Australian examsWACE
WACE Mathematics Specialist ATAR formula sheet: all eight sections and what is missing
Maths Extension 2 & Specialist Maths
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Formula sheet
The card below opens today's paper with the sheet in a drawer. The contents follow in our own layout. SCSA publishes the 2026 sheet on the Mathematics Specialist course page, so check any line against it. The sheet is valid for teaching and examining until 31 December 2026.
Formula sheet
Open formula sheetMaths Extension 2 & Specialist Maths
Differentiation and integration
\frac{d}{dx}x^n=nx^{n-1}\quad\int x^ndx=\frac{x^{n+1}}{n+1}+c,\ n\ne-1power
\frac{d}{dx}e^{ax}=ae^{ax}\quad\int e^{ax}dx=\frac{1}{a}e^{ax}+cexponential
\frac{d}{dx}\ln x=\frac{1}{x}\quad\int\frac{1}{x}dx=\ln|x|+cnatural logarithm
\frac{d}{dx}\ln f(x)=\frac{f'(x)}{f(x)}\quad\int\frac{f'(x)}{f(x)}dx=\ln|f(x)|+clogarithm of a function
\frac{d}{dx}\sin f(x)=f'(x)\cos f(x)\quad\int\sin(ax)dx=-\frac{1}{a}\cos(ax)+csine
\frac{d}{dx}\cos f(x)=-f'(x)\sin f(x)\quad\int\cos(ax)dx=\frac{1}{a}\sin(ax)+ccosine
\frac{d}{dx}\tan f(x)=f'(x)\sec^2f(x)=\frac{f'(x)}{\cos^2f(x)}\quad\int\sec^2(ax)dx=\frac{1}{a}\tan(ax)+ctangent
y=uv:\quad\frac{d}{dx}(uv)=v\frac{du}{dx}+u\frac{dv}{dx}\quad\text{or}\quad y'=f'(x)g(x)+f(x)g'(x)product rule
y=\frac{u}{v}:\quad\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}\quad\text{or}\quad y'=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}quotient rule
\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}\quad\text{or}\quad y'=f'(g(x))g'(x)chain rule
\frac{d}{dx}\left(\int_a^xf(t)dt\right)=f(x)\quad\text{and}\quad\int_a^bf'(x)dx=f(b)-f(a)fundamental theorem
Applications of calculus
\frac{dP}{dt}=kP\Leftrightarrow P=P_0e^{kt}exponential growth and decay
\frac{dP}{dt}=rP(k-P)\Leftrightarrow P=\frac{kP_0}{P_0+(k-P_0)e^{-rkt}}logistic growth
V=\pi\int_a^b\left[f(x)\right]^2dxvolume of revolution about the x-axis
V=\pi\int_c^d\left[f(y)\right]^2dyvolume of revolution about the y-axis
\text{if}\ \frac{d^2x}{dt^2}=-k^2x\ \text{then}\ x=A\sin(kt+\alpha)\ \text{or}\ x=A\cos(kt+\beta)simple harmonic motion
v^2=k^2\left(A^2-x^2\right)\quad T=\frac{2\pi}{k}\quad f=\frac{1}{T}speed, period and frequency in SHM
\delta y\approx\frac{dy}{dx}\times\delta xincrements formula
\frac{dv}{dt}\quad\text{or}\quad v\frac{dv}{dx}\quad\text{or}\quad\frac{d}{dx}\left(\frac{1}{2}v^2\right)acceleration
Functions
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}quadratic function, if f(x) = ax² + bx + c = 0
|x|=x\ \text{for}\ x\ge0,\quad|x|=-x\ \text{for}\ x<0absolute value
Statistical inference
\overline{X}-z\frac{s}{\sqrt{n}}\le\mu\le\overline{X}+z\frac{s}{\sqrt{n}}confidence interval for the population mean
n=\left(\frac{z\times s}{d}\right)^2sample size
Mensuration
A=bharea of a parallelogram
A=\frac{1}{2}bh\quad\text{or}\quad A=\frac{1}{2}ab\sin Carea of a triangle
A=\frac{1}{2}(a+b)harea of a trapezium
A=\pi r^2\quad\text{and}\quad C=2\pi r=\pi dcircle
V=Ahprism, where A is the area of the cross section
V=\frac{1}{3}Ahpyramid, where A is the area of the base
V=\pi r^2h\quad TSA=2\pi rh+2\pi r^2cylinder
V=\frac{1}{3}\pi r^2h\quad TSA=\pi rs+\pi r^2cone, where s is the slant height
V=\frac{4}{3}\pi r^3\quad TSA=4\pi r^2sphere
Vectors in 3D
\left|(a_1,a_2,a_3)\right|=\sqrt{a_1^2+a_2^2+a_3^2}magnitude
\mathbf{a}\cdot\mathbf{b}=|\mathbf{a}||\mathbf{b}|\cos\theta=a_1b_1+a_2b_2+a_3b_3dot product
\mathbf{a}\times\mathbf{b}=\left(a_2b_3-a_3b_2,\ a_3b_1-a_1b_3,\ a_1b_2-a_2b_1\right)cross product
\mathbf{r}=\mathbf{a}+\lambda\mathbf{u}line through a point with direction u
\mathbf{r}=\mathbf{a}+\lambda(\mathbf{b}-\mathbf{a})line through two points A and B
\mathbf{r}=\mathbf{a}+\lambda\mathbf{u}_1+\mu\mathbf{u}_2\quad\text{or}\quad\mathbf{r}\cdot\mathbf{n}=\mathbf{a}\cdot\mathbf{n}plane
|\mathbf{r}-\mathbf{d}|=r\quad\text{or}\quad(x-a)^2+(y-b)^2+(z-c)^2=r^2sphere
\frac{x-a_1}{u_1}=\frac{y-a_2}{u_2}=\frac{z-a_3}{u_3}Cartesian equation of a line
ax+by+cz=dCartesian equation of a plane
x=a_1+\lambda u_1,\quad y=a_2+\lambda u_2,\quad z=a_3+\lambda u_3parametric equations of a line
Complex numbers
z=a+bi,\quad\overline{z}=a-biCartesian form and conjugate
|z|=\sqrt{a^2+b^2}=r,\quad\text{Arg}(z)=\theta,\ \tan\theta=\frac{b}{a},\ -\pi<\theta\le\pimodulus and argument
|z_1z_2|=|z_1||z_2|,\quad\left|\frac{z_1}{z_2}\right|=\frac{|z_1|}{|z_2|}modulus of a product and quotient
\arg(z_1z_2)=\arg(z_1)+\arg(z_2),\quad\arg\left(\frac{z_1}{z_2}\right)=\arg(z_1)-\arg(z_2)argument of a product and quotient
z\overline{z}=|z|^2,\quad z^{-1}=\frac{1}{z}=\frac{\overline{z}}{|z|^2},\quad\overline{z_1+z_2}=\overline{z_1}+\overline{z_2},\quad\overline{z_1z_2}=\overline{z_1}\ \overline{z_2}conjugate properties
z=a+bi=r(\cos\theta+i\sin\theta)=r\ \text{cis}\ \theta,\quad\overline{z}=r\ \text{cis}(-\theta)polar form
z_1z_2=r_1r_2\ \text{cis}(\theta_1+\theta_2),\quad\frac{z_1}{z_2}=\frac{r_1}{r_2}\ \text{cis}(\theta_1-\theta_2)product and quotient in polar form
z^n=|z|^n\text{cis}(n\theta),\quad(\text{cis}\ \theta)^n=\cos n\theta+i\sin n\thetade Moivre's theorem
z^{\frac{1}{q}}=r^{\frac{1}{q}}\left(\cos\frac{\theta+2\pi k}{q}+i\sin\frac{\theta+2\pi k}{q}\right),\ k\ \text{an integer}roots of a complex number
Trigonometry
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sine rule
a^2=b^2+c^2-2bc\cos Acosine rule
\cos A=\frac{b^2+c^2-a^2}{2bc}cosine rule for an angle
\text{length of arc}=r\thetaarc length
\text{area of segment}=\frac{1}{2}r^2(\theta-\sin\theta)area of a segment
\text{area of sector}=\frac{1}{2}r^2\thetaarea of a sector
\cos^2x+\sin^2x=1,\quad1+\tan^2x=\sec^2xPythagorean identities
\cos(x\pm y)=\cos x\cos y\mp\sin x\sin ysum and difference of cosines
\sin(x\pm y)=\sin x\cos y\pm\cos x\sin ysum and difference of sines
\tan(x\pm y)=\frac{\tan x\pm\tan y}{1\mp\tan x\tan y}sum and difference of tangents
\sin2x=2\sin x\cos x,\quad\cos2x=\cos^2x-\sin^2x=2\cos^2x-1=1-2\sin^2x,\quad\tan2x=\frac{2\tan x}{1-\tan^2x}double angles
\cos A\cos B=\frac{1}{2}(\cos(A-B)+\cos(A+B)),\quad\sin A\sin B=\frac{1}{2}(\cos(A-B)-\cos(A+B))product to sum, cosines and sines
\sin A\cos B=\frac{1}{2}(\sin(A+B)+\sin(A-B)),\quad\cos A\sin B=\frac{1}{2}(\sin(A+B)-\sin(A-B))product to sum, mixed
How the exam works with the sheet
The 2026 front covers for Mathematics Specialist set out the two sections:
| Section | Reading | Working | What you may use |
|---|---|---|---|
| One: calculator-free | 5 minutes | 50 minutes | Pens, pencils, ruler and the formula sheet |
| Two: calculator-assumed | 10 minutes | 100 minutes | The formula sheet from Section One, drawing instruments, notes on two unfolded A4 sheets, and up to three calculators including CAS |
Because the sheet is retained, one copy covers both sections. For the course content, our Maths Extension 2 and Specialist Maths guide and Specialist Maths mechanics guide help.
What is not on the WACE Specialist formula sheet
- Integration by parts and substitution. No pattern is given for either method.
- Numerical methods. No trapezoidal rule, Simpson's rule or Euler's method.
- Matrices and linear transformations. Not on the sheet.
- Inverse trigonometric derivatives and integrals. Only sin, cos, tan and ln are given.
- Proof templates. There is no induction or contradiction structure.
- Sequences, series and the binomial theorem. None are printed.
- Exact trigonometric values. Identities are there, but the table of values is not.
- Vector projections and the distance from a point to a plane. Dot and cross products are given but the projection formulas are not.
How to use the sheet in the exam
- Use reading time to find the index on page 2, which tells you which page each section is on.
- Write the formula you use with the symbols matched to the question.
- In Section One, do exact working: leave surds, π and ln in your answer.
- In Section Two, put the pieces the sheet lacks on your two A4 sheets of notes.
Example 1: a volume of revolution
The curve y = √x from x = 0 to x = 4 is rotated about the x-axis. The volume line gives:
V=\pi\int_0^4\left(\sqrt{x}\right)^2dx=\pi\int_0^4x\ dx=\pi\left[\frac{x^2}{2}\right]_0^4=8\pi
This is about 25.13 cubic units. In a calculator-free section you leave it as 8π.
Example 2: cube roots of 8
To solve z³ = 8, write 8 as 8 cis 0, so r = 8 and θ = 0. The roots line with q = 3 gives:
z=8^{\frac{1}{3}}\left(\cos\frac{2\pi k}{3}+i\sin\frac{2\pi k}{3}\right)=2,\quad-1+\sqrt{3}i,\quad-1-\sqrt{3}i
These are k = 0, 1 and 2. They sit 120° apart on a circle of radius 2, which you can check in the Complex Numbers Calculator.
Example 3: sample size
You want a 95% confidence interval for a mean with a margin of error of d = 2, and the sample standard deviation is s = 12, with z = 1.96. The sample size line gives:
n=\left(\frac{z\times s}{d}\right)^2=\left(\frac{1.96\times12}{2}\right)^2=138.3
Always round up for a sample size, so you need 139 people.
Practise with the sheet open
Our Maths Extension 2 and Specialist Maths daily paper is a short timed paper of 8 questions worth 25 to 35 marks. It is not a SCSA paper. The Specialist Maths mechanics paper covers the mechanics-style calculus. Compare with the QCE Specialist Maths sheet guide.
Exam answers
The answers and a worked mark scheme come with today's paper once it is marked. They show which line of the sheet each question wanted. We do not publish official answers, past paper answers or leaked papers.
Common questions
Do you get a formula sheet in WACE Specialist Maths?
Yes. The supervisor provides a formula sheet in Section One and you retain it for Section Two.
Is the quadratic formula on the sheet?
Yes. The Functions section gives it, along with the definition of the absolute value.
Are notes allowed in the Specialist exam?
In Section Two, notes on two unfolded A4 sheets are permitted with up to three calculators.
Is integration by parts on the formula sheet?
No. The sheet has no integration by parts or substitution pattern.
How long is each section?
Section One has 5 minutes of reading and 50 minutes of working. Section Two has 10 minutes of reading and 100 minutes of working.
Revision cards
Say the answer first, then flip the card to check it.
Where to go next
- Solve it
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