Free DSST Fundamentals of College Algebra Practice Test

Question 1

Solve 3^(2x − 1) = 27^(x + 1).

Accepted Answer

x = −4

Answer

x = 4

Answer

x = −2

Answer

x = 1/2

Question 2

What is the solution set of x² − x − 12 < 0?

Accepted Answer

−3 < x < 4

Answer

x < −3 or x > 4

Answer

−4 < x < 3

Answer

x < 4

Question 3

If f(x) = 2x − 3 and g(x) = x² + 1, what is (f∘g)(−2)?

Accepted Answer

7

Answer

50

Answer

−35

Answer

−2

Question 4

A theater sold 40 tickets for $385. Adult tickets cost $12 and child tickets cost $7. How many child tickets were sold?

Accepted Answer

19

Answer

21

Answer

20

Answer

15

Question 5

Which line passes through (−2, 5) and is perpendicular to the line 2x − 3y = 6?

Accepted Answer

y = −(3/2)x + 2

Answer

y = (2/3)x + 19/3

Answer

y = (3/2)x + 8

Answer

y = −(3/2)x + 8

Question 6

The endpoints of a diameter of a circle are (−3, 7) and (5, −1). What is an equation of the circle?

Accepted Answer

(x − 1)² + (y − 3)² = 32

Answer

(x + 1)² + (y + 3)² = 32

Answer

(x − 1)² + (y − 3)² = 128

Answer

(x − 4)² + (y + 4)² = 32

Question 7

Solve x/(x − 2) = 2/(x − 2) + 3.

Accepted Answer

No solution

Answer

x = 2

Answer

x = 4

Answer

x = −2

Question 8

What are all the real solutions of x⁴ − 3x² − 4 = 0?

Accepted Answer

x = −2 and x = 2

Answer

x = −1 and x = 4

Answer

x = −2, x = −1, x = 1 and x = 2

Answer

x = 2 only

Question 9

Simplify (x² − 9)/(x² + x − 6), for values of x where the expression is defined.

Accepted Answer

(x − 3)/(x − 2)

Answer

(x + 3)/(x − 2)

Answer

(x − 3)/(x + 2)

Answer

−9/(x − 6)

Question 10

What is the remainder when P(x) = x³ − 4x² + 2x + 5 is divided by x − 3?

Accepted Answer

2

Answer

−64

Answer

5

Answer

−1

Question 11

Write (3 + 2i)/(1 − i) in the form a + bi.

Accepted Answer

1/2 + (5/2)i

Answer

1 + 5i

Answer

5/2 + (5/2)i

Answer

5/2 − (1/2)i

Question 12

Solve −3(x − 2) ≤ 2x + 1.

Accepted Answer

x ≥ 1

Answer

x ≤ 1

Answer

x ≥ −3/5

Answer

x ≤ −1

Question 13

What is the maximum value of f(x) = −2x² + 12x − 7?

Accepted Answer

11

Answer

3

Answer

−7

Answer

47

Question 14

For which values of k does x² + kx + 9 = 0 have exactly one real solution?

Accepted Answer

k = −6 or k = 6

Answer

k = 6 only

Answer

k = −3 or k = 3

Answer

k = 36

Question 15

What is the inverse of f(x) = (2x + 1)/(x − 3)?

Accepted Answer

f⁻¹(x) = (3x + 1)/(x − 2)

Answer

f⁻¹(x) = (x − 3)/(2x + 1)

Answer

f⁻¹(x) = (3x − 1)/(x + 2)

Answer

f⁻¹(x) = (2x − 1)/(x + 3)

Question 16

Write 3/(x − 2) − 2/(x + 1) as a single fraction.

Accepted Answer

(x + 7)/[(x − 2)(x + 1)]

Answer

(x − 1)/[(x − 2)(x + 1)]

Answer

(x + 5)/[(x − 2)(x + 1)]

Answer

(5x − 1)/[(x − 2)(x + 1)]

Question 17

What is the value of 27^(−2/3)?

Accepted Answer

1/9

Answer

−9

Answer

1/18

Answer

9

Question 18

Solve log₂(x) + log₂(x − 2) = 3.

Accepted Answer

x = 4 only

Answer

x = −2 and x = 4

Answer

x = 5

Answer

x = −2 only

Question 19

What is the domain of f(x) = √(6 − 2x)/(x + 1)?

Accepted Answer

x ≤ 3 and x ≠ −1

Answer

x ≥ 3

Answer

x < 3 and x ≠ −1

Answer

x ≤ 3

Question 20

Which point lies on the graph of f(x) = log₃(x − 2) + 1?

Accepted Answer

(11, 3)

Answer

(3, 0)

Answer

(5, 1)

Answer

(2, 1)

Question 21

Simplify √50 + √18 − √8.

Accepted Answer

6√2

Answer

√60

Answer

10√2

Answer

2√15

Question 22

Solve |2x − 5| ≥ 3.

Accepted Answer

x ≤ 1 or x ≥ 4

Answer

1 ≤ x ≤ 4

Answer

x ≥ 4

Answer

x ≤ −1 or x ≥ 4

Question 23

Which statement describes the graph of f(x) = (2x² − 8)/(x² − x − 2)?

Accepted Answer

A vertical asymptote at x = −1, a hole at x = 2, and a horizontal asymptote y = 2

Answer

Vertical asymptotes at x = 2 and x = −1, and a horizontal asymptote y = 2

Answer

A vertical asymptote at x = −1 and a horizontal asymptote y = 0

Answer

Vertical asymptotes at x = 1 and x = −2, and a horizontal asymptote y = 2

Question 24

Which of the following is the complete factorization of x³ − 3x² − 4x + 12?

Accepted Answer

(x − 3)(x − 2)(x + 2)

Answer

(x − 3)(x − 2)²

Answer

(x + 3)(x − 2)(x + 2)

Answer

(x − 3)(x² + 4)

Question 25

Solve √(x + 7) = x + 1.

Accepted Answer

x = 2 only

Answer

x = −3 and x = 2

Answer

x = −3 only

Answer

x = 3 only

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