Quadratic
Solve x2 − 5x + 6 = 0.
Factorise: (x − 2)(x − 3) = 0, so x = 2 or x = 3.
GCSE Maths Formulas
A revision reference for GCSE Maths. Some boards provide a formula sheet; check your board before memorizing everything.
Algebra
| Topic | Formula |
|---|---|
| Quadratic formula | x = (−b ± √(b2 − 4ac)) / 2a |
| Difference of squares | a2 − b2 = (a + b)(a − b) |
| Expanding | (a + b)2 = a2 + 2ab + b2 |
| Straight line | y = mx + c |
| Gradient | m = (y2 − y1) / (x2 − x1) |
Geometry
| Shape | Formula |
|---|---|
| Area of a triangle | A = ½ × base × height |
| Area of a trapezium | A = ½(a + b)h |
| Circumference | C = 2πr |
| Area of a circle | A = πr2 |
| Volume of a prism | V = area of cross-section × length |
| Volume of a cylinder | V = πr2h |
| Volume of a sphere | V = 4/3 πr3 |
| Volume of a cone | V = 1/3 πr2h |
| Pythagoras | a2 + b2 = c2 |
Trigonometry
| Topic | Formula |
|---|---|
| SOH CAH TOA | sin θ = O/H · cos θ = A/H · tan θ = O/A |
| Sine rule | a / sin A = b / sin B = c / sin C |
| Cosine rule | a2 = b2 + c2 − 2bc cos A |
| Area of a triangle | A = ½ab sin C |
Statistics
| Measure | Formula |
|---|---|
| Mean | sum of values / number of values |
| Median | Middle value when ordered |
| Mode | Most frequent value |
| Range | highest − lowest |
| Probability | favourable outcomes / total outcomes |
Exam-board note: AQA, Edexcel, OCR, and WJEC provide different formula sheets in different years. Always check the official advance information for your board and exam series.
Worked examples
Circle area
Find the area of a circle with radius 4 cm.
A = π × 42 = 16π ≈ 50.3 cm2.
FAQ
Is the quadratic formula on the GCSE formula sheet?
It depends on the board and series. Some boards provide it, others expect you to memorize it. Check your board’s official sheet.
Do I need to memorize π?
Use the π button on your calculator. If asked for an exact answer, leave it in terms of π.
Last updated November 1, 2026. Formulas are checked against standard references. Read the editorial policy.