Maths formulae to learn

Formulae the specification says you must know (10)

• Area of triangles, parallelograms and trapezia; volume of cuboids and other right prisms (including cylinders): triangle ½ × base × height; parallelogram base × perpendicular height; trapezium ½(a + b)h; prism (including a cylinder) area of cross-section × length
• Circumference of a circle: 2πr = πd
• Area of a circle: πr²
• Pythagoras' theorem: a² + b² = c²
• Trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
• Exact trigonometric values: sin θ and cos θ for θ = 0°, 30°, 45°, 60°, 90°; tan θ for θ = 0°, 30°, 45°, 60°
• Sine rule: a/sin A = b/sin B = c/sin C Higher
• Cosine rule: a² = b² + c² − 2bc cos A Higher
• Area of any triangle: Area = ½ab sin C Higher
• Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a Higher

On Pearson's 2026 formulae sheets (17)

The cone and sphere formulae are also printed in the questions that need them. Formulae marked Higher are only on the Higher tier sheet.

• Curved surface area of a cone: πrl
• Surface area of a sphere: 4πr²
• Volume of a sphere: (4/3)πr³
• Volume of a cone: (1/3)πr²h
• Area of a trapezium: ½(a + b)h
• Volume of a prism: area of cross section × length
• Circumference of a circle: C = 2πr = πd
• Area of a circle: A = πr²
• Pythagoras' theorem: a² + b² = c² (c is the hypotenuse)
• Trigonometry in a right-angled triangle: sin A = a/c, cos A = b/c, tan A = a/b
• Compound interest: Total accrued = P(1 + r/100)ⁿ
• Probability, OR rule: P(A or B) = P(A) + P(B) − P(A and B)
• Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a, for ax² + bx + c = 0, a ≠ 0 Higher
• Sine rule: a/sin A = b/sin B = c/sin C Higher
• Cosine rule: a² = b² + c² − 2bc cos A Higher
• Area of a triangle: Area = ½ab sin C Higher
• Probability, AND rule: P(A and B) = P(A given B) × P(B) Higher