Free Printable ACT Diagnostic Test

1.

If $\frac{x+2}{3}=\frac{x+6}{6}$ , then what is the value of x?

a)

1

b)

2

c)

4

d)

5

e)

6

2.

The value of three consecutive odd integers is 567. What is the value of the second of these three consecutive integers?

a)

175

b)

181

c)

187

d)

189

e)

193

3.

If $3x-y=7$ and $x+2y=7$ , then what is the value of xy?

a)

6

b)

9

c)

12

d)

18

e)

24

4.

If a six-sided die is thrown, what is the probability that the result of two consecutive throws will be two sixes?

a)

$\frac{1}{72}$

b)

$\frac{1}{36}$

c)

$\frac{1}{24}$

d)

$\frac{1}{3}$

e)

$\frac{1}{2}$

5.

Tim has a box with a set of 8 green, 5 blue, 6 yellow, and 7 black toys. What is the probability that a random selection would yield a blue or black toy?

a)

$\frac{5}{26}$

b)

$\frac{1}{4}$

c)

$\frac{6}{13}$

d)

$\frac{1}{2}$

e)

$\frac{15}{16}$

6.

A company has three times more researchers employed than it does support staff, while it also has twice as many support staff compared to security. If the total number of researchers, support staff, and security staff is 675, how many people work as support staff?

a)

50

b)

75

c)

100

d)

150

e)

175

7.

Rectangle A has a width of 8 centimeters and a length of 3 centimeters. Rectangle B has a width of 6 centimeters and a length of 2 centimeters. What is the ratio of the area of rectangle A compared to the area of rectangle B?

a)

1:3

b)

1:2

c)

2:1

d)

3:1

e)

4:3

8.

The ratio of x to y is 7 to 18. If the value of x is 49, then what is the value of y?

a)

25

b)

56

c)

90

d)

96

e)

126

9.

The rectangles shown below are similar. What is the value of x?

a)

9

b)

12

c)

15

d)

18

e)

24

10.

Mitch became school council president by winning 64% of the vote. If his opponent won 396 votes and all of the votes cast were valid, what was the total number of votes cast?

a)

618

b)

694

c)

791

d)

1,025

e)

1,100

11.

Given the visual shown below, the ratio of x to y is $1:\frac{4}{3}$ . What is the value of y?

a)

2

b)

3

c)

4

d)

5

e)

6

12.

Which of the following lines has a negative slope with a negative x-intercept?

a)

b)

c)

d)

e)

13.

If the point $\left(-3,y\right)$ lies on $f\left(x\right)=-3x+4$ , then what is the correct value of y?

a)

-13

b)

-5

c)

4

d)

9

e)

13

14.

The length of a diagonal of a rectangle is 5 cm, and its width is 3 cm. What is the area of the rectangle?

a)

8

b)

12

c)

15

d)

20

e)

24

15.

What is the greatest common factor of 16, 28, and 32?

a)

2

b)

3

c)

4

d)

6

e)

8

16.

The sum of 41 numbers is 1025. What is the average of these numbers?

a)

23

b)

25

c)

31

d)

41

e)

50

17.

Which of the following values of x satisfies the equation $x^2+x-12=0$

a)

-3 and 4

b)

3

c)

3 and -4

d)

4

e)

12

18.

The sum of the values $-2x$ , $x+2$ , and $3x-4$ is 12. What is the value of x?

a)

4

b)

5

c)

6

d)

7

e)

12

19.

Jennifer's parents are saving for retirement. The value of their investment can be represented with the function $FV\left(X\right)=12,500\left(1+0.09\right)^t$ , where FV is the future value of the investment while t is the time in years that has passed. Rounded to two decimals, what will be the value of their investment in 25 years?

a)

75,259.41

b)

93,321.56

c)

101,214.24

d)

107,788.51

e)

131,199.24

20.

Which of the following could be a slope of a line perpendicular to one that passes through (0,2) and (4,8)?

a)

-3

b)

$-\frac{3}{2}$

c)

$-\frac{2}{3}$

d)

1

e)

3

ACT Diagnostic Test

Total questions: 20

Worksheet time: 3600secs

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