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HSC Mathematics Standard 1 Formula Sheet

A searchable HSC Mathematics Standard 1 formula sheet with practical explanations for finance, measurement, statistics, and networks.

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. Positive gradient rises left to right, negative falls.

$m$: gradient
$c$: y-intercept
$(x_1,y_1),(x_2,y_2)$: two known points on the line

Direct proportion

y=kx

A directly proportional relationship always passes through the origin.

$k$: constant of proportionality

Reference section

B · Measurement

Metric conversions

1\text{ km}=1000\text{ m} \quad 1\text{ m}=100\text{ cm} \quad 1\text{ kg}=1000\text{ g} \quad 1\text{ L}=1000\text{ mL}

Converting to a smaller unit: multiply. Converting to a larger unit: divide.

Perimeter & area formulas

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

The height in a triangle or trapezium must be the perpendicular height, not a slanted side.

$l,w$: length, width
$b,h$: base, perpendicular height
$r$: radius
$a,b$: parallel sides of a trapezium

Volume formulas

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

1 cm³ = 1 mL, and 1000 cm³ = 1 L, linking volume to capacity.

$A_{base}$: base cross-sectional area
$h$: perpendicular height
$r$: radius

Pythagoras' theorem

c^2=a^2+b^2

Only applies to right-angled triangles. c is the hypotenuse (opposite the right angle).

$c$: hypotenuse
$a,b$: the two shorter sides

Trigonometric ratios

\sin\theta=\frac{\text{Opp}}{\text{Hyp}} \qquad \cos\theta=\frac{\text{Adj}}{\text{Hyp}} \qquad \tan\theta=\frac{\text{Opp}}{\text{Adj}}

SOH CAH TOA. Which side is opposite/adjacent depends on which angle θ is being used.

$\theta$: the reference angle (not the right angle)

Speed, distance, time

\text{Speed}=\frac{\text{Distance}}{\text{Time}}

Units of speed must match the units used for distance and time — convert first if needed.

Reference section

C · Financial Mathematics

Simple interest

I=Prn \qquad A=P(1+rn)

r must be a decimal (e.g. 5% = 0.05), and n must be in the same period as r (usually years).

$I$: interest earned
$P$: principal
$r$: rate per period (decimal)
$n$: number of periods
$A$: total amount, P+I

Overtime pay

\text{Time-and-a-half}=1.5\times\text{normal rate} \qquad \text{Double time}=2\times\text{normal rate}

Applied to hours worked beyond a standard threshold, on top of normal-rate pay for standard hours.

GST

\text{Price incl. GST}=\text{Price excl. GST}\times1.10

To reverse: divide the GST-inclusive price by 1.10, don't just subtract 10%.

Percentage discount

\text{Sale Price}=\text{Original Price}\times\left(1-\frac{\text{discount}\%}{100}\right)

Applies the discount as a percentage reduction from the original price.

Reference section

D · Statistical Analysis

Mean

\text{Mean}=\frac{\text{sum of values}}{\text{number of values}}

Data does not need to be ordered to find the mean (unlike the median).

Range

\text{Range}=\text{maximum}-\text{minimum}

A simple measure of spread, but very sensitive to a single extreme outlier.

Probability

P(\text{event})=\frac{\text{favourable outcomes}}{\text{total outcomes}} \qquad P(\text{not }A)=1-P(A)

Probability is always between 0 and 1 inclusive.

Relative frequency

\text{Relative frequency}=\frac{\text{times event occurred}}{\text{total trials}}

An experimental estimate of probability — approaches the true probability as trials increase.

Reference section

E · Networks

Degree of a vertex

\text{deg}(v)=\text{number of edges connected to } v

Only actual vertices count — a crossing of two edges elsewhere in the diagram is not a vertex unless explicitly marked.

$v$: a vertex in the network

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