The Official GCSE Maths Formula Sheet Explained
Since 2023, you are given a sheet with key formulas for your GCSE Maths exam. This means less pressure on your memory and more time to focus on problem-solving. This guide shows you exactly what’s on the official formula sheet and, just as importantly, what isn’t. 🚀
Formulas GIVEN in the Exam
This list of formulas is provided for you in all GCSE Maths papers. You don’t need to memorise them, but you absolutely need to know how and when to use them.
Area and Volume
| Shape | Formula | Notes |
|---|---|---|
| Area of a Trapezium | $A = \frac{1}{2}(a+b)h$ | ‘a’ and ‘b’ are the parallel sides and ‘h’ is the perpendicular height. |
| Volume of a Prism | Volume = Area of cross-section × length | A prism has the same cross-section all the way through. |
Circles
| Measurement | Formula |
|---|---|
| Circumference | $\pi d = 2\pi r$ |
| Area | $A = \pi r^2$ |
Higher Tier Only: Advanced Formulas
| Topic | Formula / Rule | Notes |
|---|---|---|
| Volume of Sphere | $V = \frac{4}{3}\pi r^3$ | Remember ‘r’ is radius, ‘h’ is perpendicular height, and ‘l’ is the slant height for a cone. |
| Surface Area of Sphere | $A = 4\pi r^2$ | |
| Volume of Cone | $V = \frac{1}{3}\pi r^2 h$ | |
| Curved Surface Area of Cone | $\text{Area} = \pi r l$ | |
| Quadratic Formula | $x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$ | Solves any equation in the form $ax^2 + bx + c = 0$. |
| Sine Rule | $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ | Use when you have a matching pair of a side and its opposite angle. |
| Cosine Rule | $a^2 = b^2 + c^2 – 2bc \cos A$ | Use to find a side when you have two sides and the angle between them. |
| Area of a Triangle | $\text{Area} = \frac{1}{2}ab \sin C$ | Use when you have two sides and the angle between them. |
Formulas You STILL Need to Memorise
While the formula sheet is generous, it doesn’t cover everything. These are the absolute essentials you must learn by heart.
Pythagoras & SOH CAH TOA (Right-Angled Triangles)
These fundamental tools are NOT on the formula sheet and are vital for both tiers.
(where ‘c’ is the hypotenuse)
Trigonometric Ratios (SOH CAH TOA)
SOH: Sine
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$
CAH: Cosine
$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$
TOA: Tangent
$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$
Basic Area & Volume
| Shape | Formula |
|---|---|
| Rectangle Area | Area = length × width |
| Parallelogram Area | Area = base × perpendicular height |
| Triangle Area | Area = $\frac{1}{2} \times \text{base} \times \text{height}$ |
| Cuboid Volume | Volume = length × width × height |
Tutor Insights
How should I use the formula sheet?
Don’t wait until the exam to see it for the first time. Use a copy during your revision to get familiar with the layout and what’s included. Your main skill is not memorising these specific formulas, but learning to quickly identify which one is needed for a particular problem. The formula sheet is a tool, not a replacement for understanding the concepts.
FAQs
Is the formula sheet the same for Foundation and Higher?
A: No. The Higher Tier sheet contains all the formulas from the Foundation sheet, plus the more advanced ones like the Quadratic Formula, Sine Rule, and Cosine Rule. This guide clearly marks the “Higher Tier Only” formulas.
Why isn’t Pythagoras’ Theorem on the sheet?
A: Pythagoras’ Theorem ($a^2+b^2=c^2$) is considered such a fundamental part of the GCSE curriculum that you are expected to have memorised it. The same applies to the basic SOH CAH TOA ratios.
