A Level Maths Formula Sheet
This A Level maths formula sheet summarises List MF19, the list of formulae Cambridge gives in every 9709 paper, for pure maths, mechanics and probability and statistics. It ends with the mechanics and logarithm formulas you must know because they are not on MF19.
- 58 formulas
- 5 sections
- Checked 20 October 2026
MF19 Pure: mensuration and algebra
Supplied in every 9709 paper.
- Volume of a sphere
- Surface area of a sphere
- Volume of a cone or pyramid
- Curved surface area of a cone
- Arc length (θ in radians)
- Area of a sector (θ in radians)
- Quadratic formula, for ax² + bx + c = 0 (a ≠ 0)
- Arithmetic series: nth term
- Arithmetic series: sum of n terms
- Geometric series: nth term
- Geometric series: sum of n terms (r ≠ 1)
- Geometric series: sum to infinity (|r| < 1)
- Binomial expansion (n a positive integer)
- Binomial coefficient
- Binomial series (n rational, |x| < 1)
MF19 Pure: trigonometry
Identities, compound angles and double angles.
- Tangent identity
- Pythagorean identity
- Identity with sec
- Identity with cosec
- Compound angle: sine
- Compound angle: cosine
- Compound angles: tangent
- Double angle: sine
- Double angle: cosine
- Double angle: tangent
MF19 Pure: calculus and vectors
Standard derivatives and integrals; arbitrary constants are omitted.
- Derivatives of xⁿ, ln x and eˣ
- Derivatives of sin x, cos x and tan x
- Derivatives of sec x and cosec x
- Derivatives of cot x and tan⁻¹x
- Product rule
- Quotient rule
- Parametric differentiation
- Integrals of xⁿ (n ≠ −1), 1/x and eˣ
- Integrals of sin x, cos x and sec²x
- Integral of 1/(x² + a²)
- Integration by parts
- Integral of f′(x)/f(x)
- Scalar product
MF19 Mechanics and Probability & Statistics
Constant acceleration, summary statistics and probability distributions.
- Uniformly accelerated motion
- Uniformly accelerated motion
- Mean (ungrouped data)
- Standard deviation (ungrouped data)
- Discrete random variables
- Binomial distribution B(n, p)
- Binomial mean and variance
- Geometric distribution Geo(p)
- Poisson distribution Po(λ)
- Central Limit Theorem
- Unbiased estimate of variance
Not on MF19: formulas to know
The syllabus expects you to use these, but MF19 does not list them.
- Weight
- Newton's second law
- Momentum
- Kinetic and gravitational potential energy
- Power (force in the direction of motion)
- Laws of logarithms: product
- Laws of logarithms: quotient
- Laws of logarithms: power
- Chain rule
Based on List MF19, the list of formulae and statistical tables for Cambridge International AS & A Level Mathematics 9709 (Further Mathematics sections left out) (official source), checked 20 October 2026. Always check the formula list printed in your own exam paper.
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