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 axis of symmetry of y = -3x² + 6x + 2?

A) x=-1

B) x=1

C) x=2

D) x=-2

x=-b/2a = -6/(2×-3) = -6/-6 = 1.

2 / 30

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

A) 3

B) -3

C) 9

D) -9

Set y=0: 0 = 3x-9 → x = 3.

3 / 30

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

A) x²-4

B) x²-2x+4

C) x²+4

D) x²+2x+4

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

4 / 30

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

A) x=3, y=5

B) x=5, y=3

C) x=6, y=2

D) x=4, y=4

Add: 2x=10 → x=5. Then y=8-5=3.

5 / 30

5. What is the equation of a line through (4,1) and (8,3)?

A) y=1/2x+3

B) y=1/2x-1

C) y=2x-7

D) y=x-3

slope=(3-1)/(8-4)=1/2. y-1=1/2(x-4)→y=1/2x-1.

6 / 30

6. What is the minimum value of y = (x - 2)² + 5?

A) 5

B) 2

C) 0

D) 7

The vertex is (2, 5) and since a>0, minimum y = 5.

7 / 30

7. If the roots of x²+bx+c=0 are 3 and -5, what are b and c?

A) b=-2, c=-15

B) b=2, c=-15

C) b=-2, c=15

D) b=2, c=15

Sum=3+(-5)=-2=-b→b=2. Product=3(-5)=-15=c.

8 / 30

8. Solve: x² - 4x - 12 = 0

A) x=-4, x=3

B) x=6, x=-2

C) x=4, x=-3

D) x=-6, x=2

Factor: (x-6)(x+2)=0. x=6 or x=-2.

9 / 30

9. Factor: 8x³-1

A) (2x-1)³

B) 8(x³-1)

C) (2x+1)(4x²-2x+1)

D) (2x-1)(4x²+2x+1)

Difference of cubes: (2x)³-1³=(2x-1)(4x²+2x+1).

10 / 30

10. 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).

11 / 30

11. Factor: x²+10x+25

A) (x-5)²

B) (x+5)(x-5)

C) (x+5)²

D) (x+10)(x+5)

Perfect square: (x+5)²=x²+10x+25.

12 / 30

12. Simplify: (3x+2)-(x-5)

A) 2x-3

B) 4x-3

C) 4x+7

D) 2x+7

3x+2-x+5=2x+7.

13 / 30

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

A) 1

B) 4

C) 0

D) 2

(x-1)³=(2-1)³=1.

14 / 30

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

A) 15

B) 3

C) 5

D) 7

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

15 / 30

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

A) 0

B) 10

C) -5

D) 5

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

16 / 30

16. What is f(-x) if f(x)=x³-x?

A) f(x)-2x

B) −f(x)

C) f(x)+2x

D) f(x)

f(-x)=(-x)³-(-x)=-x³+x=-(x³-x)=-f(x). Odd function.

17 / 30

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

A) x=2

B) x=1

C) x=4

D) x=3

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

18 / 30

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

A) 17

B) 18

C) 16

D) 35

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

19 / 30

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

A) 21

B) 25

C) 30

D) 15

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

20 / 30

20. Solve: (x + 2)/3 = 4

A) 9

B) 11

C) 10

D) 12

x + 2 = 12. x = 10.

21 / 30

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

A) -2

B) -4

C) 2

D) 4

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

22 / 30

22. Simplify: (x²-x-2)/(x+1)

A) x-2

B) x-1

C) x+1

D) x+2

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

23 / 30

23. What is the equation of a parabola with vertex (0,0) opening upward?

A) x=y²

B) y=x

C) y=-x²

D) y=x²

y=x² opens upward with vertex at origin.

24 / 30

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

A) 16

B) 10

C) 8

D) 12

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

25 / 30

25. If 3ˣ⁺¹ = 27, what is x?

A) 3

B) 1

C) 2

D) 4

27 = 3³. 3ˣ⁺¹ = 3³ → x+1=3 → x=2.

26 / 30

26. What are the solutions of 2x² - 18 = 0?

A) x = ±9

B) x = ±3

C) x = ±6

D) x = ±√18

2x² = 18 → x² = 9 → x = ±3.

27 / 30

27. Simplify: (x²+3x) / x

A) 3x

B) x+1

C) x+3

D) x² + 3

x(x+3)/x = x+3.

28 / 30

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

A) x = 2

B) x = -3

C) y = -3

D) y = 2

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

29 / 30

29. If 3ˣ = 9ˣ⁻¹, what is x?

A) 2

B) 3

C) 1

D) 4

9^(x-1) = 3^(2x-2). So 3ˣ = 3^(2x-2). x=2x-2. x=2.

30 / 30

30. Simplify: (x + y)² - (x - y)²

A) 2y²

B) 4xy

C) 4x²

D) 2xy

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

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