ACT MATH TEST

Pre-Algebra and Elementary Algebra

Of the 60 questions, 14 will relate to pre-algebra and 10 to elementary algebra. The pre-algebra

and elementary algebra questions will cover the following topics:

Arithmetic operations

Powers and roots

Ratio and proportion

Percent

Number theory

Linear equations with one variable

Probability and statistics

Variables and functional relationships

Substitution

Polynomials

Quadratic equations

Properties of exponent

1. On the final project in Juan's art class, 14 students earned a grade of B. Those 14 students were

exactly 20% of the total number of students in the class. How many students were in the class?

a. 28

b. 34

c. 56

d. 64

e. 70

2. What is the value of x in the following equation?

a. 2

b. 3

c. 9

d. 12

e. 18

3. At a certain construction site, there is a pile containing 55 tons of sand. Four trucks, each of

which holds 11.4 tons of sand, are filled from this pile. How many tons of sand remain in the pile?

f. 9.4

g. 16.2

h. 20.8

j. 32.2

k. 43.6

4. What is the value of 2(x – 3) + 15, if x = –2?

a. –3

b. 0

c. 5

d. 13

e. 25

ACT MATH TEST

5. Simplify:

f. –7

g. 0

h. 7

j. 14

k. 21

6. Rosie's boss is going to give her a raise of 8%. If her salary before the raise is $25,500, what

will her salary be after the raise?

a. $23,460

b. $26,500

c. $27,040

d. $27,540

e. $27,900

7. If x is a real number such that x3 = 80, between which two consecutive integers does x lie on the

number line?

f. 2 and 3

g. 3 and 4

h. 4 and 5

j. 5 and 6

k. 6 and 7

8. If 67 + a = –191, then a =

a. –258

b. –124

c. 113

d. 124

e. 258

9. Joel is 8 years older than Karen, and Karen is twice as old as Lina. If Lina is x years old, how old

is Joel in terms of x?

f. x + 8

g. 2x

h. x – 8

j. –2x

k. 2x + 8

ACT MATH TEST

10. Which of the following is a simplified form of 3a + 9b – 2a?

f. 6a + 9b

g. a + 9b

h. 12ab – 2a

j. 3a + 7ba

k. 10ab

11. If x is positive, and 2x2 – 7x – 9 = 0, then what is the value of x?

a. 1

b. 2

c. 4.5

d. 7

e. 9

12. A portable radio that normally sells for $29.55 is marked down by 20%. What is the sale price

of the radio, rounded to the nearest dollar?

a. $20

b. $21

c. $22

d. $23

e. $24

13. Which of the following is the factored form of 3d 4e3 – 15de2?

f. 3(d4e3 – 15de2)

g. 3de2(d 3e – 5)

h. 3(d4e – 15de)

j. 3d4e3 – 15de2

k. –12d3e

14. If 2u + 2 = 20, and v – 2u = –2, what is the value of v?

a. –12

b. 10

c. 12

d. 14

e. 16

ACT MATH TEST

15. At a certain store, a 7.5-pound bag of rice costs $4.80. What is the cost per ounce of rice?

(There are 16 ounces in a pound.)

f. $0.02

g. $0.03

h. $0.04

j. $0.05

k. $0.15

16. On Farm X, farm workers work 6 days per week and earn $23.00 per day, plus $0.74 per bushel

filled. If a certain farm worker earned $165.38 in a week, how many bushels did she fill in that

week?

a. 7

b. 31

c. 37

d. 68

e. 192

17. The quantity is greater than which of the following?

f. g. h. j. k.

18. What is the smallest possible sum of 2 positive integers whose product is 36?

a. 9

b. 10

c. 12

d. 13

e. 15

19. Two numbers have a greatest common factor of 6 and a least common multiple of 36. Which of

the following could be the pair of numbers?

a. 6 and 12

b. 6 and 18

c. 12 and 18

d. 12 and 24

e. 18 and 24

ACT MATH TEST

20. In the standard (x, y) coordinate plane, a line passes through the origin and the point

What is the slope of the line?

a. b. c. d. e.

21. The scores of five bowlers during the first round of a tournament are indicated in the table

below.

What is the average score of the five bowlers for the first round?

a. 186

b. 192

c. 224

d. 240

e. 312

22. Motorcycle A travels 50 miles per hour for 2.5 hours. Motorcycle B travels 30 miles per hour

for 5 hours. What is the difference between the number of miles traveled by Motorcycle A and the

number of miles traveled by Motorcycle B?

f. 0

g. 25

h. 125

j. 150

k. 275

23. For which of the following values of q is (q – 4)(q + 3) = 0?

a. 3

b. 4

c. 5

d. 6

e. 7

ACT MATH TEST

24. If pqs ≠ 0, then

f.

g.

h.

j. 2p5q7s9

k. 2p3q3s5

25. If a = 3 and b = –2, then a3b – ab3 =

f. –108

g. –78

h. –48

j. –30

k. –24

26. If (x – y)2 = x2 – 26x + y2 for all real numbers x, then y =

f. –26

g. –13

h. 13

j. 26

k. 52

27. Find the sum of the polynomials 5x2y – 2xy2 and 3xy2 – x2y.

a. 3xy2 + 2x2y

b. 4x2y + xy2

c. 5x3y3

d. 6x2y + 5xy2

e. 8x2y – 3xy2

28. Which of the following is equivalent to (–3x2)3?

f. –3x5

g. –3x6

h. –9x6

j. –27x5

k. –27x6

ACT MATH TEST

29. if calculate the value of 2x2 – 4x + 2.

f. –72

g. –28

h. –5

j. 5

k. 72

30. If 2x + 4y = 8 and 5x + 2y = 10, what is the value of y?

a. b. c. d. e.

31. Which if the following is equivalent to (a + b)2?

f. 2a + 2b

g. a2 + b2

h. (ab)2

j. a2 + 2ab + b2

k. (ab)4

Intermediate Algebra and Coordinate Geometry

Of the 60 questions, 9 will cover intermediate algebra and 9 will cover coordinate geometry. The

intermediate algebra and coordinate geometry questions will cover the following topics:

Sequences

Formulas

Quadratic formula

Functions

Composition of functions

Inequalities

Rational expressions

Roots of polynomials

Logarithms

Matrices

Number line graphs

Midpoints

Slope

Parallel lines

Graphs of polynomials

Conics

1. What is the sixth term of the arithmetic sequence 3, 6, 9, 12, ... ?

f. 13

g. 15

h. 18

j. 21

k. 24

ACT MATH TEST

2. If line segment XY is bisected by point Z, then which of the following must be true?

a.

b.

c.

d.

e.

3. A rectangle is graphed in the standard (x, y) coordinate plane. Three of the rectangle's corners

have coordinates (–4, 5), (2, 5), and (–4, –2). What are the coordinates of the fourth corner?

a. (–5, 2)

b. (4, –2)

c. (–2, 2)

d. (–4, 5)

e. (2, –2)

4. What is the slope of the line 2x – 6y = 10?

f. g. h. 0 j. k. 2

5. Which of the following is the graph of the solution set for z + 2 < 8?

a. b.

c. d.

e.

ACT MATH TEST

6. If x and y are positive numbers,

f. –3x – 4y

g.

h.

j.

k.

7. In the right triangle below, how long is side MN?

a. 6

b.

c.

d.

e.

8. Which of the answer choices best describes the graph on the number line below?

f. 1 > x > –2.5

g. 1 < x < –2.5

h. –1 < x < 2.5

j. 1 > > –2.5

k. 1 < < –2.5

9. In the right triangle below, how many meters long is side AC?

f. 5

g. 7.5

h. 10

j.

k.

ACT MATH TEST

10. The line 3x – 8y = 16 is plotted on the (x, y) coordinate plane. What is the y-intercept of the

line?

a. –4

b. –3

c. –2

d. 2

e. 4

11. Among the points on the number line below, which is the closest to

f. F

g. G

h. H

j. J

k. K

12. If m – n = 2 and m + n = then what is the value of

f. g. h. j. k. 5

13. A line is graphed on the (x, y) coordinate plane. The value of the x-coordinate for each point on

the line is 5 more than three times the value of the y-coordinate of that point. What is the slope of

the line?

f.

g.

h. 1

j. 2

k. 3

14. The equation for a certain line is 3y – x = 12. Which of the following points lies on the line?

a. (0, –10)

b. (1, 4)

c. (5, 5)

d. (–6, 2)

e. (–20, (3)

ACT MATH TEST 15. What is the value of gh, if 3g – 12 = h and

a. b. c. –4 d. e.

16. X, Y, and Z are real numbers and XYZ = π. Which of the following must be true?

f. XYZ2 = π

2

g.

h. XYZπ = 0

j.

k.

17. How many different integer values of x satisfy the inequality

a. 3

b. 4

c. 5

d. 6

e. 7

18. What is the distance, on a standard (x, y) coordinate plane, between the point (–2, 3) and the point (–5, –4)?

f. 7

g.

h. 8

j. 9

k.

19. Which of the following is equivalent to

f. g. h. 1 j. 2 k.

ACT MATH TEST

20. A cookie recipe calls for a 3:1 ratio of flour to sugar. If you put 2 cups of flour into the batter, how many cups of

sugar do you need?

a.

b. 1

c.

d. 3

e. 6

21. Line AB has points (3, 1) and (2, 4) in the standard (x, y) coordinate plane. Line CD is parallel to line AB. What is the slope of line CD?

a. –4 b. –3 c. d. e. 3

22. If log5 125 = x, then x =

a.

b.

c. 3

d. 25

e. 5125

23. At what point do the lines with the following two equations intersect?

y = 14x + 40

4x = 2y – 8

a. b. (–3, –2) c. (–3, 2) d. (3, –2) e. (3, 2)

Plane Geometry and Trigonometry

Of the 60 questions, 14 will cover plane and solid geometry and 4 will cover trigonometry. The plane geometry and trigonometry questions will cover the following topics:

Lines and angles

Perimeter

Area

Triangle

Right triangles

Similar figures

Properties of polygons

Circles

ACT MATH TEST

1. In the figure below, points G, H, and I are on the same line. What is the measure of ?

f. 35°

g. 55°

h. 75°

j. 125°

k. 145°

2. In the parallelogram below, what is the measure of ∠WZY?

a. 55° b. 75° c. 90° d. 105° e. 115°

3. A certain triangle has sides of lengths 40, 50, and 60 inches. If a similar triangle has a perimeter of 300 inches,

how many inches long is that triangle's longest side?

f. 45

g. 60

h. 80

j. 100

k. 120

4. A garden needs to be covered with grass sod. The garden has the dimensions shown below. How many square

feet of sod are required to cover the garden?

f. 720

g. 864

h. 984

j. 1,056

k. 1,200

5. A right triangle has sides of length 15, 20, and 25 meters. What is the area of the triangle in square meters?

a. 60 b. 150 c. 250 d. 625 e. 7,500

ACT MATH TEST 6. Two sides of a triangle are 17 and 18 feet. Which of the following CANNOT be the length of the third side?

a. 2 b. 8 c. 15 d. 18 e. 36

7. If the sine of a certain angle is and its cosine is what is the angle's tangent?

a. b. c. d. e.

8. In the figure below, lines a and b are parallel to each other, and lines c and d are parallel to each other. If the two angles have measures 40° and 115°, as shown, what is the measure of angle x?

f. 25° g. 35° h. 50° j. 65° k. 75°

9. What is the length of the radius of a circle with an area of 4π?

f. 1.25 g. 2 h. 2.25 j. 2.5 k. 4

10. What is the area of the shaded region below, if the radius of the inner circle is 2.5 inches and the radius of the outer circle is 5 inches?

f. 2.5π g. 6.25π h. 7.5π j. 12π k. 18.75π

ACT MATH TEST 11. A square measuring w inches on each side is removed from a rectangle of length (w + 6) inches and width (w – 1) inches. What is the remaining area, in square inches, of the rectangle?

a. 11 b. 5w – 6 c. 2w + 5 d. w

2 + 5w

e. 5w + 2

12. A tin of candy contains three flavors. There are twice as many grape candies in a tin as there are cherry candies. There are three times as many lemon candies as grape candies. If a number of apple candies, equal to the number of cherry candies already in the tin, is added to the tin, what is the probability of randomly selecting a lemon candy from the tin?

f. g. h. j. k.

13. In tossing a fair coin three consecutive times, what is the probability of getting heads on 2 consecutive tosses but NOT on three consecutive tosses? (A fair coin has an equal likelihood of a heads or tails outcome.)

f. g. h. j. k.

14. In the parallelogram ABCD shown below, AD is 7 inches long. If the perimeter of the parallelogram is 42 inches, how many inches long is CD?

f. 35 g. 29 h. 22 j. 14

k.

15. A ten-foot long ladder is propped up against an eight-foot tall building. If the ladder reaches the top of the building, what is the cosine of the angle formed by the ladder and the building?

f. g. h. 2 j. 18 k. 80

ACT MATH TEST 16. All angles in the figure below are right angles. What is the perimeter, in inches (in), of the figure below?

a. 35 b. 66 c. 70 d. 200 e. 235

17. In the figure below, if the height, width, and length are all doubled, the new surface area will be how many times its original size?

a. 2 b. 4 c. 6 d. 8 e. 24

Peterson's Practice Tests for the ACT*