WACE Mathematics Specialist formula sheet explained (SCSA)

Quick answer

The WACE Mathematics Specialist formula sheet (SCSA) is an eight-page document whose pages 3 to 7 hold the content: calculus rules, applications of calculus, vectors in 3D, complex numbers, a full trigonometry page, mensuration and two statistical inference rows. SCSA supplies it with both sections of the exam, so it is in front of you in Section One: Calculator-free as well. It gives you results to quote, not methods, and it leaves out exact trigonometric values, integration techniques, vector projections and the value of z for a confidence interval. This page describes the sheet in our own words; print the official PDF and work from that.

This guide describes the 2026 sheet (reference 2025/113749), which SCSA marks as valid for teaching and examining until 31 December 2026. It makes no claim about what the syllabus does or does not include: it says only what is printed. Past papers and marked practice questions are on the WACE Mathematics Specialist page, and the Methods formula sheet guide covers the shorter sheet for the other calculus course.

What is on the Specialist formula sheet?

Page 1 is the cover, page 2 is an index and page 8 is the copyright page. Each group below is a heading on pages 3 to 7.

The sheet closes with a note: any additional formulas the examination panel identifies as necessary will be included in the body of the particular question.

What do the details on the sheet mean?

Several rows reward a slower read. These are the ones that catch students out.

• Log integrals carry modulus signs. The integral of $\frac{1}{x}$ is printed as $\ln|x|$ and the $f'/f$ integral as $\ln|f(x)|$, so the sheet already covers negative values. Copy the modulus bars into your working.
• Derivative rows have the chain rule built in. The sine, cosine, tangent and $\ln f(x)$ derivatives are written for a general $f(x)$ and include $f'(x)$. The tangent row is printed in two forms, $f'(x)\sec^2 f(x)$ and $\frac{f'(x)}{\cos^2 f(x)}$.
• Integral rows use $ax$ only. The sine, cosine, $\sec^2$ and exponential integrals are printed for $ax$, with $\frac{1}{a}$ out the front, and the sine integral carries a minus sign. An argument like $3x+1$ is still your job to handle, and Section One marks the exact result.
• Product and quotient rule. Each is printed twice, once in $u$, $v$ notation and once in $f$, $g$ notation. They are the same rule, so use whichever matches the question.
• The logistic row. The equation is printed as $\frac{dP}{dt} = rP(k-P)$, and its solution has $e^{-rkt}$ in it, not $e^{-rt}$. The carrying capacity is $k$, and the rate that drives the exponent is the product $rk$. Misreading this is an easy way to lose a mark in a question that gives you $r$ and $k$ separately.
• Both growth rows are two-way. The exponential and logistic rows join each differential equation to its solution with a double arrow, so the general solution is printed for you.
• Volumes of revolution. The sheet prints one curve rotated about the $x$-axis and one rotated about the $y$-axis, with the integrand squared. A region between two curves is not printed.
• Simple harmonic motion. The sheet gives the two solution forms, $v^2 = k^2(A^2 - x^2)$, the period $\frac{2\pi}{k}$ and the frequency $\frac{1}{T}$, and defines $A$, $\alpha$, $\beta$, $v$ and $x$ in a line between the solution forms and the rest.
• Increments and acceleration. These sit under a grey bar with no heading. $\delta y \approx \frac{dy}{dx}\times\delta x$ is an approximation. Acceleration is printed as $\frac{dv}{dt}$, $v\frac{dv}{dx}$ and $\frac{d}{dx}\left(\frac12 v^2\right)$.
• Statistical inference symbols are not defined. The confidence interval and the sample size formula use $z$, $s$, $n$ and $d$ with no legend on the sheet and no value of $z$.
• Argument range. The sheet prints $-\pi < \theta \le \pi$ for the principal argument, so an answer outside that range is not the principal value.
• Roots. The root formula carries an integer $k$, which is how you generate each of the $q$ different roots.

What is not on the Specialist formula sheet?

This list comes from reading pages 3 to 7. It records what is printed, and nothing here says whether a result is examinable.

The left column was checked against the printed pages. The right column is our own note on where the gap can matter, not SCSA wording. Some of the items on the left may be handed to you in a question under the panel note, and some you are expected to derive.

How do you use the sheet in Section One: Calculator-free?

Section One is 5 minutes of reading and 50 minutes of working, with no calculator and no notes, so the sheet and your memory are the whole toolkit. SCSA's 2024 and 2025 Mathematics Specialist reports both call out weak algebra, and the 2025 report adds unclear presentation and singles out the notation in a three-dimensional geometry proof. Those losses sit between the printed rows, not in them. Four examples show where the sheet stops and your own working starts.

How does the sheet change in Section Two: Calculator-assumed?

You get the same sheet, plus up to three calculators (CAS included) and up to two unfolded A4 sheets of notes, with 10 minutes of reading and 100 minutes of working. So the question is what to put on your notes. Not the printed rows, which you already have. Put there the things the sheet leaves out and a CAS does not do for you: the exact trigonometric values you use, the identities not printed, the $z$-values you want and the steps a "show that" question needs.

Where do you practise with the sheet?

Do a Section One paper with the printed sheet and nothing else, then list every result you reached for that is not on it. That list is your personal not-on-the-sheet list. The marks-by-topic guides show where each group of rows gets used most: most tested topics and hardest topics. Questions that use the printed rows are in Vectors in three dimensions, Complex numbers, Rates of change and differential equations, Integration and applications of integration and Statistical inference. Dates for every WACE written exam are on the WACE exam timetable.