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Algebra Quiz with Answers

Solve equations, simplify expressions and review worked answers.

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Choose a focused 5-question round or try 10 mixed questions from all levels. You can repeat the quiz and improve your personal best.

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Scoring and personal best are saved in this browser only.

How to use the Algebra Quiz

Start an Easy, Intermediate, Advanced or Mixed round. Select one of four answers, check it, and read the full explanation before continuing. Each focused round has five questions; a mixed round has ten. Review missed questions at the end, then try another round.

Use our Algebraic Expression Calculator for extra practice. Your best score stays only in this browser.

Frequently asked questions

Is this quiz free?

Yes. Every round is free, with answers, explanations and no registration requirement.

Can I choose the difficulty?

Choose Easy, Intermediate or Advanced for a focused five-question round, or Mixed for ten questions from all levels. Try again to improve your personal best.

More practice and calculators

Continue with Algebra · Math Equation Solving or browse all learning quizzes. Check your calculations with the Algebraic Expression Calculator.

Learn Algebra Quiz topics before you start

Solving equations step by step

An equation says that two expressions have the same value. To solve x + 7 = 19, subtract 7 from both sides and obtain x = 12. Check your answer by replacing x with 12: 12 + 7 = 19. With a two-step equation, undo addition or subtraction before undoing multiplication or division. For example, 3x + 4 = 25 becomes 3x = 21 and then x = 7.

Expressions, brackets and like terms

Only like terms can be combined: 4a + 3a is 7a, but 4a + 3b cannot be simplified to 7ab. Distribute multiplication across brackets: 2(x + 5) becomes 2x + 10. A common error is multiplying the first term but forgetting the second. Test your answer by substituting a small number for x on both sides.

From factoring to simultaneous equations

To factor x² + 5x + 6, find two numbers whose sum is 5 and product is 6. They are 2 and 3, so the factorization is (x + 2)(x + 3). When two equations share two variables, adding or subtracting them can eliminate a variable. The Advanced quiz also asks you to recognize both positive and negative roots of a squared expression.

Take the Algebra Quiz above, then explore the Algebraic Expression Calculator to verify your own examples. Find other free skill checks in the quiz directory.