One of the most common questions we hear from parents is “which formulae actually need to be memorised?” This GCSE maths formula guide answers that clearly, organised by topic, and separates what you must memorise from what’s provided on the exam formula sheet across AQA, Edexcel and OCR.
What’s Given on the Exam Formula Sheet
All three major exam boards provide a formula sheet on the front of relevant papers, but it contains fewer formulae than most students assume — and Foundation and Higher tier sheets differ slightly. Typically provided formulae include: the quadratic formula, compound interest formula, area/volume of a cone and sphere, sine and cosine rules, and the trapezium area formula (on some boards). Always check your specific board’s current specification via AQA, Pearson Edexcel or OCR, since minor differences exist between boards and tiers.
Everything else — even formulae that feel like they “should” be given — must be memorised and recalled without prompting.
Number
- Percentage change = (change ÷ original) × 100 — must memorise.
- Compound interest = P(1 + r/100)ⁿ — usually given on the formula sheet.
- Simple interest = (P × R × T) ÷ 100 — must memorise.
- Standard form rules and rules of indices (multiplying, dividing, negative and fractional powers) — must memorise.
Algebra
- Quadratic formula: x = (−b ± √(b²−4ac)) ÷ 2a — given on the formula sheet, but you must know when and how to apply it.
- Expanding double and triple brackets, factorising quadratics, and completing the square — methods must be memorised; there is no formula sheet shortcut.
- nth term of a linear sequence: a + (n−1)d — must memorise.
- nth term of a quadratic sequence — the method (using half the second difference) must be memorised.
Geometry
| Formula | Status |
|---|---|
| Area of a circle = πr² | Must memorise |
| Circumference = 2πr or πd | Must memorise |
| Volume of a cuboid = l × w × h | Must memorise |
| Volume of a cone / sphere | Given on formula sheet |
| Pythagoras: a² + b² = c² | Must memorise |
| Trigonometry: SOH CAH TOA | Must memorise |
| Sine rule / cosine rule | Given on formula sheet (Higher) |
Statistics and Probability
- Mean = sum of values ÷ number of values — must memorise.
- Finding median, mode and range from a data set or frequency table — must memorise the method.
- Probability of an event = number of favourable outcomes ÷ total outcomes — must memorise.
- Estimating the mean from grouped frequency data — method must be memorised, no formula sheet support.
Tips for Remembering Formulae
Rote memorisation alone is fragile under exam pressure — a formula recalled only through repetition tends to disappear exactly when nerves are highest. These approaches build more durable, exam-proof recall:
- Derive, don’t just memorise. Understanding why the area of a trapezium formula works makes it far easier to reconstruct if you blank on exam day.
- Use flashcards with the topic name on one side and the formula on the other — see our roundup of best GCSE maths revision techniques for more on this.
- Practise recalling formulae from memory at the start of every revision session, before looking anything up.
- Write out the full formula sheet from memory once a week during exam term, to build total familiarity with what actually is (and isn’t) provided.
Formulae Students Commonly Mix Up
A handful of formula pairs cause repeated confusion because they look superficially similar. Area of a circle (πr²) and circumference (2πr or πd) are frequently swapped, especially under time pressure — a useful check is that area always involves squaring a length, giving square units, while circumference and diameter are straight lengths. Similarly, students often confuse the formula for a cone’s volume with a cylinder’s, or mix up when to use the sine rule versus the cosine rule in non-right-angled triangle questions (the cosine rule is needed whenever you know three sides, or two sides and the angle between them; the sine rule is used otherwise). Building a short personal list of “formulae I mix up” and reviewing it weekly is often more valuable than continuing to revise formulae already known securely.
Formula Differences Between Foundation and Higher
Higher tier students are expected to memorise a wider range of formulae independently, since more advanced formulae (like the sine and cosine rules) are added to their sheet in exchange for greater application demands elsewhere. If you’re unsure which tier is right for your child, our guide to GCSE Foundation vs Higher maths explains the differences in full.
It’s worth noting that having a formula provided doesn’t reduce the difficulty of a question — it simply removes one source of error. Higher tier questions involving the sine and cosine rules, for example, are typically multi-step problems that also require correctly identifying which rule applies, rearranging the formula, and interpreting the answer in context. Memorising the surrounding method matters just as much as the formula itself.
A Quick Formula Sheet Sanity Check
In the final fortnight before the exam, run through this quick checklist to confirm your formula knowledge is genuinely exam-ready:
- Can you write out every “must memorise” formula above from a blank page, with no prompts, in under ten minutes?
- Do you know which topics have a formula given on the sheet versus which require full recall — for your specific exam board and tier?
- Have you practised at least one past paper question for every formula on this list, so you know how each one is actually applied in context?
- Can you convert between related formulae — for example, rearranging the area of a circle formula to find the radius from a given area?
If you answered “no” to any of these, that’s a precise, actionable target for your remaining revision time rather than a vague sense that “more practice” is needed.
Turning Formula Knowledge Into Marks
Knowing a formula and knowing when to apply it under exam pressure are two different skills — many students can recite the quadratic formula perfectly but hesitate over whether a question actually requires it. A tutor helps bridge that gap through targeted practice. Explore GCSE Maths tuition or book a free assessment to strengthen this area.
Frequently Asked Questions
Yes, on all three major exam boards the quadratic formula is printed on the formula sheet, but students still need to know how to identify when a question requires it and how to apply it accurately.
No. Higher tier formula sheets typically include additional formulae, such as the sine and cosine rules, that Foundation tier students are not expected to know.
Around 20-25 core formulae and methods across Number, Algebra, Geometry and Statistics are not provided and must be memorised, though the exact count varies slightly by exam board.
Write out every formula you can remember from a blank page at the start of a revision session, then check against your notes — this is far more effective than simply re-reading a formula list.
