GCSE and IGCSE maths formula sheet

Q: Is there a formula sheet in GCSE maths?

Yes. AQA and Edexcel both give a short formulae sheet as an insert at Foundation and Higher tier, and OxfordAQA International GCSE and Cambridge IGCSE give their own. It lists only a few formulas, so you still have to memorise many others.

Q: Does the Cambridge IGCSE 0580 give a formula sheet?

Yes. A List of formulas is printed on page 2 of each paper, with a longer one for Extended Papers 2 and 4. It prints solids and triangle area, but not Pythagoras, trapezium area or compound interest.

Q: Is the quadratic formula given in the exam?

At AQA and Edexcel it is printed on the Higher sheet only. OxfordAQA gives it on the Extension sheet and Cambridge on the Extended list; it is not printed at Foundation or Core.

Q: Are cone and sphere formulas on the AQA sheet?

No. AQA's specification says the cone, sphere and kinematics formulas are given in the relevant question when needed. Cambridge IGCSE 0580 prints cone, sphere, cylinder and pyramid formulas on its list.

Q: Does Cambridge Additional Mathematics 0606 use the same sheet?

No. It has its own List of formulas covering circle equations, the binomial theorem, series, trigonometric identities and the sine and cosine rules. Check the current 0606 syllabus before the exam.

This page covers AQA GCSE Mathematics 8300 in detail, then shows how Pearson Edexcel GCSE 1MA1, OxfordAQA International GCSE 9260 and Cambridge IGCSE 0580 differ. The In the booklet badge means printed on the AQA formulae sheet for that tier; notes mark Higher only formulae and what the other boards print. Cambridge Additional Mathematics 0606 has its own list, covered briefly at the end.

Board	Official document
AQA GCSE Mathematics 8300 (Foundation and Higher)	Formulae Sheet insert, exams in 2026
AQA GCSE Mathematics 8300 specification	Appendix: mathematical formulae
Pearson Edexcel GCSE (9-1) Mathematics 1MA1	Higher tier Exam Aid, 2025
OxfordAQA International GCSE Mathematics 9260	Formulae Sheet, Extension
Cambridge IGCSE Mathematics 0580	Syllabus for 2025, 2026 and 2027 (List of formulas)
Cambridge IGCSE Additional Mathematics 0606	Syllabus for 2025, 2026 and 2027 (List of formulas)

In the booklet means the formula is printed in the official booklet or sheet in the exam; Learn it means students must recall it; See note means it depends on the board.

Your tier

Higher shows every formula; the 8 marked Higher only are not on the Foundation papers.

Area, perimeter and volume (AQA 8300)

Four of these are printed on the sheet at both tiers; the rest you must recall.

Formula	Equation	In the exam
Area of a trapeziuma and b are the parallel sides, h is their perpendicular separation.In the booklet	$A = \frac{1}{2} (a + b) h$	In the booklet
Volume of a prismUse it for cuboids and cylinders: a cylinder is V = πr²h.In the booklet	$V = area of cross section \times length$	In the booklet
Circumference of a circler is the radius and d is the diameter.In the booklet	$C = 2 π r = π d$	In the booklet
Area of a circleLeave answers in terms of π when asked.In the booklet	$A = π r^{2}$	In the booklet
Area of a triangleb is the base and h the perpendicular height. Not printed.Learn it	$A = \frac{1}{2} bh$	Learn it
Area of a parallelogramPerpendicular height, not the slant side.Learn it	$A = bh$	Learn it
Arc lengthFraction of the circumference; θ is the sector angle in degrees.Learn it	$l = \frac{θ}{360} \times 2 π r$	Learn it
Area of a sectorFraction of the full circle area.Learn it	$A = \frac{θ}{360} \times π r^{2}$	Learn it

Given in the question, not on the sheet (AQA 8300)

AQA's specification says these are given in the relevant question when needed, so look for them in the question stem.

Formula	Equation	In the exam
Curved surface area of a conel is the slant height. Given in the question per the AQA specification.See note	$A = π r l$	See note
Surface area of a sphereGiven in the question per the AQA specification.See note	$A = 4 π r^{2}$	See note
Volume of a sphereGiven in the question per the AQA specification.See note	$V = \frac{4}{3} π r^{3}$	See note
Volume of a coneh is the perpendicular height. Given in the question per the AQA specification.See note	$V = \frac{1}{3} π r^{2} h$	See note
Constant acceleration: velocityu initial velocity, v final velocity, a acceleration, t time. Given in the question.See note	$v = u + a t$	See note
Constant acceleration: displacements is displacement from the position at t = 0. Given in the question.See note	$s = u t + \frac{1}{2} a t^{2}$	See note
Constant acceleration: velocity and displacementGiven in the question.See note	$v^{2} = u^{2} + 2 a s$	See note

Pythagoras and trigonometry (AQA 8300)

Formula	Equation	In the exam
Pythagoras' theoremc is the hypotenuse of a right-angled triangle.In the booklet	$a^{2} + b^{2} = c^{2}$	In the booklet
Sine ratioOpposite over hypotenuse, with a opposite angle A.In the booklet	$sin A = \frac{a}{c}$	In the booklet
Cosine ratioAdjacent over hypotenuse.In the booklet	$cos A = \frac{b}{c}$	In the booklet
Tangent ratioOpposite over adjacent.In the booklet	$tan A = \frac{a}{b}$	In the booklet
Sine ruleHigher onlyHigher only. Use it with a matching side and angle pair.In the booklet	$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$	In the booklet
Cosine ruleHigher onlyHigher only. Use it for two sides and the included angle, or all three sides.In the booklet	$a^{2} = b^{2} + c^{2} - 2 b c cos A$	In the booklet
Area of any triangleHigher onlyHigher only. C is the angle between sides a and b.In the booklet	$A = \frac{1}{2} ab sin C$	In the booklet
Exact values of sineBoth tiers (Additional foundation content). Not printed.Learn it	$sin 0^{\circ} = 0, sin 3 0^{\circ} = \frac{1}{2}, sin 4 5^{\circ} = \frac{2}{2}, sin 6 0^{\circ} = \frac{3}{2}, sin 9 0^{\circ} = 1$	Learn it
Exact values of cosineCosine runs backwards through the sine values.Learn it	$cos 0^{\circ} = 1, cos 3 0^{\circ} = \frac{3}{2}, cos 4 5^{\circ} = \frac{2}{2}, cos 6 0^{\circ} = \frac{1}{2}, cos 9 0^{\circ} = 0$	Learn it
Exact values of tangenttan 90 is undefined. tan 30 can also be written 1 over root 3.Learn it	$tan 0^{\circ} = 0, tan 3 0^{\circ} = \frac{3}{3}, tan 4 5^{\circ} = 1, tan 6 0^{\circ} = 3$	Learn it

Algebra and graphs (AQA 8300)

Formula	Equation	In the exam
Quadratic formulaHigher onlyHigher only, for ax² + bx + c = 0 with a not zero. It is not on the Foundation sheet.In the booklet	$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$	In the booklet
Difference of two squaresUsed in factorising and in rationalising denominators.Learn it	$a^{2} - b^{2} = (a - b) (a + b)$	Learn it
Completed square formTurning point is at x = -b/2. Higher uses it to find turning points.Learn it	$x^{2} + b x + c = (x + \frac{b}{2})^{2} + c - \frac{b ^{2}}{4}$	Learn it
nth term of a linear sequencea is the first term and d the common difference.Learn it	$u_{n} = a + (n - 1) d$	Learn it
Equation of a straight linem is the gradient and c the y-intercept.Learn it	$y = m x + c$	Learn it
Gradient between two pointsParallel lines have equal gradients.Learn it	$m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$	Learn it
Perpendicular gradientsHigher onlyHigher only. Negative reciprocal gradients.Learn it	$m_{1} \times m_{2} = - 1$	Learn it
Circle centred on the originHigher onlyHigher only. r is the radius.Learn it	$x^{2} + y^{2} = r^{2}$	Learn it

Percentages, rates and proportion (AQA 8300)

Formula	Equation	In the exam
Compound interestP is the principal, r the percentage rate per period and n the number of periods.In the booklet	$Total accrued = P (1 + \frac{r}{100})^{n}$	In the booklet
Simple interestSame symbols as above, with t in years and r the yearly rate.Learn it	$I = \frac{P r t}{100}$	Learn it
Percentage changeAlso written as change over original, times 100.Learn it	$percentage change = \frac{new - old}{old} \times 100$	Learn it
Original value (reverse percentage)For example, after a 20% rise the multiplier is 1.2.Learn it	$original = \frac{new value}{multiplier}$	Learn it
SpeedRearrange for distance or time; check units such as m/s or km/h.Learn it	$speed = \frac{distance}{time}$	Learn it
DensityTypically g/cm³ or kg/m³.Learn it	$density = \frac{mass}{volume}$	Learn it
PressureNewtons per square metre gives pascals.Learn it	$pressure = \frac{force}{area}$	Learn it
Scale factors in similar shapesHigher onlyHigher only. k is the length scale factor.Learn it	$area scale factor = k^{2}, volume scale factor = k^{3}$	Learn it

Angles, probability and statistics (AQA 8300)

Formula	Equation	In the exam
Addition ruleBoth tiers. For mutually exclusive events the last term is zero.In the booklet	$P (A or B) = P (A) + P (B) - P (A and B)$	In the booklet
Conditional probabilityHigher onlyHigher only.In the booklet	$P (A and B) = P (A given B) P (B)$	In the booklet
Probability of an event not happeningAll probabilities of an exhaustive set add to 1.Learn it	$P (not A) = 1 - P (A)$	Learn it
Independent eventsUsed for tree diagrams. Not printed by AQA.Learn it	$P (A and B) = P (A) \times P (B)$	Learn it
Expected frequencyRelative frequency is frequency divided by total frequency.Learn it	$expected number = P (event) \times number of trials$	Learn it
Mean from a frequency tableMultiply each value by its frequency before adding.Learn it	$\overset{x}{ˉ} = \frac{\sum f x}{\sum f}$	Learn it
Sum of interior angles of a polygonn is the number of sides.Learn it	$S = (n - 2) \times 18 0^{\circ}$	Learn it
Exterior angle of a regular polygonInterior angle = 180 minus exterior angle.Learn it	$exterior angle = \frac{36 0 ^{\circ}}{n}$	Learn it

Pearson Edexcel GCSE 1MA1

The 2025 Exam Aid prints the same formulae as AQA at each tier, so the Given labels above also hold for Edexcel.

Formula	Equation	In the exam
Foundation Exam Aid printsEdexcel Foundation. There is no quadratic formula or sine and cosine rule on this sheet.In the booklet	$\frac{1}{2} (a + b) h, π r^{2}, 2 π r, a^{2} + b^{2} = c^{2}, sin A = \frac{a}{c}, P (1 + \frac{r}{100})^{n}, P (A or B)$	In the booklet
Higher Exam Aid addsEdexcel Higher. Matches the AQA Higher sheet, so the same learn list applies.In the booklet	$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}, \frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}, a^{2} = b^{2} + c^{2} - 2 b c cos A, \frac{1}{2} ab sin C, P (A and B) = P (A given B) P (B)$	In the booklet

OxfordAQA International GCSE 9260

OxfordAQA is a different board from AQA. Its Core and Extension sheets are shorter than AQA's.

Formula	Equation	In the exam
Core sheet printsOxfordAQA Core. No compound interest, quadratic formula or sine and cosine rules.In the booklet	$\frac{1}{2} (a + b) h, V = area \times length, 2 π r, π r^{2}, a^{2} + b^{2} = c^{2}, sin x = \frac{a}{c}$	In the booklet
Mutually exclusive eventsPrinted on both OxfordAQA sheets. AQA prints the general addition rule instead.See note	$P (A \cup B) = P (A) + P (B)$	See note
Extension sheet addsOxfordAQA Extension. Same as the AQA Higher sheet.In the booklet	$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}, \frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}, a^{2} = b^{2} + c^{2} - 2 b c cos A, \frac{1}{2} ab sin C$	In the booklet
Independent eventsPrinted on the OxfordAQA Extension sheet only; AQA does not print it.See note	$P (A \cap B) = P (A) \times P (B)$	See note
Compound interest (Extension)OxfordAQA Extension: n is the number of years.In the booklet	$Value of investment = P (1 + \frac{r}{100})^{n}$	In the booklet

Cambridge IGCSE Mathematics 0580

Cambridge prints a List of formulas on page 2 of every paper (Core: Papers 1 and 3; Extended: Papers 2 and 4), and a different mix from AQA.

Formula	Equation	In the exam
Cylinder: curved surface areaPrinted by Cambridge on both lists. AQA does not print it.See note	$A = 2 π r h$	See note
Cylinder: volumePrinted by Cambridge; for AQA it comes from the prism formula.See note	$V = π r^{2} h$	See note
Cone: curved surface area and volumePrinted by Cambridge. AQA gives these in the question.See note	$A = π r l, V = \frac{1}{3} π r^{2} h$	See note
Sphere: surface area and volumePrinted by Cambridge. AQA gives these in the question.See note	$A = 4 π r^{2}, V = \frac{4}{3} π r^{3}$	See note
Pyramid: volumeA is the base area, h the height. Printed by Cambridge; AQA does not list it.See note	$V = \frac{1}{3} A h$	See note
Area of a trianglePrinted by Cambridge on both lists. AQA does not print it.See note	$A = \frac{1}{2} bh$	See note
Extended list also printsExtended Papers 2 and 4 only; the Core list does not include these.In the booklet	$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}, \frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}, a^{2} = b^{2} + c^{2} - 2 b c cos A, \frac{1}{2} ab sin C$	In the booklet
Cambridge does not print: Pythagoras and trigonometryAQA prints these; for 0580 you must recall them.See note	$a^{2} + b^{2} = c^{2}, sin A = \frac{opp}{hyp}$	See note
Cambridge does not print: trapezium areaAQA prints it; the 0580 syllabus says formulas other than triangle area are not given.See note	$A = \frac{1}{2} (a + b) h$	See note
Cambridge does not print: compound interestAQA prints it; the 0580 syllabus says interest formulas are not given, so memorise it.See note	$P (1 + \frac{r}{100})^{n}$	See note
SpeedThe 0580 syllabus says knowledge of this formula is required. Formulas for density and pressure are given in the question.Learn it	$speed = \frac{distance}{time}$	Learn it

Cambridge Additional Mathematics 0606

0606 has its own List of formulas, which goes beyond any GCSE sheet above; it is not the 0580 list.

Formula	Equation	In the exam
Equation of a circleCentre (a, b), radius r. Printed on the 0606 list; AQA GCSE only needs the origin case.See note	$(x - a)^{2} + (y - b)^{2} = r^{2}$	See note
Binomial theoremPrinted on the 0606 list; not part of GCSE 8300.See note	$(a + b)^{n} = a^{n} + (1 n) a^{n - 1} b + (2 n) a^{n - 2} b^{2} + \dots + b^{n}$	See note
Sum to infinity of a geometric seriesPrinted on the 0606 list; not part of GCSE 8300.See note	$S_{\infty} = \frac{a}{1 - r}, ∣ r ∣ < 1$	See note

Learn these: not in the booklet

Area of a triangle $A = \frac{1}{2} bh$ Not printed by AQA, Edexcel or OxfordAQA.
Area of a parallelogram $A = bh$
Arc length and sector area $\frac{θ}{360} \times 2 π r an d \frac{θ}{360} \times π r^{2}$
Exact trigonometric values $sin 3 0^{\circ} = \frac{1}{2}, cos 6 0^{\circ} = \frac{1}{2}, sin 4 5^{\circ} = cos 4 5^{\circ} = \frac{2}{2}, tan 6 0^{\circ} = 3$
Speed, density, pressure $speed = \frac{d}{t}, density = \frac{m}{V}, pressure = \frac{F}{A}$
Simple interest $I = \frac{P r t}{100}$
Percentage change $\frac{new - old}{old} \times 100$
Independent events $P (A and B) = P (A) \times P (B)$
Mean from a frequency table $\overset{x}{ˉ} = \frac{\sum f x}{\sum f}$
Interior angle sum of a polygon $(n - 2) \times 18 0^{\circ}$
Straight line $y = m x + c, m_{1} m_{2} = - 1$ The perpendicular gradient rule is Higher tier.
Difference of two squares $a^{2} - b^{2} = (a - b) (a + b)$
Similar shapes (Higher) $area scale factor k^{2}, volume scale factor k^{3}$

Study booklets for your board

Our printable version of each board's official booklet: everything it prints (formulas, constants, data and statistical tables) in the board's own order, plus what you must learn and exam tips. Choose your board, then click a booklet to open it or use Download to save the PDF.

AQA3 booklets

GCSE Maths 8300 Higher tierPDF, 3 pages, 0.4 MB
Download
GCSE Maths 8300 Foundation tierPDF, 3 pages, 0.3 MB
Download
Level 2 Certificate in Further Maths 8365PDF, 4 pages, 0.4 MB
Download

Edexcel3 booklets

GCSE Maths 1MA1 Higher tierPDF, 4 pages, 0.4 MB
Download
GCSE Maths 1MA1 Foundation tierPDF, 3 pages, 0.4 MB
Download
International GCSE Further Pure Maths 4PM1PDF, 4 pages, 0.4 MB
Download

Cambridge3 booklets

IGCSE Maths 0580 Extended tierPDF, 4 pages, 0.5 MB
Download
IGCSE Maths 0580 Core tierPDF, 3 pages, 0.4 MB
Download
IGCSE and O Level Additional Maths 0606 and 4037PDF, 4 pages, 0.4 MB
Download

OxfordAQA2 booklets

International GCSE Maths 9260 Extension tier (higher)PDF, 4 pages, 0.4 MB
Download
International GCSE Maths 9260 Core tier (foundation)PDF, 2 pages, 0.3 MB
Download

How to use the formula sheet in the exam

Open the sheet on the first page of the paper and note which formulas are printed, so you stop trying to recall them.
Check your tier: the Foundation sheet has no quadratic formula, sine rule, cosine rule or conditional probability.
Read each question stem for cone, sphere or acceleration formulas; AQA gives these in the question, not on the sheet.
Label your triangle with opposite, adjacent and hypotenuse before using the sheet's a, b, c ratios.
For compound interest, make n match the compounding period: 3 years of yearly interest means n = 3, but monthly means n = 36.

Common questions

Is there a formula sheet in GCSE maths?

Yes. AQA and Edexcel both give a short formulae sheet as an insert at Foundation and Higher tier, and OxfordAQA International GCSE and Cambridge IGCSE give their own. It lists only a few formulas, so you still have to memorise many others.

Does the Cambridge IGCSE 0580 give a formula sheet?

Yes. A List of formulas is printed on page 2 of each paper, with a longer one for Extended Papers 2 and 4. It prints solids and triangle area, but not Pythagoras, trapezium area or compound interest.

Is the quadratic formula given in the exam?

At AQA and Edexcel it is printed on the Higher sheet only. OxfordAQA gives it on the Extension sheet and Cambridge on the Extended list; it is not printed at Foundation or Core.

Are cone and sphere formulas on the AQA sheet?

No. AQA's specification says the cone, sphere and kinematics formulas are given in the relevant question when needed. Cambridge IGCSE 0580 prints cone, sphere, cylinder and pyramid formulas on its list.

Does Cambridge Additional Mathematics 0606 use the same sheet?

No. It has its own List of formulas covering circle equations, the binomial theorem, series, trigonometric identities and the sine and cosine rules. Check the current 0606 syllabus before the exam.

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Formulas checked against the official documents linked above. Boards update their booklets from time to time: always practise with the version your exam uses.