"IGCSE maths formula sheet" is searched by students who have heard that a sheet is given and want to know what is on it, and by parents comparing the two boards. The answer changed in 2025, when Cambridge started printing a list of formulas on every 0580 paper for the first time, and it differs between Cambridge and Edexcel and between tiers. This page gives both sheets exactly as the exam prints them, then the longer list of what is not given and must be memorised, with a printable of both. The board and tier facts are in IGCSE vs GCSE.
Download the IGCSE maths formula sheet, both boards, with the memorise list (PDF) (the Cambridge list, the Edexcel Foundation and Higher sheets, and the formulas you must know by topic; two pages, free).
Cambridge IGCSE 0580: the list of formulas (from 2025)
Printed on page 2 of every paper, Core and Extended, since the 2025 syllabus. The paper structure from 2025: Paper 1 (Core) and Paper 2 (Extended) are non-calculator; Paper 3 (Core) and Paper 4 (Extended) are calculator papers.
| Given on all papers (Core and Extended) | |
|---|---|
| Area of a triangle, base b, height h | A = ½ b h |
| Area of a circle of radius r | A = π r² |
| Circumference of a circle of radius r | C = 2 π r |
| Curved surface area of a cylinder, radius r, height h | A = 2 π r h |
| Curved surface area of a cone, radius r, sloping edge l | A = π r l |
| Surface area of a sphere of radius r | A = 4 π r² |
| Volume of a prism, cross-sectional area A, length l | V = A l |
| Volume of a pyramid, base area A, height h | V = ⅓ A h |
| Volume of a cylinder, radius r, height h | V = π r² h |
| Volume of a cone, radius r, height h | V = ⅓ π r² h |
| Volume of a sphere of radius r | V = 4⁄3 π r³ |
| Given on Extended papers only (Papers 2 and 4) | |
|---|---|
| The quadratic formula, for ax² + bx + c = 0, a ≠ 0 | x = (−b ± √(b² − 4ac)) / 2a |
| The sine rule, triangle ABC | a / sin A = b / sin B = c / sin C |
| The cosine rule | a² = b² + c² − 2bc cos A |
| Area of a triangle | Area = ½ ab sin C |
Not given by Cambridge, on any paper: the area of a trapezium, Pythagoras, the right-angled trigonometric ratios, and everything in the memorise list below.
Edexcel International GCSE Mathematics A (4MA1): the formulae sheets
Printed at the front of each paper (page 2), and the paper says you must not write on it.
| Foundation tier (Papers 1F and 2F) | |
|---|---|
| Area of a trapezium | ½ (a + b) h |
| Volume of a prism | area of cross section × length |
| Volume of a cylinder | π r² h |
| Curved surface area of a cylinder | 2 π r h |
| Higher tier (Papers 1H and 2H): the four above, plus | |
|---|---|
| Sum to n terms of an arithmetic series | Sₙ = n⁄2 [2a + (n − 1)d] |
| The quadratic formula, for ax² + bx + c = 0, a ≠ 0 | x = (−b ± √(b² − 4ac)) / 2a |
| The sine rule, triangle ABC | a / sin A = b / sin B = c / sin C |
| The cosine rule | a² = b² + c² − 2bc cos A |
| Area of a triangle | ½ ab sin C |
| Volume of a cone | ⅓ π r² h |
| Curved surface area of a cone | π r l |
| Volume of a sphere | 4⁄3 π r³ |
| Surface area of a sphere | 4 π r² |
Not given by Edexcel: the area and circumference of a circle (Cambridge gives these, Edexcel does not), the volume of a pyramid, Pythagoras, the trigonometric ratios, and the memorise list below. Both papers allow a calculator on 4MA1.
The two boards compared
| Formula | Cambridge 0580 | Edexcel 4MA1 |
|---|---|---|
| Area of triangle ½bh, area and circumference of circle | Given, all papers | Not given |
| Area of trapezium | Not given | Given, both tiers |
| Prism and cylinder volume, cylinder curved surface | Given | Given |
| Cone volume and curved surface, sphere volume and surface | Given, all papers | Higher only |
| Pyramid volume | Given | Not given |
| Quadratic formula, sine rule, cosine rule, ½ab sin C | Extended only | Higher only |
| Arithmetic series sum | Not given (not in the syllabus) | Higher only |
What you must memorise, by topic
Number. Percentage change = change ÷ original × 100. Simple interest = P × r × t ÷ 100. Compound growth: amount = P(1 + r/100)ⁿ. Standard form a × 10ⁿ with 1 ≤ a < 10. Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ, a^(1/n) = ⁿ√a. Surds: √a × √b = √(ab); rationalise by multiplying by the surd. Upper and lower bounds: half the unit of rounding either way.
Algebra. Gradient = (y₂ − y₁)/(x₂ − x₁). Equation of a line y = mx + c; parallel lines share m; perpendicular gradients multiply to −1 (Extended and Higher). Midpoint ((x₁ + x₂)/2, (y₁ + y₂)/2); distance √((x₂ − x₁)² + (y₂ − y₁)²). Difference of two squares a² − b² = (a + b)(a − b). Completing the square (Extended and Higher). The nth term of an arithmetic sequence a + (n − 1)d. Direct proportion y = kx, inverse y = k/x. Edexcel Higher only: dy/dx of axⁿ is naxⁿ⁻¹.
Geometry and measure. Pythagoras a² + b² = c². The right-angled ratios: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Exact values: sin 30 = ½, cos 60 = ½, sin 45 = cos 45 = √2/2, tan 45 = 1, sin 60 = cos 30 = √3/2, tan 30 = 1/√3, tan 60 = √3 (non-calculator papers). Angle sum of a polygon (n − 2) × 180; exterior angles sum to 360. Area of a parallelogram b × h; area of a trapezium ½(a + b)h on Cambridge. Arc length = θ/360 × 2πr; sector area = θ/360 × πr². Circle theorems: angle in a semicircle 90°, angle at the centre twice the angle at the circumference, angles in the same segment equal, opposite angles of a cyclic quadrilateral sum to 180°, tangent perpendicular to the radius, the alternate segment theorem (Extended and Higher). Similar shapes: lengths × k, areas × k², volumes × k³. Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
Statistics and probability. Mean = sum ÷ count; the mean from a grouped table uses midpoints; median is the middle value; range is largest minus smallest. P(A or B) = P(A) + P(B) for mutually exclusive events; P(A and B) = P(A) × P(B) for independent events; tree diagrams multiply along branches and add across. Relative frequency = frequency ÷ total.
Sets and functions (Cambridge Extended). Set notation ∪, ∩, ∈, ⊂, the complement A′, n(A); the number in the union n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Composite function fg(x) = f(g(x)); the inverse f⁻¹ found by swapping x and y and rearranging.
A formula you have used fifty times in homework is not one you need to revise; the ones to drill are the ones used three times a year: the cosine rule's arrangement for an angle, the sector area, the compound-growth power, the exact trig values. The printable has the list by topic for ticking off.
Where to get help
A 1-on-1 online class for IGCSE maths with a tutor who holds a master's in mathematics and teaches both Cambridge 0580 (Core and Extended, including the non-calculator papers from 2025) and Edexcel 4MA1 (Foundation and Higher): the syllabus in the board's order, past papers marked to the mark scheme from the first term, and the formulas learned in the topic they belong to rather than from a list. UK after-school and Gulf and Asian evening hours, every class recorded, £8 to £10 an hour. The free 30-minute first class is a real lesson on the topic the student is on. The June 2025 grade boundaries are in Edexcel IGCSE grade boundaries 2025.
Download the IGCSE maths formula sheet, both boards, with the memorise list (PDF)
Questions parents ask
1Is there a formula sheet in IGCSE maths?
2What formulas are given in Cambridge IGCSE maths 0580?
3What formulas are given in Edexcel IGCSE maths 4MA1?
4What formulas do I have to memorise for IGCSE maths?
5Is the formula sheet the same on the calculator and non-calculator papers?
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