GCSE Maths formulas to learn

AQA (8300), Edexcel (1MA1) and OCR (J560) all teach the same list of formulas, set by the Department for Education. It sorts them into three groups: formulas you must know, formulas you must know or be able to derive, and formulas that will be given in the question when you need them.

Since 2022 every board has also handed out a formulae sheet in the exam, and Ofqual has made it a requirement for the rest of the current specifications. It covers the first two groups, with the Higher only ones on the Higher sheet. The last column shows where each formula appears on the 2026 sheets.

Practise with marked questions

Formulas the specification says to know

GCSE Maths formulas students are expected to know
Formula	What it is for	On the 2026 sheet
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$	The quadratic formula: solves $ax^2 + bx + c = 0$ , where $a \neq 0$	Higher sheet
$C = 2\pi r = \pi d$	Circumference of a circle	Both sheets
$A = \pi r^2$	Area of a circle	Both sheets
$a^2 + b^2 = c^2$	Pythagoras’ theorem, in a right-angled triangle with hypotenuse $c$	Both sheets
$\sin A = \dfrac{a}{c},\ \cos A = \dfrac{b}{c},\ \tan A = \dfrac{a}{b}$	Trigonometric ratios in a right-angled triangle with hypotenuse $c$	Both sheets
$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$	Sine rule, in any triangle	Higher sheet
$a^2 = b^2 + c^2 - 2bc\cos A$	Cosine rule, in any triangle	Higher sheet
$\text{Area} = \tfrac{1}{2}ab\sin C$	Area of any triangle from two sides and the angle between them	Higher sheet

Formulas to know or be able to derive

GCSE Maths formulas to know or derive
Formula	What it is for	On the 2026 sheet
$\tfrac{1}{2}(a + b)h$	Area of a trapezium, where $a$ and $b$ are the parallel sides	Both sheets
$V = \text{area of cross section} \times \text{length}$	Volume of a prism (a cylinder is a prism)	Both sheets
$P\left(1 + \dfrac{r}{100}\right)^n$	Compound interest: total accrued on principal $P$ at $r\%$ per period for $n$ periods	Both sheets
$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$	Probability of A or B	Both sheets
$P(A \text{ and } B) = P(A \text{ given } B)\,P(B)$	Probability of A and B (conditional probability)	Higher sheet

Formulas given in the question

You do not need to memorise these: when a question needs one, it is printed in that question.

GCSE Maths formulas given in the question
Formula	What it is for	On the 2026 sheet
$\pi rl$	Curved surface area of a cone, slant height $l$	Given in the question
$4\pi r^2$	Surface area of a sphere	Given in the question
$\tfrac{4}{3}\pi r^3$	Volume of a sphere	Given in the question
$\tfrac{1}{3}\pi r^2h$	Volume of a cone	Given in the question
$v = u + at$	Kinematics, constant acceleration	Given in the question
$s = ut + \tfrac{1}{2}at^2$	Kinematics, constant acceleration	Given in the question
$v^2 = u^2 + 2as$	Kinematics, constant acceleration	Given in the question

What the formulae sheet does not cover

The sheet is short. Nothing on it covers the area of a rectangle, a triangle ( $\tfrac{1}{2} \times \text{base} \times \text{height}$ ) or a parallelogram, the volume of a cuboid, angle facts such as angles in a triangle adding to 180°, the equation of a straight line $y = mx + c$ , or the laws of indices. These are part of the content of both tiers, so learn them.

Having the sheet does not tell you which formula a question needs. Practise picking the formula from the information in the question, then substituting and rearranging, and keep the sheet for checking.

Practise these with marked questions

Exam-style questions for every topic, free to read. Answer them online and Exaim marks each answer against the mark scheme, showing which marks you earned.