IGCSE Maths Formula Sheet

Multiply the base by the perpendicular height and halve the result. Works for any triangle as long as you use the perpendicular height, not the slant side.

Square the radius and multiply by π. Remember that radius is half the diameter — a common source of mistakes in exam questions.

The distance around a circle. You can also write this as C = πd where d is the diameter.

Imagine unrolling the curved surface into a rectangle — its width is the circumference (2πr) and its height is h.

Here l is the slant height, not the vertical height. If given the vertical height, use Pythagoras to find l first.

Exactly four times the area of a great circle. This formula is given on the exam paper.

Find the cross-sectional area and multiply by the length. This works for any prism — triangular, trapezoidal, or irregular.

One-third of the base area times the perpendicular height. Works for any pyramid shape, not just square-based.

The base is a circle (πr²) multiplied by the height — it's just a circular prism.

One-third of the cylinder with the same base and height. Use the vertical height, not the slant height.

Cube the radius, multiply by 4π/3. Watch for questions that give the diameter instead of the radius.

Solves ax² + bx + c = 0 when factorising is difficult. The discriminant (b² − 4ac) tells you how many solutions exist: positive = 2, zero = 1, negative = none.

Use when you have a side and its opposite angle. Can be flipped (sin A/a) when finding angles. Essential for non-right-angled triangles.

Use when you have two sides and the included angle (SAS), or all three sides (SSS). Rearrange to find an angle: cos A = (b² + c² − a²) / 2bc.

When you know two sides and the included angle but not the perpendicular height. Appears frequently in Paper 4 extended questions.