Enhance Your Skills with Our ACT Algebra Practice Test/Quiz

Report a question

What's wrong with this question?
You cannot submit an empty report. Please add some details.

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 does it mean graphically if the discriminant = 0?

A) One x-intercept (tangent to x-axis)

B) No x-intercepts

C) Two x-intercepts

D) Infinite x-intercepts

Discriminant=0 → one repeated root → parabola touches x-axis once.

2 / 30

2. What is the domain of f(x) = √(x - 4)?

A) All real numbers

B) x ≥ 4

C) x > 4

D) x ≤ 4

For √(x-4) to be real, x - 4 ≥ 0, so x ≥ 4.

3 / 30

3. Solve: 3/x = 6/8

A) x=18

B) x=16

C) x=2

D) x=4

Cross multiply: 6x=24. x=4.

4 / 30

4. What is the value of (x-1)(x+1)(x²+1) when x=2?

A) 21

B) 15

C) 25

D) 30

(1)(3)(5)=15.

5 / 30

5. If h(x) = x² - 4x, what is h(6)?

A) 12

B) 14

C) 18

D) 10

h(6) = 36 - 24 = 12.

6 / 30

6. What is the intersection of y=x+1 and y=x²-1?

A) (0,1) and (-1,0)

B) (3,4) and (-1,0)

C) (1,2) and (-2,-1)

D) (2,3) and (-1,0)

x+1=x²-1. x²-x-2=0. (x-2)(x+1)=0. x=2,y=3 or x=-1,y=0.

7 / 30

7. What is the product of roots of x² - 5x + 6 = 0?

A) -6

B) 6

C) 5

D) -5

Product of roots = c/a = 6/1 = 6.

8 / 30

8. Simplify: (x + y)² - (x - y)²

A) 4xy

B) 2y²

C) 2xy

D) 4x²

(x+y)²=x²+2xy+y², (x-y)²=x²-2xy+y². Difference=4xy.

9 / 30

9. Simplify: 3x² + 2x - x² + 4x

A) 4x² + 6x

B) 2x² + 6x

C) 2x² - 6x

D) 3x² + 6x

Explanation: Combine like terms: (3-1)x² + (2+4)x

10 / 30

10. If f(x) = 2ˣ, what is f(3)?

A) 9

B) 8

C) 16

D) 6

f(3) = 2³ = 8.

11 / 30

11. Factor: 5x²-20

A) 5(x-4)(x+4)

B) 5(x²-4)

C) 5(x+2)(x-2)

D) Both A and B

5(x²-4)=5(x+2)(x-2). Both A and B are correct.

12 / 30

12. Simplify: (x⁴)/(x²)

A) x⁶

B) x

C) x⁸

D) x²

x⁴/x² = x^(4-2) = x².

13 / 30

13. What is the quadratic with roots -3 and 7?

A) x²+4x+21

B) x²+4x-21

C) x²-4x+21

D) x²-4x-21

Sum=-3+7=4=-b/a, so b=-4. Product=-21=c. x²-4x-21.

14 / 30

14. If f(x) = 2x + 3, what is f⁻¹(x)?

A) (3-x)/2

B) 2x-3

C) (x-3)/2

D) (x+3)/2

y = 2x+3 → x = 2y+3 → y = (x-3)/2.

15 / 30

15. What is the value of log₅(125)?

A) 2

B) 4

C) 5

D) 3

5³=125. log₅(125)=3.

16 / 30

16. Solve: 3x-4 ≥ 2x+1

A) x≥5

B) x≤-5

C) x≤5

D) x≥-5

x≥5.

17 / 30

17. Solve: e^x = e³

A) x=ln3

B) x=e

C) x=3

D) x=e³

If bases are equal, exponents are equal. x=3.

18 / 30

18. Simplify: √50 + √18

A) 68√2

B) 4√5+3√2

C) 8√2

D) 10√2

√50=5√2, √18=3√2. Sum=8√2.

19 / 30

19. What is the slope of 4x + 2y = 8?

A) -4

B) -2

C) 2

D) 4

Rewrite: 2y = -4x + 8 → y = -2x + 4. Slope = -2.

20 / 30

20. Simplify: log(x²) - log(x)

A) log(x)

B) 2log(x)

C) log(x²-x)

D) log(x/2)

log(x²)-log(x)=log(x²/x)=log(x).

21 / 30

21. Solve: 3x/4 = 9

A) 12

B) 10

C) 8

D) 16

3x=36. x=12.

22 / 30

22. Simplify: (x+2)/(x²-4)

A) 1/(x-2)

B) (x+2)/(x-2)

C) 1/(x+2)

D) x/(x-2)

x²-4=(x+2)(x-2). Simplified: 1/(x-2).

23 / 30

23. If f(x)=3x+k and f(2)=11, what is k?

A) 7

B) 3

C) 5

D) 9

6+k=11. k=5.

24 / 30

24. If f(x)=x+3 and g(x)=2x, what is (g∘f)(x)?

A) 2(x+3)

B) 2x+3

C) Both B and C

D) 2x+6

g(f(x))=g(x+3)=2(x+3)=2x+6. Both B and C are equal.

25 / 30

25. Solve: 3x+5 > 4x-2

A) x>-7

B) x<-7

C) x>7

D) x<7

3x-4x>-2-5. -x>-7. x<7.

26 / 30

26. If f(x) = √(x + 9), what is the domain?

A) x > 9

B) x ≥ -9

C) x ≥ 9

D) x > 0

x + 9 ≥ 0 → x ≥ -9.

27 / 30

27. If f(x) = x² and g(x) = 2x - 1, what is g(f(3))?

A) 18

B) 17

C) 35

D) 16

f(3)=9. g(9)=2(9)-1=17.

28 / 30

28. Solve: x² + 4x + 4 = 0

A) x = 4

B) x = -2

C) x = -4

D) x = 2

(x+2)² = 0. x = -2 (double root).

29 / 30

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

A) x=4

B) x=5

C) x=3

D) x=2

25=5². x-1=2. x=3.

30 / 30

30. Simplify: (4x³y²) / (2xy)

A) 8x²y

B) 2x³y

C) 4x²y²

D) 2x²y

4/2=2, x³/x=x², y²/y=y. Answer: 2x²y.

Your score is
The average score is 25%
0%

🎯 Register FREE to save your score and unlock 1000+ more free quizzes!

👉 Register Now — It’s Free!

📚 StudyRightWay

Pages

Resources

Legal

Connect

Course has been added to your cart