Looking for a clear Edexcel IGCSE higher Maths formula sheet? This guide brings together every formula given on the official sheet, explains when each one is useful, and lists the key formulas you still need to memorise.
It is written for Edexcel International GCSE Mathematics A (4MA1) Higher students. Use it alongside past papers, class notes and the official specification. For individual help, Sophie offers IGCSE Maths tutoring, or you can contact Sophie.
Official formula sheet
Download the official Edexcel IGCSE Higher formulae sheet (PDF)
What the formula sheet gives you
The Edexcel IGCSE Higher formula sheet is included in your exam paper and contains more formulae than the Foundation sheet. Knowing exactly what is provided means you can focus your memorisation time on the formulas that are not given.
Arithmetic series
Sum to n terms: Sₙ = n/2 × [2a + (n − 1)d], where a is the first term, d is the common difference and n is the number of terms. This is used when a question asks for the sum of an arithmetic sequence rather than a single term.
Area of trapezium
Area = ½(a + b)h, where a and b are the parallel sides and h is the perpendicular height. Identify the two parallel sides clearly before substituting — this is where most errors occur.
Quadratic equation
x = (−b ± √(b² − 4ac)) / 2a, used when ax² + bx + c = 0 and the equation does not factorise neatly. Always identify a, b and c before substituting, and remember the ± gives two possible solutions.
Trigonometry in non-right-angled triangles
Sine rule: a/sin A = b/sin B = c/sin C. Use this when you have a matching side-angle pair and one other side or angle.
Cosine rule: a² = b² + c² − 2bc cos A. Use this when you have two sides and the included angle, or all three sides and need an angle.
Area of triangle: Area = ½ab sin C. Use this when two sides and the included angle are known and no height is given.
Cone
Volume of cone = ⅓πr²h. Curved surface area of cone = πrl, where l is the slant height (not the vertical height h). Use Pythagoras to find l if the question gives r and h instead.
Prism and cylinder
Volume of prism = area of cross section × length. Volume of cylinder = πr²h. Curved surface area of cylinder = 2πrh. These are the same as the Foundation sheet.
Sphere
Volume of sphere = 4/3 πr³. Surface area of sphere = 4πr². Both use the radius. Note the surface area formula covers the entire surface — there is no distinction between curved and flat faces as with a cylinder.
Formulas you must memorise
Everything below is needed for the Higher exam and is not on the formula sheet.
Area, perimeter and circles
Area of rectangle = length × width
Area of triangle = ½ × base × height
Area of circle = πr²
Circumference = 2πr
Arc length = (θ/360) × 2πr
Area of sector = (θ/360) × πr²
Arc and sector formulas are not given but appear regularly. Memorise them as the "fraction of the full circle" times the corresponding circle formula.
Pythagoras and right-angled trigonometry
a² + b² = c² (Pythagoras' theorem)
sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOHCAHTOA)
Trigonometric identity: sin²θ + cos²θ = 1
tan θ = sin θ ÷ cos θ
Coordinate geometry
Equation of a straight line: y = mx + c
Gradient = (y₂ − y₁) ÷ (x₂ − x₁)
Perpendicular gradient = −1/m (the negative reciprocal of the original gradient)
Distance between two points = √((x₂ − x₁)² + (y₂ − y₁)²)
Equation of a circle centred at the origin: x² + y² = r²
Speed, density and pressure
Speed = distance ÷ time. Density = mass ÷ volume. Pressure = force ÷ area. None of these are on the formula sheet.
Percentages and growth
Percentage change = (change ÷ original) × 100
Compound interest / exponential growth: Amount = P × (1 + r/100)ⁿ
Sequences
nth term of arithmetic sequence: a + (n − 1)d (note the sum formula is given, but the nth term is not)
nth term of geometric sequence: arⁿ⁻¹, where a is the first term and r is the common ratio
Histograms
Frequency density = frequency ÷ class width. This is needed to draw and interpret histograms and is never given on the sheet.
How to use this formula sheet in revision
Split your revision into two lists: formulas given and formulas to memorise. Drill the second list using retrieval practice — cover the page, write from memory, check, and repeat the ones you missed. The most common exam error with given formulas is substituting into the wrong one or misidentifying which letter represents which measurement. Practise labelling diagrams carefully before substituting.
For the sine and cosine rules in particular, draw the triangle, label all known sides and angles with the letters from the formula, and then substitute. Skipping the labelling step is where most marks are lost on these questions.
