A-Level Maths Formula Booklet: What's Included and How to Use It

The A-Level maths formula booklet is one of the most misunderstood resources students have access to during their exams. Many assume it contains every formula they’ll need, only to lose marks because they didn’t memorise the basics. Others know it exists but struggle to navigate it efficiently under exam pressure.

Understanding what’s in your formula booklet – and what’s deliberately left out – is essential for A-Level maths success. Here’s everything you need to know.

Do All Exam Boards Provide a Formula Booklet?

Yes, but the content varies by exam board:

AQA provides a formula booklet covering pure maths, statistics, and mechanics
Edexcel provides a formula booklet with similar coverage
OCR provides a formula booklet (called the “Mathematical Formulae and Statistical Tables”)

All three boards include the more complex formulas you’ll need, but they expect you to know fundamental formulas from memory. The booklet is provided at the start of each exam paper and is the same for AS and A-Level.

What’s Inside the A-Level Maths Formula Booklet?

The formula booklet is typically 5-8 pages long and organised into sections:

Pure Mathematics

Included:

Binomial expansion for any power (including negative and fractional)
Trigonometric identities (sin²θ + cos²θ = 1, addition formulas, double angle formulas)
Differentiation formulas (standard derivatives, chain rule, product rule, quotient rule)
Integration formulas (standard integrals, integration by parts, reduction formulas)
Sequences and series (arithmetic and geometric series sums)
Maclaurin series expansions
Numerical methods (Newton-Raphson, trapezium rule)

NOT included – must memorise:

Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
Laws of logarithms: log(ab) = log a + log b, log(a/b) = log a - log b, log(aⁿ) = n log a
Differentiation basics: d/dx(xⁿ) = nxⁿ⁻¹
Integration basics: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c
Area of a trapezium: A = ½(a + b)h
Circle properties: circumference = 2πr, area = πr²

Statistics

Included:

Probability distributions (binomial, normal)
Mean and variance formulas for discrete distributions
Standard normal distribution table (Z-tables)
Hypothesis testing formulas
Correlation and regression formulas

NOT included – must memorise:

Mean: x̄ = Σx / n
Standard deviation: you need to know the concept, though calculation formulas are given
Basic probability rules: P(A or B) = P(A) + P(B) - P(A and B)

Mechanics

Included:

Constant acceleration equations (SUVAT equations)
Formulae for projectile motion
Moments formulas
Centre of mass formulas

NOT included – must memorise:

Newton’s second law: F = ma
Weight: W = mg
Work done: W = Fs
Power: P = Fv

Key Differences Between Exam Boards

While all three boards provide comprehensive formula booklets, there are subtle differences:

AQA formula booklet is organised clearly by topic with helpful labels. The statistics section includes critical value tables for hypothesis testing.

Edexcel formula booklet follows a similar structure but uses slightly different notation in some places (particularly in mechanics). Make sure you’re familiar with how your board writes formulas.

OCR formula booklet is the most comprehensive, including extensive statistical tables (normal distribution, binomial cumulative distribution). OCR students often find they need to reference the booklet less during pure maths but more during statistics.

All boards expect the same foundational knowledge. Don’t assume switching exam boards will reduce what you need to memorise.

What You MUST Memorise (Not in the Booklet)

These formulas appear in almost every exam but are deliberately excluded from the formula booklet:

Pure Maths Must-Know Formulas

Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
Completing the square: x² + bx = (x + b/2)² - (b/2)²
Laws of indices: xᵃ × xᵇ = xᵃ⁺ᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ
Laws of logarithms: (as listed above)
Straight line equation: y = mx + c, or y - y₁ = m(x - x₁)
Gradient formula: m = (y₂ - y₁) / (x₂ - x₁)
Circle equation: (x - a)² + (y - b)² = r²
Basic differentiation: d/dx(xⁿ) = nxⁿ⁻¹
Basic integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c (for n ≠ -1)
Trigonometric values: sin 0°, sin 30°, sin 45°, sin 60°, sin 90° (and corresponding cos and tan values)

Statistics Must-Know Formulas

Mean: x̄ = Σx / n
Variance: Var(X) = E(X²) - [E(X)]²
Standard deviation: σ = √variance
Probability basics: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Mechanics Must-Know Formulas

F = ma (Newton’s second law)
W = mg (weight)
Work done: W = Fs
Power: P = Fv (or P = W/t)

If you can’t recall these instantly, you’ll struggle in exams. These form the foundation for more complex problems.

How to Use the Formula Booklet Effectively

Having access to the formula booklet doesn’t mean you should rely on it for everything. Here’s how to use it strategically:

1. Know Where Everything Is

Before your exam, spend time familiarising yourself with the booklet’s layout. Know that:

Pure maths formulas are at the front
Statistics formulas are in the middle
Mechanics formulas are at the back
Statistical tables (Z-tables, critical values) are at the very end

In the exam, you don’t want to waste 30 seconds flipping pages looking for the binomial distribution formula.

2. Memorise Common Formulas Anyway

Even though the formula booklet contains certain equations, you should memorise the ones you use frequently:

Trigonometric identities (sin²θ + cos²θ = 1, double angle formulas)
Standard derivatives and integrals
SUVAT equations

Why? Because looking up formulas repeatedly breaks your concentration and wastes time. Memorise what you use often; reference what you use rarely.

3. Check Your Notation

The formula booklet uses specific notation. Make sure you understand:

What each symbol means (Σ for sum, μ for mean, σ for standard deviation)
How fractions are written (some formulas use horizontal bars, others use division symbols)
Subscript and superscript meanings

Misreading notation is a common source of error. If you’re unsure what a symbol means, check the key at the front of the booklet.

4. Don’t Just Copy – Understand

Copying a formula from the booklet and blindly substituting numbers won’t always work. Exam questions often require you to:

Rearrange the formula for a different variable
Combine multiple formulas
Recognise which formula applies to a given scenario

Understanding how formulas are derived and what each term represents makes them easier to apply correctly.

5. Practise with the Booklet

Do past papers with the formula booklet beside you, just as you will in the real exam. This helps you:

Learn which formulas you naturally remember and which you need to look up
Build speed in finding formulas
Avoid over-reliance on the booklet for basic formulas

Timed practice is essential. You need to balance speed with accuracy.

Common Mistakes Students Make with the Formula Booklet

Mistake 1: Assuming everything is in there

The quadratic formula is NOT in the booklet. Neither are basic differentiation or integration rules. Don’t lose easy marks by searching for something that isn’t there.

Mistake 2: Not understanding when to use a formula

The booklet gives you the formula for integration by parts, but it won’t tell you when integration by parts is the right method to use. That’s why understanding concepts matters as much as knowing formulas.

Mistake 3: Misreading formulas under pressure

Exam pressure leads to errors. Students mix up similar-looking formulas (e.g., binomial distribution mean vs variance) or misread subscripts. Slow down when referencing the booklet.

Mistake 4: Wasting time looking up basic formulas

If you’re flipping to the booklet to find the quadratic formula or the formula for the area of a circle, you’re losing precious time. Commit fundamental formulas to memory.

Mistake 5: Forgetting to use the statistical tables

The back of the formula booklet contains Z-tables and other statistical tables. Many students forget these exist and try to work out probabilities manually. Use the tables – they’re there to save you time.

How to Memorise What’s Not in the Booklet

You can’t rely on the formula booklet for everything. Here’s how to memorise the essentials:

Create a Formula Sheet

Write out all the formulas NOT in the booklet on a single A4 page. Organise by topic (pure, stats, mechanics). Keep this sheet visible on your desk while revising.

Use Active Recall

Cover your formula sheet and write out as many formulas as you can remember. Check what you missed, then try again. Repeat until you can recall them all without help.

Apply Formulas in Context

Memorising formulas in isolation doesn’t work. Do past paper questions that require you to use each formula. The more you apply a formula, the better you’ll remember it.

Test Yourself Regularly

Quiz yourself on key formulas before every revision session. Use flashcards, apps like Anki, or simply write them out from memory. Spaced repetition is far more effective than cramming.

Strategies for Different A-Level Maths Papers

Paper 1 and 2 (Pure Maths)

Pure maths papers test your problem-solving ability more than your memorisation. The formula booklet helps with:

Complex trigonometric identities
Standard integrals for unfamiliar functions
Series expansions

But you’ll still need instant recall of quadratic formula, differentiation basics, and logarithm laws.

Paper 3 (Statistics and Mechanics)

Statistics papers require frequent reference to the booklet for:

Distribution formulas (binomial, normal)
Hypothesis testing critical values
Statistical tables

Mechanics papers include SUVAT equations in the booklet, but you should memorise F = ma and related formulas. Mechanics questions often require quick recall to set up equations.

How UpGrades Helps with A-Level Maths Formulas

Knowing formulas is only half the battle – you need to recognise which formula applies to each question and use it accurately under pressure. UpGrades provides:

Targeted practice questions that test formula application, not just recall
Instant feedback showing you where errors occur (wrong formula vs calculation mistake)
Adaptive difficulty that focuses on the formulas and techniques you struggle with most

With UpGrades, you’ll build the confidence to decide quickly whether to reference the formula booklet or rely on memory. The result? Faster, more accurate exam performance across pure maths, statistics, and mechanics.

Final Tips for Using the A-Level Maths Formula Booklet

Familiarise yourself with the booklet before exam day – Know where every section is
Memorise fundamentals – The booklet is for complex formulas, not basics like the quadratic formula
Practise with the booklet – Use it during timed past paper practice
Don’t rely on it for everything – Memorise what you use frequently
Check your notation – Make sure you understand what every symbol means

The A-Level maths formula booklet is a powerful resource, but only if you know how to use it effectively. Combine smart booklet usage with strong foundational knowledge, and you’ll approach your exams with the confidence that comes from genuine understanding – not just memorisation.