The A-Level Maths Formula Booklet: What's Given and What You Must M…

Every A-Level Maths exam board provides a formula booklet in the exam room, and one of the most common mistakes students make is assuming it contains more than it actually does. Relying on a formula that isn't there — or wasting time searching for one that you should already know — costs marks and time you cannot afford. This guide sets out, topic by topic, what tends to be provided and what you need to have memorised cold.

Note that the exact contents vary slightly between exam boards (AQA, Edexcel, OCR, WJEC), so you should always check your own board's formula booklet directly before the exam. This article describes the general pattern shared across boards to help you build a memorisation checklist.

Why this distinction matters

The formula booklet is designed to hold results that are long, easily misquoted, or not central to demonstrating understanding — things like the quadratic formula's variants for more complex cases, or standard distribution formulae. It deliberately does not include the basic building blocks that the specification expects you to know automatically, because those are considered core knowledge you should be able to produce instantly, without flicking through pages, under exam time pressure.

Pure mathematics: what's usually given

The formula booklet typically provides:

The binomial expansion formula for (1 + x)^n with the general term
Standard trigonometric identities in their compound and double-angle forms (sin(A±B), cos(A±B), tan(A±B), double angle formulae)
The formulae for the sum of arithmetic and geometric series
Some standard integrals and derivatives, often listed in a table (usually the less obvious ones, such as tan x, sec²x, and certain forms involving 1/x)
Small angle approximations for sin θ, cos θ and tan θ
The remainder and factor theorem statement in some specifications

Pure mathematics: what you must memorise

You are expected to know without looking:

The quadratic formula and how to complete the square
Laws of indices and logarithms (including change of base)
Basic differentiation and integration rules for polynomials, e^x, and ln x
The derivatives and integrals of sin x and cos x (though some boards list higher-order trig derivatives in the booklet, the basic ones are expected knowledge)
Chain rule, product rule and quotient rule (the booklet gives the general formula but you need to know how and when to apply each)
Definitions of the discriminant and how it relates to the nature of roots
Circle theorems and coordinate geometry formulae such as the equation of a circle, gradient of a line, and distance between two points
The basic Pythagorean trig identity, sin²θ + cos²θ = 1

This is exactly the kind of area where our guide to choosing the right integration method becomes useful, because knowing which standard integral applies before reaching for the booklet saves valuable time.

Statistics: what's usually given

Formulae for the product moment correlation coefficient
The standard normal distribution table (or you're expected to use your calculator, depending on board)
Formulae linking binomial and Poisson distributions to their mean and variance
Hypothesis testing critical value formulae in some cases
The formula for the equation of a regression line

Statistics: what you must memorise

How to calculate mean, variance and standard deviation from raw or grouped data
The conditions under which the binomial distribution is a valid model
How to interpret a hypothesis test conclusion in context (this is a skill, not a formula, but it is one of the most heavily penalised areas when done poorly)
Basic probability rules: addition rule, multiplication rule, conditional probability
How to read and use large data set contexts if your board includes one

Mechanics: what's usually given

Formulae for the SUVAT equations of motion (these are typically provided, though many students memorise them anyway because they're used so often)
Formulae for the coefficient of friction (F = μR) in some specifications
Centre of mass formulae for standard shapes in some specifications

Mechanics: what you must memorise

Newton's second law, F = ma, and how to construct force diagrams
How to resolve forces into perpendicular components (horizontal/vertical or parallel/perpendicular to a slope)
The relationship between weight, mass and g (W = mg)
How moments work: the principle that for equilibrium, sum of clockwise moments equals sum of anticlockwise moments
How to set up and solve problems involving connected particles and pulleys

Our mechanics revision guide walks through each of these question types with worked approaches, which is a natural next step once you know exactly which formulae you need to bring to the table yourself.

A practical way to learn the memorised set

Trying to memorise a long list the night before an exam rarely works. Instead:

Build your own one-page summary. Writing out the formulae you must know by hand, rather than copying and pasting, embeds them far better than passive reading.
Test yourself blind. Cover your summary sheet and try to reproduce it from memory, checking only afterwards. Repeat this every few days rather than once.
Use formulae inside actual problems, not in isolation. Memorising sin²θ + cos²θ = 1 as an abstract fact is far weaker than seeing it appear naturally while simplifying a trigonometric expression in a real question from past papers.
Time yourself finding things in the booklet. During timed practice papers, practise physically locating the formulae that are provided so that on exam day you aren't hunting through unfamiliar pages for the first time.
Revisit the list on a schedule, not just once. A revision timetable that schedules short, spaced repetitions of your formula list across several weeks will embed it far more reliably than a single cramming session.

Formula booklet vs mark scheme expectations

It's worth noting that even when a formula is given in the booklet, you are still expected to know how to apply it correctly and interpret the output. Examiners' reports consistently highlight cases where students quoted the correct formula from the booklet but substituted values incorrectly or misinterpreted what the result meant in context — particularly in hypothesis testing and mechanics. Memorising isn't just about the formula itself; it's about understanding when and how each one is used, which is best built through consistent practice with past papers and resources rather than by flashcard memorisation alone.

If you find that despite learning the right formulae, you still lose marks applying them under exam conditions, that's usually a sign you need more guided practice interpreting results — a tutor through A-Level Maths Tutoring can work through past exam questions with you and pinpoint exactly where application, rather than recall, is breaking down.

Takeaway

The formula booklet is a safety net for long or easily-misquoted results, not a substitute for core knowledge. Build a clear list, by topic, of what your specific exam board provides and what it doesn't, memorise the "must-know" list through active recall and spaced repetition, and practise applying both sets of formulae inside real exam questions from past papers so that recall becomes automatic rather than a source of exam-day panic.

Checking your specific exam board's booklet

Because the exact split between provided and memorised formulae differs slightly between AQA, Edexcel, OCR and WJEC, it is worth downloading your own board's formula booklet directly from their website early in your revision, rather than relying on generic advice alone. Print it out and annotate it: highlight the formulae you already know instinctively in one colour, and the ones you regularly need to check in another. This turns a passive reference document into an active revision tool, and it also means that on exam day, you already know roughly where in the booklet to find each result rather than searching from scratch.

It's also worth comparing your annotated booklet against a handful of past papers to see how frequently each provided formula actually appears in questions. Some formulae in the booklet are used in almost every paper (the binomial expansion, standard integrals), while others appear rarely. Prioritise practising the ones that appear often, since fluency with those has a disproportionate effect on your overall mark, even though technically all of them are "given" to you.

Common misconceptions about the formula booklet

A few misconceptions come up repeatedly among students preparing for these exams:

"If it's in the booklet, I don't need to understand it." Understanding when and how to apply a formula is a separate skill from being able to read it off a page, and it is this application skill that is actually assessed.
"The booklet has everything I need for mechanics." In practice, many of the most commonly tested mechanics relationships — Newton's second law, resolving forces, the definition of moments — are not formally listed as formulae in the booklet at all, because they are considered core conceptual knowledge rather than results to be quoted.
"I can look things up quickly enough in the exam, so I don't need to memorise anything extra." Time pressure in a real exam is far higher than when practising at home, and repeatedly flicking through a multi-page booklet during a timed paper is a significant and avoidable time cost across the full exam.

Avoiding these misconceptions early in your revision, and testing yourself honestly against them, will save considerable time in the final weeks before the exam, when your focus should be on refining technique using past papers rather than still working out which formulae you actually know.