GCSE Maths · Topic guide
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.
Worked examples & mini quiz
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.
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.
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1. Expand and simplify: 4(2x − 3) − 2(x + 5)
Correct: 6x − 228x − 12 − 2x − 10 = 6x − 22.
2. Which is a correct simplification of 3x² + 2x − x² + x?
Correct: 2x² + 3xCombine x² terms: 2x². Combine x terms: 3x.
3. A correct first step to solve (2x + 1)/3 = 5 is:
Correct: Multiply both sides by 3Eliminate the denominator by multiplying both sides by 3.
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