Enhance Your Skills with Our ACT Algebra Practice Test/Quiz

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30 random questions |30 minutes | Questions are randomized every attempt. Good luck!

ACT Math - Algebra Practice Test

Test your ACT algebra skills with 30 random practice test questions. Great for students preparing for the ACT math section!

1 / 30

1. What is the y-intercept of y = x² - 5x + 6?

A) -6

B) 5

C) -5

D) 6

Set x=0: y=6.

2 / 30

2. If h(x) = x² - 4 and k(x) = x + 2, what is h(x)/k(x) for x ≠ -2?

A) x²-2

B) x+2

C) x-2

D) x-4

(x²-4)/(x+2)=(x+2)(x-2)/(x+2)=x-2.

3 / 30

3. Factor: x³+x²-x-1

A) (x+1)(x²-1)

B) (x+1)²(x-1)

C) (x²-1)(x+1)

D) (x-1)(x+1)²

x²(x+1)-(x+1)=(x+1)(x²-1)=(x+1)²(x-1).

4 / 30

4. What is 16^(0.75)?

A) 8

B) 12

C) 16

D) 4

16^(3/4)=(16^(1/4))³=2³=8.

5 / 30

5. What is the value of (2x - 3)(3x + 1) when x = 0?

A) 3

B) 1

C) 0

D) -3

(2(0)-3)(3(0)+1)=(-3)(1)=-3.

6 / 30

6. For what x is f(x)=x²-4x minimum?

A) x=2

B) x=4

C) x=0

D) x=-2

Vertex x=-b/2a=-(-4)/(2)=2.

7 / 30

7. What is the value of x³-3x²+3x-1 when x=2?

A) 2

B) 0

C) 4

D) 1

(x-1)³=(2-1)³=1.

8 / 30

8. Which is the equation of a vertical line through (-3, 2)?

A) y = 2

B) y = -3

C) x = 2

D) x = -3

A vertical line through x = -3 is x = -3.

9 / 30

9. What is the inverse of f(x)=2x-4?

A) 2x+4

B) x/4+2

C) (x+4)/2

D) x/2+2

y=2x-4. x=2y-4. y=(x+4)/2.

10 / 30

10. What is the solution set of |x + 1| < 3?

A) x < 2

B) x > 2 or x < -4

C) -4 < x < 2

D) x > -4

|x+1| < 3 → -3 < x+1 < 3 → -4 < x < 2.

11 / 30

11. Solve: 3x/4 = 9

A) 12

B) 8

C) 10

D) 16

3x=36. x=12.

12 / 30

12. Solve: 5 - 2(3x + 1) = -9

A) x=3

B) x=4

C) x=1

D) x=2

5-6x-2=-9. 3-6x=-9. -6x=-12. x=2.

13 / 30

13. If 4(x - 2) = 2(x + 6), what is x?

A) 5

B) 8

C) 14

D) 10

4x - 8 = 2x + 12. 2x = 20. x = 10.

14 / 30

14. Solve: 5^(x-1)=25

A) x=3

B) x=4

C) x=5

D) x=2

25=5². x-1=2. x=3.

15 / 30

15. What is f(f(2)) if f(x) = x + 3?

A) 9

B) 10

C) 7

D) 8

f(2)=5. f(5)=8.

16 / 30

16. What is the slope of the line passing through (2, 3) and (6, 7)?

A) 2

B) 0

C) 1

D) 4

slope = (7-3)/(6-2) = 4/4 = 1.

17 / 30

17. What is the value of log₂(1)?

A) undefined

B) 1

C) 2

D) 0

log₂(1) = 0 because 2⁰ = 1.

18 / 30

18. What is the discriminant of x²+4x+4=0?

A) 4

B) 0

C) 16

D) 8

b²-4ac=16-16=0. One repeated root.

19 / 30

19. What is the domain of f(x) = 1/√(2x-6)?

A) x ≤ 3

B) x > 3

C) x < 3

D) x ≥ 3

2x-6 > 0 → x > 3 (strict — can't have 0 in denominator).

20 / 30

20. Solve: 5x-2 ≤ 3x+6

A) x≥-4

B) x≤-4

C) x≤4

D) x≥4

2x≤8. x≤4.

21 / 30

21. What is the x-intercept of y = 3x - 9?

A) 9

B) 3

C) -9

D) -3

Set y=0: 0 = 3x-9 → x = 3.

22 / 30

22. Solve: x²+6x+9=0

A) x=3

B) x=-3

C) x=±3

D) x=−3 only (double)

(x+3)²=0. x=-3 (double root).

23 / 30

23. If f(x)=ln(x), what is f(e²)?

A) 2e

B) ln2

C) e

D) 2

ln(e²)=2.

24 / 30

24. What is the value of (2x+3y)² when x=1, y=2?

A) 16

B) 49

C) 64

D) 8

2(1)+3(2)=2+6=8. 8²=64.

25 / 30

25. Factor: x² - 9

A) (x-3)(x-3)

B) (x+9)(x-1)

C) (x+3)(x-3)

D) (x-9)(x+1)

Difference of squares: x² - 9 = (x+3)(x-3).

26 / 30

26. What is the value of log₅(125)?

A) 2

B) 3

C) 5

D) 4

5³=125. log₅(125)=3.

27 / 30

27. Simplify: log(x²) - log(x)

A) 2log(x)

B) log(x)

C) log(x²-x)

D) log(x/2)

log(x²)-log(x)=log(x²/x)=log(x).

28 / 30

28. What is the equation of a line parallel to y = -2x + 3 through (0, 1)?

A) y = 2x + 1

B) y = 2x - 1

C) y = -2x - 1

D) y = -2x + 1

Parallel lines have same slope. m=-2, b=1: y = -2x + 1.

29 / 30

29. What is the quotient when x³-8 is divided by x-2?

A) x²+4

B) x²+2x+4

C) x²-2x+4

D) x²-4

Difference of cubes: x³-8=(x-2)(x²+2x+4).

30 / 30

30. What is the sum of solutions of |x|=5?

A) -5

B) 10

C) 5

D) 0

x=5 or x=-5. Sum=0.

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