FREE Algebra Basic Concepts Questions and Answers 2026 October

Sample Algebra Test Practice Questions

Try these questions from our free Algebra Test practice tests. The correct answer and an explanation follow each question.

1. In the system y = 4x - 3 and y = 4x + 1, how many solutions exist?

   • A. None
   • B. One
   • C. Two
   • D. Infinitely many

   Answer: A. None

   Both lines have slope 4 but different intercepts, making them parallel with no intersection.

2. Which function graphs as a straight line?

   • A. f(x) = x²
   • B. f(x) = 2x + 1
   • C. f(x) = √x
   • D. f(x) = 1/x

   Answer: B. f(x) = 2x + 1

   f(x) = 2x + 1 is a linear function and graphs as a straight line.

3. What is the vertex of y = (x - 3)² + 5?

   • A. (3, 5)
   • B. (-3, 5)
   • C. (3, -5)
   • D. (-3, -5)

   Answer: A. (3, 5)

   In vertex form y = a(x - h)² + k, the vertex is (h, k) = (3, 5).

4. Solve for x: 5(x - 2) = 15

   • A. x = 1
   • B. x = 3
   • C. x = 5
   • D. x = 7

   Answer: C. x = 5

   Divide both sides by 5 to get x - 2 = 3, then add 2 to get x = 5.

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