A-Level Maths Formula Sheet: Every Formula You Need to Know

What you're actually given in the exam

Every A-Level Maths exam comes with a formula booklet. But knowing what's in it — and what isn't — is one of the most overlooked revision advantages.

Students who don't know the formula booklet content waste time deriving things they could look up. Students who rely on it for things that aren't there panic at the wrong moment.

What the formula booklet contains

The Edexcel, AQA, and OCR formula booklets all contain similar content:

Pure Mathematics:

• Quadratic formula
• Laws of logarithms
• Trigonometric identities (including compound angle formulae: sin(A±B), cos(A±B), tan(A±B))
• Double angle formulae
• Differentiation and integration of standard functions (sin, cos, tan, eˣ, ln x)
• Integration by parts formula
• Trapezium rule

Statistics:

• Binomial probability formula
• Normal distribution standardisation formula
• Mean and variance formulae for discrete distributions

Mechanics:

• Constant acceleration equations (suvat)
• Newton's second law (F = ma)

What is NOT in the booklet (must memorise)

This is where most students fall short. These must be in your head:

Algebra:

• Factor theorem: if f(a) = 0, then (x − a) is a factor
• Sum of an arithmetic series: Sₙ = n/2(2a + (n−1)d)
• Sum of a geometric series: Sₙ = a(1 − rⁿ)/(1 − r)
• Sum to infinity: S∞ = a/(1 − r) for |r| < 1

Trigonometry:

• CAST diagram and exact values: sin30°=½, cos60°=½, tan45°=1, sin45°=cos45°=1/√2, sin60°=cos30°=√3/2
• Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ

Calculus:

• Chain rule: dy/dx = dy/du × du/dx
• Product rule: d/dx(uv) = u(dv/dx) + v(du/dx)
• Quotient rule: d/dx(u/v) = (v·du/dx − u·dv/dx)/v²
• Standard derivatives: d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x, d/dx(sin x) = cos x, d/dx(cos x) = −sin x

Vectors:

• Magnitude of vector: |ai + bj + ck| = √(a² + b² + c²)
• Dot product: a·b = |a||b|cosθ

Statistics:

• P(A∪B) = P(A) + P(B) − P(A∩B)
• P(A|B) = P(A∩B)/P(B)

The formula memorisation method that actually works

Reading formulas is not memorisation. The only method that works:

1. 1Cover the formula completely
2. 2Write it from memory on a blank sheet
3. 3Check — if wrong, understand why, don't just read it again
4. 4Space it out: test yourself on each formula 24 hours later, then 3 days, then a week

The reason most students "know" a formula but can't apply it under pressure is because they've only ever seen it — never recalled it cold. Infinity Stars practice questions require you to select and apply the right formula unprompted, which builds that automatic recall.

A-level maths formula you will almost certainly need in your exam

These appear on virtually every paper:

• Integration by parts (always at least one question)
• Binomial expansion for (1 + x)ⁿ where n is not a positive integer
• The trapezium rule
• Arc length and sector area: l = rθ, A = ½r²θ
• Logarithm change of base
• Hypothesis testing critical values (check your board's specific booklet)

Knowing these cold — not having to search the booklet — saves you 3–5 minutes per paper. Over three papers, that's 10–15 minutes of checking time.