GCSE Maths formulas you need to memorise
There's a lot of confusion about which GCSE Maths formulas your child has to learn by heart, partly because the rules changed and a formula sheet is now provided in the exam. This guide cuts through it: what you still have to memorise, what's given to you, and how to actually make the important ones stick.
In this guide
First: there's now a formula sheet
The big change to know about is that the main exam boards (AQA, Edexcel and OCR) now include a formula sheet in the GCSE Maths exam. That's genuinely helpful, but it catches students out in two ways: they assume everything is on it (it isn't, far from it), or they never look at the sheet beforehand and waste time hunting for formulas in the exam.
So the single most important step is this: download the official formula sheet for your child's exact board and exam year, and read it. Know what's on it so they don't memorise it needlessly, and know what's missing so they learn that properly. The lists below are a reliable general guide, but boards do tweak the sheet, so always confirm against the current document for your board and tier.
The mistake I see most: a student who "knows" the formula sheet has the quadratic formula on it, relaxes, and then can't actually use it under pressure because they never practised choosing it. Having a formula handed to you is worthless if you don't recognise when the question is asking for it. Knowing when to use a formula matters far more than where it's written down.
Formulas you still need to memorise
These are the everyday formulas that are not usually on the sheet, so your child needs them committed to memory. They turn up constantly, on both tiers, and they're the ones most worth drilling.
Compound measures
- Speed = distance ÷ time
- Density = mass ÷ volume
- Pressure = force ÷ area
Area
- Area of a rectangle = base × height
- Area of a triangle = ½ × base × height
- Area of a parallelogram = base × height
- Area of a trapezium = ½ × (a + b) × height
- Area of a circle = π × r²
- Circumference of a circle = π × diameter = 2 × π × r
Volume
- Volume of a cuboid = length × width × height
- Volume of a prism = area of cross-section × length
- Volume of a cylinder = π × r² × height
Pythagoras and basic trigonometry
- Pythagoras' theorem: a² + b² = c² (for a right-angled triangle)
- sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent (remember it as SOH CAH TOA)
Graphs and sequences
- Equation of a straight line: y = mx + c
- Gradient = change in y ÷ change in x
- The nth term of an arithmetic sequence (recognising and building the rule)
Formulas that are usually given to you
These tend to appear on the formula sheet, so your child usually doesn't need to memorise them, but they absolutely must know when to reach for each one and how to use it. Treat the list as "check it's on your sheet, then practise applying it", not "ignore it".
- The quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a
- The sine rule and the cosine rule (Higher)
- Area of a triangle = ½ab sin C (Higher)
- Volume of a sphere = ⁴⁄₃ × π × r³, and surface area of a sphere = 4 × π × r² (Higher)
- Volume of a cone = ⅓ × π × r² × height, and curved surface area of a cone = π × r × slant height (Higher)
Because the exact contents of the sheet vary by board and can change year to year, this is the part to double-check against your child's own formula sheet rather than take on trust.
Foundation vs Higher
The core formulas, areas, volumes, compound measures, basic trigonometry, are needed on both tiers. Higher tier then layers more on top: the sine and cosine rules, the area-of-a-triangle rule, and the spheres-and-cones formulas, plus exact trigonometric values for angles like 30°, 45° and 60°. If your child is on Higher, those extras are exactly where the marks they're missing often hide. (Not sure which tier suits your child? I've written a separate guide on choosing between Foundation and Higher.)
How to actually memorise them
Reading a list of formulas does almost nothing; the brain forgets a list it only looked at. What works is active recall: your child covers the formula, writes it from memory, then checks. Getting it wrong and correcting it is where the learning actually happens.
- Flashcards, tested both ways. Name on one side, formula on the other, and crucially also the reverse: show the formula and ask what it's for and when you'd use it.
- Use them in real questions. A formula learnt inside a past-paper question sticks far better than one learnt off a poster, because it's tied to recognising the type of problem.
- Little and often. Five minutes of recall most days beats an hour the night before. Space it out and the formulas move into long-term memory.
- Write your own one-page sheet. The act of condensing every must-know formula onto a single page is revision in itself, and it shows up the gaps fast.
How you can help as a parent
This is one area where you can help directly without remembering any maths yourself. Hold the flashcards and test your child, you don't need to understand the formula to read it off the back of a card and check their answer. Five minutes in the car or over breakfast, done regularly, is genuinely effective. Beyond that, help them find and print their board's formula sheet, and encourage the little-and-often habit rather than the night-before cram.
If certain topics behind the formulas, trigonometry and the harder Higher-tier work are the usual culprits, never quite click, that's where a few focused one-to-one sessions make the biggest difference, and it's exactly what I do.
Common questions
Do you get a formula sheet in GCSE Maths?
Yes. AQA, Edexcel and OCR now provide a formula sheet in the GCSE Maths exam, but it only covers some formulae. You still have to memorise many of the core ones yourself, so download your own board's current sheet and check exactly what is and isn't on it.
Is the quadratic formula given in the GCSE Maths exam?
On the current formula sheets for the main boards the quadratic formula is provided, but you still need to know when and how to use it, and you should confirm it's on your board's sheet for your exam year, as the contents can change.
Are the GCSE Maths formulas different for Foundation and Higher tier?
The core formulae overlap, but Higher tier expects more, such as the trigonometric rules and the volumes and surface areas of spheres and cones. Always work from the formula list for your tier and board.