Learn Maths with IbrahimOnline Maths & Science Tuition
Free Formula Sheet

Edexcel A Level Maths Formula Sheet

Every formula in the Pearson Edexcel A Level Mathematics (9MA0) formulae booklet, plus every formula students must learn by heart for pure maths, statistics and mechanics. Read it here or download the PDF.

At a Glance

Pearson Edexcel A Level Mathematics

A formulae booklet is provided in every paper, and a calculator is allowed. This page shows exactly what is on it, and the formulas that are not given, which students most often forget.

Given in the Exam22 formulas in the booklet
Learn by Heart21 formulas to learn, the same for every board
Read it online ↓Edexcel A Level revision checklist →
Formula Sheet

Edexcel A Level Maths Formulas

Everything in the formulae booklet, grouped into pure maths, mechanics and statistics, then the formulas you must learn.

1Given in Your Exam

These formulas are in the Edexcel "Mathematical Formulae and Statistical Tables" booklet. You don't need to memorise them, but learn when and how to use each one. It also includes tables: binomial cumulative probabilities, percentage points of the normal distribution, critical values for correlation coefficients and random numbers.

Pure

Sphere and Cone
Surface area of a sphere = 4πr2
Curved surface area of a cone = πr × slant height
Arithmetic Series
Sn = 12n(a + l) = 12n[2a + (n − 1)d]
a is the first term, l the last term, d the common difference
Binomial Series
(a + b)n = an + (n1)an−1b + … + (nr)an−rbr + … + bn
(nr) = n!r!(n − r)!
For positive whole numbers n
General Binomial Expansion
(1 + x)n = 1 + nx + n(n − 1)2!x2 + … + n(n − 1)…(n − r + 1)r!xr + …
Valid for |x| < 1 when n is negative or a fraction
Logarithms and Exponentials
loga x = logb xlogb a
ex ln a = ax
Change of base
Geometric Series
Sn = a(1 − rn)1 − r
S∞ = a1 − r for |r| < 1
a is the first term, r the common ratio
Compound Angle Formulae
sin(A ± B) = sin A cos B ± cos A sin B
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) = tan A ± tan B1 ∓ tan A tan B
Sum-to-Product Formulae
sin A + sin B = 2 sin A + B2 cos A − B2
sin A − sin B = 2 cos A + B2 sin A − B2
cos A + cos B = 2 cos A + B2 cos A − B2
cos A − cos B = −2 sin A + B2 sin A − B2
Small Angle Approximations
sin θ ≈ θ
cos θ ≈ 1 − θ22
tan θ ≈ θ
θ in radians
Differentiation From First Principles
f′(x) = limh→0 f(x + h) − f(x)h
Derivatives of Trig Functions
tan kx → k sec2 kx
sec kx → k sec kx tan kx
cot kx → −k cosec2 kx
cosec kx → −k cosec kx cot kx
f(x) → f′(x)
Quotient Rule
y = uv ⇒ dydx = vdudx − udvdxv2
Standard Integrals
sec2 kx → 1ktan kx
tan kx → 1kln|sec kx|
cot kx → 1kln|sin kx|
cosec kx → −1kln|cosec kx + cot kx|
sec kx → 1kln|sec kx + tan kx|
Add + c to each
Integration by Parts
∫udvdx dx = uv − ∫vdudx dx
The Trapezium Rule
∫ab y dx ≈ h2{(y0 + yn) + 2(y1 + … + yn−1)}
h = b − an
Newton–Raphson Method
xn+1 = xn − f(xn)f′(xn)

Mechanics

Constant Acceleration (suvat)
v = u + at
s = ut + 12at2
s = vt − 12at2
s = 12(u + v)t
v2 = u2 + 2as
Motion in a straight line with constant acceleration

Statistics

Probability
P(A′) = 1 − P(A)
P(A ∩ B) = P(A)P(B|A)
P(A|B) = P(B|A)P(A)P(B|A)P(A) + P(B|A′)P(A′)
Independent: P(A ∩ B) = P(A)P(B)
Probability: A or B
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Standard Deviation and IQR
Sxx = Σ(x − x̄)2 = Σx2 − (Σx)2n
σ = √Sxxn or √Σx2n − x̄2
IQR = Q3 − Q1
The Binomial Distribution
If X ~ B(n, p):
P(X = x) = (nx)px(1 − p)n−x
Mean = np
Variance = np(1 − p)
Sample Mean From a Normal Distribution
X̄ ~ N(μ, σ2n)
X̄ − μσ/√n ~ N(0, 1)
Used in hypothesis tests for the mean

2Learn These by Heart

These are not given in the exam. Students lose marks on them every year.

Algebra and Functions

The Quadratic Formula
x = −b ± √b2 − 4ac2a
Laws of Indices
ax × ay = ax+y
ax ÷ ay = ax−y
(ax)y = axy
Laws of Logarithms
x = an ⇔ n = loga x
loga x + loga y = loga(xy)
loga x − loga y = logaxy
k loga x = loga(xk)
a > 0, x > 0
Straight Lines
y − y1 = m(x − x1)
Perpendicular: m1m2 = −1
nth Terms of Sequences
Arithmetic: un = a + (n − 1)d
Geometric: un = arn−1

Trigonometry

Sine Rule, Cosine Rule and Area
asin A = bsin B = csin C
a2 = b2 + c2 − 2bc cos A
Area = 12ab sin C
Pythagorean Identities
cos2A + sin2A ≡ 1
sec2A ≡ 1 + tan2A
cosec2A ≡ 1 + cot2A
Double Angle Formulae
sin 2A ≡ 2 sin A cos A
cos 2A ≡ cos2A − sin2A
tan 2A ≡ 2 tan A1 − tan2A
cos 2A can also be written as 2cos²A − 1 or 1 − 2sin²A
Arc Length and Sector Area
s = rθ
A = 12r2θ
θ in radians

Mensuration

Circles
C = 2πr = πd
A = πr2
Pythagoras' Theorem
c2 = a2 + b2
c is the hypotenuse
Trapezium and Prism
Area of a trapezium = 12(a + b)h
Volume of a prism = area of cross-section × length

Calculus and Vectors

Standard Derivatives
xn → nxn−1
sin kx → k cos kx
cos kx → −k sin kx
ekx → kekx
ln x → 1x
f(x) → f′(x)
Product and Chain Rules
(fg)′ = f′g + fg′
ddxf(g(x)) = f′(g(x))g′(x)
Standard Integrals
xn → xn+1n + 1 (n ≠ −1)
cos kx → 1ksin kx
sin kx → −1kcos kx
ekx → 1kekx
1x → ln|x|
Add + c to each
Reverse Chain Rule and Area
∫f′(g(x))g′(x) dx = f(g(x)) + c
Area under a curve = ∫ab y dx (y ≥ 0)
Magnitude of a Vector
|xi + yj + zk| = √x2 + y2 + z2

Mechanics

Forces and Newton's Second Law
Weight = mg
Friction: F ≤ μR
F = ma
Use g = 9.8 m s⁻² unless told otherwise
Variable Acceleration
v = drdt
a = dvdt = d2rdt2
r = ∫v dt
v = ∫a dt

Statistics

Mean
x̄ = Σxn = ΣfxΣf
Standardising a Normal Variable
Z = X − μσ, where X ~ N(μ, σ2)

Download the PDF

Different Exam Board?

Formula Sheets for Every Board

AQA A LevelFormula sheet · 7357OCR A LevelFormula sheet · H240OCR MEI A LevelFormula sheet · H640All Formula SheetsGCSE, IGCSE and A Level
Knowing the Formula Is Half the Job

Learn When and How to Use Each One

Book a free 90-minute lesson and I'll show your child how to pick the right formula and use it to get full marks.

Book Your Free Lesson

Let's Find the Right Starting Point for Your Child

Fill in the short form and we'll get back to you with available times for a free 90-minute first lesson. Prefer to talk? Message us on WhatsApp.

Email Usmathstutoringbyibrahim@gmail.com

Parent Enquiry Form

Takes under a minute. Only the starred fields are needed.

Which Subject? *
Add more detail (optional)
We usually reply within 30 minutes (9am–9pm UK time).
Book a Free 90-Minute Lesson