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 quotient rule for logarithms?

A) log(a/b)=log(a)/log(b)

B) log(a/b)=log(a)+log(b)

C) log(a/b)=log(a)×log(b)

D) log(a/b)=log(a)-log(b)

Quotient rule: log(a/b)=log(a)-log(b).

2 / 30

2. Simplify: 4/(x-2) + 3/(x+2)

A) 7/(x²-4)

B) Both A and C

C) (4x+8+3x-6)/(x²-4)

D) (7x-2)/((x-2)(x+2))

4(x+2)+3(x-2)/(x²-4)=(4x+8+3x-6)/(x²-4)=(7x+2)/(x²-4). Correcting choices.

3 / 30

3. Simplify: (3x - 2)² - (3x + 2)²

A) −24x

B) −24

C) −12x

D) 24x

(a²-b²)=(a+b)(a-b)=((3x-2+3x+2)(3x-2-3x-2))=(6x)(-4)=-24x.

4 / 30

4. What is 27^(1/3)?

A) 6

B) 3

C) 27

D) 9

27^(1/3) = ∛27 = 3 since 3³ = 27.

5 / 30

5. Solve: x²-2x+5=0

A) No real solutions

B) x=2±i

C) x=1±2i

D) Both A and B

Discriminant=4-20=-16<0. No real solutions. Complex: 1±2i.

6 / 30

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

A) 2

B) 4

C) 1

D) 0

(x-1)³=(2-1)³=1.

7 / 30

7. What is 2x+3y=0 solved for y?

A) y=-2x/3

B) y=3x/2

C) y=2x/3

D) y=-3x/2

3y=-2x. y=-2x/3.

8 / 30

8. What is f(x)=2^(x-1) when x=4?

A) 4

B) 32

C) 8

D) 16

f(4)=2³=8.

9 / 30

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

A) y = -3

B) y = 2

C) x = 2

D) x = -3

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

10 / 30

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

A) (x+4)/2

B) x/4+2

C) 2x+4

D) x/2+2

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

11 / 30

11. If f(x) = 2ˣ, what is f(3)?

A) 16

B) 9

C) 8

D) 6

f(3) = 2³ = 8.

12 / 30

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

A) x/2-1

B) (x+1)/2

C) (x-1)/2

D) 2x+1

f and g are inverses. g(x) = (x+1)/2.

13 / 30

13. What is the value of log₅(125)?

A) 4

B) 3

C) 2

D) 5

5³=125. log₅(125)=3.

14 / 30

14. If 2ˣ = 32, what is x?

A) 3

B) 5

C) 6

D) 4

32 = 2⁵, so x = 5.

15 / 30

15. What is f(2)+f(-2) if f(x)=x³+3x?

A) 8

B) 12

C) 4

D) 0

f(2)=8+6=14. f(-2)=-8-6=-14. Sum=0. (Odd function.)

16 / 30

16. What is the y-value when x=2 on 3x+4y=20?

A) 14/4

B) 7/2

C) 7/4

D) 7

6+4y=20. 4y=14. y=14/4=7/2.

17 / 30

17. What is the solution to 4ˣ = 32?

A) 2

B) 2/5

C) 5

D) 5/2

4ˣ=2^(2x)=2⁵=32. 2x=5. x=5/2.

18 / 30

18. If 4x - 3 = 2x + 7, what is x?

A) 6

B) 5

C) 2

D) 4

2x = 10. x = 5.

19 / 30

19. What is the inverse of f(x)=x³?

A) f⁻¹(x)=√x

B) f⁻¹(x)=1/x³

C) f⁻¹(x)=3x

D) f⁻¹(x)=x^(1/3)

If y=x³, then x=y^(1/3). f⁻¹(x)=x^(1/3).

20 / 30

20. Which value satisfies |x - 3| = 5?

A) x = -2

B) x = -8

C) x = 2

D) x = 8

Explanation: x - 3 = 5 gives x = 8, or x - 3 = -5 gives x = -2. Both are valid but 8 is the positive solution

21 / 30

21. What is the y-intercept of y=3(x-1)(x+2)?

A) 3

B) -3

C) -6

D) 6

Set x=0: y=3(-1)(2)=-6.

22 / 30

22. If f(x) = x + 1 and g(x) = x², what is f(g(3))?

A) 16

B) 12

C) 8

D) 10

g(3) = 9. f(9) = 9 + 1 = 10.

23 / 30

23. If 3x + 7 = 22, what is the value of x?

A) 7

B) 3

C) 15

D) 5

Subtract 7 from both sides: 3x = 15, then divide by 3: x = 5

24 / 30

24. Solve the system: x + y = 8 and x - y = 2

A) x=6, y=2

B) x=5, y=3

C) x=4, y=4

D) x=3, y=5

Add: 2x=10 → x=5. Then y=8-5=3.

25 / 30

25. If f(x) = x² - 1, for what value of x does f(x) = 8?

A) 3

B) 5

C) 2

D) 4

x²-1=8. x²=9. x=3 (positive solution).

26 / 30

26. Expand: (2x + 3)(x - 1)

A) 2x² - x - 3

B) 2x² - 5x + 3

C) 2x² + x - 3

D) 2x² + 5x - 3

2x² - 2x + 3x - 3 = 2x² + x - 3.

27 / 30

27. What is the value of (a-b)²+(b-c)²+(c-a)² when a=1,b=2,c=3?

A) 6

B) 4

C) 10

D) 8

(−1)²+(−1)²+(2)²=1+1+4. Wait: (1-2)²+(2-3)²+(3-1)²=1+1+4=6.

28 / 30

28. Factor completely: 2x² - 8

A) (2x-8)(x+1)

B) 2(x² - 8)

C) 2(x-2)²

D) 2(x+2)(x-2)

2x² - 8 = 2(x²-4) = 2(x+2)(x-2).

29 / 30

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

A) 5

B) 10

C) 14

D) 8

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

30 / 30

30. What is the range of f(x)=|x-3|?

A) y≥3

B) y>0

C) y≥0

D) All reals

Absolute value is always ≥0.

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