GCSE Maths last-minute formulas you must know

Introduction

With your GCSE Maths exam just days away, you don't have time to relearn the whole specification — but you do have time to lock down the formulas that come up again and again. Some formulas are given on the formula sheet; many are not, and you're expected to recall them from memory. This guide pulls together the last-minute formulas you must know, organised by topic, so you can spend your final revision sessions where they count.

Examiners reward correct method as well as the final answer. Knowing the right formula — and writing it down before you substitute numbers — protects your marks even if you slip up on the arithmetic.

Number and algebra

• The quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a. This is given at Higher tier, but learn it anyway so you can use it instantly.
• Difference of two squares: a² − b² = (a + b)(a − b).
• Compound interest: final amount = P × (1 + r/100)ⁿ, where P is the principal, r the rate and n the number of periods.
• nth term of an arithmetic sequence: a + (n − 1)d, where a is the first term and d the common difference.

Geometry and measures

• Area of a circle: πr². Circumference: 2πr (or πd).
• Area of a trapezium: ½(a + b)h.
• Volume of a prism: area of cross-section × length.
• Volume of a cylinder: πr²h. Surface area of a cylinder: 2πr² + 2πrh.
• Pythagoras' theorem: a² + b² = c², for the sides of a right-angled triangle.

Trigonometry (right-angled triangles)

Remember SOH CAH TOA:

• sinθ = opposite / hypotenuse
• cosθ = adjacent / hypotenuse
• tanθ = opposite / adjacent

And learn the exact trig values for 0°, 30°, 45°, 60° and 90° — they are commonly tested and not always given.

Higher-tier trigonometry

• The sine rule: a / sinA = b / sinB = c / sinC.
• The cosine rule: a² = b² + c² − 2bc·cosA.
• Area of a triangle: ½ab·sinC.

Statistics and probability

• Mean: sum of values ÷ number of values.
• Probability of A or B (mutually exclusive): P(A) + P(B).
• Probability of A and B (independent): P(A) × P(B).
• Speed, distance, time: speed = distance ÷ time. Density: mass ÷ volume. Pressure: force ÷ area.

How to revise formulas in your last few days

Don't just read the list — that's passive and it won't stick. Use active recall instead:

1. Write each formula on a flashcard with the name on one side and the formula on the other.
2. Test yourself: see the name, write the formula from memory, then check.
3. Focus your time on the ones you get wrong — that's where the marks are hiding.
4. Practise applying each formula to a past-paper question, not just reciting it. Knowing when to use a formula matters as much as knowing it.

You can build a deck of formula flashcards in minutes with Partielo and test yourself with active recall: create your GCSE Maths flashcards on Partielo and make your last few revision sessions count.

Conclusion

You don't need to memorise everything in the last few days — you need to be certain of the formulas that come up every year. Lock down the quadratic formula, the circle and volume formulas, Pythagoras, the trig ratios and rules, and the key statistics formulas. Test yourself with active recall rather than re-reading, and always write the formula down before you substitute. Walk into that exam knowing the tools are at your fingertips. Good luck.