Resources · IGCSE · Formulas

IGCSE maths formula sheet:
what is given,
what must be learned

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 IGCSE maths formula list is short,
and the boards disagree on it

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).

Formulas the IGCSE papers print for you, by board and tier

Every formula that appears on either board's printed list. Anything not in this table is not given on the formula page.

FormulaGiven in exam?Notes
Area of triangle = ½bhCambridge: Core and Extended. Edexcel: noEdexcel candidates learn it
Area of circle = πr²Cambridge: Core and Extended. Edexcel: noEdexcel candidates learn it
Circumference = 2πrCambridge: Core and Extended. Edexcel: noEdexcel candidates learn it
Area of trapezium = ½(a + b)hEdexcel: Foundation and Higher. Cambridge: noCambridge candidates learn it
Volume of prism = cross-section area × lengthYes, both boards, every tier
Volume of cylinder = πr²hYes, both boards, every tier
Curved surface area of cylinder = 2πrhYes, both boards, every tier
Volume of pyramid = ⅓ × base area × heightCambridge: Core and Extended. Edexcel: no
Volume of cone = ⅓πr²hCambridge: both tiers. Edexcel: Higher onlyEdexcel Foundation: learn it or expect it in the question
Curved surface area of cone = πrlCambridge: both tiers. Edexcel: Higher onlyl is the slant height
Volume of sphere = ⁴⁄₃πr³Cambridge: both tiers. Edexcel: Higher only
Surface area of sphere = 4πr²Cambridge: both tiers. Edexcel: Higher only
Quadratic formulaCambridge Extended and Edexcel HigherNot needed at Core or Foundation
Sine rule and cosine ruleCambridge Extended and Edexcel HigherCosine rule printed in the form for a side
Area of triangle = ½ab sin CCambridge Extended and Edexcel Higher
Sum of an arithmetic seriesEdexcel Higher onlyNot 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 formulas IGCSE students must memorise

None of these is printed on either board's formula page. The notes say which tiers need them.

FormulaGiven in exam?Notes
Percentage change = change ÷ original × 100NoAll tiers
Compound growth: P(1 + r/100)n; depreciation uses (1 − r/100)nNoAll tiers; Cambridge states interest formulas are not given
Reverse percentage: original = new amount ÷ multiplierNoAll tiers; after a 15% rise, divide by 1.15
Standard form A × 10n, 1 ≤ A < 10NoAll tiers
Index laws, including a0 = 1 and an = 1/anNoAll tiers; fractional indices at Extended and Higher
Surds: √a × √b = √(ab)NoCambridge Extended, Edexcel Higher
Bounds: half a unit either side of the rounded valueNoAll tiers; bounds of calculations at Extended and Higher
Speed = distance ÷ timeNoAll tiers; Cambridge expects it known
Density = mass ÷ volume; pressure = force ÷ areaNot on the list; usually in the questionCambridge gives rate formulas other than speed in the question, and Edexcel does the same for pressure
Difference of two squares: a² − b² = (a + b)(ab)NoUsed most at Extended and Higher
Completing the square: x² + bx = (x + b/2)² − (b/2)²NoCambridge Extended, Edexcel Higher
nth term of a linear sequence: dn + (ad)NoAll tiers
Proportion: y = kx, y = k/x, and squared or rooted formsNoAlgebraic form at Cambridge Extended and Edexcel Higher
Differentiation: y = axn gives dy/dx = naxn−1NoCambridge Extended, Edexcel Higher; turning points where dy/dx = 0

Geometry and trigonometry formulas not printed on IGCSE papers

This is where most “I didn't know that was on the sheet” moments happen.

FormulaGiven in exam?Notes
Pythagoras: a² + b² = c²NoAll tiers, both boards
sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adjNoAll tiers, both boards
Arc length = θ/360 × 2πr; sector area = θ/360 × πr²NoAll tiers, both boards
Gradient = change in y ÷ change in x; y = mx + cNoAll tiers
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)NoCambridge Extended; Edexcel from Foundation
Length of a line segment by Pythagoras on the coordinatesNoCambridge Extended, Edexcel Higher
Perpendicular gradients multiply to −1NoCambridge Extended, Edexcel Higher
Interior angles of an n-sided polygon = (n − 2) × 180°NoAll tiers; exterior angles sum to 360°
Similar shapes: lengths × k, areas × k², volumes × k³NoCambridge Extended, Edexcel Higher
Cosine rule rearranged for an angle: cos A = (b² + c² − a²) ÷ 2bcNoThe printed version is for a side
Exact values of sin, cos and tan at 0°, 30°, 45°, 60° (and 90° for sin and cos)NoRequired at Cambridge Extended (E6.3)
Magnitude of a vector (x, y) = √(x² + y²)NoCambridge Extended, Edexcel Higher

Probability and statistics results to know by heart for IGCSE

FormulaGiven in exam?Notes
P(not A) = 1 − P(A)NoAll tiers
Mutually exclusive events: P(A or B) = P(A) + P(B)NoAll tiers
Independent events: P(A and B) = P(A) × P(B)NoAll tiers
Expected frequency = probability × number of trialsNoAll tiers
Estimated mean = Σ(frequency × midpoint) ÷ ΣfrequencyNoAll tiers
Interquartile range = upper quartile − lower quartileNoCambridge Extended, Edexcel Higher
Frequency density = frequency ÷ class widthNoCambridge Extended, Edexcel Higher
Conditional probabilityNoCambridge Extended works it from diagrams and tables; its syllabus says formula notation is not required

Ten IGCSE formulas to learn first if time is short

These turn up on almost every paper and appear on no tier's formula list.

Six habits that make an IGCSE formula list worth marks

Knowing a formula is half the job;
choosing it is the other half

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 class

Other IGCSE maths guides for UAE students

Is there a formula sheet in the IGCSE maths exam?
Yes. Cambridge 0580 prints a list of formulas on page 2 of each paper, longer at Extended than at Core. Edexcel 4MA1 includes a formulae sheet in each paper: four formulas at Foundation and thirteen at Higher.
Is Pythagoras' theorem given in IGCSE maths?
No. Neither Cambridge 0580 nor Edexcel 4MA1 prints Pythagoras' theorem or the SOH CAH TOA ratios at any tier, so both have to be known by heart.
Is the quadratic formula given?
Only on the higher tiers: Cambridge Extended and Edexcel Higher both print it. Core and Foundation candidates are not expected to use it.
Can my child take their own formula sheet into the exam?
No. Only the formulas printed in the paper may be used; anything brought in on paper or written on a calculator case breaks the exam rules.
How do I know which formula list applies to my child?
Check the paper code on a school test: 0580 is Cambridge, 4MA1 is Edexcel, and the paper number shows the tier. If you are unsure, WhatsApp a photo of the cover to +91 78781 48026 and we will tell you. Class prices are on the UAE pricing page.
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