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SACE Stage 2 Mathematical Methods formula sheet: what is on it, and the notes you add

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Formula sheet

The card below opens today's Year 12 paper with the sheet in a drawer. The contents follow in our own layout. The SACE Board prints the sheet on one page in two columns and says it has been provided in examinations since November 2022. Check any line against the Board's Mathematical Methods external assessment page and its past papers.

Formula sheet

Year 11 Maths Advanced & Methods

Open formula sheet

Properties of derivatives

\frac{d}{dx}\left(f(x)g(x)\right)=f'(x)g(x)+f(x)g'(x)product rule
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{\left[g(x)\right]^2}quotient rule
\frac{d}{dx}f(g(x))=f'(g(x))g'(x)chain rule

Quadratic equations

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}solution of ax² + bx + c = 0

Discrete random variables

\mu_X=\sum xp(x)mean or expected value
\sigma_X=\sqrt{\sum\left[x-\mu_X\right]^2p(x)}standard deviation

Bernoulli distribution

\sqrt{p(1-p)}standard deviation, with mean p

Binomial distribution

\sqrt{np(1-p)}standard deviation, with mean np
\Pr(X=k)=C_k^np^k(1-p)^{n-k}probability of k successes from n trials

Population proportions

\hat{p}=\frac{X}{n}sample proportion
\sqrt{\frac{p(1-p)}{n}}standard deviation of the sample proportion, with mean p
\hat{p}-z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\le p\le\hat{p}+z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}confidence interval for the population proportion

Continuous random variables

\mu_X=\int_{-\infty}^{\infty}xf(x)dxmean or expected value
\sigma_X=\sqrt{\int_{-\infty}^{\infty}\left[x-\mu_X\right]^2f(x)dx}standard deviation

Normal distributions

f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}probability density function
Z=\frac{X-\mu}{\sigma}standardising

Sampling and confidence intervals

\overline{x}-z\frac{\sigma}{\sqrt{n}}\le\mu\le\overline{x}+z\frac{\sigma}{\sqrt{n}}confidence interval for the population mean

How the exam works with the sheet

The Board's 2025 Mathematical Methods paper lists its materials as question booklet 1, question booklet 2, the formula sheet and your registration label:

ItemDetail
Subject code2MHS20, on Monday 2 November in the 2026 timetable
Total time130 minutes
Total marks100 (53 in question booklet 1, which is allowed about 65 minutes)
Formula sheetProvided, one page
NotesTwo unfolded A4 sheets (four sides) of your own handwritten notes
CalculatorsApproved calculators may be used; the front cover asks you to list them
AnswersThree significant figures unless told otherwise

That notes rule changes how you should read the sheet. The Board gives you the statistics formulas and leaves the calculus and trigonometry to you. Our VCE Methods guide and WACE Methods sheet guide show how Victoria and Western Australia handle the same gap.

What is not on the SACE Methods formula sheet

  • Basic derivatives and integrals. Nothing for x^n, e^x, ln x, sin x or cos x, and no antiderivatives of any kind.
  • Logarithm and index laws. None are given.
  • Trigonometry. No identities, no exact values and no area or sine rule.
  • Sequences and finance. Not on the sheet.
  • The binomial mean. The sheet gives the standard deviation, and the text says the mean is np.
  • The trapezoidal rule and area formulas. Not given.
  • Values of z. The sheet says z is determined by the confidence level, but gives no table.

How to use the sheet in the exam

  1. Use the first few minutes to see what the sheet covers so you do not search for a formula that is not there.
  2. Write the formula from the sheet before you substitute, then show each step: the paper asks for appropriate working and steps of logic.
  3. Notice that the standard deviation lines are written as the square root, so the variances are the squares.
  4. Round to three significant figures unless told otherwise.

Example 1: standardising

Marks are normally distributed with mean 65 and standard deviation 8. A student scores 72. The standardising line gives:

Z=\frac{X-\mu}{\sigma}=\frac{72-65}{8}=0.875

That is 0.875 standard deviations above the mean, so your calculator's normal distribution function gives a probability of about 0.809 below 72.

Example 2: the standard deviation of a sample proportion

A population has p = 0.35 and a sample of n = 400 is taken. The sheet gives the standard deviation of the sample proportion:

\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.35\times0.65}{400}}=0.0238

Its mean is p = 0.35, so about 95% of sample proportions fall within two of these standard deviations, between 0.302 and 0.398.

Example 3: a confidence interval for a mean

A sample of 100 has mean 52 and the population standard deviation is 15. For 95% confidence, z = 1.96:

52\pm1.96\times\frac{15}{\sqrt{100}}=52\pm2.94,\quad49.1\le\mu\le54.9

The sheet gives the shape, but you decide z from the confidence level.

Practise with the sheet open

Our Year 12 Maths Advanced and Methods daily paper is a short timed paper of 8 questions worth 25 to 35 marks. It is not a SACE paper. Practise with a graphics calculator and a page of your own notes, as you will in the exam. The Year 11 paper covers the earlier topics.

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 SACE Mathematical Methods?
Yes. The SACE Board provides a one-page formula sheet with the Stage 2 examination.
Can I bring notes into the SACE Methods exam?
Yes. The Board's exam rules page allows two unfolded A4 sheets (four sides) of your own handwritten notes.
Is the quadratic formula on the SACE Methods sheet?
Yes. It is the second item on the left column.
Are derivatives like d/dx e^x on the sheet?
No. Only the product, quotient and chain rules are given.
How long is the exam?
130 minutes, with a total of 100 marks in the 2025 paper.

Revision cards

Say the answer first, then flip the card to check it.

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