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TCE Mathematics Methods (MTM415117) information sheet: what TASC gives you

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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. TASC reissued the sheet as version 3 in September 2026 with minor changes for mathematical clarity, and publishes it on the TASC Mathematics Methods page. Check any line against it before you rely on it.

Formula sheet

Year 11 Maths Advanced & Methods

Open formula sheet

Function study: quadratic formula

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

Function study: graph shapes

The sheet draws each shape with its labelled turning point or asymptotes and gives its equation.

y=a(x-h)^2+kquadratic
y=a(x-h)^3+kcubic
y=\frac{a}{x-h}+khyperbola
y=\frac{a}{(x-h)^2}+ktruncus
y=a\sqrt{x-h}+ksquare root
y=a\times b^{x-h}+kexponential
y=a\log_n(x-h)+klogarithmic

Function study: graphical transformations

TransformationEffect
y = −f(x)reflects y = f(x) in the x axis
y = f(−x)reflects y = f(x) in the y axis
y = af(x)a dilation of y = f(x) by factor a in the direction of the y axis
y = f(ax)a dilation of y = f(x) by factor 1/a in the direction of the x axis
y = f(x − h)a translation of y = f(x) by h units to the right
y = f(x) + ka translation of y = f(x) by k units upwards

Index laws

a^x\times a^y=a^{x+y}product
a^x\div a^y=a^{x-y}quotient
\left(a^x\right)^y=a^{x\times y}power of a power
(a)^{\frac{1}{y}}=\sqrt[y]{a}fractional index
(a)^{\frac{x}{y}}=\sqrt[y]{a^x}general fractional index

Log laws and useful log results

\log_axy=\log_ax+\log_ayproduct
\log_a\left(\frac{x}{y}\right)=\log_ax-\log_ayquotient
\log_ax^n=n\log_axpower
\log_ax=\frac{\log_bx}{\log_ba}change of base
\log_ay=xdefinition: if y = a^x
\log_a1=0,\quad\ln1=0,\quad\log_aa=1,\quad\ln e=1useful results

Inverse functions and binomial expansion

f\left(f^{-1}(x)\right)=f^{-1}\left(f(x)\right)=xinverse functions
(x+y)^n={}^nC_0x^n+{}^nC_1x^{n-1}y+{}^nC_2x^{n-2}y^2+\ldots+{}^nC_{n-1}xy^{n-1}+{}^nC_ny^nbinomial expansion

Circular functions: conversion and identities

\text{multiply by }\frac{180}{\pi}radians to degrees
\text{multiply by }\frac{\pi}{180}degrees to radians
\sin^2x+\cos^2x=1Pythagorean identity
\tan x=\frac{\sin x}{\cos x}tangent
\cot x=\frac{1}{\tan x}cotangent
\sec x=\frac{1}{\cos x}secant
\text{cosec}\ x=\frac{1}{\sin x}cosecant

Circular functions: exact values

xsin xcos xtan x
0010
π/61/2√3/2√3/3
π/4√2/2√2/21
π/3√3/21/2√3
π/210undefined
π0−10
3π/2−10undefined
2π010

Circular functions: graphs and equations

y=a\sin n(x+b)+c\quad\text{or}\quad y=a\cos n(x+b)+csine or cosine with amplitude, period, phase and vertical shift
\text{amplitude }|a|,\quad\text{period }\frac{2\pi}{|n|}amplitude and period of those graphs
y=a\tan n(x+b)+c,\quad\text{period }\frac{\pi}{|n|}tangent graph
x=n\pi+(-1)^n\arcsin a,\ n\text{ an integer}solving sin x = a
x=2n\pi\pm\arccos a,\ n\text{ an integer}solving cos x = a
x=n\pi+\arctan a,\ n\text{ an integer}solving tan x = a

Calculus: definition of the derivative

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}derivative from first principles

Calculus: differentiation formulae

FunctionDerivative
xⁿnxⁿ⁻¹
sin xcos x
cos x−sin x
tan xsec² x or 1/cos² x
eˣeˣ
logₑ x or ln x1/x

Calculus: integration formulae

FunctionIntegral
aax + c
xⁿxⁿ⁺¹/(n + 1) + c
(ax + b)ⁿ(ax + b)ⁿ⁺¹/(a(n + 1)) + c
eˣeˣ + c
1/xln|x| + c
sin x−cos x + c
cos xsin x + c

Calculus: differentiation rules

\frac{d}{dx}\left(f(x)g(x)\right)=f(x)g'(x)+f'(x)g(x)\quad\text{or}\quad\frac{d}{dx}(uv)=v\frac{du}{dx}+u\frac{dv}{dx}product rule
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{g(x)f'(x)-f(x)g'(x)}{\left(g(x)\right)^2}\quad\text{or}\quad\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}quotient rule
\frac{d}{dx}g(f(x))=g'(f(x))f'(x)\quad\text{or, if }y=f(u),\ u=g(x):\ \frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}chain rule

Probability distributions

{}^nC_r=\frac{n!}{r!(n-r)!}combinations
n!=n(n-1)(n-2)\times\ldots\times3\times2\times1factorial
\Pr(X=x)={}^nC_xp^x(1-p)^{n-x}binomial probability
\mu=npbinomial mean
\sigma^2=np(1-p)binomial variance
E(X)=\sum x\cdot\Pr(X=x)discrete random variable: expected value
\sigma^2=E\left(X^2\right)-\left[E(X)\right]^2discrete random variable: variance
z=\frac{x-\mu}{\sigma}standard normal

The 68, 95 and 99.7 approximations

WithinShare of the data
1 standard deviation of the mean68%
2 standard deviations95%
3 standard deviations99.7%

Sample proportion and confidence intervals

\hat{p}=\frac{X}{n}sample proportion
E(\hat{p})=pmean of the sample proportion
\sigma_{\hat{p}}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}standard deviation of the sample proportion
\left(\hat{p}-z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\ \hat{p}+z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)confidence interval, with z = 1.96 for 95%
M=z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}margin of error

How the exam works with the sheet

TASC's external assessment specifications for Mathematics Methods set a written exam of three hours with an extra 15 minutes of preparation time, and list the information sheet and a TASC-approved calculator as the approved materials:

PartMarksTimeCalculator
Section A80About 80 minutesNot allowed. Five parts of 16 marks: functions and graphs, circular functions, differential calculus, integral calculus, and statistics and probability
Section B100The rest of the examCalculators may be used once Section A is collected, 80 minutes after the start

The two sections are in separate question-and-response booklets. Students may start Section B at any point, but cannot use a calculator for it in the first 80 minutes. The specifications document is dated February 2022, so treat the times as a guide and check your own exam instructions. See how other states handle the same job in our WACE Methods sheet guide and SACE Methods sheet guide.

What is not on the TASC Methods information sheet

  • Numerical integration. No trapezoidal rule or Simpson's rule.
  • Areas and volumes. No area, volume or surface area formulas, and no area under a curve line.
  • Sequences, series and finance. None are printed.
  • Double-angle and compound-angle identities. The sheet has only the Pythagorean, tangent and reciprocal identities.
  • The derivatives of other powers of e and of the logarithm to other bases. Only eˣ and ln x are given.
  • Variance of a continuous random variable and the normal density function. Only the standard normal z formula is given.
  • Values of z for other confidence levels. The sheet gives z = 1.96 for 95% only.

How to use the sheet in the exam

  1. In Section A, use exact values from the table, so leave answers in surd and π form.
  2. Write the line you use, then substitute: the specifications say answers with no working earn at most partial marks on items worth two or more marks.
  3. For integrals of a linear bracket, such as (ax + b)ⁿ, use the sheet's line rather than substitution.
  4. In Section B, switch to your calculator for numerical work, but still show the setup.

Example 1: the chain rule

Differentiate sin(3x²). The sheet gives the derivative of sin x and the chain rule g'(f(x)) f'(x), with f(x) = 3x²:

\frac{d}{dx}\sin\left(3x^2\right)=\cos\left(3x^2\right)\times6x=6x\cos\left(3x^2\right)

Check that you have multiplied by the derivative of the inside, 6x.

Example 2: integrating a bracket

Find\int(2x+1)^4dx. The integral table gives (ax + b)ⁿ with a = 2 and n = 4:

\int(2x+1)^4dx=\frac{(2x+1)^5}{2\times5}+c=\frac{(2x+1)^5}{10}+c

The factor of a in the denominator is easy to miss.

Example 3: a trigonometric equation

Solve 2 sin x = √3 for x in radians. Then sin x = √3 ÷ 2, and the exact values table gives arcsin(√3/2) = π/3, so the equation line gives:

x=n\pi+(-1)^n\frac{\pi}{3},\quad n\text{ an integer}

In [0, 2π] these are π/3 (n = 0) and 2π/3 (n = 1). Practise in the Trigonometry 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 TASC paper. Practise the first half without a calculator, then check with one. The Year 11 paper covers functions and graphs.

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 TCE Mathematics Methods?
Yes. TASC lists the Mathematics Methods Information Sheet as approved material in the external exam.
Are exact trigonometric values on the sheet?
Yes, with a CAST diagram, which most other states do not give.
Can I use a calculator in the TCE Methods exam?
Not in Section A. Calculators may be used in Section B once Section A is collected, 80 minutes after the start.
How long is the exam?
Three hours, plus 15 minutes of preparation time.
Is the trapezoidal rule on the sheet?
No.

Revision cards

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

Where to go next

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Australia · TCETCE Maths Methods: Level 4 course, TASC exam, awardsTCE Maths Methods (MTM415117): five examined criteria, the two-section TASC exam, awards EA to PA, the 2026 date and a daily practice paper.