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How to Learn the GCSE Maths Formulae Not on the Sheet

Check which formulae your GCSE maths sheet gives you, then build a short recall list for the rest and test it with cards and spaced reviews.

Flat illustration of blank cream flashcards beside a brass compass, a protractor and a set square on a cream background with teal and coral shapes, with open space on the left.

Every GCSE maths student has stared at a question, knowing the method exists somewhere in their head, and not being able to write the formula down. The fix is not to memorise everything. It is to find out which formulae your exam gives you, and then learn the rest properly. This guide shows how to build that list in ten minutes and turn it into a short recall routine.

Start with the formulae sheet your exam board gives you

AQA publishes a formulae sheet for each tier of GCSE Maths (8300). The 2026 Foundation sheet lists the area of a trapezium, the volume of a prism, the circumference and area of a circle, Pythagoras' theorem, sin, cos and tan in a right-angled triangle, compound interest, and the addition rule for probability. The 2026 Higher sheet adds the quadratic formula, the sine rule, the cosine rule and the area of a triangle using sin C. You can read both on AQA's own pages: the Foundation formulae sheet and the Higher formulae sheet. Both are marked for exams in 2026 only, so check that you are looking at the version for your own exam series, and check your teacher's advice if you sit a different board.

One more fact helps with planning. On AQA's specification at a glance page, Paper 1 is non-calculator and Papers 2 and 3 allow a calculator. Each paper is 1 hour 30 minutes and 80 marks. That matters because on Paper 1 you have to use your recalled formulae without a calculator, so practise some questions that way.

Step 1: Build your own "not given" list

The sheet tells you what you will be handed. Your job is to list what is missing. Work through these steps with a pen and your revision guide.

  1. Copy out the headings on your tier's sheet, so you know exactly what is covered.
  2. Scan your revision guide or the specification topics for every formula, rule or fact you use in calculations.
  3. Cross out anything that is on the sheet.
  4. What remains is your learn list. For many students it includes speed, distance and time, density, mass and volume, the volume of a cone and sphere, the volume of a cylinder (the sheet's prism rule covers it, but it helps to know it directly), the area of a triangle as half base times height, the angle sum of a polygon, the equation of a straight line, and the mean from a frequency table.

Do not trust a list from a friend or a video without checking it against the sheet. Sheets can change between exam series, so build your list from the document for your own year.

Step 2: Turn each formula into a question

A formula copied ten times feels familiar, but familiarity is not the same as being able to recall it. Retrieval practice means recalling information from memory with little prompting, and the Chartered College of Teaching notes it is now widely used in classrooms, although it also says the evidence from UK classroom studies is still limited (see this article on low-stakes retrieval practice). So treat it as a sensible habit, not a magic trick.

Put each item on one side of a card as a question, and write the answer on the back:

  • Front: "Density in terms of mass and volume?" Back: density = mass ÷ volume.
  • Front: "Volume of a cylinder?" Back: pi × r² × h.
  • Front: "Interior angle sum of a polygon with n sides?" Back: (n − 2) × 180 degrees.

Add a unit or a quick sketch where it helps. A cylinder card with a tiny diagram is easier to retrieve than a bare line of symbols.

Step 3: Test yourself, then check

Shuffle the cards and say or write each answer before you flip it. Sort them into "right first time" and "needed a look". Only the second pile gets another round that day. Keep going until the pile is empty, then stop. Ten to fifteen minutes is enough.

Step 4: Space the reviews

Come back to the cards on a planned day rather than cramming the night before. If you are not sure how to plan the gaps, our guide to a spaced repetition study schedule shows a simple pattern you can copy. Cards you get right move to a longer gap, and cards you miss come back sooner.

A worked example: density

Here is how one formula becomes a skill. Suppose a question says a metal block has a mass of 540 g and a volume of 200 cm³, and asks for its density.

  1. Recall the formula from the card: density = mass ÷ volume.
  2. Substitute the values: 540 ÷ 200.
  3. Calculate: 2.7.
  4. Add the unit: 2.7 g/cm³.
  5. Check: a block that is heavier than its volume in cm³ suggests a density above 1, so 2.7 is sensible.

Now rearrange the same formula. If the density is 2.7 g/cm³ and the volume is 50 cm³, then mass = density × volume = 2.7 × 50 = 135 g. Practise both directions, because exam questions often ask for the mass or the volume instead of the density.

Step 5: Use the formulae in mixed questions

Recalling a formula is only half the job. After a few days, take a set of mixed questions and name the formula before you start each one. If you pick the wrong one, add that question type to your cards. Over time your list shrinks, because the formulae you keep getting right earn longer gaps.

A short checklist for the week before the exam

  • Your learn list is written down, and it matches the sheet for your tier.
  • Every card has been right first time at least twice, on different days.
  • You have used each formula in at least one exam-style question.
  • You know which paper is non-calculator and have practised without one.

The aim is simple. Let the sheet carry the formulae it is allowed to carry, and spend your effort on the ones it does not. That keeps your revision small, specific and easy to repeat.