Free Printable ACT Math Questions

1.

If x = –6, y = 4, and z = 2, what is the value of xyz – xy ?

a)

-72

b)

-48

c)

-24

d)

12

e)

24

2.

If a = 9, b = 1, and c = –5, what does (a + b – c)(a – b + c) equal?

a)

-25

b)

15

c)

25

d)

45

e)

55

3.

What is the value of 2 ∙ 4^(p+q) when p = 3 and q = –1 ?

a)

0

b)

1

c)

4

d)

32

e)

64

4.

If x = –1, y = 4, and z = 3, what is the value of $xy+\frac{\text{yz}}{\text{x-z}}-xz?$

a)

-11

b)

-10

c)

-4

d)

2

e)

4

5.

If m = 10, n = 2, and p = –3, what does (m – n + p)(n – p) equal?

a)

-11

b)

-5

c)

5

d)

11

e)

25

6.

Which of the following expressions is equivalent to (a – 4)(4a – 3) ?

a)

$4a^2+12$

b)

$4a^2-19a+12$

c)

$4a^2+19a+12$

d)

$4a^2-12a+12$

e)

$4a^2+12a+12$

7.

The expression (4x – 6y)(4y + 5x) is equivalent to:

a)

7xy

b)

44xy

c)

$20x^2+46xy−24y^2$

d)

$20x^2-14xy-24y^2$

e)

$-18x^2y^2$

8.

The expression (4z – 5)(5z + 4) is equivalent to which of the following?

a)

9z−1

b)

9z+1

c)

$20z^2-20$

d)

$20z^2-9z-20$

e)

$20z^2+9z-20$

9.

If x = –1, y = 4, and z = 3, what is the value of

$xy+\frac{\text{yz}}{\text{x-z}}-xz?$

a)

-11

b)

-10

c)

-4

d)

2

e)

4

10.

The expression (5a²+ 6b)(5a²- 6b) is equivalent to which of the following?

a)

25a⁴−36b²

b)

25a⁴−12b²

c)

25a⁴+36b²

d)

10a⁴−36b²

e)

10a⁴−12b²

11.

What is the area, in square meters, of the figure ?

a)

62

b)

82

c)

320

d)

420

e)

520

12.

What is the area, in square feet, of the hexagon ABCDEF shown below?

a)

57

b)

45

c)

35

d)

30

e)

25

13.

In the figure below, the angles at ∠FAB, ∠FDE, and ∠BDC are right angles. What is the perimeter of the polygon, in inches?

a)

32

b)

38

c)

42

d)

48

e)

112

14.

What is the area, in square feet, of the figure below?

a)

$25\ \frac{1}{4}$

b)

$24\ \frac{1}{2}$

c)

$21\ \frac{1}{2}$

d)

$21\ \frac{1}{4}$

e)

Cannot be determined from the given information

15.

Ted is planting a garden on his L-shaped plot of land. As shown below, the design for his garden has right angles at each corner. Ted plans to buy seeds for crops, and he knows that each packet of seeds covers 25 square feet of soil. Based on this knowledge, what is the minimum number of packets that Ted will need to buy in order to cover each square foot of his garden with plants?

a)

2

b)

3

c)

4

d)

5

e)

7

16.

The expression $\left(5x+3y^2\right)\ \left(5x-3y^2\right)$ is equivalent to:

a)

$10x^2+6y^4$

b)

$25x^2+9y^4$

c)

$10x^2-6y^4$

d)

$25x^2-9y^4$

e)

$25x^2-6y^4$

17.

If 7(x-7) = -15, then x=?

a)

$-\frac{64}{7}$

b)

$-\frac{34}{7}$

c)

$-\frac{15}{7}$

d)

$\frac{34}{7}$

e)

$\frac{64}{7}$

18.

The daily fee for admission to the Florida Fun 'n Sun Amusement Park is $45 per adult and $25 per child. Daily admission fees are paid for a adults and c children. which of the following expressions gives the total amount, in dollars, collected for daily fees?

a)

45a+25c

b)

45c+25a

c)

$25\left(a+c\right)$

d)

$70\left(a+c\right)$

e)

$25\left(a+c\right)+45a$

19.

Natalie makes $9.50 per hour for up to 40 hours a week working ata local bookstore. She is paid an overtime wage of 1.5 times her regular pay for every hour she works over 40 hours. If Natalie works 43 hours in a week, how much will she make that week?

a)

$380.00

b)

$394.25

c)

$408.50

d)

$422.00

e)

$422.75

20.

Dicounted tickets to the cinema cost $6.00 each. James spent $72.00 on discounted tickets, $54.00 less than he would have spent if he had bought the tickets without the discount. What is the price of a ticket without a discount?

a)

$6.00

b)

$6.50

c)

$10.50

d)

$12.00

e)

$16.50

21.

Which of the following mathematical expressions is equivalent to the verbal expression "A number, y, cubed is 42 more than the product of 13 and y"?

a)

$3y=42+13y$

b)

$3y=42y+13y$

c)

$y^3=42-13y$

d)

$y^3=42+y^{13}$

e)

$y^3=42+13y$

22.

A rectangle has a perimeter of 24 meters and an area of 35 square meters. What is the length, in meters, of the longest side?

a)

1

b)

3

c)

5

d)

7

e)

8

23.

If k = 7, j = 4, p = -5, what does $\left(k+j\right)\left(k+p-j\right)\ equal\ ?$

a)

-22

b)

0

c)

22

d)

44

e)

88

24.

Jason's class projects are graded on a scale of 250 points. Jason has received scores of 245,215,220, and 224 for his first four projects. Jason worked out his average score on prjects thus far. In order to maintain the average grade on projects, what grade must Jason receive on his 5th and final class project?

a)

200

b)

215

c)

224

d)

226

e)

245

25.

A pool consisting of a square and two semicircles has dimensions shown. What is the outside perimeter, in meters, of the pool

a)

$16+8\pi$

b)

$16+16\pi$

c)

$32+16\pi$

d)

$32+32\pi$

e)

$64+32\pi$

26.

For $\Delta ABC$ , shown below, which of the following is an expression for y in terms of x?

a)

$\sqrt[]{x^2-49}$

b)

$\sqrt[]{x^2+49}$

c)

$\sqrt[]{x^2-7}$

d)

$\sqrt[]{x^2+7}$

e)

$\sqrt[]{x-7}$

27.

If $4^x=52$ , then which of the following must be true?

a)

$1<x<2$

b)

$2<x<3$

c)

$3<x<4$

d)

$4<x<5$

e)

$x>5$

28.

In $\Delta ABC$ , the sum of the measures of $\angle A\ and\ \angle B$ is $66\degree$ .

What is the measure of $\angle C$ ?

a)

$57\degree$

b)

$66\degree$

c)

$90\degree$

d)

$114\degree$

e)

$124\degree$

29.

In the figure, line AD $\parallel$ BE, $\overline{AC}$ bisects $\angle DAB,\ and\ \overline{BC}$ bisects $\angle DAB$ is $76\degree,$ what is the measure of $\angle ACB$ ?

a)

$60\degree$

b)

$70\degree$

c)

$80\degree$

d)

$90\degree$

e)

$100\degree$

30.

A rectangle with a perimeter of 30 centimeters is twice as long as it is wide. What is the area of the rectangle in square centimeters?

a)

15

b)

25

c)

50

d)

100

e)

125

31.

For 2 consecutive integers, the result of adding the smaller integer and four times the larger integer is 84. What are the 2 integers?

a)

15,16

b)

16,17

c)

17,18

d)

18,19

e)

19,20

32.

If $4^x=52$ , then which of the following must be true?

a)

$1<x<2$

b)

$2<x<3$

c)

$3<x<4$

d)

$4<x<5$

e)

$x>5$

33.

In $\Delta ABC$ , the sum of the measures of $\angle A\ and\ \angle B$ is $66\degree$ .

What is the measure of $\angle C$ ?

a)

$57\degree$

b)

$66\degree$

c)

$90\degree$

d)

$114\degree$

e)

$124\degree$

34.

A function $f\left(x\right)$ is defined as $f\left(x\right)=-7x^2$ . What is $f\left(-2\right)$ ?

a)

-121

b)

-28

c)

28

d)

98

e)

121

35.

At an ice cream parlor, patrons make their own sundaes from 5 flavors of ice cream, 2 sauces, 4 toppings and 3 fruits. How many different sundaes can be made by a patron who chooses exactly 1 ice cream flavor, 1 sauce, 1 topping and 1 fruit?

a)

14

b)

24

c)

60

d)

64

e)

120

36.

The base of a triangle is four times the bse of a smaller triangle. The two trianlges have the same height. The area of the smaller triangle is A square units. The area of the larger triangle is $kA$ square units. Which of the following is the value of k?

a)

$\frac{1}{4}$

b)

$\frac{1}{2}$

c)

1

d)

2

e)

4

37.

What is the common multiple of 30,40, and 70?

a)

84

b)

120

c)

840

d)

1,200

e)

84,000

38.

The bacteria population of a nutrient broth grows according to the equation $y=21\left(3\right)^t$ , where t represents time in days and y represents the population.According to this equation, which answer will represent the bacteria population of the nutrient broth after 5 days?

a)

63

b)

315

c)

1,701

d)

5,103

e)

15,309

39.

Mind Beats Audio is designing a box for its new line of professional headphones. The box is a rectangular prism that is 28 centimeters long, 19 centimeters wide, and has a volume of 6,384 cubic centimeters. What is the height, in centimeters, of the box?

a)

10

b)

12

c)

19

d)

48

e)

63

40.

Four points L,M,N and P, lie on a circle with a circumference of 18 units. Point M is 4 units counterclockwise from point L. Point N is 6 units clockwise from point L. Point P is 9 units counterclockwise from point L. Moving clockwise and starting with point L, in what order are the points arranged?

a)

L,M,N,P

b)

L,MP,N

c)

L,P,M,N

d)

L,N,M,P

e)

L,N,P,M

ACT Math Questions

Total questions: 40

Worksheet time: 40mins

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