c. When y = 0, which of the following best describes the solutions for x ? entertainment $125 $219 food $254 clothes $120 gas $182 insurance A C D B O x y

Paper 37 · ACT September 2015 · Form 72C · Math Test

What is the product of the complex numbers (−3i + 4) and (3i + 4) ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The radius of the base of the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, θ, of the angle formed by a slant height of the cone and a radius?

Paper 37 · ACT September 2015 · Form 72C · Math Test

To make a 750-piece jigsaw puzzle more challenging, a puzzle company includes 5 extra pieces in the box along with the 750 pieces, and those 5 extra pieces do not fit anywhere in the puzzle. If you buy such a puzzle box, break the seal on the box, and immediately select 1 piece at random, what is the probability that it will be 1 of the extra pieces?

Paper 37 · ACT September 2015 · Form 72C · Math Test

What fraction lies exactly halfway between and ? 7 5 θ 5 _ _ 7 7 _ _ 5 5 _ _ 7 7 _ _ 5 7 _ _ 5 1 _ _ 5 1 ___ _ 755 1 ___ _ 750 5 ___ _ 755 5 ___ _ 750 3 _ _ 4 2 _ _ 3 3 _ _ 5 5 _ _ 6 7 __ _ 12 9 __ _ 16 17 __ _ 24 GO ON TO THE NEXT PAGE. 2 2 25. Last month, Lucie had total expenditures of $900. The pie chart below breaks down these expenditures by category. The category in which Lucie’s expenditures were greatest is what percent of her total expenditures, to the nearest 1% ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

A 15-foot wall is how many inches long in the scale drawing?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Gianna will install tile on the portion of the floor that will NOT be covered by cabinets. What is the area, in square feet, of the portion of the floor that will NOT be covered by cabinets?

Paper 37 · ACT September 2015 · Form 72C · Math Test

CC Installations’ estimate consists of a $650.00 charge for labor, plus a fixed charge per cabinet. The labor charge and the charge per cabinet remain the same for any number of cabinets built and installed. CC Installations would give Gianna what estimate if the craft room were to have twice as many cabinets as Gianna is planning to have? window cabinets door 2 ft deep 15 ft wall 12 ft wall cabinets Use the following information to answer questions 33–35.

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following is the graph of the region 1 < x + y < 2 in the standard (x,y) coordinate plane?

Paper 37 · ACT September 2015 · Form 72C · Math Test

What is the difference between the mean and the median of the set {3, 8, 10, 15} ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following describes a true relationship between the functions f(x) = (x − 3)2 + 2 and g(x) = x + 1 graphed below in the standard (x,y) coordinate plane? 2 −1 1 −2 y x y 2 −1 1 −2 x 2 1 1 2 y x 2 −1 −1 2 y x 2 −1 1 −2 y x y x O 1 _ _ 2 GO ON TO THE NEXT PAGE. 2 2 Gianna is converting a 12-foot-by-15-foot room in her house to a craft room. Gianna will install tile herself but will have CC Installations build and install the cabinets. The scale drawing shown below displays the location of the cabinets in the craft room (0.25 inch represents 2 feet). Cabinets will be installed along one of the 12-foot walls from floor to ceiling, and 4 cabinets that are each 3 feet tall will be installed in the middle of the room. These are the only cabinets that will be installed, and each of them will be 2 feet wide and 2 feet deep. CC Installations has given Gianna an estimate of $2,150.00 for building and installing the cabinets.

Paper 37 · ACT September 2015 · Form 72C · Math Test

What is the slope of CD ___ ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

When ABCD is reflected over the y-axis to A′B′C′D′, what are the coordinates of D′ ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Given f(x) = x − and g(x) = , what is f 1g1 22? O y x B(3,4) C(9,4) A(2,1) D(12,1) 5 __ _ 21 3 _ _ 2 1 _ _ 2 1 _ _ x 1 _ _ x 3 _ _ 2 2 _ _ 3 3 _ _ 2 Use the following information to answer questions 39–41.

Paper 37 · ACT September 2015 · Form 72C · Math Test

A formula to estimate the monthly payment, p dollars, on a short-term loan is p = where a dollars is the amount of the loan, r is the annual interest rate expressed as a decimal, and y years is the length of the loan. When a is multiplied by 2, what is the effect on p ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The points E(6,4) and F(14,12) lie in the standard (x,y) coordinate plane shown below. Point D lies on EF ___ between E and F such that the length of EF ___ is 4 times the length of DE ___ . What are the coordinates of D ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Given that a3 4 = 3 4 for some real number a, what is x + z ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

A container is full of water. After 10 cups of water are added, the container is full. What is the volume of the container, in cups? 1 _ _ 2 ary + a ________ _ 12y y x O E(6,4) F(14,12) 27 z x y 6 4 2 1 4 _ _ 3 27 __ _ 2 1 _ _ 8 3 _ _ 4 1 _ _ 3 1 _ _ 2 GO ON TO THE NEXT PAGE. 2 2 Trapezoid ABCD is graphed in the standard (x,y) coordinate plane below.

Paper 37 · ACT September 2015 · Form 72C · Math Test

Source question 47. Refer to the source image.

Paper 37 · ACT September 2015 · Form 72C · Math Test

+ = ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The shaded region in the graph below represents the solution set to which of the following systems of inequalities? (x − 1)2 + (y − 2)2 < 9 (x − 1)2 + (y − 2)2 < 9 (x − 1)2 + (y − 2)2 > 9 (x − 1)2 + (y − 2)2 > 9 (x − 1) > 3 y x (x − 1)2 + (y − 2)2 = 9 y = − x + 2 4√" 3 + 2√" 2 ___________ _ √" 5 4√" 3 + 2√" 2 ___________ _ √" 6 6 _________ √" 2 + √" 3 6 ___ _ √" 5 8 ___ _ √" 6 2 ___ _ √" 3 4 ___ _ √" 2

Paper 37 · ACT September 2015 · Form 72C · Math Test

You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters by 30 centimeters and is filled with water to a depth of 20 centimeters. The object sinks to the bottom, and the water level goes up 0.25 centimeters. What is the volume, in cubic centimeters, of the object?

Paper 37 · ACT September 2015 · Form 72C · Math Test

If x:y = 5:2 and y:z = 3:2, what is the ratio of x:z ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following is the solution statement for the inequality shown below? −5 < 1 − 3x < 10

Paper 37 · ACT September 2015 · Form 72C · Math Test

A formula for the surface area (A) of the rectangular solid shown below is A = 2lw + 2lh + 2wh where l represents length; w, width; and h, height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor?

Paper 37 · ACT September 2015 · Form 72C · Math Test

A dog eats 7 cans of food in 3 days. At this rate, how many cans of food does the dog eat in 3 + d days? h l w 7 _ _ 3 d __ 3 7 _ _ 3 7 __ _ 3d 7 _ _ 3 d __ 3 7d __ _ 3 GO ON TO THE NEXT PAGE. 2 2 47. Only tenth-, eleventh-, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school’s total student population is 86:255, and the ratio of eleventh graders to the school’s total student population is 18:51. If 1 student is chosen at random from the entire school, which grade is that student most likely to be in?

Paper 37 · ACT September 2015 · Form 72C · Math Test

Kelly asked 120 students questions about skiing. The results of the poll are shown in the table below. After completing the poll, Kelly wondered how many of the students polled had skied both cross-country and downhill. How many of the students polled indicated that they had skied both cross-country and downhill?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The square below is divided into 3 rows of equal area. In the top row, the region labeled A has the same area as the region labeled B. In the middle row, the 3 regions have equal areas. In the bottom row, the 4 regions have equal areas. What fraction of the square’s area is in a region labeled A ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The functions y = sin,x and y = sin(x + a) + b, for constants a and b, are graphed in the standard (x,y) coordinate plane below. The functions have the same maximum value. One of the following statements about the values of a and b is true. Which statement is it? Question Yes No

Paper 37 · ACT September 2015 · Form 72C · Math Test

Which of the following number line graphs shows the solution set to the inequality ⎪x − 5⎪ < −1 ?

Paper 37 · ACT September 2015 · Form 72C · Math Test

As part of a probability experiment, Elliott is to answer 4 multiple-choice questions. For each question, there are 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly?

Paper 37 · ACT September 2015 · Form 72C · Math Test

The sides of an acute triangle measure 14 cm, 18 cm, and 20 cm, respectively. Which of the following equations, when solved for θ, gives the measure of the smallest angle of the triangle? (Note: For any triangle with sides of length a, b, and c that are opposite angles A, B, and C, respectively, = = and c2 = a2 + b2 − 2ab cos,C.) = 182 + 202 − 2(18)(20)cos,θ = 142 + 182 − 2(14)(18)cos,θ 4 x 6 x 6 4 x 6 4 x x (empty set) 6 4 6 4 27 __ _ 81 12 __ _ 81 4 __ _ 81 3 __ _ 81 1 __ _ 81 sin,C _____ c sin,B _____ b sin,A _____ a 1 __ _ 18 sin,θ ____ _ 14 1 __ _ 20 sin,θ ____ _ 14 1 __ _ 14 sin,θ ____ _ 20 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.