A level Maths formula booklet: how to use it

By The STEM-Tutor team · Updated October 2026

Every A level Maths exam comes with a formula booklet, but it does not contain everything. Here is how to use it well and what you still need to learn.

Every board has its own booklet

Edexcel, AQA and OCR each publish their own A level Maths formula booklet, and Cambridge International has its own list for its syllabus. The contents are similar but not identical, so download the current booklet for your board from the official exam board website and use that one in every practice paper.

What booklets typically include

• Some series results, such as the binomial series and arithmetic and geometric series sums
• Some trigonometric identities and less common derivatives and integrals
• Numerical methods, such as the trapezium rule and Newton-Raphson
• Statistical distributions and tables, such as binomial and normal distribution information

What you usually need to memorise

Many essentials are not in every booklet, so it is safest to know them by heart:

• The quadratic formula and completing the square
• Laws of indices and logarithms
• sin²x + cos²x = 1 and tan x = sin x / cos x
• Derivatives and integrals of xⁿ, e^x, ln x, sin x and cos x
• The product, quotient and chain rules
• The SUVAT equations for mechanics
• Exact trigonometric values, such as sin 30° = ½

How to use the booklet in the exam

1. Know where everything is. Use the booklet in every practice paper so you can find a formula in seconds.
2. Know what it does not say. It gives formulas, not when to use them.
3. Copy the formula first. Writing it before substituting earns method marks and reduces errors.

A quick way to learn the rest

1. List every formula you need that is not in your board's booklet.
2. Rewrite the list from memory once a week.
3. Use each formula in mixed questions, not just as flashcards.

See the full A level Maths topic list for what each formula belongs to.

Worked examples using the booklet

These examples show how formulas in a typical booklet are used in real questions. Check that your own board's booklet includes each result before relying on it.

Example 1: the binomial series

Expand (1 + 2x)⁻¹ up to the term in x³, and state when it is valid.

• The booklet gives (1 + x)ⁿ = 1 + nx + n(n − 1)x²/2! + n(n − 1)(n − 2)x³/3! + … for |x| < 1.
• Replace x with 2x and use n = −1: 1 + (−1)(2x) + (−1)(−2)(2x)²/2 + (−1)(−2)(−3)(2x)³/6.
• This simplifies to 1 − 2x + 4x² − 8x³.
• It is valid when |2x| < 1, so |x| < ½.

Example 2: the trapezium rule

Estimate ∫₀² x² dx using four strips.

• Strip width h = 0.5. The y-values at x = 0, 0.5, 1, 1.5, 2 are 0, 0.25, 1, 2.25 and 4.
• Area ≈ (h/2)[y₀ + y₄ + 2(y₁ + y₂ + y₃)] = 0.25 × [0 + 4 + 2(3.5)] = 2.75.
• The exact answer is 8/3 ≈ 2.667. The rule overestimates here because the curve is convex: each trapezium sits slightly above the curve.

Example 3: Newton-Raphson

Use x_n+1 = x_n − f(x_n)/f'(x_n) with f(x) = x² − 2 and x₀ = 1.5 to approximate √2.

• f'(x) = 2x.
• x₁ = 1.5 − 0.25/3 = 1.41667 (5 d.p.).
• x₂ = 1.41667 − 0.00694/2.83333 ≈ 1.41422, already very close to √2 = 1.41421…

Results worth memorising, with examples

Laws of logarithms

log a + log b = log(ab), log a − log b = log(a/b) and k log a = log(a^k). For example, log₂8 + log₂4 = log₂32 = 5.

Exact trigonometric values

The two triangles above give every exact value you need: sin 30° = ½, cos 30° = √3/2, tan 60° = √3, sin 45° = cos 45° = √2/2. Sketch them in the margin of a non-calculator question rather than memorising a table.

Basic calculus

d/dx(xⁿ) = nxⁿ⁻¹ and ∫xⁿ dx = xⁿ⁺¹/(n + 1) + c. For example, d/dx(4x³) = 12x² and ∫6x² dx = 2x³ + c.

A five-minute booklet audit

1. Download your board's current booklet.
2. Go through the A level Maths topic list and, for each formula you use, note whether it is in the booklet.
3. Highlight everything that is not in the booklet. That is your memorisation list.
4. Stick the list on your wall and test yourself weekly.

Practice questions

Try each one before opening the answer.

More examples: arithmetic and geometric series

Example 4: sum of an arithmetic series

Find the sum of the first 20 terms of 3, 7, 11, 15, …

• First term a = 3, common difference d = 4, n = 20.
• S_n = (n/2)[2a + (n − 1)d] = 10 × [6 + 76] = 820.

Example 5: sum to infinity of a geometric series

Find the sum to infinity of 8 + 4 + 2 + 1 + …

• a = 8 and r = ½. Because |r| < 1, the series converges.
• S_∞ = a/(1 − r) = 8/(1 − ½) = 16.

Common mistakes with the booklet

• Using a formula outside its conditions. The binomial series for a negative or fractional power only works when the expression is valid, for example |x| < 1. Always state the range.
• Copying a formula but changing the variable wrongly. If you replace x with 2x, every x becomes 2x, including inside the powers.
• Radians versus degrees. Calculus results for sin and cos in the booklet assume radians.
• Searching for something that is not there. Wasting two minutes hunting for the quadratic formula costs more than learning it.

Frequently asked questions

Can I write in the formula booklet during the exam?

Rules depend on the board and the exam centre, so ask your teacher or exams officer. Either way, practise without writing in it.

Is the Further Maths booklet the same?

No. Further Maths booklets add results for topics such as complex numbers, matrices, series and further calculus. Download the right one for your course.

When should I start using the booklet?

From the first week of Year 12. Students who only open it in May lose time finding things in the exam.