Mathematics Standard 1 Formula Sheet

Measurement

Limits of accuracy

\displaystyle \text{Absolute error} = \frac{1}{2} \times \text{precision}

\displaystyle \text{Upper bound} = \text{measurement} + \text{absolute error}

\displaystyle \text{Lower bound} = \text{measurement} - \text{absolute error}

Length

\displaystyle l = \frac{\theta}{360} \times 2\pi r

Area

\displaystyle A = \frac{\theta}{360} \times \pi r^{2}

\displaystyle A = \frac{h}{2}\,(a + b)

\displaystyle A \approx \frac{h}{2}\,(d_{f} + d_{l})

Surface area

\displaystyle A = 2\pi r^{2} + 2\pi r h

\displaystyle A = 4\pi r^{2}

Volume

\displaystyle V = \frac{1}{3} A h

\displaystyle V = \frac{4}{3} \pi r^{3}

Trigonometry

\displaystyle \sin A = \frac{\mathrm{opp}}{\mathrm{hyp}},\; \cos A = \frac{\mathrm{adj}}{\mathrm{hyp}},\; \tan A = \frac{\mathrm{opp}}{\mathrm{adj}}

\displaystyle A = \frac{1}{2} ab \sin C

\displaystyle \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

\displaystyle c^{2} = a^{2} + b^{2} - 2ab \cos C

\displaystyle \cos C = \frac{a^{2} + b^{2} - c^{2}}{2ab}

Financial Mathematics

\displaystyle FV = PV(1 + r)^{n}

Straight-line method of depreciation

\displaystyle S = V_{0} - Dn

Declining-balance method of depreciation

\displaystyle S = V_{0}(1 - r)^{n}

Statistical Analysis

\displaystyle \begin{aligned} \text{An outlier is a score} \\ \text{less than } & Q_{1} - 1.5 \times IQR \\ \text{or more than } & Q_{3} + 1.5 \times IQR \end{aligned}

\displaystyle z = \frac{x - \mu}{\sigma}

Normal distribution

Approximately 68% of scores have z-scores between -1 and 1

Approximately 95% of scores have z-scores between -2 and 2

Approximately 99.7% of scores have z-scores between -3 and 3

Mathematics Standard 1Formula Sheet