The GCSE Maths Formula Sheet

La méthode, étape par étape

1. 1

   Check your board's current formulae page

   AQA, Edexcel and OCR each publish what is provided

   The provided list is specified in each board's specification and has changed in recent years. Working from an out-of-date list is a genuine risk, so the check should be against the current specification rather than an older revision guide.

2. 2

   Memorise the area and perimeter formulae

   circle area πr², circumference 2πr, trapezium ½(a+b)h

   The common two-dimensional formulae are generally expected to be known. These appear on almost every paper, so they should be automatic regardless of what any sheet provides.

3. 3

   Memorise the core algebra and trigonometry

   quadratic formula, SOHCAHTOA, Pythagoras

   Pythagoras and the right-angled trigonometric ratios are expected knowledge. The quadratic formula's status has varied between boards and series, which is precisely why it should be memorised anyway.

4. 4

   Know the exact trigonometric values

   sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 45° = √2/2

   Higher tier requires exact values for 0, 30, 45, 60 and 90 degrees, and they are needed on the non-calculator paper where no calculator can supply them. These are pure recall and are examined regularly.

5. 5

   Treat every formula as memorisable anyway

   the safest revision assumes nothing is provided

   A student who knows a formula loses nothing when it turns out to be printed. A student relying on a sheet that does not include it loses the question. The asymmetry makes over-preparation the rational choice.

Why the distinction matters

Revision time is finite, and knowing which formulae are printed lets a student spend it on the ones that are not. But the calculation is asymmetric: the cost of memorising something unnecessarily is a few minutes, and the cost of not knowing something assumed to be provided is an entire question.

For that reason we treat the provided list as a safety net rather than a revision plan. It is genuinely useful to know what is there, and it should never be the reason a formula goes unlearned.

• Check the current specification, not an old guide
• 2D area and perimeter formulae — know them
• Pythagoras and SOHCAHTOA — know them
• Exact trig values for 0/30/45/60/90 — know them
• Anything provided is a bonus, not a plan

Formulae on the non-calculator paper

Exact trigonometric values matter most on Paper 1, where a calculator cannot be consulted. A student who knows that sin 30° is exactly ½ can answer questions that are otherwise inaccessible without one.

The same applies to π. Answers left in terms of π require knowing the circle formulae precisely, since an approximate value is neither available nor wanted.

Having the formula is not the same as using it

A printed formula sheet does not tell a student which formula a question needs. Recognising that a problem calls for the cosine rule rather than Pythagoras is the actual skill, and no sheet supplies it.

This is why practice on mixed past papers matters more than formula memorisation past a point. Students generally lose more marks to selecting the wrong approach than to forgetting the formula for the right one.

How we handle formulae

We check the current specification for the student's board at the start of the course, because the provided list has changed and revision guides lag behind. Then we teach every formula as though none were given.

We spend the saved time on recognition instead — mixed question sets where the student must decide which tool applies. That is where the marks actually are, and it is the part a formula sheet can never help with.