GCSE Maths formulae sheet (Higher tier): The complete guide for 2026

Good news for anyone sitting GCSE Maths in 2026: Every major exam board (AQA, Edexcel, OCR, and WJEC/Eduqas) gives you a formulae sheet in every paper. That includes Paper 1 (non-calculator), Paper 2, and Paper 3. You don't have to memorise every formula on the sheet to score on questions that use them.

There's a catch, though. The sheet is shorter than students often think. It prints Pythagoras' theorem, the trig ratios SOH CAH TOA, the sine and cosine rules, the quadratic formula, a few specific area and volume formulas, the compound interest formula, and two probability rules. It does NOT print the volume of a sphere, the volume of a cone, or the curved surface area of a cone. Those still need to be memorised.

This guide lists what's actually on the AQA Higher tier sheet, then covers the formulas that students often assume are there but aren't. It finishes with practical advice on how to use the sheet under exam conditions so you don't waste seconds hunting for something that isn't printed.

The AQA Higher tier sheet is one page. It's grouped under five headings: Perimeter, area and volume; the quadratic formula; Pythagoras' theorem and trigonometry; compound interest; and probability. The Edexcel, OCR, and Eduqas Higher tier sheets are very close to identical in content.

Worth highlighting: Pythagoras' theorem (a² + b² = c²) and the basic trig ratios (sin A = a/c, cos A = b/c, tan A = a/b) ARE printed on the sheet. SOH CAH TOA is not given as a mnemonic, but the three ratios are written out, with a labelled right-angled triangle diagram next to them. The sine rule and cosine rule sit underneath, with a separate labelled triangle.

The shapes whose formulas are printed are very specific: Trapezium area, prism volume, circle circumference, and circle area. Notice what's missing. There's no rectangle, no parallelogram, no cuboid, no cylinder, no sphere, no cone.

Plenty of formulas you'd expect to see on the sheet aren't there at all. Examiners assume you know these from memory, and questions involving them are routine on every paper. If you can't recall any of these under pressure, you'll lose easy marks.

The ones students most commonly assume are on the sheet, but aren't, are the volume of a sphere ((4/3)πr³), the volume of a cone ((1/3)πr²h), and the curved surface area of a cone (πrl). These three need memorising. They've been on the off-sheet list since the 2022 introduction of the formulae sheet, and Ofqual has not added them since.

Work through the list below and check that each formula is automatic. If you hesitate on any of them, write them on a flashcard and drill them daily until they're obvious.

Having the sheet in front of you is only useful if you know how to use it. Three habits separate students who get full benefit from the sheet from students who waste time on it.

First, learn the layout in advance. Download the exact sheet your board uses (the AQA version is called 'AQA GCSE Mathematics Higher Tier Formulae Sheet') and put it next to you for every past paper you do. By the time the real exam comes, you should know where the sine rule lives without thinking.

Second, only reach for the sheet when you genuinely need it. If a triangle question gives you the perpendicular height, don't look up (1/2)ab sin C. Use base × height ÷ 2 from memory. The sheet is a backup, not your first port of call.

Third, practise applying each formula in the form the sheet gives it. The quadratic formula on the sheet looks straightforward, but plugging in negative coefficients and surds without sign slips takes practice. The cosine rule rearrangement, cos A = (b² + c² - a²) / 2bc, is NOT given on the sheet. You have to derive it from the printed form a² = b² + c² - 2bc cos A whenever a question asks you for an angle from three sides. Examiners know this and test it.

All four major UK boards (AQA, Edexcel, OCR, and WJEC/Eduqas) provide a formulae sheet on the current GCSE Maths specifications. The contents are essentially identical because Ofqual coordinated the policy across boards.

The small differences are in layout, ordering, and labelling rather than in which formulas appear. Edexcel and OCR put the trigonometry section in a slightly different position. Eduqas sometimes uses slightly different variable letters in its cosine rule statement. None of this changes what you can use the sheet for.

If you're sitting Foundation tier, your sheet is shorter than the Higher one. The quadratic formula, sine rule, cosine rule, and (1/2)ab sin C are all Higher tier only and do not appear on the Foundation sheet. The Foundation sheet still gives you trapezium area, prism volume, circle circumference, and circle area, plus Pythagoras and the basic trig ratios.

The first common mistake is looking up something on the sheet when it isn't there. Students sometimes spend 30 seconds hunting for the volume of a cone on the formulae sheet before remembering it isn't printed. The off-sheet list above is the antidote: Memorise it once, properly, and you won't waste exam time.

The second is mis-applying the cosine rule. The sheet only gives the form a² = b² + c² - 2bc cos A, which finds a side from two sides and the included angle. When the question gives you three sides and asks for an angle, you need to rearrange to cos A = (b² + c² - a²) / 2bc. Many students stare at the printed form and get stuck instead of rearranging.

The third is forgetting that the area of a triangle formula on the sheet, (1/2)ab sin C, needs C to be the angle between sides a and b. If you pick the wrong angle, the answer is wrong. Label your triangle properly before plugging in.

The fourth is misreading the quadratic formula. The negative sign in front of b and the ± symbol both need to be applied carefully. Plug in for a, b, c carefully, square b before subtracting 4ac, and remember to divide the entire numerator by 2a (not just one part of it).

The fifth is using the wrong probability rule. P(A or B) = P(A) + P(B) - P(A and B) handles two events that might overlap. Some students drop the final subtraction when the two events are not mutually exclusive, which double-counts the overlap. Read the question to see whether the events can both happen.

Even with the sheet in front of you, the students who score grade 8 and 9 still treat the on-sheet formulas like they have to know them from scratch. Two reasons.

One, fluency is fast. If you know the quadratic formula by heart, you can plug numbers in within seconds. If you have to read it off the sheet first, that takes ten to twenty seconds you could spend on the next question. Across a long paper those seconds add up.

Two, you can spot the right formula faster. Knowing in your head that 'two sides and an included angle for a triangle area means (1/2)ab sin C' is the difference between solving a four-mark question in 90 seconds and spending five minutes guessing. The sheet doesn't tell you which formula applies; it only prints them. Pattern recognition is the skill that converts the sheet into marks.

The other reason fluency pays off is that the sheet doesn't help with rearrangement. The quadratic formula on the sheet is in standard form, but you might need to rearrange a question like 3x² - 5 = 2x into ax² + bx + c = 0 form first. The compound interest formula assumes you can identify the principal, rate, and number of periods from a worded question. The cosine rule, as we've said, sometimes needs rearranging before you can use it. Practising past papers with the sheet open, until each manipulation is second nature, is what closes the gap between students who 'have the sheet' and students who 'use the sheet well'.