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HSC Mathematics Standard 2 Formula Sheet

A searchable HSC Mathematics Standard 2 formula sheet with equations, variables, explanations, and linked revision topics.

These formulas are rendered as real mathematics rather than images. Read the definition, check every variable, and follow the topic link to see the idea in context. Always confirm the permitted official booklet or sheet for your examination session.

Reference section

A · Algebra

Linear equation of a line

y=mx+c \qquad m=\frac{y_2-y_1}{x_2-x_1}

m is the gradient, c is the y-intercept.

$m$: gradient
$c$: y-intercept

Exponential model

N(t)=N_0\cdot r^t

r is the growth/decay factor, not the raw percentage rate — e.g. 6% growth means r=1.06, 6% decay means r=0.94.

$N(t)$: quantity at time t
$N_0$: initial quantity
$r$: growth (>1) or decay (0<r<1) factor per period
$t$: number of periods

Reference section

B · Measurement

Area formulas

A_{rect}=lw \qquad A_{tri}=\frac12bh \qquad A_{circle}=\pi r^2 \qquad A_{trap}=\frac12(a+b)h \qquad A_{parallelogram}=bh

The height in a triangle/trapezium must be the perpendicular height.

Volume formulas

V_{prism}=A_{base}h \qquad V_{cylinder}=\pi r^2h \qquad V_{cone}=\frac13\pi r^2h \qquad V_{sphere}=\frac43\pi r^3

For similar figures with linear scale factor k: length scales by k, area by k², volume by k³.

Pythagoras' theorem & trig ratios

c^2=a^2+b^2 \qquad \sin\theta=\frac{\text{Opp}}{\text{Hyp}} \quad \cos\theta=\frac{\text{Adj}}{\text{Hyp}} \quad \tan\theta=\frac{\text{Opp}}{\text{Adj}}

c is the hypotenuse. Ensure your calculator is in degree mode.

$a,b,c$: triangle sides, c the hypotenuse
$\theta$: the reference angle

Sine rule & cosine rule

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \qquad a^2=b^2+c^2-2bc\cos A

Sine rule: angle-side opposite pair known. Cosine rule: SSS or SAS. Watch for the ambiguous case with the sine rule.

$a,b,c$: sides opposite angles A,B,C

Area of a triangle (trig form)

\text{Area}=\frac12ab\sin C

C must be the angle included between the two given sides a and b.

$a,b$: two sides
$C$: the included angle

Speed conversion

\text{km/h} \to \text{m/s: multiply by } \frac{5}{18}

The reverse conversion (m/s to km/h) multiplies by 18/5 (i.e. 3.6).

Reference section

C · Financial Mathematics

Compound interest

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

r and n must match the compounding period. Interest earned is A−P, not A itself.

$A$: final amount
$P$: principal
$r$: rate per period (%)
$n$: number of periods

Declining-balance depreciation

S=V_0\left(1-\frac{r}{100}\right)^n

Never reaches exactly zero. Same form as compound interest but decreasing.

$S$: salvage value
$V_0$: original value
$r$: depreciation rate per period (%)
$n$: number of periods

Straight-line depreciation

S=V_0-Dn

Decreases by a fixed dollar amount D each period — can reach exactly zero.

$S$: salvage value
$V_0$: original value
$D$: fixed depreciation per period
$n$: number of periods

Future value of an annuity

FV=M\left[\frac{(1+i)^n-1}{i}\right]

i and n must both match the contribution period (e.g. both monthly).

$FV$: future value
$M$: regular contribution
$i$: interest rate per period (decimal)
$n$: number of contributions

Reference section

D · Statistical Analysis

Mean and quartiles

\bar{x}=\frac{\sum x_i}{n} \qquad IQR=Q_3-Q_1

Data must be ordered before finding quartiles. IQR is less sensitive to outliers than the range.

$\bar{x}$: mean
$Q_1,Q_3$: lower and upper quartiles

Standard deviation

s=\sqrt{\frac{\sum(x_i-\bar{x})^2}{n-1}}

Calculated using technology. A smaller s means data is more tightly clustered around the mean.

$s$: sample standard deviation
$x_i$: each data value
$\bar{x}$: the mean

z-score

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

Empirical rule: ~68% of data within 1σ of μ, ~95% within 2σ, ~99.7% within 3σ.

$z$: standardized score
$x$: raw value
$\mu$: mean
$\sigma$: standard deviation

Independent events

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

For events without replacement, the second probability changes based on the first outcome.

$A,B$: independent events

Reference section

E · Networks

Float time

\text{Float} = LST - EST

Zero float means the activity is on the critical path — it cannot be delayed without delaying the whole project.

$LST$: latest start time
$EST$: earliest start time

Critical path / project duration

\text{Project duration} = \max(\text{total duration of each path})

The critical path is the LONGEST path through the network, not the shortest.

Reviewed by the Study to Learn editorial team · Updated 2026-07-24