Topic explanation
Gradients of Curves is part of the Algebra strand in GCSE Maths. Interpret gradient at a point as instantaneous rate; link to context (e.g. velocity).
Exam papers from AQA, Edexcel, OCR assess fluency (short questions) and reasoning (multi-mark). Practise reading command words (“show that”, “hence”, “give your answer in the form…”) before you rearrange algebra or interpret a result.
Key formulas & rules
- Expanding: single bracket, double brackets, watch signs on every term
- Factorising: HCF first, then pairs/quadratics; difference of two squares a² − b²
- Rearranging: inverse operations in reverse order; keep equality balanced
Common mistakes
- Arithmetic and sign errors when simplifying expressions involving gradients of curves.
- Not answering in the required form (fraction vs decimal, surd vs rounded).
- Missing a final sentence that interprets the result in context when the question is applied.
Exam tips
- Underline key words in the question: “exact”, “integer”, “give reasons”.
- Estimate or use inverse operations to sanity-check answers when a calculator is allowed.
- Use StudyVector practice filtered to “Gradient as Rate of Change” to drill exam-style questions on this skill.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
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