Algebra 2 Practice Test

About This Algebra 2 Practice Test

This 20-question test reviews the broader function and equation skills developed after Algebra 1. The set includes quadratic equations, complex numbers, rational simplification, radical equations, exponentials and logarithms, composition and inverse functions, the Remainder Theorem, polynomial factoring, nonlinear systems, sequences, vertices, asymptotes, domains, and binomial coefficients.

Questions are intentionally mixed so that the correct method must be selected from the structure of the problem.

Topics Included

• Quadratic equations and vertex form ideas.
• Complex-number arithmetic.
• Rational expressions and restrictions.
• Radical, exponential, and logarithmic equations.
• Function composition and inverses.
• Polynomial factoring and the Remainder Theorem.
• Arithmetic and geometric sequences.
• Domains, asymptotes, and binomial expansion.

Problem-Solving Strategy

1. Identify the function or equation family.
2. Record restrictions before simplifying.
3. Choose an algebraic form that exposes the structure.
4. Check potential extraneous or excluded solutions.
5. Interpret the result in the context of the question.

Common Errors

Frequent mistakes include losing domain restrictions after cancellation, accepting an invalid logarithmic root, confusing a function inverse with a reciprocal, mishandling i², or using an arithmetic-sequence rule on a geometric sequence.

Practice Format

Each selection reveals a worked explanation and a review of the distractors. The final score is based on all 20 questions and separately reports skipped items.