Formulae Sheet for GCSE
GCSE Mathematics Formulae Sheet
This page presents the exam-style formulae sheet used in GCSE Mathematics. Wording is kept concise and no extra hints are added, to mirror the exam context.
- Higher / Foundation: use the toggle on the right to filter what you will see in your paper.
- How to revise: do not rely on memorising; practise when and how to apply each formula.
- Disclaimer: always check your school/exam board for the latest official sheet.
Where a and b are the lengths of the parallel sides and h is their perpendicular separation:
Area of a trapezium: \( \frac{1}{2}(a + b)h \)
Volume of a prism: area of cross section × length
Circumference of a circle: \( 2\pi r = \pi d \)
Area of a circle: \( \pi r^2 \)
The solution of \( ax^2 + bx + c = 0 \)
where a ≠ 0
\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
In any right-angled triangle:
\( a^2 + b^2 = c^2 \)
In any right-angled triangle ABC where a, b and c are the length of the sides and c is the hypotenuse:
\( \sin A = \frac{a}{c}, \cos A = \frac{b}{c}, \tan A = \frac{a}{b} \)
In any triangle ABC where a, b and c are the length of the sides:
Sine rule: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \)
Cosine rule: \( a^2 = b^2 + c^2 - 2bc \cos A \)
Area of triangle: \( \frac{1}{2} ab \sin C \)
Where \( P \) is the principal amount, \( r \) is the interest rate, and \( n \) is the number of times interest is compounded:
Total accrued = \( P\left(1 + \frac{r}{100}\right)^n \)
Where \( P(A) \) is the probability of outcome A:
and P (B) is the probability of outcome B:
\( P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \)
\( P(A \text{ and } B) = P(A \text{ given } B) P(B) \)
