IGCSE Mathematics Formula Sheet
Some formulae are given on the 0580 paper and others are not, and the ones most often needed under pressure are the ones that are not. Learn the whole list and the distinction stops mattering.
This sheet gathers every formula the 0580 syllabus uses, grouped so that related results sit together. Check which formulae are printed on your own paper, since what is provided varies between papers and syllabus versions, and treat anything printed as a bonus rather than something to rely on.
Area, perimeter and volume
| Shape | Formula |
|---|---|
| Triangle | area = half x base x perpendicular height |
| Parallelogram | area = base x perpendicular height |
| Trapezium | area = half x (a + b) x h, where a and b are the parallel sides |
| Circle | circumference = 2 pi r, area = pi r2 |
| Arc and sector | arc = (angle over 360) x 2 pi r, sector = (angle over 360) x pi r2 |
| Prism | volume = cross sectional area x length |
| Cylinder | volume = pi r2 h, curved surface area = 2 pi r h |
| Cone | volume = one third pi r2 h, curved surface area = pi r l |
| Sphere | volume = four thirds pi r3, surface area = 4 pi r2 |
| Pyramid | volume = one third x base area x perpendicular height |
Algebra and number
| Result | Formula |
|---|---|
| Quadratic formula | x = (minus b plus or minus the square root of (b2 minus 4ac)) divided by 2a |
| Discriminant | b2 minus 4ac, deciding the number of real roots |
| Gradient | m = (y2 minus y1) divided by (x2 minus x1) |
| Straight line | y = mx + c |
| Midpoint | ((x1 + x2) over 2, (y1 + y2) over 2) |
| Length of a line | the square root of ((x2 minus x1)2 + (y2 minus y1)2) |
| Compound interest | final amount = P x (1 + r over 100)n |
| Simple interest | I = P R T divided by 100 |
| Percentage change | change divided by original, multiplied by 100 |
Trigonometry and statistics
| Result | Formula |
|---|---|
| Pythagoras | a2 + b2 = c2, with c the hypotenuse |
| Right-angled ratios | sin = opposite over hypotenuse, cos = adjacent over hypotenuse, tan = opposite over adjacent |
| Sine rule | a divided by sin A = b divided by sin B = c divided by sin C |
| Cosine rule | a2 = b2 + c2 minus 2bc cos A |
| Area of any triangle | area = half a b sin C |
| Mean from a frequency table | sum of fx divided by sum of f |
| Frequency density | frequency divided by class width |
| Interquartile range | upper quartile minus lower quartile |
How to use this sheet
- Write the formula before substituting. On 0580 that line is frequently a method mark on its own.
- For cones and pyramids, check whether the question gives the perpendicular height or the slant height.
- Keep answers in terms of pi through the working and convert to a decimal only at the end.
- Give final answers to three significant figures unless the question says otherwise, and angles to one decimal place.
- Learn which formulae are printed on your paper, but revise all of them anyway.
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Frequently asked questions
Are all IGCSE Maths formulae given in the exam?
No. Cambridge prints some on the paper, typically several mensuration and trigonometry results, but many are expected from memory, including the quadratic formula in some papers, gradient, midpoint, compound interest and the statistics results. Check what appears on your own paper.
What is the difference between the sine rule and the cosine rule?
Use the sine rule when you have a side together with the angle opposite it, forming a matching pair. Use the cosine rule when you have three sides, or two sides and the angle between them, since in those cases no matching pair exists.
Which height do I use for a cone?
Use the perpendicular height for the volume and the slant height for the curved surface area. The radius, perpendicular height and slant height form a right-angled triangle, so Pythagoras converts between them when only one is given.
To how many figures should I give my answers?
Three significant figures unless the question specifies otherwise, with angles given to one decimal place. Keep full accuracy on your calculator throughout the working and round only the final answer, since rounding early shifts the third figure.
Practise the topics this sheet supports
Other reference sheets
Written to the published Cambridge IGCSE syllabuses. Always check the formula list and data sheet issued with your own paper, since the material provided differs between subjects and syllabus versions. Last reviewed 2026-08-12.