One of the most important strategic decisions in your A-Level Mathematics preparation is knowing what is in the formula book and what you must memorise. The AQA formula book is provided in the exam and contains many key results — but it does not contain everything. If you rely on the formula book for something that is not there, you will waste precious time and may lose marks.
This lesson provides a comprehensive breakdown of what is given and what must be committed to memory.
Spec Mapping — This lesson develops transferable exam-skill content for AQA 7357 Papers 1, 2 and 3, drawing on the contents of the AQA formula booklet and the must-memorise list. Refer to the official AQA specification document for exact wording.
What Is the AQA Formula Book?
The AQA Mathematical Formulae and Statistical Tables booklet is provided to every candidate in all three exam papers. It contains:
Key formulae for pure mathematics
Key formulae for mechanics
Key formulae for statistics
Statistical tables (binomial cumulative distribution function, percentage points of the normal distribution, etc.)
You will receive a clean copy — you cannot take your own annotated version into the exam.
Pure Mathematics: What IS in the Formula Book
The following results are provided in the AQA formula book. You do not need to memorise these, but you must know how to use them.
Mensuration
Surface area of a sphere: 4πr2
Area of the curved surface of a cone: πrl (where l is slant height)
Binomial Series
The general binomial expansion for (1 + x)ⁿ where n is not a positive integer:
(a+b)n=r=0∑n(rn)an−rbrwhere (rn)=r!(n−r)!n!(1+x)n=1+nx+2!n(n−1)x2+⋯(for positive integer n, this terminates)
Note: The formula book gives the general binomial expansion (for non-integer n). The basic expansion for positive integer n — and the formula for binomial coefficients — must be memorised.
Key Distinction: The addition formulae (sin(A±B), cos(A±B), etc.) and double angle formulae ARE in the formula book. The Pythagorean identities (sin2+cos2=1 and its variants) are NOT. You must memorise them.
Quadratic Formula
x=[−b±b2−4ac]/2a
Discriminant
b2−4ac>0b2−4ac=0b2−4ac<0⇒two distinct real roots⇒one repeated root⇒no real roots
Mechanics: What You MUST Memorise
All mechanics formulae must be memorised — none are given in the AQA formula book for A-Level Maths (they are only in the Further Maths book).
Where: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.
Exam Tip: You must know all five SUVAT equations. In any kinematics problem, identify the three known quantities and the one unknown, then select the equation that does not contain the fifth (unwanted) quantity.
Newton's Laws of Motion
First law: A body remains at rest or moves with constant velocity unless acted upon by a resultant force.
Second law:F=ma (resultant force = mass × acceleration).
Third law: For every action, there is an equal and opposite reaction.
Weight
W=mg
where g=9.8m/s2 (or as specified in the question).
Friction
F≤μR — friction ≤ coefficient of friction × normal reaction
F=μR — at the point of sliding (when friction is limiting)
Moments
Moment = Force × Perpendicular distance from the pivot
For equilibrium: sum of clockwise moments = sum of anticlockwise moments
Resolving Forces
On an inclined plane at angle θ:Component parallel to the plane:Component perpendicular to the plane:mgsinθmgcosθ
Projectiles
Horizontal:x=Vcosθ×t (constant velocity, no acceleration)
Mean of grouped data:Variance:Standard deviation:xˉ=∑f∑fxσ2=∑f∑f(x−xˉ)2=∑f∑fx2−xˉ2σ=varianceFor coded data: if y=bx−a, then xˉ=byˉ+a and σx=b×σy
Hypothesis Testing
Binomial test:H0:p=p0H1:p>p0(or p<p0 or p=p0)Significance level: usually 5% or 1%Compare P(X≥observed) or P(X≤observed) with the significance levelNormal test (for means):H0:μ=μ0Test statistic: Z=σ/nxˉ−μ0Compare with critical value from tables
Exam Tip: When conducting a hypothesis test, always state H₀ and H₁, define the test statistic, find the p-value or critical region, and write a conclusion in context. Saying "reject H₀" without interpretation will lose you marks.
Trigonometric Identities: The Full Picture
This is a frequent source of confusion, so here is a clear summary:
Given in the formula book (do NOT memorise — just know where to find them)
sin(A±B), cos(A±B), tan(A±B)
sin2A, cos2A, tan2A
Small angle approximations
NOT in the formula book (MUST memorise)
sin2θ+cos2θ≡1
tanθ≡cosθsinθ
1+tan2θ≡sec2θ (derived from dividing sin2+cos2=1 by cos2θ)
1+cot2θ≡cosec2θ (derived from dividing sin2+cos2=1 by sin2θ)
Exact values: sin0∘, sin30∘, sin45∘, sin60∘, sin90∘ and corresponding cos and tan values
Exact trigonometric values (must know)
Angle
sin
cos
tan
0∘
0
1
0
30∘ (6π)
21
23
31
45∘ (4π)
22
22
1
60∘ (3π)
23
21
3
90∘ (2π)
1
0
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Integration Techniques: What Is Expected Without the Formula Book
You must be able to perform the following integrations from memory, without reference to the formula book:
Power rule for xⁿ (including negative and fractional powers)
eˣ and eᵏˣ
sin x, cos x, sin kx, cos kx
1/x (giving ln|x|)
Integration by substitution — the method must be known; specific substitutions may be suggested in the question
Integration by parts — the formula ∫u dv = uv − ∫v du must be memorised
Partial fractions — decomposition technique must be known
Using trigonometric identities to rewrite integrands (e.g., using cos 2A = 1 − 2sin²A to integrate sin²x)
The formula book provides integrals for sec², tan, cot, cosec, and sec — you do not need to memorise these.
Tips for Using the Formula Book Effectively
Before the exam
Get a copy of the AQA formula book and practise using it during revision
Know the layout — where are the trig identities? Where are the statistical tables?
Practise finding formulae quickly — in the exam, fumbling through pages wastes time
Mark up your own revision copy with notes about when each formula is used (you cannot take this into the exam, but it helps you learn the structure)
During the exam
Check immediately if you cannot remember a formula — it might be in the book
Do not waste time deriving formulae that are provided — use them directly
Copy formulae carefully — transcription errors are a common source of lost marks
Use the statistical tables for binomial cumulative probabilities and normal distribution critical values rather than trying to calculate them
Common mistakes with the formula book
Mistake
Consequence
Assuming laws of logarithms are given
They are NOT — you must memorise them
Looking for SUVAT equations
They are NOT in the A-Level Maths formula book
Confusing the general binomial expansion with the integer version
The book gives the general version; you must know how to use both
Not using the statistical tables
The cumulative binomial tables save enormous time
Misreading the normal distribution table
Check whether you need P(Z < z) or P(Z > z)
Synoptic Links
This topic connects to:
Trigonometry identities and equations (aqa-alevel-maths-pure-1 / trigonometry) — knowing which trig results are printed versus memorised drives equation-solving speed in the exam.
Normal distribution and statistical tables (aqa-alevel-maths-statistics / normal-distribution) — the printed z-table and percentage-points table underpin every Paper 3 normal-distribution question.
Integration by parts and standard integrals (aqa-alevel-maths-calculus-applications / integration-by-parts) — the booklet's integral table sets the boundary between standard recall and memorised technique.
Summary
The AQA formula book provides addition formulae, double angle formulae, small angle approximations, advanced derivatives and integrals, the trapezium rule, Newton-Raphson, and statistical tables.
You must memorise: laws of logarithms, basic derivatives and integrals (xⁿ, sin, cos, eˣ, 1/x), SUVAT equations, Newton's laws, probability rules, binomial conditions, Pythagorean trig identities, exact trig values, quadratic formula, factor theorem, equations of lines and circles, and integration by parts formula.
Know the layout of the formula book so you can find things quickly.
Practise with the formula book during revision so you are comfortable using it under exam conditions.
Exam Tip: Make flash cards for every formula NOT in the book. Test yourself daily in the weeks leading up to the exam. The single biggest reason students lose marks is forgetting formulae they assumed were given.
Deeper Strategy: AQA Formula Book and What to Memorise