Edexcel A Level maths formula booklet (9MA0)

This page covers Pearson Edexcel A Level Mathematics 9MA0, using the booklet Mathematical Formulae and Statistical Tables and Appendix 1 of the specification, which lists what you must recall. Use it to tick off what you can find in the exam and to build your memory list. Edexcel International A Level and AQA A Level Maths booklets are similar, with the differences named in the last section.

Board	Official document
Pearson Edexcel A Level Mathematics 9MA0 (main board)	Mathematical Formulae and Statistical Tables, Issue 1, July 2017 (Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics, code P54458A)
Pearson Edexcel A Level Mathematics 9MA0 specification	Specification Issue 4, February 2020, Appendix 1: Formulae
Pearson Edexcel International A Level Mathematics	Mathematical Formulae and Statistical Tables, Issue 2, January 2021
AQA A Level Mathematics 7357	Formulae for A-level Mathematics, v1.2, August 2017

In the booklet means the formula is printed in the official booklet or sheet in the exam; Learn it means students must recall it.

Algebra, sequences and series

The booklet prints the series sums and both binomial expansions, but not the nth term formulas.

Formula	Equation	In the exam
Binomial expansion, positive integer nn is a positive integer. The binomial coefficient is also written nCr.In the booklet	$(a + b)^{n} = a^{n} + (1 n) a^{n - 1} b + (2 n) a^{n - 2} b^{2} + \dots + (r n) a^{n - r} b^{r} + \dots + b^{n}$	In the booklet
Binomial coefficientIn the booklet	$(r n) =^{n} C_{r} = \frac{n !}{r ! ( n - r )!}$	In the booklet
Binomial expansion, any nValid for \|x\| < 1 and any real n. For (a + bx)ⁿ, take out aⁿ first.In the booklet	$(1 + x)^{n} = 1 + n x + \frac{n ( n - 1 )}{1 \times 2} x^{2} + \dots + \frac{n ( n - 1 ) \dots ( n - r + 1 )}{1 \times 2 \times \dots \times r} x^{r} + \dots$	In the booklet
Arithmetic series, sum of n termsa is the first term, d the common difference, l the last term.In the booklet	$S_{n} = \frac{1}{2} n (a + l) = \frac{1}{2} n [2 a + (n - 1) d]$	In the booklet
Geometric series, sum of n termsr is the common ratio.In the booklet	$S_{n} = \frac{a ( 1 - r ^{n} )}{1 - r}$	In the booklet
Geometric series, sum to infinityOnly valid when the series converges.In the booklet	$S_{\infty} = \frac{a}{1 - r} for ∣ r ∣ < 1$	In the booklet
Arithmetic progression, nth termLearn it	$u_{n} = a + (n - 1) d$	Learn it
Geometric progression, nth termLearn it	$u_{n} = a r^{n - 1}$	Learn it

Quadratics, indices and logarithms

Only the change of base and the exponential identity are printed. The log laws are not.

Formula	Equation	In the exam
Quadratic formulaFor ax²+bx+c=0. Not in the booklet.Learn it	$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$	Learn it
Laws of indicesLearn it	$a^{x} a^{y} = a^{x + y}, a^{x} \div a^{y} = a^{x - y}, (a^{x})^{y} = a^{x y}$	Learn it
Change of baseIn the booklet	$lo g_{a} x = \frac{l o g _{b} x}{l o g _{b} a}$	In the booklet
Exponential identityIn the booklet	$e^{x l n a} = a^{x}$	In the booklet
Definition of a logarithmLearn it	$x = a^{n} ⟺ n = lo g_{a} x (a > 0, x > 0)$	Learn it
Sum and difference of logsLearn it	$lo g_{a} x + lo g_{a} y = lo g_{a} (x y), lo g_{a} x - lo g_{a} y = lo g_{a} (\frac{x}{y})$	Learn it
Power law of logsLearn it	$k lo g_{a} x = lo g_{a} (x^{k})$	Learn it

Trigonometry

The addition and sum to product identities are printed. The sine rule, cosine rule and double angle identities are not.

Formula	Equation	In the exam
Sine additionIn the booklet	$sin (A \pm B) = sin A cos B \pm cos A sin B$	In the booklet
Cosine additionNote the sign flips.In the booklet	$cos (A \pm B) = cos A cos B \mp sin A sin B$	In the booklet
Tangent additionIn the booklet	$tan (A \pm B) = \frac{t a n A \pm t a n B}{1 \mp t a n A t a n B} (A \pm B \neq = (k + \frac{1}{2}) π)$	In the booklet
Sum of sinesIn the booklet	$sin A + sin B = 2 sin \frac{A + B}{2} cos \frac{A - B}{2}$	In the booklet
Difference of sinesIn the booklet	$sin A - sin B = 2 cos \frac{A + B}{2} sin \frac{A - B}{2}$	In the booklet
Sum of cosinesIn the booklet	$cos A + cos B = 2 cos \frac{A + B}{2} cos \frac{A - B}{2}$	In the booklet
Difference of cosinesIn the booklet	$cos A - cos B = - 2 sin \frac{A + B}{2} sin \frac{A - B}{2}$	In the booklet
Small angle approximationsOnly when θ is in radians.In the booklet	$sin θ \approx θ, cos θ \approx 1 - \frac{θ ^{2}}{2}, tan θ \approx θ$	In the booklet
Sine ruleLearn it	$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$	Learn it
Cosine ruleLearn it	$a^{2} = b^{2} + c^{2} - 2 b c cos A$	Learn it
Area of a triangleLearn it	$Area = \frac{1}{2} ab sin C$	Learn it
Pythagorean identitiesLearn it	$cos^{2} A + sin^{2} A = 1, sec^{2} A = 1 + tan^{2} A, cosec^{2} A = 1 + cot^{2} A$	Learn it
Double angle identitiesLearn it	$sin 2 A = 2 sin A cos A, cos 2 A = cos^{2} A - sin^{2} A, tan 2 A = \frac{2 t a n A}{1 - t a n ^{2} A}$	Learn it
Arc length and sector areaAngle θ in radians.Learn it	$s = r θ, A = \frac{1}{2} r^{2} θ$	Learn it

Differentiation

The booklet prints first principles, the reciprocal trig derivatives and the quotient rule. The basic derivatives, product rule and chain rule are not printed.

Formula	Equation	In the exam
First principlesIn the booklet	$f^{'} (x) = lim_{h \to 0} \frac{f ( x + h ) - f ( x )}{h}$	In the booklet
TangentIn the booklet	$f (x) = tan k x \Rightarrow f^{'} (x) = k sec^{2} k x$	In the booklet
SecantIn the booklet	$f (x) = sec k x \Rightarrow f^{'} (x) = k sec k x tan k x$	In the booklet
CotangentIn the booklet	$f (x) = cot k x \Rightarrow f^{'} (x) = - k cosec^{2} k x$	In the booklet
CosecantIn the booklet	$f (x) = cosec k x \Rightarrow f^{'} (x) = - k cosec k x cot k x$	In the booklet
Quotient ruleIn the booklet	$\frac{d}{d x} (\frac{f ( x )}{g ( x )}) = \frac{f ^{'} ( x ) g ( x ) - f ( x ) g ^{'} ( x )}{( g ( x ) ) ^{2}}$	In the booklet
Power of xLearn it	$\frac{d}{d x} (x^{n}) = n x^{n - 1}$	Learn it
Sine and cosineLearn it	$\frac{d}{d x} (sin k x) = k cos k x, \frac{d}{d x} (cos k x) = - k sin k x$	Learn it
Exponential and logLearn it	$\frac{d}{d x} (e^{k x}) = k e^{k x}, \frac{d}{d x} (ln x) = \frac{1}{x}$	Learn it
Exponential with base aStated in the specification guidance as a result students are expected to know.Learn it	$\frac{d}{d x} (a^{k x}) = k a^{k x} ln a$	Learn it
Sum ruleLearn it	$\frac{d}{d x} [f (x) + g (x)] = f^{'} (x) + g^{'} (x)$	Learn it
Product ruleLearn it	$\frac{d}{d x} [f (x) g (x)] = f^{'} (x) g (x) + f (x) g^{'} (x)$	Learn it
Chain ruleLearn it	$\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) g^{'} (x)$	Learn it

Integration

The booklet prints the trig integrals and integration by parts. The standard integrals of powers, sine, cosine and exponentials are not printed.

Formula	Equation	In the exam
Secant squaredIn the booklet	$\int sec^{2} k x d x = \frac{1}{k} tan k x + c$	In the booklet
TangentIn the booklet	$\int tan k x d x = \frac{1}{k} ln ∣ sec k x ∣ + c$	In the booklet
CotangentIn the booklet	$\int cot k x d x = \frac{1}{k} ln ∣ sin k x ∣ + c$	In the booklet
CosecantTwo equivalent forms are printed.In the booklet	$\int cosec k x d x = - \frac{1}{k} ln ∣ cosec k x + cot k x ∣ + c = \frac{1}{k} ln tan (\frac{1}{2} k x) + c$	In the booklet
SecantTwo equivalent forms are printed.In the booklet	$\int sec k x d x = \frac{1}{k} ln ∣ sec k x + tan k x ∣ + c = \frac{1}{k} ln tan (\frac{1}{2} k x + \frac{1}{4} π) + c$	In the booklet
Integration by partsIn the booklet	$\int u \frac{d v}{d x} d x = uv - \int v \frac{d u}{d x} d x$	In the booklet
Power of xLearn it	$\int x^{n} d x = \frac{1}{n + 1} x^{n + 1} + c (n \neq = - 1)$	Learn it
Cosine and sineLearn it	$\int cos k x d x = \frac{1}{k} sin k x + c, \int sin k x d x = - \frac{1}{k} cos k x + c$	Learn it
Exponential and 1 over xLearn it	$\int e^{k x} d x = \frac{1}{k} e^{k x} + c, \int \frac{1}{x} d x = ln ∣ x ∣ + c (x \neq = 0)$	Learn it
Reverse chain ruleLearn it	$\int f^{'} (g (x)) g^{'} (x) d x = f (g (x)) + c$	Learn it
Area under a curveLearn it	$Area = \int_{a}^{b} y d x (y \geq 0)$	Learn it

Numerical methods

Formula	Equation	In the exam
Trapezium rulen is the number of strips, so there are n+1 ordinates.In the booklet	$\int_{a}^{b} y d x \approx \frac{1}{2} h {(y_{0} + y_{n}) + 2 (y_{1} + y_{2} + \dots + y_{n - 1})}, h = \frac{b - a}{n}$	In the booklet
Newton-Raphson iterationSolves f(x)=0. It fails if f′(x_n) is zero or close to zero.In the booklet	$x_{n + 1} = x_{n} - \frac{f ( x _{n} )}{f ^{'} ( x _{n} )}$	In the booklet

Coordinate geometry, vectors and mensuration

Only the sphere and cone areas are printed. Everything else here is recall.

Formula	Equation	In the exam
Surface area of a sphereIn the booklet	$A = 4 π r^{2}$	In the booklet
Curved surface area of a coneIn the booklet	$A = π r \times slant height$	In the booklet
CircleLearn it	$C = 2 π r = π d, A = π r^{2}$	Learn it
Trapeziuma and b are the parallel sides, h the perpendicular distance between them.Learn it	$Area = \frac{1}{2} (a + b) h$	Learn it
PrismLearn it	$Volume = area of cross section \times length$	Learn it
Equation of a straight lineGradient m, passing through (x1, y1).Learn it	$y - y_{1} = m (x - x_{1})$	Learn it
Perpendicular linesLearn it	$m_{1} m_{2} = - 1$	Learn it
Magnitude of a vectorLearn it	$∣ x i + y j + z k ∣ = x^{2} + y^{2} + z^{2}$	Learn it

Statistics

The booklet also prints the binomial cumulative tables, normal percentage points, product moment correlation critical values and random numbers.

Formula	Equation	In the exam
ComplementIn the booklet	$P (A^{'}) = 1 - P (A)$	In the booklet
Addition lawIn the booklet	$P (A \cup B) = P (A) + P (B) - P (A \cap B)$	In the booklet
Multiplication lawIn the booklet	$P (A \cap B) = P (A) P (B ∣ A)$	In the booklet
Conditional probability (Bayes form)In the booklet	$P (A ∣ B) = \frac{P ( B ∣ A ) P ( A )}{P ( B ∣ A ) P ( A ) + P ( B ∣ A ^{'} ) P ( A ^{'} )}$	In the booklet
Independent eventsIn the booklet	$P (B ∣ A) = P (B), P (A ∣ B) = P (A), P (A \cap B) = P (A) P (B)$	In the booklet
Standard deviationIn the booklet	$Standard deviation = Variance$	In the booklet
Interquartile rangeIn the booklet	$IQR = Q_{3} - Q_{1}$	In the booklet
SxxIn the booklet	$S_{xx} = \sum (x_{i} - \overset{x}{ˉ})^{2} = \sum x_{i}^{2} - \frac{( \sum x _{i} ) ^{2}}{n}$	In the booklet
Standard deviation from SxxIn the booklet	$σ = \frac{S _{xx}}{n} or \frac{\sum x ^{2}}{n} - \overset{x}{ˉ}^{2}$	In the booklet
Binomial distribution, probabilityX is B(n, p).In the booklet	$P (X = x) = (x n) p^{x} (1 - p)^{n - x}$	In the booklet
Binomial distribution, mean and varianceIn the booklet	$E (X) = n p, Var (X) = n p (1 - p)$	In the booklet
Sample mean of a normal populationFor a random sample of n observations from N(μ, σ²).In the booklet	$\frac{X ˉ - μ}{σ / n} \sim N (0, 1)$	In the booklet
Mean of a data setLearn it	$\overset{x}{ˉ} = \frac{\sum x}{n} = \frac{\sum f x}{\sum f}$	Learn it
Standardising a normal variableLearn it	$Z = \frac{X - μ}{σ} where X \sim N (μ, σ^{2})$	Learn it

Mechanics

Only the constant acceleration equations are printed. The force and variable acceleration results are not.

Formula	Equation	In the exam
Constant acceleration: velocityu initial velocity, v final velocity, a acceleration, t time, s displacement.In the booklet	$v = u + a t$	In the booklet
Constant acceleration: displacement from uIn the booklet	$s = u t + \frac{1}{2} a t^{2}$	In the booklet
Constant acceleration: displacement from vIn the booklet	$s = v t - \frac{1}{2} a t^{2}$	In the booklet
Constant acceleration: no timeIn the booklet	$v^{2} = u^{2} + 2 a s$	In the booklet
Constant acceleration: average velocityIn the booklet	$s = \frac{1}{2} (u + v) t$	In the booklet
Variable accelerationUse when acceleration changes with time. Do not use the equations of constant acceleration.Learn it	$v = \frac{d r}{d t}, a = \frac{d v}{d t} = \frac{d ^{2} r}{d t ^{2}}, r = \int v d t, v = \int a d t$	Learn it
Newton's second lawLearn it	$F = ma$	Learn it
Weightg is 9.8 m s⁻² unless the question says otherwise.Learn it	$W = m g$	Learn it
FrictionEquality when the object is moving or on the point of moving (limiting friction).Learn it	$F \leq μ R$	Learn it
Moment of a forceNot listed in the specification formulae, but needed for moments questions.Learn it	$Moment = force \times perpendicular distance$	Learn it

How the Edexcel IAL and AQA booklets differ

All three are the same course in spirit but the booklets are not identical. Check the one printed for your exam. The 'given' column below refers to the Edexcel 9MA0 booklet.

Formula	Equation	In the exam
Cosine rulePrinted in the Edexcel IAL booklet (Pure P1). Not printed in the 9MA0 or AQA booklets.Learn it	$a^{2} = b^{2} + c^{2} - 2 b c cos A$	Learn it
Poisson distributionPrinted in the Edexcel IAL booklet (Statistics S2). Not part of 9MA0 A Level Mathematics.Learn it	$P (X = x) = e^{- λ} \frac{λ ^{x}}{x !}, E (X) = Var (X) = λ$	Learn it
Normal probability density functionPrinted in the Edexcel IAL booklet (Statistics S1). Not printed in the 9MA0 or AQA booklets.Learn it	$f (x) = \frac{1}{σ 2 π} e^{- \frac{1}{2} (\frac{x - μ}{σ})^{2}}$	Learn it
Integral of f dash over fPrinted in the AQA booklet. Not printed in the 9MA0 booklet.Learn it	$\int \frac{f ^{'} ( x )}{f ( x )} d x = ln ∣ f (x) ∣ + c$	Learn it
Change of base for logsIn the 9MA0 and IAL booklets. Not in the AQA booklet.In the booklet	$lo g_{a} x = \frac{l o g _{b} x}{l o g _{b} a}$	In the booklet
Sum to product identitiesIn the 9MA0 and IAL booklets. Not in the AQA booklet.In the booklet	$sin A + sin B = 2 sin \frac{A + B}{2} cos \frac{A - B}{2}$	In the booklet
Small angle approximationsIn the 9MA0 and AQA booklets. Not found in the IAL booklet.In the booklet	$sin θ \approx θ, cos θ \approx 1 - \frac{θ ^{2}}{2}$	In the booklet

Learn these: not in the booklet

Quadratic formula $x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
Laws of indices $a^{x} a^{y} = a^{x + y}, a^{x} \div a^{y} = a^{x - y}, (a^{x})^{y} = a^{x y}$
Laws of logarithms $lo g_{a} x + lo g_{a} y = lo g_{a} (x y), lo g_{a} x - lo g_{a} y = lo g_{a} (x / y), k lo g_{a} x = lo g_{a} x^{k}$
Sine rule $\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$
Cosine rule $a^{2} = b^{2} + c^{2} - 2 b c cos A$
Area of a triangle $\frac{1}{2} ab sin C$
Double angle $sin 2 A = 2 sin A cos A, cos 2 A = cos^{2} A - sin^{2} A, tan 2 A = \frac{2 t a n A}{1 - t a n ^{2} A}$
Pythagorean identities $cos^{2} A + sin^{2} A = 1, sec^{2} A = 1 + tan^{2} A, cosec^{2} A = 1 + cot^{2} A$
Arc length and sector area (radians) $s = r θ, A = \frac{1}{2} r^{2} θ$
nth terms $u_{n} = a + (n - 1) d, u_{n} = a r^{n - 1}$
Straight line $y - y_{1} = m (x - x_{1}), m_{1} m_{2} = - 1$ The second result is the condition for perpendicular lines.
Derivatives $\frac{d}{d x} x^{n} = n x^{n - 1}, \frac{d}{d x} sin k x = k cos k x, \frac{d}{d x} cos k x = - k sin k x, \frac{d}{d x} e^{k x} = k e^{k x}, \frac{d}{d x} ln x = \frac{1}{x}, \frac{d}{d x} a^{k x} = k a^{k x} ln a$
Product and chain rules $(f g)^{'} = f^{'} g + f g^{'}, \frac{d}{d x} f (g (x)) = f^{'} (g (x)) g^{'} (x)$
Integrals $\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + c, \int cos k x d x = \frac{s i n k x}{k} + c, \int sin k x d x = - \frac{c o s k x}{k} + c, \int e^{k x} d x = \frac{e ^{k x}}{k} + c, \int \frac{1}{x} d x = ln ∣ x ∣ + c$
Standardising $Z = \frac{X - μ}{σ}; m e an \overset{x}{ˉ} = \frac{\sum f x}{\sum f}$
Mechanics $F = ma, W = m g, F \leq μ R, v = \frac{d r}{d t}, a = \frac{d v}{d t}$

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.

AQA2 booklets

A Level Maths 7357PDF, 5 pages, 0.5 MB
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A Level Further Maths 7367PDF, 13 pages, 1.1 MB
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Edexcel1 booklet

AS and A Level Maths and Further Maths 8MA0, 9MA0, 8FM0, 9FM0PDF, 29 pages, 2.6 MB
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Edexcel International (IAL)1 booklet

International AS and A Level Maths, Further Maths and Pure MathsPDF, 23 pages, 2.3 MB
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Cambridge1 booklet

AS and A Level Maths 9709 and Further Maths 9231 MF19PDF, 16 pages, 1.3 MB
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OxfordAQA1 booklet

International AS and A Level Maths 9660PDF, 29 pages, 4.1 MB
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How to use the formula sheet in the exam

Learn the not-given list first: the booklet will not rescue you on the quadratic formula or the cosine rule.
Open the booklet at the start and mark the pages for series, trig identities and integrals so you can find them in seconds.
Check signs for cos(A plus or minus B) and the tan addition formula. The sign flips between the two sides.
Use the trapezium rule and Newton-Raphson formulae from the booklet, then write each substitution on its own line to protect method marks.
For mechanics, check whether acceleration is constant before choosing the SUVAT equations. If it varies, differentiate or integrate instead.

Common questions

Is there a formula sheet in the Edexcel A Level Maths exam?

Yes. You are given the booklet Mathematical Formulae and Statistical Tables in Papers 1, 2 and 3. It also holds the statistical tables and cannot be removed from the exam room.

Is the quadratic formula in the A Level maths formula booklet?

No. Edexcel lists it in Appendix 1 of the specification as a formula you must recall, along with the log laws, sine and cosine rules, double angle identities and basic derivatives and integrals.

Are the SUVAT equations given in A Level Maths?

Yes, the five constant acceleration equations are printed in the mechanics section. The variable acceleration results, F = ma and F ≤ μR are not printed, so learn them.

Which statistical tables are in the Edexcel 9MA0 booklet?

The ones needed for A Level Mathematics are the binomial cumulative distribution function, percentage points of the normal distribution, critical values for the product moment correlation coefficient and random numbers.

Is the AQA or Edexcel IAL formula booklet the same?

Mostly, but not exactly. AQA's booklet is shorter and has no log, sum to product or probability complement formulae, while the IAL booklet is split by unit and adds items such as the cosine rule and Poisson distribution.

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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.

Edexcel A Level maths formula booklet: what is given and what to learn

In short