HSC Maths Cheat Sheet: Every Formula You Actually Need (Printable)

Last updated: 24 July 2026

The HSC gives you a formula sheet in the exam. But it's crowded and not organised by what actually comes up. This cheat sheet cuts through that noise — just the formulas you'll reach for, grouped by topic, with quick examples.

Print this. Stick it on your wall. Take a photo for your phone. Use it during topic drills until you don't need it anymore.

Algebra

Formula	Example
Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$	$x^2 - 5x + 6 = 0$ → $x = 2, 3$
Discriminant: $\Delta = b^2 - 4ac$	$\Delta > 0$ → 2 roots, $\Delta = 0$ → 1 root, $\Delta < 0$ → 0 real roots
Log rules: $\log ab = \log a + \log b$ , $\log(a/b) = \log a - \log b$ , $\log a^n = n\log a$	$\log 100 = 2$
Exponential: $A = Pe^{rt}$	Continuous growth/decay

Calculus

Formula	Example
$\frac{d}{dx}x^n = nx^{n-1}$	$\frac{d}{dx}x^3 = 3x^2$
$\frac{d}{dx}e^x = e^x$	Derivative of $e^x$ is itself
$\frac{d}{dx}\sin x = \cos x$	$\frac{d}{dx}\cos x = -\sin x$
Product rule: $(uv)' = u'v + uv'$	$\frac{d}{dx}x^2\sin x = 2x\sin x + x^2\cos x$
Chain rule: $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$	$\frac{d}{dx}\sin(2x) = 2\cos(2x)$
$\int x^n dx = \frac{x^{n+1}}{n+1} + C$	$\int x^2 dx = \frac{x^3}{3} + C$
$\int e^x dx = e^x + C$	—
Area under curve: $\int_a^b f(x) dx$	Between curve and x-axis
Trapezoidal rule: $\int_a^b f(x)dx \approx \frac{h}{2}[f(a) + 2\sum f(x_i) + f(b)]$	Where $h = (b-a)/n$

Trigonometry

Formula	Example
$\sin^2\theta + \cos^2\theta = 1$	Identity. Rearranges to $\sin^2 = 1 - \cos^2$
$\tan\theta = \frac{\sin\theta}{\cos\theta}$	—
Sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$	For non-right triangles
Cosine rule: $c^2 = a^2 + b^2 - 2ab\cos C$	Rearranges to find angles
Area: $A = \frac{1}{2}ab\sin C$	For non-right triangles

Extension formulas:

$\sin(A + B) = \sin A\cos B + \cos A\sin B$
$\cos(A + B) = \cos A\cos B - \sin A\sin B$
$\sin 2A = 2\sin A\cos A$
$\cos 2A = \cos^2 A - \sin^2 A = 2\cos^2 A - 1 = 1 - 2\sin^2 A$

Probability and Statistics

Formula	Notes
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$	Union: don't double-count overlap
$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$	Conditional: restrict to B
68-95-99.7 rule	Within 1/2/3 SD of mean
$z = \frac{x - \mu}{\sigma}$	Standardised score

Finance

Formula	Notes
$A = P(1 + r)^n$	Compound interest
$FV = M\frac{(1 + r)^n - 1}{r}$	Future value of annuity
$PV = M\frac{1 - (1 + r)^{-n}}{r}$	Present value / loan
$r$ is rate per period, $n$ is number of periods	Match the compounding frequency

Extension 1: Vectors

Formula	Notes
$\mathbf{a} \cdot \mathbf{b} = \lVert \mathbf{a} \rVert \lVert \mathbf{b} \rVert \cos\theta$	Dot product = angle finder
Perpendicular: $\mathbf{a} \cdot \mathbf{b} = 0$	Zero dot = right angle
$\text{proj}_{\mathbf{b}}\mathbf{a} = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{b} \cdot \mathbf{b}}\mathbf{b}$	Vector projection

Extension 2: Complex Numbers

Formula	Notes
$z = x + iy = r(\cos\theta + i\sin\theta)$	Cartesian ↔ polar
De Moivre: $(\cos\theta + i\sin\theta)^n = \cos(n\theta) + i\sin(n\theta)$	Powers made easy
Conjugate: $z \times \overline{z} = \lvert z \rvert^2$	Product with conjugate = real

Quick exam tips

Show working. Method marks are real marks. Even if you can do it in your head, write the steps.
Draw a diagram. For geometry, vectors, trig — sketch first.
Check the domain. Multiple solutions in trig? Domain determines which count.
Use your formula sheet. During topic drills, have it open. Train your eye for where things are.
If stuck for 5 minutes, move. The easy marks are elsewhere in the paper.

Print this, work through it during topic drills, and by exam day it'll be muscle memory.

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