Binomial Expansion (|x| < 1)
For non-integer n, expansion valid for |x| < 1. Remember to state range.
(1 + x)^n = 1 + nx + n(n − 1)x²/2! + n(n − 1)(n − 2)x³/3! + ⋯ Edexcel International A Level WMA01/WMA02/WMA03
🧮 Edexcel International A Level Maths Formula Sheet 2025
Pure maths, mechanics and statistics formulas aligned to the Edexcel International A Level syllabus — summarised for Paper 1–4 preparation.
Pure Mathematics Mechanics Statistics
Everything You Need for Edexcel A Level Mathematics
Whether you are sitting the AS or full A Level, this formula sheet organises differentiation, integration, series, vectors, kinematics and probability formulas with short reminders to help you avoid common mistakes.
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Pure maths identities with exam-ready notes
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Mechanics equations with vector form reminders
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Statistics formulas for discrete and continuous models
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Tips to pair formulas with Edexcel command words
Algebra, Trigonometry & Series
Arithmetic & Geometric Progressions
a first term, d common difference, r common ratio, uₙ nth term, Sₙ sum to n terms.
Arithmetic nth term
uₙ = a + (n − 1)d Arithmetic sum
Sₙ = n/2 [2a + (n − 1)d] Geometric nth term
uₙ = ar^{n−1} Geometric sum (finite)
Sₙ = a(1 − rⁿ)/(1 − r) Geometric sum (|r| < 1)
S∞ = a/(1 − r) Trigonometric Identities
x angle in radians unless stated; A, B general angles.
sin²x + cos²x = 1 1 + tan²x = sec²x 1 + cot²x = cosec²x sin(A ± B) = sinA cosB ± cosA sinB cos(A ± B) = cosA cosB ∓ sinA sinB cos2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x Radian Measure
θ in radians. Applicable when |θ| is small.
Arc length
s = rθ Sector area
A = ½ r²θ Small angle approximations
sinθ ≈ θ, tanθ ≈ θ, cosθ ≈ 1 − θ²/2 Differentiation & Integration
Core Rules
a constant multiplier, n real power, x differentiation variable.
d(xⁿ)/dx = nx^{n−1} d(e^{ax})/dx = ae^{ax} d(ln x)/dx = 1/x d(sin ax)/dx = a cos ax d(cos ax)/dx = −a sin ax d(tan ax)/dx = a sec² ax Product & Chain Rule
u and v differentiable functions of x; y dependent variable; intermediate variable u used in chain rule.
Product
d(uv)/dx = u dv/dx + v du/dx Chain
dy/dx = dy/du × du/dx Quotient
d(u/v)/dx = (v du/dx − u dv/dx) / v² Integration Basics
a constant, C integration constant, x integration variable.
∫ xⁿ dx = x^{n+1}/(n + 1) + C (n ≠ −1) ∫ e^{ax} dx = (1/a) e^{ax} + C ∫ 1/x dx = ln|x| + C ∫ sin ax dx = −(1/a) cos ax + C ∫ cos ax dx = (1/a) sin ax + C Definite Integrals & Area
Sketch functions to ensure correct limits and order.
Fundamental Theorem
∫ₐᵇ f'(x) dx = f(b) − f(a) Area between curves
Area = ∫ₐᵇ [y_upper − y_lower] dx Differential Equations
Separate variables where possible: ∫ (1/g(y)) dy = ∫ f(x) dx + C.
Vectors & Coordinate Geometry
Vector Basics
a, b vectors with components a₁,a₂,a₃ etc.; |a| magnitude; d direction vector; t scalar parameter.
Magnitude
|a| = √(a₁² + a₂² + a₃²) Unit vector
â = a / |a| Scalar (dot) product
a · b = |a||b| cos θ Vector equation of line
r = a + t d Planes
n is normal vector; a is position vector on plane.
Cartesian form
r · n = a · n General equation
ax + by + cz = d Distance & Angle
Points use coordinates (x₁,y₁,z₁) etc.; d₁, d₂ direction vectors; n plane normal.
Distance between points
√[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²] Angle between lines
cos θ = (d₁ · d₂) / (|d₁||d₂|) Angle between line & plane
sin θ = (|d · n|)/(|d||n|) Mechanics: Kinematics & Forces
Use vector notation for displacement, velocity and acceleration where appropriate.
Equations of Motion (constant acceleration)
v = final velocity, u = initial velocity, a = acceleration, s = displacement.
v = u + at s = ut + ½ at² v² = u² + 2as s = ½ (u + v)t Newton's Laws & Resultant Forces
F resultant force, m mass, g gravitational field strength, μ coefficient of friction, R normal reaction.
Second Law
F = ma Weight
W = mg Friction
F_f = μR Momentum & Impulse
m mass, v velocity, Δ(mv) change in momentum, F applied force, t time interval. For collisions, resolve along line of centres and apply restitution if given.
Momentum = mv Impulse = Ft = Δ(mv) Work, Energy & Power
F constant force, d displacement along force, θ angle between directions, m mass, v speed, g gravitational field strength.
Kinetic Energy
KE = ½ mv² Gravitational Potential Energy
GPE = mgh Work done by constant force
W = Fd cos θ Power
P = Work / Time = Fv Statistics & Probability
Measures of Location & Spread
x observed value, f frequency, x̄ mean, σ standard deviation.
Mean (discrete)
x̄ = Σ (x f) / Σ f Variance
σ² = Σ f(x − x̄)² / Σ f Standard Deviation
σ = √σ² Probability Rules
P( ) denotes probability; A, B events; ∩ intersection, ∪ union.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) Conditional probability: P(A|B) = P(A ∩ B) / P(B) Mutually exclusive: P(A ∩ B) = 0 Binomial Distribution
n number of trials, r successful outcomes, p probability of success on each trial. Requires fixed n, two outcomes, constant p, independence.
Probability
P(X = r) = C(n, r) p^r (1 − p)^{n − r} Mean
E(X) = np Variance
Var(X) = np(1 − p) Normal Distribution
x data value, μ population mean, σ standard deviation, z standardised score. Use tables for Φ(z); sketch and shade region before calculating probabilities.
Standardisation
z = (x − μ) / σ Correlation & Regression
n number of (x,y) pairs; Σ sums across data; r product moment correlation coefficient; a intercept, b slope.
Product moment correlation
r = [nΣxy − (Σx)(Σy)] / √{[nΣx² − (Σx)²][nΣy² − (Σy)²]} Least squares regression
y = a + bx, b = [nΣxy − (Σx)(Σy)] / [nΣx² − (Σx)²] How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Quote Formula, Then Apply
Edexcel examiners award method marks when you state the relevant formula before substitution — especially in integration and statistics questions.
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Sketch for Sign Checks
Draw quick graphs or motion diagrams to confirm limits, signs and directions before plugging values into calculus or mechanics formulas.
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Link Papers Together
Pure maths often underpins mechanics or statistics parts. Note which pure topics feed into applied questions to save revision time.
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Rehearse Calculator Workflow
Practise entering regression, normal distribution and vector calculations on your calculator so you can reproduce them quickly in the exam.
Perfect Your A Level Maths Strategy
Train with Edexcel specialists who help you blend concise working with convincing reasoning across Papers 1–4. Custom question banks and feedback accelerate your score gains.
References the Edexcel International AS & A Level Mathematics (WMA01/WMA02/WMA03) specification including Pure Mathematics, Mechanics, and Statistics.
State assumptions (e.g., light string, particle model, normal approximation conditions) whenever you apply these formulas in long-form answers.