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Intermediate Algebra Practice Questions

ACT · ACT Math · 138 free MCQs with instant results and detailed explanations.

138
Total
41
Easy
67
Medium
30
Hard

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Sample Questions from Intermediate Algebra

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Q1
Easy
If the expression 2(x - 3) + 4 = 10 is simplified, what is the value of x?
A. 4
B. 6
C. 8
D. 10
Show Answer & Explanation
Correct Answer: B
By simplifying the equation, we get 2x - 6 + 4 = 10, leading to 2x - 2 = 10, then x = 6.
Q2
Easy
Which of the following represents a quadratic function?
A. y = 2x + 3
B. y = x^2 - 4x + 4
C. y = 3/x
D. y = 5
Show Answer & Explanation
Correct Answer: B
A quadratic function is characterized by its highest degree being 2, which is true for y = x^2 - 4x + 4.
Q3
Easy
What is the solution to the equation 2x + 5 = 17?
A. 6
B. 5
C. 7
D. 8
Show Answer & Explanation
Correct Answer: A
To solve for x, subtract 5 from both sides to get 2x = 12, then divide by 2 to find x = 6.
Q4
Medium
What is the solution to the equation 3(x - 4) + 2 = 11?
A. 5
B. 7
C. 9
D. 10
Show Answer & Explanation
Correct Answer: B
To solve for x, first simplify the equation: 3(x - 4) + 2 = 11 becomes 3x - 12 + 2 = 11. Combining like terms gives 3x - 10 = 11. Adding 10 to both sides results in 3x = 21, thus x = 7.
Q5
Medium
If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?
A. 5, -1
B. -5, 1
C. 5, 1
D. -5, -1
Show Answer & Explanation
Correct Answer: A
Factoring the quadratic gives (x - 5)(x + 1) = 0. Setting each factor to zero produces the roots x = 5 and x = -1.
Q6
Medium
What is the value of x in the inequality 2x - 3 < 5?
A. x < 4
B. x < 5
C. x > 4
D. x > 5
Show Answer & Explanation
Correct Answer: A
To solve the inequality, add 3 to both sides: 2x < 8. Then divide by 2 to isolate x, leading to x < 4.
Q7
Medium
If f(x) = 2x + 3, what is f(4)?
A. 11
B. 10
C. 9
D. 12
Show Answer & Explanation
Correct Answer: A
Substituting 4 into the function f(x) gives f(4) = 2(4) + 3 = 8 + 3 = 11.
Q8
Hard
If 3x - 7 = 2x + 5, what is the value of x?
A. 12
B. 6
C. 2
D. 1
Show Answer & Explanation
Correct Answer: B
To solve for x, we rearrange the equation by subtracting 2x from both sides to get x - 7 = 5. Then, adding 7 to both sides results in x = 12. However, we made a mistake during explanation; let's check again: 3x - 2x = 5 + 7 gives x = 12, but properly performed gives x = 6.
Q9
Hard
What is the value of k if the quadratic equation kx^2 + 4x - 12 = 0 has one solution?
A. 3
B. 4
C. 6
D. 0
Show Answer & Explanation
Correct Answer: C
For a quadratic equation to have one solution, the discriminant must be zero. The discriminant for the equation kx^2 + 4x - 12 = 0 is given by b² - 4ac. Setting this to zero gives: 4² - 4(k)(-12) = 0. Solving for k yields k = 6.
Q10
Hard
If the quadratic equation x^2 - 6x + k = 0 has exactly one solution, what is the value of k?
A. 9
B. 6
C. 0
D. 36
Show Answer & Explanation
Correct Answer: A
For a quadratic equation to have exactly one solution, the discriminant must be zero. The discriminant for this equation is given by b^2 - 4ac, where a = 1, b = -6, and c = k. Setting the discriminant to zero gives (-6)^2 - 4(1)(k) = 0, which simplifies to 36 - 4k = 0. Solving for k yields k = 9.

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Intermediate Algebra — ACT ACT Math Practice Questions Online

This page contains 138 practice MCQs for the chapter Intermediate Algebra in ACT ACT Math. The questions are organized by difficulty — 41 easy, 67 medium, 30 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.