GCSE Maths · Topic guide
GCSE Maths algebra revision
Algebra is the backbone of GCSE Maths papers: you'll see it in number, geometry and probability questions. Examiners reward clear working, correct notation (especially negatives and indices), and answers that match the form asked for — 'simplify', 'solve', 'expand'. Higher tier adds quadratics, rearranging formulae and proof-style steps; foundation focuses on linear equations and substitution. Get comfortable manipulating expressions before you speed up under time pressure.
Common mistakes in exams
- Dropping negative signs when expanding brackets or collecting terms.
- Adding unlike terms (e.g. treating x² and x as the same).
- Forgetting to apply an operation to every term inside a bracket.
- Giving a decimal when the question asks for an exact fraction or simplified surd.
Worked examples & mini quiz
GCSE Maths: Algebra essentials
Start every algebra question by writing the equation or expression clearly. Simplify before you solve: expand brackets, collect like terms, then isolate the unknown. For linear equations, balance both sides with the same add/subtract and multiply/divide steps.
Worked examples
Example 1
Solve 3(x − 2) = 2x + 4
Expand: 3x − 6 = 2x + 4. Subtract 2x: x − 6 = 4. Add 6: x = 10. Check: LHS = 3(8) = 24, RHS = 20 + 4 = 24.
Example 2
Simplify 2a³b × 4ab²
Multiply coefficients: 2 × 4 = 8. Add powers of a: a³ × a = a⁴. Add powers of b: b × b² = b³. Answer: 8a⁴b³.
Mini quiz (3 questions)
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1. Expand and simplify: 4(2x − 3) − 2(x + 5)
- A.6x − 22
- B.6x − 2
- C.10x − 22
- D.6x + 2
Show answer
Correct: 6x − 22
8x − 12 − 2x − 10 = 6x − 22.
2. Which is a correct simplification of 3x² + 2x − x² + x?
- A.2x² + 3x
- B.4x² + 3x
- C.2x² + x
- D.3x³
Show answer
Correct: 2x² + 3x
Combine x² terms: 2x². Combine x terms: 3x.
3. A correct first step to solve (2x + 1)/3 = 5 is:
- A.Multiply both sides by 3
- B.Subtract 1 from the left only
- C.Cross-multiply by 5
- D.Expand the fraction
Show answer
Correct: Multiply both sides by 3
Eliminate the denominator by multiplying both sides by 3.
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