GCSE Maths Formula Sheet: Essential Formulas for Your Exam

Picture a familiar mock-exam scene: a student sits down, flips to the formula sheet, and spends four minutes hunting for “area of a rectangle.” It’s not there. Never has been. Four minutes lost, panic sets in, and the rest of the paper goes downhill. Don’t be that student. This guide is part of our complete GCSE Maths revision guide — visit there for an overview of all topics and revision strategies. The good news? Your exam does hand you a formula sheet with many equations you’ll need. The catch? Not everything’s on it, and knowing which formulas you’ve got to memorise yourself can genuinely be the difference between a grade 7 and a grade 9.

So here’s your complete guide to the GCSE maths formula sheet — what’s on it, what’s not, and how to actually use the thing under pressure.

What is the GCSE Maths Formula Sheet?

It’s a single page. That’s it. You get it in both Foundation and Higher tier papers, and it contains roughly 15-20 formulas covering geometry, algebra, and a handful of statistical bits.

All the major boards — AQA, Edexcel, OCR — provide this sheet. The layouts differ slightly, but the formulas themselves? Largely the same across all of them. If you’ve seen one, you’ve basically seen them all.

Which Formulas Are Included on the Sheet?

Geometry and Mensuration

• Circumference of a circle: C = πd or C = 2πr
• Area of a circle: A = πr²
• Curved surface area of a cylinder: A = 2πrh
• Volume of a cylinder: V = πr²h
• Volume of a prism: V = area of cross-section × length
• Volume of a cone: V = ⅓πr²h
• Curved surface area of a cone: A = πrl (where l is slant height)
• Volume of a sphere: V = ⁴⁄₃πr³
• Surface area of a sphere: A = 4πr²
• Pythagoras’ theorem: a² + b² = c²

Trigonometry

• Sine rule: a/sin A = b/sin B = c/sin C
• Cosine rule: a² = b² + c² - 2bc cos A
• Area of a triangle: Area = ½ab sin C

Quadratic Formula

• Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

Some boards also throw in compound interest (Total = P(1 + r/100)ⁿ) and simple interest (Interest = (P × r × t) / 100). Depends on the board. Check your specific exam board’s specimen papers — don’t assume.

Formulas You MUST Memorise (Not on the Sheet)

These don’t appear on the formula sheet. Full stop. You need them in your head before you walk into that exam hall.

Basic Operations

Fractions — adding, subtracting, multiplying, dividing. Percentages — finding them, percentage increase, percentage decrease. Ratios — dividing amounts in given ratios. None of this is given to you. It’s assumed knowledge.

Algebra

• Expanding brackets: (a + b)(c + d) = ac + ad + bc + bd
• Factorising: Reversing expansion
• Difference of two squares: a² - b² = (a + b)(a - b)
• Rearranging formulas: Making a different letter the subject

Geometry Basics

This is where students get caught out. Every. Single. Year.

• Area of a rectangle: A = length × width
• Area of a triangle: A = ½ × base × height (the basic version, not the sine one)
• Area of a trapezium: A = ½(a + b)h
• Area of a parallelogram: A = base × height
• Perimeter: Sum of all sides

Area of a trapezium is one of the formulas most often dropped in mocks — students who can’t recall it under pressure routinely skip the entire question rather than work it out from first principles. It’s not on the sheet. Drill these until they’re automatic — no thinking required.

Speed, Distance, Time

First, speed = distance ÷ time. Then distance = speed × time. Finally, time = distance ÷ speed. Draw the triangle if it helps. Most students find it does.

Density

Density = mass ÷ volume. Same triangle trick works here.

Probability

• Probability: P(event) = number of favourable outcomes ÷ total number of outcomes
• Combined events: P(A and B) = P(A) × P(B) (for independent events)

Statistics

• Mean: sum of values ÷ number of values
• Range: highest value - lowest value
• Median: the middle value when data’s ordered
• Mode: the most frequent value

You need these instantly. If you’re hesitating, you’re already losing time.

How Formulas Differ by Topic

Algebra

Algebra’s more about methods than formulas, honestly. You need to know how to solve linear equations (3x + 5 = 14, that sort of thing), how to crack simultaneous equations using elimination or substitution, how to complete the square, and how to factorise quadratics.

The quadratic formula IS on the sheet. But you still need to substitute values correctly and simplify surds — the sheet doesn’t do that bit for you.

Geometry and Measures

Most geometry formulas for circles, cones, spheres, and cylinders? On the sheet. Basic area formulas for rectangles, triangles, trapeziums, parallelograms? Not on the sheet.

You also need to know how to convert between units — cm to m, mm to cm, all of that. Plus angle rules: angles in parallel lines, angles in polygons, circle theorems. Why does this matter? Because a 5-mark question might test the formula AND the angle knowledge together.

Ratio and Proportion

Ratio questions don’t really need formula memorisation. They need method understanding: how to simplify ratios, how to divide amounts in a given ratio, how to scale recipes or maps, direct and inverse proportion. It’s procedural, not formulaic.

Statistics and Probability

Mean, median, mode, range. That’s it. You must know how to calculate all four without looking anything up. The formula sheet doesn’t include these because — in the examiners’ view — they’re fundamental. Sound obvious? Half the cohort still muddles median and mode under pressure.

Trigonometry

Basic SOHCAHTOA is NOT on the formula sheet. Memorise it:

• sin θ = opposite ÷ hypotenuse
• cos θ = adjacent ÷ hypotenuse
• tan θ = opposite ÷ adjacent

The sine rule and cosine rule ARE provided because they’re more complex. But you can’t use the complex stuff if you don’t know the basics.

How to Use the Formula Sheet Effectively in Your Exam

1. Familiarise Yourself Beforehand

Download the formula sheet from your exam board’s website — just search “AQA GCSE maths formula sheet” or whatever board you’re on — or view our organised formula sheets for a clean reference. Keep it on your desk during revision. Use it when you’re doing past papers so finding formulas becomes quick and automatic.

2. Don’t Rely on It for Everything

This is arguably where most students go wrong. Just because a formula’s on the sheet doesn’t mean you should look it up every single time. Memorise formulas you use frequently — area of a circle, Pythagoras — so you can work faster. Save the formula sheet for the occasional check.

3. Know When You Need It

If a question mentions circles, cones, or spheres, check the sheet for volume or surface area formulas. Non-right-angled triangles? Check for sine rule or cosine rule. Quadratic equations that won’t factorise nicely? That’s when you pull out the quadratic formula.

But if a question asks for area of a rectangle, triangle, or trapezium — recall from memory. Speed, distance, time? Memory. Mean, median, mode? Memory. None of those are on the sheet, and hunting for them wastes precious minutes.

4. Check Your Substitution

The formula sheet gives you the formula. It doesn’t do the substitution for you. The most common substitution mistakes: using diameter instead of radius (or vice versa), forgetting to square the radius in area or volume calculations, and having your calculator in radians when the question’s in degrees.

Always write out the formula, substitute values clearly, then calculate. This makes errors much easier to spot — both for you and for the examiner awarding method marks.

Common Mistakes Students Make with Formulas

A particularly costly substitution error: writing A = πr² but then substituting the diameter the question gave. If the question says “a circle has diameter 10 cm,” the wrong answer is A = π × 10² = 314.2 cm². The right answer is A = π × 5² = 78.5 cm². This shows up in almost every mock series. Circle the word “diameter” or “radius” in the question — literally draw a ring round it — then check you’ve used the right value before calculating.

Mistake 1: Looking for formulas that aren’t there

Students waste ages searching for area of a rectangle or the formula for mean. Not there. Know what’s NOT on the sheet before you go in.

Mistake 2: Using the wrong formula

Confusing circumference with area, using the wrong volume formula — it costs easy marks. Does the question ask for surface area or volume? Perimeter or area? Read it twice.

Mistake 3: Not showing working

Even when you use the formula sheet, show your working. Write the formula, substitute the numbers, then calculate. You can still earn method marks even if your final answer’s wrong.

Mistake 4: Forgetting units

If the question gives measurements in centimetres but asks for volume in cubic metres, you must convert. Unit-conversion errors are a quiet but reliable way to lose 4–6 marks across a single paper — every dropped mark feels small in isolation, but they add up fast. Always check units in the question AND in what they’re asking for.

Mistake 5: Misreading the formula

The quadratic formula has ± in it. Students often forget to calculate both solutions. The sine rule can be written upside down. Make sure you actually understand how to read and apply each formula, not just where to find it.

Memory Techniques for GCSE Maths Formulas

Since many formulas aren’t on the sheet, you need proper memorisation strategies. Not just reading them over and over — that doesn’t work.

1. Create a Formula Flashcard Set

Write each formula on one side, an example question on the back. Test yourself daily. Focus hard on the ones you keep forgetting.

2. Use Mnemonics

SOHCAHTOA for trigonometry. BIDMAS for order of operations. The DST triangle for speed, distance, time. The triangle diagrams are underrated — they work brilliantly for density too.

3. Practise Application, Not Just Memorisation

Memorising formulas in isolation? Waste of time. Do past paper questions that require each formula. The more you use a formula in context, the better it sticks.

A useful drill for students who freeze on formula-heavy questions: cover the numbers and ask “what type of problem is this? What formula do I associate with that type?” Train the brain to pattern-match first. The calculation comes after.

4. Group Formulas by Topic

Don’t try to memorise 50 random formulas. Group them: geometry (areas, perimeters), algebra (quadratic formula, rearranging), statistics (mean, median, mode), trigonometry (SOHCAHTOA, sine and cosine rules). Recall becomes much easier during exams when you can think “this is a geometry question, so I need geometry formulas.”

How to Revise Formulas for Foundation vs Higher Tier

Foundation Tier: Focus on basic area formulas — rectangle, triangle, trapezium. Memorise SOHCAHTOA for right-angled triangles. Know how to use Pythagoras’ theorem. Understand simple probability and statistics: mean, median, mode. The formula sheet covers most geometry volume formulas you’ll need at this tier.

Higher Tier: Everything from Foundation, plus sine and cosine rules for non-right-angled triangles, the quadratic formula (memorise it anyway for speed, even though it’s on the sheet), completing the square, circle theorems, and more complex probability like tree diagrams and conditional probability.

Higher tier questions assume faster formula recall because they’re testing problem-solving, not just calculation. You don’t have time to hunt.

How UpGrades Helps with GCSE Maths Formulas

Knowing formulas is step one. You also need to recognise which formula applies to a given question, substitute values correctly, rearrange formulas when needed, and do all of this under time pressure.

UpGrades gives you targeted practice that tests your ability to select and apply the right formula. With instant feedback, you’ll quickly see which formulas you’re confident with, which ones you’re misapplying, and where your calculation errors creep in.

The adaptive system makes sure you spend time on the areas you actually find hardest — not the stuff you’ve already nailed. Combine smart formula revision with UpGrades’ exam-style practice, and you’ll walk into your GCSE maths exam properly prepared.

Final Checklist for GCSE Maths Formula Success

• Download and familiarise yourself with your exam board’s formula sheet
• Memorise all formulas NOT on the sheet (area of rectangle, triangle, trapezium; speed/distance/time; mean/median/mode)
• Practise using the formula sheet during timed past papers
• Create a one-page summary of formulas you must memorise
• Test yourself on formula application, not just recall
• Check units carefully in every question
• Always show your working, even when using the formula sheet

The GCSE maths formula sheet is a helpful resource. It’s not a crutch. Master the fundamentals that aren’t on the sheet, know when to reference what is on the sheet, and you’ll be ready for whatever your exam throws at you.

How to Use This Guide

Ignore the people who tell you to colour-code your formula revision notes with twelve different highlighters. It looks productive. It isn’t. Instead, print the “must memorise” section and stick it somewhere you’ll see it daily — bathroom mirror, inside your planner, on the fridge. Test yourself on those formulas until they’re instant. Then work through past papers with the actual formula sheet in front of you, so you get used to the real setup. If you’re still mixing up which formulas are given and which aren’t, come back here and use that checklist. The students who do best aren’t the ones who revise longest — they’re the ones who know exactly what they need to memorise and what they can look up. Get that sorted, and you’re already ahead.

Related GCSE Maths Guides

• Quadratic formula guide — step-by-step examples and the discriminant explained
• Algebra revision guide — from simplifying expressions to solving quadratics
• Geometry and measures guide — angles, shapes, and trigonometry
• GCSE Physics equation sheet guide — all equations explained with worked examples

Useful Resources

• GCSE Maths subject page — all exam boards, topics, and revision support
• Formula sheets for all subjects — download official formula sheets from every exam board
• 2026 exam timetable — check your Maths exam dates

Ready to practise? Try GCSE Maths questions on UpGrades to find and fix your weak spots.