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Formula

Perimeter, area and volume

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: \( \pi r^2 \)

Quadratic formula

The solution of \( ax^2 + bx + c = 0 \)

where a ≠ 0

\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Pythagoras' Theorem and Trigonometry

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: \( \frac{1}{2} ab \sin C \)

Compound Interest

Where \( P \) is the principal amount, \( r \) is the interest rate, and \( n \) is the number of times interest is compounded:

Total accrued = \( P\left(1 + \frac{r}{100}\right)^n \)

Probability

Where \( P(A) \) is the probability of outcome A:

and P (B) is the probability of outcome B:

\( P(A \text{ or } B) \)\(= P(A) + P(B) - P(A \text{ and } B) \)

\( P(A \text{ and } B) = P(A \text{ given } B) P(B) \)

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GCSE Exam Board

✓Edexcel AQA OCR

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