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Free Year 10 Algebra Worksheets

10 free algebra resources for Year 10: 7 worksheets, 2 study guides, 1 test. Answers included.

Patterns, expressions, equations, functions and graphs. In Year 10, Year 10 prepares students for senior courses: quadratics, simultaneous equations, surds, trigonometry and logarithms, plus data analysis.

Students will practise: understanding that the solution to simultaneous equations satisfies both equations at once; solving by substitution when one variable is already the subject; solving by elimination, including multiplying an equation to match coefficients; setting up and solving simultaneous equations from a word problem; understanding the standard form of a quadratic equation; factorising monic quadratics and special cases; solving quadratic equations using the null factor law; using the quadratic formula and the discriminant.

Recommended learning path

  1. 1Simultaneous Equations: Substitution and Elimination
  2. 2Quadratics Cheat Sheet: Factorising and Solving
  3. 3Year 10 Quadratics Topic Test
Type:
Level:

Worksheets

Printable practice with an answer sheet.

  • Worksheet

    Year 10 Factorising and Solving Quadratics Worksheet — Level 2

    Factorise monic quadratics and solve quadratic equations by factorising. Expected-level practice for this year group. This Year 10…

    Difficulty
    Level 2 · Standard
    Time
    15 min
    Questions
    10 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Simultaneous Equations Worksheet — Level 2

    Solve pairs of linear equations by elimination or substitution. Expected-level practice for this year group. This Year 10 worksheet has 8…

    Difficulty
    Level 2 · Standard
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Factorising and Solving Quadratics Worksheet — Level 2 (Set 2)

    Factorise monic quadratics and solve quadratic equations by factorising. Expected-level practice for this year group. This Year 10…

    Difficulty
    Level 2 · Standard
    Time
    15 min
    Questions
    10 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Factorising and Solving Quadratics Worksheet — Level 3

    Factorise monic quadratics and solve quadratic equations by factorising. A challenge set for students ready to stretch further. This Year…

    Difficulty
    Level 3 · Challenge
    Time
    15 min
    Questions
    10 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Simultaneous Equations Worksheet — Level 3

    Solve pairs of linear equations by elimination or substitution. A challenge set for students ready to stretch further. This Year 10…

    Difficulty
    Level 3 · Challenge
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Solving Linear Equations Worksheet — Level 3

    One-step, two-step and equations with brackets or variables on both sides. A challenge set for students ready to stretch further. This…

    Difficulty
    Level 3 · Challenge
    Time
    15 min
    Questions
    12 questions
    Answers
    Answers included
  • Worksheet

    Year 10 Expanding Brackets Worksheet — Level 3

    Expand single brackets, then binomial products. A challenge set for students ready to stretch further. This Year 10 worksheet has 12…

    Difficulty
    Level 3 · Challenge
    Time
    15 min
    Questions
    12 questions
    Answers
    Answers included

Topic Tests

End-of-topic tests covering the whole topic.

  • Topic Test

    Year 10 Quadratics Topic Test

    Expanding binomials, factorising and solving quadratic equations in a 45-minute Year 10 test with marks and fully worked solutions.

    Difficulty
    Level 3 · Challenge
    Time
    45 min
    Questions
    18 questions
    Answers
    Answers included

Study Guides

Clear explanations, examples and tips.

  • Study Guide

    Simultaneous Equations: Substitution and Elimination

    Shows Year 10 students how to solve a pair of linear equations by substitution and by elimination, including when to multiply an equation…

    Difficulty
    Level 2 · Standard
    Time
    20 min

Cheat Sheets

Formulas and rules at a glance.

  • Cheat Sheet

    Quadratics Cheat Sheet: Factorising and Solving

    A one-page summary of everything needed to factorise and solve quadratic equations: the sum-and-product method, common factors, difference…

    Difficulty
    Level 3 · Challenge
    Time
    15 min

Common questions

What do Year 10 students learn about algebra?

Patterns, expressions, equations, functions and graphs. At Year 10, our resources focus on: understanding that the solution to simultaneous equations satisfies both equations at once; solving by substitution when one variable is already the subject; solving by elimination, including multiplying an equation to match coefficients; setting up and solving simultaneous equations from a word problem.

Where should we start?

Read the study guide first, then start with the Level 1 or Level 2 worksheet. Finish with the topic test.

Are answers included?

Yes — every worksheet has an answer sheet. Maths answer sheets show the working; English tasks include model answers or success criteria.

How to use these resources

  1. Start with the Level 1 worksheet for the topic — if it's easy, move up a level.
  2. Use the answer sheet's working, not just the final answer, to check the method.
  3. Finish a topic with the topic test to see whether the skill is secure.
  4. Two or three short sessions a week beat one long one.

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