The Cambridge IGCSE Maths formula sheet
From 2025, every Cambridge IGCSE Mathematics (0580) paper prints a list of formulas on page 2. That list is useful, but short. Here is exactly what it gives you at Core and Extended, and the formulas you still need to know by heart.
On this page
Where the formulas are
The 0580 syllabus for 2025, 2026 and 2027 says that a list of formulas is provided on page 2 of the examination papers. There are two versions: one for Core (Papers 1 and 3) and one for Extended (Papers 2 and 4). Cambridge also says clearly that not all required formulas are given, so the syllabus notes tell you which ones you must know.
Remember the other big change in this syllabus: Papers 1 and 2 are non-calculator, and Papers 3 and 4 allow a calculator.
Given on Core papers (1 and 3)
- Area of a triangle: A = ½bh
- Area of a circle: A = πr², and circumference C = 2πr
- Curved surface area of a cylinder: A = 2πrh
- Curved surface area of a cone: A = πrl, where l is the sloping edge
- Surface area of a sphere: A = 4πr²
- Volume of a prism: V = Al, where A is the cross-sectional area and l the length
- Volume of a pyramid: V = ⅓Ah
- Volume of a cylinder: V = πr²h
- Volume of a cone: V = ⅓πr²h
- Volume of a sphere: V = (4/3)πr³
Extra formulas on Extended papers (2 and 4)
Extended papers give everything above, plus:
- The quadratic formula: for ax² + bx + c = 0 with a ≠ 0, x = (−b ± √(b² − 4ac)) / 2a
- The sine rule: a/sin A = b/sin B = c/sin C
- The cosine rule: a² = b² + c² − 2bc cos A
- Area of a triangle: ½ab sin C
Formulas you must still learn
These are not on the list, but questions expect you to use them.
- Pythagoras' theorem: a² + b² = c² for a right-angled triangle.
- Right-angled trigonometry: sin, cos and tan as ratios of sides (SOHCAHTOA).
- Area of a rectangle, parallelogram and trapezium: for the trapezium, ½(a + b)h.
- Arc length and sector area as fractions of the circle: (θ/360) × 2πr and (θ/360) × πr².
- Gradient, midpoint and length of a line segment, and y = mx + c.
- Speed, distance and time, and density = mass ÷ volume.
- Percentage change, simple and compound interest: compound interest uses P(1 + r/100)n.
- Interior and exterior angles of polygons: the interior angles of an n-sided polygon sum to (n − 2) × 180°.
- Probability rules, such as P(not A) = 1 − P(A).
Using a given formula
A cone has radius 6 cm and height 8 cm. Find its volume and its curved surface area, leaving π in your answers.
- Volume from the list: V = ⅓πr²h = ⅓ × π × 36 × 8 = 96π cm³.
- The curved surface needs the sloping edge l, which is not given: l = √(6² + 8²) = 10 cm by Pythagoras.
- Curved surface area = πrl = π × 6 × 10 = 60π cm². The list gave both formulas, but you had to know Pythagoras.
An Extended non-calculator question
Solve x² − 4x − 1 = 0, giving your answers in surd form.
- The quadratic formula is given: x = (4 ± √(16 + 4)) / 2 = (4 ± √20) / 2.
- √20 = 2√5, so x = 2 ± √5.
- Simplifying surds is not on the formula list: it is a skill you must have for Paper 2.
Non-calculator tips for Papers 1 and 2
Half of your marks now come from a paper without a calculator, so the formula list is only part of the preparation.
- Keep answers in terms of π or as surds when asked: 36π is a complete answer.
- Simplify before you multiply: ⅓ × 36 × 8 is easier as 12 × 8.
- Know your squares, cubes and simple roots up to at least 15² and 5³.
- Practise written methods for long multiplication and division of decimals.
How to use the list in the exam
- Glance at page 2 at the start so you know what is there.
- Write the formula before substituting: method marks are often awarded for a correct formula with correct values.
- Check units, especially for areas (cm²) and volumes (cm³).
- On non-calculator papers, leave answers in terms of π when the question asks.
Common mistakes
- Assuming Pythagoras or SOHCAHTOA will be given: they are not.
- Using the height of a cone where the sloping edge l is needed, or the other way round.
- Forgetting the ⅓ in the volume of a cone or pyramid.
- Rounding too early in multi-step calculator questions.
Practice questions
Try each one before opening the answer.
Q1. Find the volume of a sphere of radius 3 cm, in terms of π.
Show answer
Q2. In triangle ABC, a = 9 cm, A = 30° and B = 45°. Find b.
Show answer
Q3. A cylinder has radius 4 cm and height 10 cm. Find its total surface area in terms of π.
Show answer
Q4. Interior angle of a regular hexagon?
Show answer
Frequently asked questions
Is there a formula sheet in IGCSE Maths?
For Cambridge 0580 from 2025, yes: a list of formulas is printed on page 2 of every paper, with a longer list for Extended.
Is the quadratic formula given in Core?
No. The quadratic formula, sine rule, cosine rule and ½ab sin C are on the Extended list only.
Is Edexcel IGCSE the same?
No. Edexcel International GCSE Mathematics A has its own formulae page. Check your own board's papers.
Key takeaways
- 0580 prints a list of formulas on page 2 of every paper.
- Core: areas, surfaces and volumes.
- Extended adds the quadratic formula, sine and cosine rules and ½ab sin C.
- Pythagoras, SOHCAHTOA and many others are not given.
- Papers 1 and 2 are non-calculator.