FREE Algebra Basic Concepts Questions and Answers 2026

Sample Algebra Test Practice Questions

Try these questions from our free Algebra Test practice tests. The correct answer and an explanation follow each question. Practice with the free Algebra practice test on PracticeTestGeeks (98 questions with answer explanations).

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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Free Algebra Test Study Tools

Interactive Algebra Test resources on PracticeTestGeeks, free to start:

• Algebra Test practice test — 98 questions with instant scoring and answer explanations
• Algebra Test flashcards — review key terms and concepts card by card
• Algebra Test study guide — topic-by-topic overview of what the exam covers
• Algebra Test cheat sheet — one-page printable summary for last-minute review