Edexcel GCSE Maths

GCSE Maths formulae

What's on the formulae sheet in the exam, and the rules and facts you still need to know yourself.

Yes, you get a formulae sheet. Ofqual requires exam boards to give GCSE Maths candidates a formulae sheet, including in the November resits; it was first required for 2025, 2026 and 2027, and in May 2026 Ofqual decided to keep it for the rest of the life of the current GCSEs. Pearson provides it as an "Exam Aid" insert with each 1MA1 question paper. Foundation and Higher get different sheets, and the formulae for cones, spheres and the volume of a pyramid are printed inside a question whenever it needs them. The sheet holds every formula on the Department for Education's list of formulae that GCSE students would normally have to memorise, which is why students officially "will not need to memorise formulae". It does not hold the everyday rules and facts the specification still expects you to know and use, such as the area of a triangle, arc length, speed == distance ÷\div time and the exact trig values, so make sure you know those.

Given on the formulae sheet

FormulaWhen to use it
Area of a trapeziumArea=12(a+b)h\text{Area} = \tfrac{1}{2}(a + b)ha and b are the parallel sides; h is the perpendicular height between them, not the slanted side.
Volume of a prismVolume=area of cross section×length\text{Volume} = \text{area of cross section} \times \text{length}Works for any solid with the same cross-section all the way through, including a cylinder (πr² × length).
Circumference of a circleC=2πr=πdC = 2\pi r = \pi dUse πd if you are given the diameter, 2πr if you are given the radius.
Area of a circleA=πr2A = \pi r^2Square the radius, not the diameter: halve d first.
Pythagoras' theorema2+b2=c2a^2 + b^2 = c^2Right-angled triangles only; c is the hypotenuse, the longest side, opposite the right angle. Square and add to find the hypotenuse; square and subtract to find a shorter side.
Trigonometric ratios (right-angled triangles)sin⁡A=accos⁡A=bctan⁡A=ab\sin A = \frac{a}{c} \qquad \cos A = \frac{b}{c} \qquad \tan A = \frac{a}{b}On the sheet's diagram a is opposite angle A, b is adjacent to it and c is the hypotenuse. Label your own triangle the same way before choosing, and use sin⁻¹, cos⁻¹ or tan⁻¹ to find an angle.
Compound interestTotal accrued=P(1+r100)n\text{Total accrued} = P\left(1 + \frac{r}{100}\right)^{n}P is the amount invested, r the percentage rate per period and n the number of periods. It gives the total, not just the interest: subtract P if the question asks for the interest. For depreciation or decay use (1 − r/100) instead.
Probability of A or BP(A or B)=P(A)+P(B)−P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)For mutually exclusive events P(A and B) = 0, so you just add.

Extra formulae on the Higher sheet only

FormulaWhen to use it
Quadratic formulaHigherx=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}Solves ax² + bx + c = 0 where a ≠ 0. Rearrange so one side is zero first, and keep the signs of a, b and c: if b is negative, −b is positive, and put negative values in brackets when you square them.
Sine ruleHigherasin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}Any triangle; use it when you know a side and its opposite angle as a pair. To find an angle, flip it so the sines are on top: sin A / a = sin B / b.
Cosine ruleHighera2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc\cos AAny triangle; use it with two sides and the angle between them, or with all three sides to find an angle (rearrange to cos A = (b² + c² − a²) ÷ (2bc)). Work out b² + c² − 2bc cos A in one go on your calculator; a common slip is subtracting 2bc before multiplying by cos A.
Area of a triangle using sineHigherArea=12absin⁡C\text{Area} = \tfrac{1}{2}ab\sin CC must be the angle between sides a and b.
Probability of A and B (conditional)HigherP(A and B)=P(A given B) P(B)P(A \text{ and } B) = P(A \text{ given } B)\,P(B)If A and B are independent, P(A given B) = P(A), so this becomes P(A) × P(B).

Given in the question when it is needed

FormulaWhen to use it
Volume of a sphereV=43πr3V = \tfrac{4}{3}\pi r^3Printed in the question when needed, not on the sheet. For a hemisphere, halve it.
Surface area of a sphereA=4πr2A = 4\pi r^2Printed in the question when needed. A hemisphere's total surface also includes its flat circle, πr².
Volume of a coneV=13πr2hV = \tfrac{1}{3}\pi r^2 hPrinted in the question when needed; h is the perpendicular height.
Curved surface area of a coneA=πrlA = \pi r lPrinted in the question when needed; l is the slant height, not the perpendicular height. Add πr² for the base if the question wants the total.
Volume of a pyramidV=13×area of base×hV = \tfrac{1}{3} \times \text{area of base} \times hPearson announced on 31 January 2025 that it will print this in the question when it is needed, as it does for cones and spheres; h is the perpendicular height.

Not on the sheet: number and ratio

FormulaWhen to use it
Percentage changePercentage change=changeoriginal×100\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100Always divide by the original amount, not the new one.
Percentage multipliers and reverse percentagesnew=original×(1±r100)original=newmultiplier\text{new} = \text{original} \times \left(1 \pm \frac{r}{100}\right) \qquad \text{original} = \frac{\text{new}}{\text{multiplier}}A 15% increase is × 1.15 and a 15% decrease is × 0.85. To find the original after a change, divide by the multiplier; never take the percentage of the new amount.
Simple interestInterest=P×r100×n\text{Interest} = P \times \frac{r}{100} \times nInterest is the same every year; compare with compound interest on the sheet.
Standard formA×10n,1≤A<10,  n an integerA \times 10^{n}, \quad 1 \le A < 10, \; n \text{ an integer}The first number must be at least 1 and less than 10.
Laws of indicesam×an=am+nam÷an=am−n(am)n=amna^m \times a^n = a^{m+n} \qquad a^m \div a^n = a^{m-n} \qquad (a^m)^n = a^{mn}Add powers when multiplying, subtract when dividing, multiply for a power of a power.
Zero and negative indicesa0=1a−n=1ana^0 = 1 \qquad a^{-n} = \frac{1}{a^n}A negative power means 'one over', not a negative number.
Fractional indicesHighera1n=anamn=(an)ma^{\frac{1}{n}} = \sqrt[n]{a} \qquad a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^mTake the root first, then the power, to keep the numbers small.
Multiplying surdsHighera×b=ab\sqrt{a} \times \sqrt{b} = \sqrt{ab}Use it to simplify, e.g. √12 = √4 × √3 = 2√3; there is no such rule for adding.
Direct and inverse proportiony=kxy=kxy = kx \qquad y = \frac{k}{x}Find k from one pair of values, then use the equation. Higher papers also use powers and roots, such as y = kx² or y = k/√x.
Speed, distance and timespeed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}Check the units match, e.g. km and hours give km/h. Convert minutes to hours by dividing by 60: 20 minutes is 1/3 of an hour, not 0.2.
Densitydensity=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}e.g. g/cm³. Rearrange for mass or volume as needed.
Pressurepressure=forcearea\text{pressure} = \frac{\text{force}}{\text{area}}Force in newtons over area in m² gives N/m².

Not on the sheet: algebra

FormulaWhen to use it
Equation of a straight liney=mx+cy = mx + cm is the gradient and c is where the line crosses the y-axis. Parallel lines have the same m.
Gradient between two pointsm=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}Change in y over change in x; keep the points in the same order on top and bottom.
Difference of two squaresa2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)Spot it whenever you have one square minus another.
Perpendicular gradientsHigherm1×m2=−1m_1 \times m_2 = -1The perpendicular gradient is the negative reciprocal: flip it and change the sign.
Completing the squareHigherx2+bx+c=(x+b2)2−(b2)2+cx^2 + bx + c = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + cHalve the coefficient of x; the result also gives the turning point of the graph.
Equation of a circle, centre the originHigherx2+y2=r2x^2 + y^2 = r^2r is the radius, so x² + y² = 25 has radius 5. The tangent at a point is perpendicular to the radius there.

Not on the sheet: geometry and measures

FormulaWhen to use it
Area of a rectangleArea=length×width\text{Area} = \text{length} \times \text{width}The building block for compound shapes: split the shape into rectangles, triangles and other shapes you know.
Area of a triangleArea=12×base×height\text{Area} = \tfrac{1}{2} \times \text{base} \times \text{height}Height is perpendicular to the base.
Area of a parallelogramArea=base×perpendicular height\text{Area} = \text{base} \times \text{perpendicular height}Use the perpendicular height, not the slanted side.
Volume of a cuboidV=length×width×heightV = \text{length} \times \text{width} \times \text{height}A special case of the prism formula on the sheet.
Volume of a cylinderV=πr2hV = \pi r^2 hThe prism formula with a circular cross-section.
Curved surface area of a cylinderA=2πrhA = 2\pi r hUnrolls to a rectangle: circumference × height. Add the two circular ends, 2πr², for the total surface area.
Arc lengthArc length=θ360×2πr\text{Arc length} = \frac{\theta}{360} \times 2\pi rθ is the angle at the centre in degrees.
Area of a sectorArea=θ360×πr2\text{Area} = \frac{\theta}{360} \times \pi r^2The same fraction of the full circle as the arc.
Angles in a polygonSum of interior angles=(n−2)×180∘\text{Sum of interior angles} = (n - 2) \times 180^\circn is the number of sides. Exterior angles of any polygon add up to 360°, so each exterior angle of a regular polygon is 360° ÷ n, and interior + exterior = 180°.
Exact trigonometric values0∘30∘45∘60∘90∘sin⁡01222321cos⁡13222120tan⁡03313\begin{array}{c|ccccc} & 0^\circ & 30^\circ & 45^\circ & 60^\circ & 90^\circ \\ \hline \sin & 0 & \frac{1}{2} & \frac{\sqrt{2}}{2} & \frac{\sqrt{3}}{2} & 1 \\ \cos & 1 & \frac{\sqrt{3}}{2} & \frac{\sqrt{2}}{2} & \frac{1}{2} & 0 \\ \tan & 0 & \frac{\sqrt{3}}{3} & 1 & \sqrt{3} & \end{array}You need these without a calculator, especially on the non-calculator paper (Paper 1). √2/2 is the same as 1/√2 and √3/3 is the same as 1/√3; tan 90° is not required.
Similar shapes: area and volumeHigherlength scale factor k  ⇒  area k2,  volume k3\text{length scale factor } k \;\Rightarrow\; \text{area } k^2, \; \text{volume } k^3Find k from a pair of matching lengths first.

Not on the sheet: probability and statistics

FormulaWhen to use it
Probability of an event not happeningP(not A)=1−P(A)P(\text{not } A) = 1 - P(A)All the probabilities of the outcomes add up to 1.
Expected frequencyExpected frequency=P(A)×number of trials\text{Expected frequency} = P(A) \times \text{number of trials}An estimate of how often the outcome will happen, not a guarantee.
Relative frequencyRelative frequency=number of times it happensnumber of trials\text{Relative frequency} = \frac{\text{number of times it happens}}{\text{number of trials}}An estimate of the probability from an experiment; more trials give a more reliable estimate.
Independent eventsP(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)Multiply along the branches of a tree diagram; only when one event does not affect the other.
Mean from a frequency tableMean=∑fx∑f\text{Mean} = \frac{\sum fx}{\sum f}For grouped data use the midpoint of each class for x; the answer is an estimate.
RangeRange=largest value−smallest value\text{Range} = \text{largest value} - \text{smallest value}Always a single number, not 'from … to …'.
Interquartile rangeHigherIQR=upper quartile−lower quartile\text{IQR} = \text{upper quartile} - \text{lower quartile}The spread of the middle half of the data, so extreme values do not affect it.
Frequency densityHigherFrequency density=frequencyclass width\text{Frequency density} = \frac{\text{frequency}}{\text{class width}}Plot this, not frequency, on a histogram; area of a bar gives the frequency.

Using formulae in the exam

  • Before the exam, read Pearson's Exam Aid for your tier so you know what is on it and where; in the exam you get a clean copy as an insert, and you cannot bring your own.
  • The sheet lists formulae but never tells you which one a question needs. Practise past papers with the sheet beside you so choosing becomes quick.
  • Write the formula down, then substitute the numbers. Method marks are often given for a correct substitution even if the final answer slips.
  • For right-angled triangles, label the sides opposite, adjacent and hypotenuse first, then pick sin, cos or tan to match.
  • Cone, sphere and pyramid formulae are not on the sheet: look for them printed in the question itself.
  • Keep your calculator in degree mode for trigonometry, and keep full accuracy until the final answer.

Questions students ask

Do you get a formula sheet in GCSE Maths in 2027?
Yes. Ofqual requires exam boards to provide formulae sheets in GCSE Maths exams in 2025, 2026 and 2027, and in May 2026 it decided to keep them for the rest of the life of the current GCSEs, including resits. For Edexcel 1MA1, Pearson includes the sheet as an Exam Aid insert with every question paper.
Is there a formula sheet for the November 2026 resit?
Yes. Ofqual's decision explicitly covers the November GCSE Maths exams in 2025, 2026 and 2027 as well as the summer exams. Pearson's 2026 Exam Aid is headed "2026 Assessment Window", and Pearson says its content has not changed since 2025.
What is the difference between the Foundation and Higher formula sheets?
Both have the trapezium, prism, circle, Pythagoras, right-angled trigonometry, compound interest and P(A or B)P(A \text{ or } B) formulae. The Higher sheet also has the quadratic formula, the sine rule, the cosine rule, 12absin⁡C\tfrac{1}{2}ab\sin C and P(A and B)=P(A given B)P(B)P(A \text{ and } B) = P(A \text{ given } B)P(B).
Can I take my own formula sheet into the exam?
No. Pearson's Exam Aid says you may not take it into the exam; an identical clean copy is provided inside the question paper on the day.
Which GCSE Maths formulae do I still need to know?
Officially you will not need to memorise formulae: everything on the government's list of GCSE Maths formulae is on the sheet. But the specification still expects you to know and use everyday rules that are not on it, for example the area of a triangle, arc length and sector area, speed, density and pressure, y=mx+cy = mx + c, percentage change and the exact trigonometric values. Higher students also need frequency density, perpendicular gradients and the equation of a circle.

Sources

Checked against these documents on 18 October 2026. Pearson's own Exam Aid is the final word: read it for your tier before the exam.