AQA A-Level Maths Formula Booklet: What's Included and What You Must Memorise

One of the most common questions A-Level Maths students ask is: "Will this formula be given to me in the exam?" It is a fair question, because the answer makes a real difference to how you prepare. If a formula is in the booklet, you need to know how to use it. If it is not in the booklet, you need to know it from memory and know how to use it.

AQA provides a formula booklet for all A-Level Maths exams (Pure, Statistics, and Mechanics). The booklet is the same for AS and A-Level, and it is available on the AQA website so you can familiarise yourself with it before the exam. But simply knowing the booklet exists is not enough. You need to understand what is in it, what is not, and how to use it effectively under exam pressure.

This guide breaks down the AQA A-Level Maths formula booklet section by section, highlights the key formulas you must memorise, and gives you practical strategies for making the most of the booklet in the exam.

What the Formula Booklet Contains

The AQA formula booklet is organised into sections that align with the areas of the specification. Here is a summary of what you will find.

Pure Mathematics

The pure maths section of the booklet includes several important results that you do not need to memorise:

Binomial Series: The general binomial expansion for (1 + x) to the power n, where n is not a positive integer, is provided. This includes the condition that the expansion is valid for |x| < 1.

Logarithms and Exponentials: The change of base formula for logarithms is given: log_a(x) = log_b(x) / log_b(a).

Trigonometric Identities: The booklet provides several compound angle and double angle formulas:

sin(A +/- B) = sinA cosB +/- cosA sinB
cos(A +/- B) = cosA cosB -/+ sinA sinB
tan(A +/- B) = (tanA +/- tanB) / (1 -/+ tanA tanB)

Differentiation: The booklet provides differentiation from first principles definition, as well as a table of standard derivatives including tan(kx), sec(x), cot(x), cosec(x), and the results for differentiating inverse trig functions (arcsin, arccos, arctan).

Integration: A table of standard integrals is provided, including results for sec^2(kx), tan(x), cot(x), cosec(x), and sec(x). These are results that would be difficult to derive quickly in an exam, so they are given.

Numerical Methods: The trapezium rule formula is provided.

Statistics

The statistics section contains:

Probability and Statistical Distributions: The formulas for the binomial distribution and the standard normal distribution are given. The booklet also includes the relationship between the mean and variance for discrete and continuous distributions.

Statistical Tables: The booklet includes percentage points of the normal distribution, critical values for correlation coefficients, and other tables you need for hypothesis testing. You do not need to memorise these values -- they are looked up from the tables.

Mechanics

The mechanics section is relatively short:

Kinematics: The five SUVAT equations for constant acceleration are provided. This is worth noting because many students spend time memorising all five when they are actually given in the booklet.

What You Must Memorise

This is the crucial section. Everything that is not in the booklet must be committed to memory. Here are the key formulas and results you need to learn, organised by topic.

Quadratics and Algebra

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a. Although basic, this is not in the booklet.
Discriminant conditions: b^2 - 4ac > 0 (two real roots), = 0 (one repeated root), < 0 (no real roots).
Completing the square: You need to be able to do this, not just apply a formula.
Factor and remainder theorems: Know the statements and how to apply them.

Coordinate Geometry

Equation of a straight line: y - y1 = m(x - x1).
Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2).
Distance between two points: sqrt((x2 - x1)^2 + (y2 - y1)^2).
Circle equation: (x - a)^2 + (y - b)^2 = r^2.
Condition for perpendicular lines: m1 x m2 = -1.

Sequences and Series

Arithmetic series: nth term = a + (n-1)d, sum = n/2(2a + (n-1)d) or n/2(a + l).
Geometric series: nth term = ar^(n-1), sum of n terms = a(1 - r^n)/(1 - r), sum to infinity = a/(1 - r) for |r| < 1.
Sigma notation: You need to be fluent in converting between sigma notation and expanded series.

Trigonometry

The booklet gives you the compound angle formulas, but you must memorise:

Basic trig values: sin, cos, and tan of 0, 30, 45, 60, and 90 degrees (and their radian equivalents).
CAST diagram or unit circle: To determine the sign of trig functions in each quadrant.
Pythagorean identities: sin^2(x) + cos^2(x) = 1. You also need to know the derived identities: 1 + tan^2(x) = sec^2(x) and 1 + cot^2(x) = cosec^2(x).
Small angle approximations: sin(x) is approximately x, cos(x) is approximately 1 - x^2/2, tan(x) is approximately x (where x is in radians).
Reciprocal trig functions: sec(x) = 1/cos(x), cosec(x) = 1/sin(x), cot(x) = 1/tan(x).

Calculus -- Differentiation

You must memorise the standard derivatives for basic functions:

y = x^n gives dy/dx = nx^(n-1).
y = sin(x) gives dy/dx = cos(x).
y = cos(x) gives dy/dx = -sin(x).
y = e^(kx) gives dy/dx = ke^(kx).
y = ln(x) gives dy/dx = 1/x.
y = a^(kx) gives dy/dx = ka^(kx) ln(a).

You must also memorise:

Product rule: d/dx(uv) = u(dv/dx) + v(du/dx).
Quotient rule: d/dx(u/v) = (v(du/dx) - u(dv/dx)) / v^2.
Chain rule: dy/dx = dy/du x du/dx.

Note that while the product and quotient rules are fundamental tools, the booklet does not list them as standalone formulas. Relying on the booklet for these would waste valuable time and suggests a lack of fluency. Treat them as formulas you must know by heart.

Calculus -- Integration

You need to memorise the reverse of the basic differentiation results:

Integral of x^n dx = x^(n+1)/(n+1) + c (for n not equal to -1).
Integral of 1/x dx = ln|x| + c.
Integral of e^(kx) dx = (1/k)e^(kx) + c.
Integral of sin(kx) dx = -(1/k)cos(kx) + c.
Integral of cos(kx) dx = (1/k)sin(kx) + c.

You must also know:

Integration by parts: Integral of u(dv/dx) dx = uv - integral of v(du/dx) dx.
Integration by substitution: The method, not a single formula.
Trapezium rule: This is in the booklet, but you must understand how to apply it.

Vectors

Position vectors, direction vectors, and the scalar product: a.b = |a||b|cos(theta).
Condition for perpendicular vectors: a.b = 0.

Logarithms

Laws of logarithms: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), log(a^n) = n log(a).
Key results: log_a(a) = 1, log_a(1) = 0, and e^(ln x) = x.

Statistics -- Formulas to Memorise

While the booklet provides distribution formulas, you must memorise:

Mean of a frequency distribution: x-bar = sum(fx) / sum(f).
Coding formulas: How to calculate the mean and standard deviation from coded data.
Conditions for a binomial distribution: fixed number of trials, two outcomes, constant probability, independent trials.
Normal distribution standardisation: z = (x - mu) / sigma.
Conditions for using a normal approximation to a binomial: np > 5 and n(1-p) > 5, with continuity correction.
Hypothesis testing process: Defining H0 and H1, choosing significance level, calculating test statistic, comparing with critical value, stating conclusion in context.

Mechanics -- Formulas to Memorise

The SUVAT equations are in the booklet, but you must memorise:

Newton's second law: F = ma.
Weight: W = mg (typically g = 9.8 m/s^2).
Friction: F = mu R (where mu is the coefficient of friction and R is the normal reaction force).
Moments: Moment = Force x perpendicular distance from the pivot.
Resolving forces: How to resolve forces into horizontal and vertical components.

How to Use the Formula Booklet Effectively

Having the booklet in the exam is only helpful if you know how to use it well. Here are some practical tips:

Familiarise Yourself Before the Exam

Download the AQA formula booklet from the AQA website and use it regularly during your revision. By exam day, you should know exactly where everything is. You should not be discovering its contents for the first time in the exam hall.

Do Not Over-Rely on It

The booklet is a safety net, not a substitute for knowledge. If you have to look up every formula, you will lose significant time. The students who perform best are the ones who have memorised the key formulas and only use the booklet as a quick reference for the less common results.

Know What Is Not There

This is just as important as knowing what is there. If you walk into the exam assuming the quadratic formula is in the booklet (it is not), you have a problem. Make a list of the formulas you know are not provided and make sure they are locked into your memory.

Cross-Reference with Questions

When you come across a question that seems to require a formula you cannot remember, check the booklet. It might be there in a slightly different form. For example, the compound angle formulas can be used to derive the double angle formulas, which are not always listed separately.

Use It During Practice

When you do past papers, use the booklet as you would in the real exam. This builds the habit of knowing where to look and helps you identify which formulas you still need to memorise.

Common Traps and Misconceptions

There are a few areas where students regularly get caught out:

Assuming SUVAT is not in the booklet. Many students spend hours memorising the five SUVAT equations when they are provided. Use that time to memorise something that is not given.

Confusing which trig identities are provided. The compound angle formulas are in the booklet. The Pythagorean identities (sin^2 + cos^2 = 1 and its variants) are not. Know the difference.

Not memorising the laws of logarithms. These are not in the booklet and come up in nearly every exam. They should be automatic.

Forgetting integration by parts. The formula for integration by parts is not in the booklet. You need to know it and be able to apply it fluently, including knowing when to use it twice (for integrals like x^2 e^x).

Building Your Formula Fluency

The most effective way to memorise formulas is to use them repeatedly in context. Simply reading a list of formulas is passive and does not build the recall you need under exam pressure. Instead:

Do practice questions. Every time you use a formula in a question, you reinforce it.
Write formulas from memory. At the start of each revision session, write out the formulas you are trying to learn without looking at your notes. Check afterwards and focus on the ones you missed.
Use flashcards. Create cards with the formula name on one side and the formula on the other. Review them using spaced repetition.
Time yourself. Can you write out all the formulas for a given topic in two minutes? If not, keep practising.

Prepare with LearningBro

LearningBro's A-Level Maths exam preparation course is designed to build exactly the kind of fluency you need. Each lesson focuses on a specific topic from the AQA specification, with practice questions that require you to recall and apply the formulas you need to memorise. Built-in flashcards with spaced repetition help you lock key formulas into your long-term memory.

Try a free lesson preview to see how the course works, and start building the formula fluency that will give you confidence on exam day.

Good luck with your revision. You have got this.