GCSE Maths formulas: the formula sheet and what you still need to know

The exact contents depend on your exam board and tier, so always use your own board's sheet. The Higher tier sheets typically group formulas under headings like these:

Foundation sheets cover the formulas relevant to Foundation content.

Check your board's sheet, but these are commonly needed and often not provided:

• Area: rectangle $lw$, triangle $\tfrac{1}{2}bh$, parallelogram $bh$.
• Volume of a prism: area of cross-section × length; cuboid $lwh$.
• Compound measures: speed $= \dfrac{\text{distance}}{\text{time}}$, density $= \dfrac{\text{mass}}{\text{volume}}$, pressure $= \dfrac{\text{force}}{\text{area}}$.
• Straight lines: gradient $= \dfrac{\text{change in } y}{\text{change in } x}$, $y = mx + c$, parallel lines have equal gradients.
• Percentage change: $\dfrac{\text{change}}{\text{original}} \times 100$.
• Angle facts: angles on a straight line add to 180°, in a triangle 180°, around a point 360°, exterior angles of a polygon 360°.
• Circle equation (Higher): $x^2 + y^2 = r^2$.

Even when a formula is on the sheet, knowing it saves time and helps you spot which one a question needs.

• Practise with the actual sheet for your board and tier, so you know where everything is without searching.
• Write down the formula first in your working, then substitute. Method marks are often given for a correct substitution even if the final answer is wrong.
• Check units before and after: area in units², volume in units³.
• Don't let the sheet replace understanding. The sheet tells you the cosine rule; it doesn't tell you that a triangle with two sides and the included angle needs it.

In triangle ABC, AB = 7 cm, AC = 9 cm and angle A = 50°. Find BC.

You know two sides and the angle between them, so use the cosine rule:

so $BC \approx 7.0$ cm. If instead you knew two angles and a side, or a side and its opposite angle, you'd use the sine rule. The formulas are on the sheet; choosing correctly is your job.

Rather than copying out a list, practise questions that make you choose and use each formula, mixed together so you have to decide which one fits. Test yourself a few days later on the ones you got wrong. See how to revise for GCSE Maths and interleaved practice. For topic practice, see our GCSE Maths pages.