CMClearMathAcademy

Algebra II Final Exam

A free Algebra II lesson from the “Trigonometry and Modeling” unit, with a worked example and practice problems including step-by-step solutions.

An independent 52-question sample across all 13 course units. Review exercises prepare you for the skills; final questions use a separate bank. This assessment samples calculation, interpretation, and reasoning. Its score is evidence about these questions, not an external readiness certification. Written reasoning requires separate review.

What you'll learn

Why it matters: The Algebra II readiness test mirrors what college placement exams, ACT/SAT math, and pre-calculus diagnostics expect. The skill is identifying which Algebra II tool each problem is asking for — equations, functions, polynomials, exponentials, logs, or trig — and applying it cleanly.

Worked example

Problem. Evaluate log base 2 of 16.

  1. Ask: 2 to what power equals 16?
  2. 2^4 = 16.
  3. So the logarithm is 4.

Answer: 4

Lesson preview: this page shows 5 practice items. The interactive activity contains 50 practice items and 52 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. If f(x) = 3x + 2, find f(8).

Show solution
  1. 3(8) + 2 = 26.

Answer: 26

2. For f(x) = 1/(x + 4), what value is excluded?

Show solution
  1. x + 4 cannot be zero.

Answer: -4

3. The vertex of y = (x - 6)^2 - 1 is...

Choices: (6, -1) · (-6, -1) · (6, 1) · (-6, 1)

Show solution
  1. Vertex form gives (h, k).

Answer: (6, -1)

4. Factor x^2 - 7x + 12.

Choices: (x - 3)(x - 4) · (x + 3)(x + 4) · (x - 2)(x - 6) · (x - 1)(x - 12)

Show solution
  1. 3 and 4 multiply to 12 and add to 7.

Answer: (x - 3)(x - 4)

5. Find the discriminant of x^2 - 6x + 9 = 0.

Show solution
  1. 36 - 36 = 0.

Answer: 0

Practice this interactively with instant feedback and an AI tutor.

Practice Algebra II Final Exam Take the free placement check

More Algebra II lessons