Formulas given in the exam
These are printed on page 2 of every paper. Extended papers include everything on the Core list plus the four marked Extended. Everything else applies to Core and Extended.
| Quantity | Formula |
|---|---|
| Area of a triangle | A = ½bh |
| Area of a circle | A = πr² |
| Circumference of a circle | C = 2πr |
| Curved surface area of a cylinder | A = 2πrh |
| Curved surface area of a cone | A = πrl |
| Surface area of a sphere | A = 4πr² |
| Volume of a prism | V = Al |
| Volume of a pyramid | V = ⅓Ah |
| Volume of a cylinder | V = πr²h |
| Volume of a cone | V = ⅓πr²h |
| Volume of a sphere | V = ⁴⁄₃πr³ |
| Quadratic formula, for ax² + bx + c = 0 Extended | x = (−b ± √(b² − 4ac)) ÷ 2a |
| Sine rule Extended | a ÷ sin A = b ÷ sin B = c ÷ sin C |
| Cosine rule Extended | a² = b² + c² − 2bc cos A |
| Area of a triangle (two sides and the included angle) Extended | Area = ½ab sin C |
Not given: learn these
| Quantity | Formula |
|---|---|
| Pythagoras' theorem | a² + b² = c² |
| Trigonometric ratios | sin θ = opp ÷ hyp, cos θ = adj ÷ hyp, tan θ = opp ÷ adj |
| Area of a rectangle | A = lw |
| Area of a parallelogram | A = bh |
| Area of a trapezium | A = ½(a + b)h |
| Arc length | (θ ÷ 360) × 2πr |
| Area of a sector | (θ ÷ 360) × πr² |
| Speed | speed = distance ÷ time |
| Simple interest | I = PRT ÷ 100 |
| Compound interest | A = P(1 + r ÷ 100)ⁿ |
| Gradient of a line | m = (y₂ − y₁) ÷ (x₂ − x₁) |
| Equation of a straight line | y = mx + c |
| Midpoint of a line segment | ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) |
| Length of a line segment | √((x₂ − x₁)² + (y₂ − y₁)²) |
| Exact trigonometric values Extended | sin and cos of 0°, 30°, 45°, 60°, 90°; tan of 0°, 30°, 45°, 60° |
Papers and calculators
| Paper | Tier | Calculator | Time and marks |
|---|---|---|---|
| Paper 1 | Core | Not allowed | 1 h 30 min, 80 marks |
| Paper 2 | Extended | Not allowed | 2 h, 100 marks |
| Paper 3 | Core | Scientific calculator | 1 h 30 min, 80 marks |
| Paper 4 | Extended | Scientific calculator | 2 h, 100 marks |
Graphical and algebraic calculators are not allowed. On calculator papers, use the π button or 3.142, and give non-exact answers to 3 significant figures (angles in degrees to 1 decimal place) unless the question says otherwise.
How to use this sheet
- Learn the second table until you can write every formula from memory: none of it is printed in the exam.
- Practise with the printed list in front of you, so you know where each formula is on page 2.
- Rates other than speed, such as density and pressure, are given in the question when needed.
- Source: Cambridge IGCSE Mathematics 0580 syllabus for 2025–2027 (PDF).