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WACE Mathematics Methods ATAR formula sheet: every line, and what to learn yourself

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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. SCSA's 2026 sheet is dated 2025 and published on the SCSA Mathematics Methods page, so check any line against it before you rely on it.

Formula sheet

Year 11 Maths Advanced & Methods

Open formula sheet

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-b}=ae^{ax-b}\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+c,\ x>0natural logarithm
\frac{d}{dx}\ln f(x)=\frac{f'(x)}{f(x)}\quad\int\frac{f'(x)}{f(x)}dx=\ln f(x)+c,\ f(x)>0logarithm of a function
\frac{d}{dx}\sin(ax-b)=a\cos(ax-b)\quad\int\sin(ax-b)dx=-\frac{1}{a}\cos(ax-b)+csine
\frac{d}{dx}\cos(ax-b)=-a\sin(ax-b)\quad\int\cos(ax-b)dx=\frac{1}{a}\sin(ax-b)+ccosine
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
\delta y\approx\frac{dy}{dx}\times\delta xincrements formula
\frac{dP}{dt}=kP\Leftrightarrow P=P_0e^{kt}exponential growth and decay

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

Trigonometry

\sin^2x+\cos^2x=1Pythagorean identity
\tan x=\frac{\sin x}{\cos x}tangent

Logarithms

x=\log_ab\Leftrightarrow a^x=bdefinition
a^{\log_ab}=b\quad\text{and}\quad\log_a\left(a^b\right)=binverse properties
\log_amn=\log_am+\log_anproduct
\log_a\frac{m}{n}=\log_am-\log_anquotient
\log_a\left(m^k\right)=k\log_ampower
\log_ex=\ln xnatural logarithm

Probability

P(A')=1-P(A)complement
P(A\cup B)=P(A)+P(B)-P(A\cap B)addition rule
P(A|B)=\frac{P(A\cap B)}{P(B)}conditional probability

Random variables and probability distributions

\mu=p\quad\sigma^2=p(1-p)Bernoulli distribution
P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}\quad\mu=np\quad\sigma^2=np(1-p)binomial distribution
P(X=x)=P(x)\quad\mu=E(X)=\sum xp(x)\quad\sigma^2=\sum(x-\mu)^2p(x)discrete random variable
P(a\le X\le b)=\int_a^bp(x)dxcontinuous random variable
\mu=E(X)=\int_{-\infty}^{\infty}xp(x)dxexpected value of a continuous variable
\sigma^2=\int_{-\infty}^{\infty}(x-\mu)^2p(x)dxvariance of a continuous variable

Sample proportions

\hat{p}=\frac{X}{n}sample proportion
E(\hat{p})=pmean
\sigma=\sqrt{\frac{p(1-p)}{n}}standard deviation
E=z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}margin of error
\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

How the exam works with the sheet

The Mathematics Methods ATAR examination has two sections. The syllabus design brief and the 2025 exam covers say this about the sheet and what you may bring:

SectionShareReadingWorkingWhat you may use
One: calculator-free35%5 minutes50 minutesPens, pencils, ruler and the formula sheet. No special items.
Two: calculator-assumed65%10 minutes100 minutesThe formula sheet from Section One, drawing instruments, notes on two unfolded A4 sheets, and up to three calculators including CAS

There is a changeover period of up to 15 minutes during which you cannot work. The syllabus assumes you have a calculator with CAS capability for Section Two. Our VCE Methods guide shows how Victoria differs, and the QCE Methods sheet guide covers Queensland.

What is not on the WACE Methods formula sheet

  • The quadratic formula. Learn it and the discriminant.
  • Exact trigonometric values and the double-angle identities. The sheet has only sin² + cos² = 1 and tan = sin ÷ cos.
  • The derivative of tan x and of a^x. Only the exponential e^(ax − b), the natural logarithm, sine and cosine are given.
  • Sequences and series. There are no arithmetic or geometric formulas.
  • The trapezoidal rule and Simpson's rule. Neither is printed.
  • The binomial theorem. Only the binomial distribution is given.
  • Normal distribution and z-values. The sheet gives margin of error but not the value of z.
  • Integrals of powers of a linear function. There is no line for the integral of (ax + b) to the power n, so you divide by a yourself.

How to use the sheet in the exam

  1. Use the Section One reading time to find the page for calculus, then the page for probability.
  2. Write the formula you will use and the substituted values before you simplify, because markers need working for any question worth more than 2 marks.
  3. Look for the matching form. The sine and cosine rows are written for (ax − b), so a bracket with a coefficient is already covered.
  4. Keep the sheet for Section Two: it is retained, so you do not need to hand it in.

Example 1: an integral with a coefficient

Find\int e^{2x-3}dx. The exponential integral line is for e^(ax), and the same coefficient rule works for e^(ax − b), so with a = 2:

\int e^{2x-3}dx=\frac{1}{2}e^{2x-3}+c

Differentiating back with the line d/dx e^(ax − b) = ae^(ax − b) returns e^(2x − 3), which confirms it. Practise it in the Calculus course.

Example 2: exponential growth

A population is 500 and grows to 800 after 3 years. With P = P₀e^(kt), the value of k comes from 800 = 500e^(3k):

k=\frac{\ln1.6}{3}=0.1567,\qquad P(10)=500e^{1.567}\approx2395

The population doubles every ln 2 ÷ k = 4.4 years, so the sheet's growth line answers several questions at once.

Example 3: a confidence interval

In a survey of 150 people, 60% say they prefer the new design, so p-hat = 0.6, and you use z = 1.96. The sheet's margin of error line gives:

E=1.96\sqrt{\frac{0.6\times0.4}{150}}=0.0784\quad\text{so}\quad0.522\le p\le0.678

The sheet gives the formula but not z: take it from your CAS or the question.

Practise with the sheet open

Our Year 12 Maths Advanced and Methods paper is a short timed paper of 8 questions worth 25 to 35 marks. It is not a SCSA paper. Use it as a short mock for Section One style working without a calculator, then check with a calculator. The Year 11 paper covers earlier units.

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 Maths Methods?
Yes. The supervisor provides a formula sheet in Section One, and you retain it for Section Two.
Can I bring notes into the WACE Methods exam?
In Section Two, notes on two unfolded A4 sheets are permitted. Section One allows no special items.
Is the quadratic formula on the WACE Methods formula sheet?
No. Learn it.
How long is the Methods exam?
Section One has 5 minutes of reading and 50 minutes of working. Section Two has 10 minutes of reading and 100 minutes of working.
How much is each section worth?
Section One is 35% and Section Two is 65% of the examination.

Revision cards

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

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