Mathematics Higher Tier Formula Sheet

Perimeter, area and volume

Trapezium

Where a and b are the lengths of the parallel sides and h is their perpendicular separation:

\displaystyle \quad \text{Area of a trapezium} = \frac{1}{2} (a + b) h

Prism

\displaystyle \text{Volume of a prism} = \text{area of cross section} \times \text{length}

Circle

Where r is the radius and d is the diameter:

\displaystyle \quad \text{Circumference of a circle} = 2\pi r = \pi d

\displaystyle \quad \text{Area of a circle} = \pi r^{2}

Quadratic formula

The solution of ax² + bx + c = 0

where a ≠ 0

\displaystyle \qquad x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Compound Interest

Where P is the principal amount, r is the interest rate over a given period and n is number of times that the interest is compounded:

\displaystyle \quad \text{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:

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

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

Pythagoras’ Theorem and Trigonometry

In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:

\displaystyle \quad 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:

\displaystyle \quad \sin A = \frac{a}{c} \quad \cos A = \frac{b}{c} \quad \tan A = \frac{a}{b}

In any triangle ABC where a, b and c are the length of the sides:

\displaystyle \quad \text{sine rule: } \ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

\displaystyle \quad \text{cosine rule: } \ a^2 = b^2 + c^2 - 2bc \cos A

\displaystyle \quad \text{Area of triangle} = \frac{1}{2} ab \sin C

Mathematics Higher TierFormula Sheet