GCSE Maths formulas and facts

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• Area of a trapezium½(a + b)h, where a and b are the parallel sides and h is the perpendicular height between them.
• Area of a triangle from two sides and the angle between them½ab sin C
• Circumference of a circleC = πd = 2πr
• Area of a circleA = πr²
• Arc length of a sector with angle θ°(θ/360) × 2πr
• Area of a sector with angle θ°(θ/360) × πr²
• Volume of a prismArea of the cross-section × length
• Volume of a cylinderπr²h
• Volume of a cone⅓πr²h
• Volume of a sphere(4/3)πr³
• Pythagoras’ theorema² + b² = c², where c is the hypotenuse: the side opposite the right angle.
• sin θ, cos θ and tan θ in a right-angled trianglesin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent.
• Exact values of sin 30° and cos 60°Both are ½.
• Exact values of sin 60° and cos 30°Both are √3/2.
• Exact values of sin 45° and cos 45°Both are √2/2 (which is 1/√2).
• Exact values of tan 30°, tan 45° and tan 60°tan 30° = √3/3 (which is 1/√3), tan 45° = 1, tan 60° = √3.
• The sine rulea/sin A = b/sin B = c/sin C
• The cosine rulea² = b² + c² − 2bc cos A
• The quadratic formula for ax² + bx + c = 0x = (−b ± √(b² − 4ac)) / 2a
• Sum of the interior angles of a polygon with n sides(n − 2) × 180°
• Sum of the exterior angles of any polygon360°
• Alternate angles on parallel linesEqual (the Z shape).
• Co-interior angles on parallel linesAdd up to 180° (the C or U shape).
• Angle at the centre of a circleTwice the angle at the circumference standing on the same arc.
• Angle in a semicircle90°
• Opposite angles in a cyclic quadrilateralAdd up to 180°.
• Angle between a tangent and the radius at the point of contact90°
• Gradient of the line through (x₁, y₁) and (x₂, y₂)(y₂ − y₁) ÷ (x₂ − x₁)
• Equation of a straight liney = mx + c, where m is the gradient and c is the y-intercept.
• Gradients of perpendicular linesThey multiply to −1, so m₂ = −1/m₁.
• Equation of a circle with centre (0, 0) and radius rx² + y² = r²
• Speed, distance and timespeed = distance ÷ time
• Density, mass and volumedensity = mass ÷ volume
• Pressure, force and areapressure = force ÷ area
• Percentage change(change ÷ original amount) × 100
• Compound growth: £P at r% a year for n yearsP × (1 + r/100)ⁿ
• aᵐ × aⁿ, aᵐ ÷ aⁿ and (aᵐ)ⁿaᵐ⁺ⁿ, aᵐ⁻ⁿ and aᵐⁿ
• a⁰ and a⁻ⁿ (a not 0)a⁰ = 1 and a⁻ⁿ = 1/aⁿ
• P(A or B) when A and B cannot both happenP(A) + P(B)
• P(A and B) when A and B are independentP(A) × P(B)