VCE Specialist Maths formula sheet: what is on it and what is not (VCAA)

Quick answer

The VCE Specialist Mathematics formula sheet (VCAA) is six pages of tables in seven sections: mensuration, complex numbers, data analysis and probability, calculus, kinematics, vectors, and circular functions. It is handed out with Exam 1, which is technology-free with no notes, and Exam 2 has its own sheet with the same content. It prints a long list of derivatives and antiderivatives, integration by parts, Euler's method, surface area and arc length integrals, de Moivre's theorem, line and plane equations and the circular function identities, but not algebra rules, exact values or most integration techniques. This page describes the sheet in our own words; print the official PDF from the VCAA Specialist Mathematics examination page and work from that.

This guide describes the sheets VCAA links for Specialist Mathematics (marked 2024 on the cover; no 2026-dated sheet was listed when we checked on 21 October 2026) under the VCE Mathematics Study Design accredited for 2023 to 2027. In 2026 Exam 1 is on Monday 9 November and Exam 2 on Wednesday 11 November. Past papers and marked questions are on the VCE Specialist Mathematics page.

What is on the VCE Specialist Maths formula sheet?

Each section has a heading, and the pages run in this order. Here is each one in plain words.

Mensuration

Eight rows: the area of a circle segment (written in terms of the radius and the angle at the centre), the volume of a cylinder, cone, pyramid and sphere, the area of a triangle from two sides and the included angle, and the sine rule and cosine rule. Note what is missing: there is no row for the area of a whole circle or a sector.

Algebra, number and structure (complex numbers)

Six statements. Cartesian and polar (cis) form of a complex number, its modulus, the range printed for the principal argument, the product and quotient of two numbers in polar form, and de Moivre's theorem. Everything else about complex numbers, including conjugates, roots of polynomials and the geometry of loci, is yours to bring.

Data analysis, probability and statistics

• The expected value and variance of a linear function of one random variable, and of a sum of independent random variables with different coefficients.
• The expected value and variance of a sum of independent, identically distributed variables, in terms of $n$, $\mu$ and $\sigma^2$.
• The approximate confidence interval for a population mean, written with the sample standard deviation $s$ and a $z$ value.
• The mean and variance of the sample mean $\overline{X}$.

The sheet does not tell you which $z$ to use, how $s$ is calculated, or what shape the distribution of $\overline{X}$ has.

Calculus

The biggest section, spread over two pages. Page one is a two-column table with a derivative on the left and an antiderivative on the right.

• Derivatives of a power of $x$, $e^{ax}$, the natural logarithm, and sine, cosine, tangent, cotangent, secant and cosecant of $ax$, plus the inverse sine, inverse cosine and inverse tangent of $ax$.
• Antiderivatives of the matching forms, including $\sec^2$, $\operatorname{cosec}^2$, secant times tangent and cosecant times cotangent, three inverse circular forms with $a^2$ in the denominator, a power of a linear expression $(ax+b)$, and $\frac{1}{ax+b}$. The antiderivative of $\frac{1}{x}$ is printed with an absolute value inside the logarithm. The last two rows have no printed derivative, as the cells are shaded out.
• Product, quotient and chain rules, and integration by parts.
• Euler's method, as the step rule for $x$ and $y$ with step size $h$.
• Arc length for parametric curves, and surface area of revolution in four forms: Cartesian about the $x$-axis, Cartesian about the $y$-axis, and parametric about each axis.

Kinematics

Acceleration written four ways, as $\frac{d^2x}{dt^2}$, $\frac{dv}{dt}$, $v\frac{dv}{dx}$ and the derivative of $\frac{1}{2}v^2$, and the four constant acceleration formulas.

Vectors in two and three dimensions

• Position as a vector function of $t$, its magnitude, and its derivative.
• The scalar (dot) product in both its angle form and its component form, and the cross product written as a determinant and expanded.
• The vector and parametric equations of a line.
• The vector, parametric and Cartesian equations of a plane.

Circular functions

The Pythagorean identities for sine and cosine, tangent and secant, and cotangent and cosecant. The sum and difference formulas for sine, cosine and tangent, the double angle formulas (cosine in all three of its forms), and the formulas for $\sin^2(ax)$ and $\cos^2(ax)$ in terms of $\cos(2ax)$. The last pair is what you reach for when you need to integrate a squared sine or cosine.

What is not on the formula sheet?

This list comes from reading the printed pages, not from the study design. Each item is absent from the sheet, so it has to come from memory in Exam 1, and from memory or your bound reference in Exam 2. Whether a given item can be examined is a question for the study design.

The left column was checked against the printed pages. The right column is our own note on where a gap can matter, not VCAA wording.

Are the Exam 1 and Exam 2 formula sheets the same?

Yes, on the files VCAA currently links. We compared the text of the two PDFs and the only differences are the exam number on the cover and in the page headers. The practical differences between the papers sit elsewhere:

Calculator and bound reference rules are from VCAA's 2026 Exams Navigator and the study design. Both exams start with 15 minutes of reading time, which matches the 9:00 am to 10:15 am and 11:45 am to 2:00 pm slots on the timetable. The Methods version of this sheet is a different document, covered in the VCE Methods formula sheet guide. Exam dates for every study are on the VCE exam timetable.

How do you use the sheet in the technology-free Exam 1?

The sheet saves you remembering a formula. It does not save you the algebra, and it is the algebra that Exam 1 marks. Three short examples show where the sheet stops and your own work starts.

Where do you practise with the sheet?

AusGrader holds VCAA Specialist Mathematics past exams with marked practice questions. Do an Exam 1 paper with only the printed sheet beside you and no calculator, and write down every rule you needed that is not printed. That list is more useful than anyone else's. For which topics carry marks, see most tested topics and hardest topics. The topic pages for calculus, space and measurement, algebra, number and structure and data analysis, probability and statistics hold the questions that use the matching sections of the sheet.