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HSC

Mathematics Standard 1Formula Sheet

Measurement

Limits of accuracy

Absolute error=12×precision\displaystyle \text{Absolute error} = \frac{1}{2} \times \text{precision}
Upper bound=measurement+absolute error\displaystyle \text{Upper bound} = \text{measurement} + \text{absolute error}
Lower bound=measurement−absolute error\displaystyle \text{Lower bound} = \text{measurement} - \text{absolute error}

Length

l=θ360×2πr\displaystyle l = \frac{\theta}{360} \times 2\pi r

Area

A=θ360×πr2\displaystyle A = \frac{\theta}{360} \times \pi r^{2}
A=h2 (a+b)\displaystyle A = \frac{h}{2}\,(a + b)
A≈h2 (df+dl)\displaystyle A \approx \frac{h}{2}\,(d_{f} + d_{l})

Surface area

A=2πr2+2πrh\displaystyle A = 2\pi r^{2} + 2\pi r h
A=4πr2\displaystyle A = 4\pi r^{2}

Volume

V=13Ah\displaystyle V = \frac{1}{3} A h
V=43πr3\displaystyle V = \frac{4}{3} \pi r^{3}

Trigonometry

sin⁡A=opphyp,  cos⁡A=adjhyp,  tan⁡A=oppadj\displaystyle \sin A = \frac{\mathrm{opp}}{\mathrm{hyp}},\; \cos A = \frac{\mathrm{adj}}{\mathrm{hyp}},\; \tan A = \frac{\mathrm{opp}}{\mathrm{adj}}
A=12absin⁡C\displaystyle A = \frac{1}{2} ab \sin C
asin⁡A=bsin⁡B=csin⁡C\displaystyle \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
c2=a2+b2−2abcos⁡C\displaystyle c^{2} = a^{2} + b^{2} - 2ab \cos C
cos⁡C=a2+b2−c22ab\displaystyle \cos C = \frac{a^{2} + b^{2} - c^{2}}{2ab}
Financial Mathematics
FV=PV(1+r)n\displaystyle FV = PV(1 + r)^{n}

Straight-line method of depreciation

S=V0−Dn\displaystyle S = V_{0} - Dn

Declining-balance method of depreciation

S=V0(1−r)n\displaystyle S = V_{0}(1 - r)^{n}
Statistical Analysis
An outlier is a scoreless than Q1−1.5×IQRor more than Q3+1.5×IQR\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}
z=x−μσ\displaystyle z = \frac{x - \mu}{\sigma}

Normal distribution

Normal distribution curve
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