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VCE Mathematical Methods formula sheet: what is on it, and what is not

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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 VCAA published the sheets for all VCE mathematics exams in August 2024 in a redesigned layout, and the sheet is on the VCAA Mathematical Methods pages. Check any line against it before you rely on it.

Formula sheet

Year 11 Maths Advanced & Methods

Open formula sheet

Mensuration

A=\frac{1}{2}(a+b)harea of a trapezium
A=2\pi rhcurved surface area of a cylinder
V=\pi r^2hvolume of a cylinder
V=\frac{1}{3}\pi r^2hvolume of a cone
V=\frac{1}{3}Ahvolume of a pyramid
V=\frac{4}{3}\pi r^3volume of a sphere
A=\frac{1}{2}bc\sin(A)area of a triangle

Calculus

\frac{d}{dx}\left(x^n\right)=nx^{n-1}\quad\int x^ndx=\frac{1}{n+1}x^{n+1}+c,\ n\ne-1power
\frac{d}{dx}\left((ax+b)^n\right)=an(ax+b)^{n-1}\quad\int(ax+b)^ndx=\frac{1}{a(n+1)}(ax+b)^{n+1}+c,\ n\ne-1power of a linear function
\frac{d}{dx}\left(e^{ax}\right)=ae^{ax}\quad\int e^{ax}dx=\frac{1}{a}e^{ax}+cexponential
\frac{d}{dx}\left(\log_e(x)\right)=\frac{1}{x}\quad\int\frac{1}{x}dx=\log_e(x)+c,\ x>0natural logarithm
\frac{d}{dx}(\sin(ax))=a\cos(ax)\quad\int\sin(ax)dx=-\frac{1}{a}\cos(ax)+csine
\frac{d}{dx}(\cos(ax))=-a\sin(ax)\quad\int\cos(ax)dx=\frac{1}{a}\sin(ax)+ccosine
\frac{d}{dx}(\tan(ax))=\frac{a}{\cos^2(ax)}=a\sec^2(ax)tangent
\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}product rule
\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}quotient rule
\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}chain rule
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}Newton's method
Area\approx\frac{x_n-x_0}{2n}\left[f(x_0)+2f(x_1)+2f(x_2)+\ldots+2f(x_{n-2})+2f(x_{n-1})+f(x_n)\right]trapezium rule approximation

Probability

\Pr(A)=1-\Pr(A')complement
\Pr(A\cup B)=\Pr(A)+\Pr(B)-\Pr(A\cap B)addition rule
\Pr(A|B)=\frac{\Pr(A\cap B)}{\Pr(B)}conditional probability
\mu=E(X)mean
var(X)=\sigma^2=E\left((X-\mu)^2\right)=E\left(X^2\right)-\mu^2variance
\binom{n}{x}=\frac{n!}{x!(n-x)!}binomial coefficient

Probability distributions

DistributionProbabilityMeanVariance
discretePr(X = x) = p(x)μ = Σ x p(x)σ² = Σ (x − μ)² p(x)
binomialPr(X = x) = C(n, x) pˣ (1 − p)ⁿ⁻ˣμ = npσ² = np(1 − p)
continuousPr(a < X < b) = ∫ f(x) dx from a to bμ = ∫ x f(x) dxσ² = ∫ (x − μ)² f(x) dx

Sample proportions

\hat{P}=\frac{X}{n}sample proportion
E(\hat{P})=pmean
sd(\hat{P})=\sqrt{\frac{p(1-p)}{n}}standard deviation
\left(\hat{p}-z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\ \hat{p}+z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)approximate confidence interval

How the two exams work with the sheet

The VCAA's 2025 Methods papers give these conditions:

ItemExamination 1Examination 2
Reading time15 minutes15 minutes
Writing time1 hour2 hours
Content9 questions, 40 marksSection A: 20 multiple-choice questions, 20 marks. Section B: 4 questions, 60 marks
TechnologyNone: no calculator or softwareOne approved CAS calculator or CAS software, and one scientific calculator
NotesNone of any kindOne bound reference
Formula sheetSuppliedSupplied

The sheet is identical in both, so the same lines serve a technology-free paper and a CAS paper. For other states' Methods sheets, see the QCE, WACE, SACE and TCE guides, and our VCE Maths Methods guide for the course.

What is not on the VCE Methods formula sheet

  • The quadratic formula. Not printed, in either exam.
  • Trigonometric identities and exact values. No identities, no double angles and no table of exact values.
  • Logarithm and index laws. None are given.
  • The normal distribution. No density function, z-score line or 68-95-99.7 rule, so these come from your CAS in Exam 2.
  • Sequences and finance. Not in the Methods study design sheet.
  • The binomial theorem. Only the binomial coefficient and distribution are given.
  • Antiderivatives of tan and the general logarithm. Only the integrals of x^n, powers of a linear function, e^(ax), 1/x, sine and cosine are given.

How to use the sheet in the exam

  1. During reading time in Exam 1, check which lines you need: it is technology-free, so exact answers matter.
  2. Write the line from the sheet first, then substitute.
  3. In Exam 1, leave answers exact unless told otherwise, with surds, π and logarithms intact.
  4. In Exam 2, use the CAS for the arithmetic, but show the setup in Section B.

Example 1: Newton's method

Starting at x₀ = 1.5, apply Newton's method to f(x) = x² − 2 to approximate √2. With f'(x) = 2x, the sheet line gives:

x_1=1.5-\frac{1.5^2-2}{2\times1.5}=1.5-\frac{0.25}{3}=1.4167,\qquad x_2=1.4142

The true value of √2 is 1.41421, so two steps already agree to four decimal places.

Example 2: the trapezium rule

Estimate\int_1^3\frac{1}{x}dxwith 4 strips. The points x = 1, 1.5, 2, 2.5 and 3 give heights 1, 0.667, 0.5, 0.4 and 0.333:

\frac{3-1}{2\times4}\left[1+2(0.667+0.5+0.4)+0.333\right]=0.25\times4.467=1.117

The exact value is loge 3 = 1.099, so the trapezium rule overestimates because the curve is convex.

Example 3: a power of a linear function

Differentiate (3x − 2)⁵. The sheet gives d/dx of (ax + b)ⁿ with a = 3 and n = 5:

\frac{d}{dx}\left((3x-2)^5\right)=3\times5(3x-2)^4=15(3x-2)^4

The factor 15 is the coefficient a times the power n. Practise this in the Calculus course.

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 VCAA paper. Sit it without technology for the Exam 1 style, then check with your CAS. The Year 11 paper covers 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 VCE Methods?
Yes. The VCAA supplies the same formula sheet with Examination 1 and Examination 2.
Can I bring notes into VCE Methods Exam 1?
No. Students are not permitted to bring technology or notes of any kind into Exam 1.
What can I bring into Methods Exam 2?
One bound reference, one approved CAS calculator or software, and one scientific calculator.
Is the quadratic formula on the VCE Methods sheet?
No. You must know it.
How long are the exams?
Exam 1 has 15 minutes of reading and 1 hour of writing. Exam 2 has 15 minutes of reading and 2 hours of writing.

Revision cards

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

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