Both IGCSE maths boards print a short formula list inside every paper, and it covers far less than most students assume. This sheet sets out exactly what Cambridge 0580 and Edexcel 4MA1 give at each tier, and everything else your child has to carry in their head.
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The short answer
Cambridge 0580 prints a list of formulas on page 2 of every paper; Edexcel 4MA1 prints a formulae sheet inside every paper. Neither prints Pythagoras' theorem, the trigonometric ratios or arc length, so those have to be learned.
The two lists are not even the same shape. Cambridge gives the area of a circle and of a triangle but not the trapezium; Edexcel gives the trapezium but not the circle. A student practising from the other board's papers can be caught out either way.
Sources: the Cambridge 0580 syllabus for 2025–2027 (List of formulas) and the Pearson 4MA1 specification (Appendices 4 and 5).
Printed on the paper
Every formula that appears on either board's printed list. Anything not in this table is not given on the formula page.
| Formula | Given in exam? | Notes |
|---|---|---|
| Area of triangle = ½bh | Cambridge: Core and Extended. Edexcel: no | Edexcel candidates learn it |
| Area of circle = πr² | Cambridge: Core and Extended. Edexcel: no | Edexcel candidates learn it |
| Circumference = 2πr | Cambridge: Core and Extended. Edexcel: no | Edexcel candidates learn it |
| Area of trapezium = ½(a + b)h | Edexcel: Foundation and Higher. Cambridge: no | Cambridge candidates learn it |
| Volume of prism = cross-section area × length | Yes, both boards, every tier | |
| Volume of cylinder = πr²h | Yes, both boards, every tier | |
| Curved surface area of cylinder = 2πrh | Yes, both boards, every tier | |
| Volume of pyramid = ⅓ × base area × height | Cambridge: Core and Extended. Edexcel: no | |
| Volume of cone = ⅓πr²h | Cambridge: both tiers. Edexcel: Higher only | Edexcel Foundation: learn it or expect it in the question |
| Curved surface area of cone = πrl | Cambridge: both tiers. Edexcel: Higher only | l is the slant height |
| Volume of sphere = ⁴⁄₃πr³ | Cambridge: both tiers. Edexcel: Higher only | |
| Surface area of sphere = 4πr² | Cambridge: both tiers. Edexcel: Higher only | |
| Quadratic formula | Cambridge Extended and Edexcel Higher | Not needed at Core or Foundation |
| Sine rule and cosine rule | Cambridge Extended and Edexcel Higher | Cosine rule printed in the form for a side |
| Area of triangle = ½ab sin C | Cambridge Extended and Edexcel Higher | |
| Sum of an arithmetic series | Edexcel Higher only | Not on the Cambridge 0580 syllabus |
Edexcel's Foundation sheet has four formulas: trapezium, prism, cylinder volume and cylinder curved surface area. The Higher sheet has thirteen.
Number and algebra
None of these is printed on either board's formula page. The notes say which tiers need them.
| Formula | Given in exam? | Notes |
|---|---|---|
| Percentage change = change ÷ original × 100 | No | All tiers |
| Compound growth: P(1 + r/100)n; depreciation uses (1 − r/100)n | No | All tiers; Cambridge states interest formulas are not given |
| Reverse percentage: original = new amount ÷ multiplier | No | All tiers; after a 15% rise, divide by 1.15 |
| Standard form A × 10n, 1 ≤ A < 10 | No | All tiers |
| Index laws, including a0 = 1 and a−n = 1/an | No | All tiers; fractional indices at Extended and Higher |
| Surds: √a × √b = √(ab) | No | Cambridge Extended, Edexcel Higher |
| Bounds: half a unit either side of the rounded value | No | All tiers; bounds of calculations at Extended and Higher |
| Speed = distance ÷ time | No | All tiers; Cambridge expects it known |
| Density = mass ÷ volume; pressure = force ÷ area | Not on the list; usually in the question | Cambridge gives rate formulas other than speed in the question, and Edexcel does the same for pressure |
| Difference of two squares: a² − b² = (a + b)(a − b) | No | Used most at Extended and Higher |
| Completing the square: x² + bx = (x + b/2)² − (b/2)² | No | Cambridge Extended, Edexcel Higher |
| nth term of a linear sequence: dn + (a − d) | No | All tiers |
| Proportion: y = kx, y = k/x, and squared or rooted forms | No | Algebraic form at Cambridge Extended and Edexcel Higher |
| Differentiation: y = axn gives dy/dx = naxn−1 | No | Cambridge Extended, Edexcel Higher; turning points where dy/dx = 0 |
Shape and space
This is where most “I didn't know that was on the sheet” moments happen.
| Formula | Given in exam? | Notes |
|---|---|---|
| Pythagoras: a² + b² = c² | No | All tiers, both boards |
| sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj | No | All tiers, both boards |
| Arc length = θ/360 × 2πr; sector area = θ/360 × πr² | No | All tiers, both boards |
| Gradient = change in y ÷ change in x; y = mx + c | No | All tiers |
| Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) | No | Cambridge Extended; Edexcel from Foundation |
| Length of a line segment by Pythagoras on the coordinates | No | Cambridge Extended, Edexcel Higher |
| Perpendicular gradients multiply to −1 | No | Cambridge Extended, Edexcel Higher |
| Interior angles of an n-sided polygon = (n − 2) × 180° | No | All tiers; exterior angles sum to 360° |
| Similar shapes: lengths × k, areas × k², volumes × k³ | No | Cambridge Extended, Edexcel Higher |
| Cosine rule rearranged for an angle: cos A = (b² + c² − a²) ÷ 2bc | No | The printed version is for a side |
| Exact values of sin, cos and tan at 0°, 30°, 45°, 60° (and 90° for sin and cos) | No | Required at Cambridge Extended (E6.3) |
| Magnitude of a vector (x, y) = √(x² + y²) | No | Cambridge Extended, Edexcel Higher |
Data and chance
| Formula | Given in exam? | Notes |
|---|---|---|
| P(not A) = 1 − P(A) | No | All tiers |
| Mutually exclusive events: P(A or B) = P(A) + P(B) | No | All tiers |
| Independent events: P(A and B) = P(A) × P(B) | No | All tiers |
| Expected frequency = probability × number of trials | No | All tiers |
| Estimated mean = Σ(frequency × midpoint) ÷ Σfrequency | No | All tiers |
| Interquartile range = upper quartile − lower quartile | No | Cambridge Extended, Edexcel Higher |
| Frequency density = frequency ÷ class width | No | Cambridge Extended, Edexcel Higher |
| Conditional probability | No | Cambridge Extended works it from diagrams and tables; its syllabus says formula notation is not required |
First ten
These turn up on almost every paper and appear on no tier's formula list.
Using the list
Knowing versus choosing
Most lost marks on formula questions are not forgotten formulas. They are the right formula used in the wrong place — sector area where the question wanted arc length, or the sine rule where only the cosine rule works.
In a free 55-minute ClassArc class, the teacher gives your child mixed exam questions on a shared worksheet and watches which formula they reach for, line by line. Afterwards you hear which gaps are worth closing first, and whether a weekly class is needed at all.
If a student can say when a formula does not apply, they know it.
The test we use in classKeep going
Every 0580 and 4MA1 topic tagged by tier, to rate green, amber or red.
Rate the topicsThe order to revise in, non-calculator practice, and a twelve-week plan.
Plan revisionWeekly one-to-one classes on either board, on UAE evenings.
Find out moreFormula questions
First class
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Last updated · May 2026
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Last updated · May 2026
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