## Formulae - GCSE Maths formulae sheet

A list of all the formulae needed for your GCSE maths exam. Click a formula for an interactive example to show how it is used.

If you are entered for Foundation tier then you must know all the formulae marked 'F'. Higher tier students must learn the whole list!

Formula | Tier? | How to use the formula in words: | In Algebra: |
---|---|---|---|

Area of a Rectangle | F | Multiply the length by the width. | \(A = L × W\) |

Area of a Triangle | F | Multiply the base by the perpendicular height and divide by two. | \(A = \frac{1}2{}bh\) |

Area of a Parallelogram | F | Multiply the base by the height. | \(A = b × h\) |

Area of a Trapezium | F | Add together the parallel sides and multiply by the height. Divide your answer by two. | \(A = \frac{1}{2}(a + b)h\) |

Area of a Circle | F | Square the radius and multiply by pi. | \(A = πr^{2}\) |

Circumference of a Circle | F | Double the radius and multiply by pi or multiply the diameter by pi. | \(C = 2πr\) or \(C = πd\) |

Volume of a Cuboid | F | Multiply the length by the width by the height. | \(V = lwh\) |

Volume of a Prism | F | Multiply the cross sectional area of the prism by its length. | n/a |

Volume of a Sphere | H | Cube the radius and multiply by pi. Multiply your answer by four then divide by three. | \(V = \frac{4}{3}πr^{3}\) |

Surface Area of a Sphere | H | Square the radius and multiply by pi. Multiply your answer by four. | \(A = 4πr^{2}\) |

Volume of a Cone | H | Square the base radius of the cone and multiply by pi. Multiply your answer by the perpendicular height. Divide your answer by three. | \(V = \frac{1}{3}πr^{2}h\) |

Curved Surface Area of a Cone | H | Multiply the base radius of the cone by pi. Multiply your answer by the length of the side of the cone. | \(A = πrl\) |

Volume of a Pyramid | H | Multiply the area of the base by the perpendicular height. Divide your answer by three. | n/a |

Sine Rule | H | n/a | \(\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}\) |

Cosine Rule | H | n/a | \(a^{2} = b^{2} + c^{2} - 2bc Cos A\) |

Area of any Triangle | H | n/a | \(\frac{1}{2}ab Sin C\) |

Quadratic Equation | H | n/a | \(x = \frac{-b ± \sqrt{b^{2} - 4ac}}{2a}\) |