Uni-Sine
Australian exams
Australian examsQCE

QCE Mathematical Methods formula book: every formula and what is missing

Published 6 min read

Papers reset in

Formula sheet

The card below opens today's paper with the book in a drawer, so you practise the way you will sit the exam. The contents follow in our own layout. The QCAA publishes the book as a Creative Commons PDF dated June 2026, so check any line against the QCAA Mathematical Methods page before you rely on it.

Formula sheet

Year 11 Maths Advanced & Methods

Open formula sheet

Mensuration

C=2\pi rcircumference of a circle
A=\pi r^2area of a circle
A=bharea of a parallelogram
A=\frac{1}{2}(a+b)harea of a trapezium
A=\frac{1}{2}bharea of a triangle
S=\pi rs+\pi r^2total surface area of a cone
S=2\pi rh+2\pi r^2total surface area of a cylinder
S=4\pi r^2surface area of a sphere
V=\frac{1}{3}\pi r^2hvolume of a cone
V=\pi r^2hvolume of a cylinder
V=Ahvolume of a prism
V=\frac{1}{3}Ahvolume of a pyramid
V=\frac{4}{3}\pi r^3volume of a sphere

Graph equations

y=a(x-h)^2+kquadratic, turning point form
y=a(x-x_1)(x-x_2)quadratic, factorised form
y=a(x-h)^3+kcubic, turning point form
y=a(x-x_1)(x-x_2)(x-x_3)cubic, factorised form
(x-h)^2+(y-k)^2=r^2circle
y=a\sqrt{x-h}+ksquare root
y=\frac{a}{x-h}+kreciprocal
y=r^{(x-h)}+kexponential, where r > 0
y=\log_a(x-h)+klogarithmic, where a > 1
y=a\sin(b(x-h))+ksine
y=a\cos(b(x-h))+kcosine

Logarithms

a^x=b\Leftrightarrow x=\log_a(b)exponents and logarithms
\log_a(x)+\log_a(y)=\log_a(xy)sum of logarithms
\log_a(x)-\log_a(y)=\log_a\left(\frac{x}{y}\right)difference of logarithms
\log_a\left(x^n\right)=n\log_a(x)power of a logarithm
\log_a(x)=\frac{\log_b(x)}{\log_b(a)}change of base
\log_a(1)=0logarithm of 1
\log_a(a)=1logarithm of the base

Calculus

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}definition of the derivative
\int_a^bf(x)dx\approx\text{limit of sums }\sum_if(x_i)\delta x_iintegral as a limit of sums
\int_a^bf(x)dx=F(b)-F(a)fundamental theorem
\frac{d}{dx}\left(f(x)+g(x)\right)=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)derivative of a sum
\int\left(f(x)+g(x)\right)dx=\int f(x)dx+\int g(x)dxintegral of a sum
\int kf(x)dx=k\int f(x)dxconstant multiple of an integral
\frac{d}{dx}x^n=nx^{n-1}power rule
\int x^ndx=\frac{x^{n+1}}{n+1}+cintegral of a power, n not equal to −1
\frac{d}{dx}e^x=e^x,\quad\frac{d}{dx}e^{f(x)}=f'(x)e^{f(x)},\quad\int e^xdx=e^x+cexponential
\frac{d}{dx}\ln(x)=\frac{1}{x},\quad\frac{d}{dx}\ln(f(x))=\frac{f'(x)}{f(x)},\quad\int\frac{1}{x}dx=\ln(x)+c\ \text{for}\ x>0natural logarithm
\frac{d}{dx}\sin(x)=\cos(x),\quad\frac{d}{dx}\sin(f(x))=f'(x)\cos(f(x)),\quad\int\sin(x)dx=-\cos(x)+csine
\frac{d}{dx}\cos(x)=-\sin(x),\quad\frac{d}{dx}\cos(f(x))=-f'(x)\sin(f(x)),\quad\int\cos(x)dx=\sin(x)+ccosine
\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}chain rule, if y = f(u) and u = g(x)
\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
\int_a^bf(x)dx\approx\frac{w}{2}\left[f(x_0)+2\left(f(x_1)+f(x_2)+f(x_3)+\ldots+f(x_{n-1})\right)+f(x_n)\right]trapezoidal rule, where w = (b − a)/n

Trigonometry

c^2=a^2+b^2-2ab\cos(C)cosine rule
\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}sine rule
\text{area}=\frac{1}{2}bc\sin(A)area of a triangle
\sin^2(A)+\cos^2(A)=1Pythagorean identity

Statistics

(x+y)^n=x^n+\binom{n}{1}x^{n-1}y+\ldots+\binom{n}{r}x^{n-r}y^r+\ldots+y^nbinomial theorem
P(X=r)=\binom{n}{r}p^r(1-p)^{n-r}binomial probability
E(X)=\mu=\sum p_ix_idiscrete random variable, mean
Var(X)=\sum p_i(x_i-\mu)^2discrete random variable, variance
\sqrt{Var(X)}discrete random variable, standard deviation
E(X)=\mu=\int_{-\infty}^{\infty}xp(x)dxcontinuous random variable, mean
Var(X)=\sigma^2=\int_{-\infty}^{\infty}(x-\mu)^2p(x)dxcontinuous random variable, variance
pBernoulli distribution, mean
p(1-p)Bernoulli distribution, variance
npbinomial distribution, mean
np(1-p)binomial distribution, variance
psample proportion, mean
\sqrt{\frac{p(1-p)}{n}}sample proportion, 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 for p
z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}approximate margin of error
P\left(\overline{A}\right)=1-P(A)complementary probability
P(A\cup B)=P(A)+P(B)-P(A\cap B)general addition rule
P(A\cap B)=P(A)P(B)independent events
P(A\cap B)=P(A|B)P(B)conditional probability

When you get the book

The Mathematical Methods syllabus sets one external examination of two papers, and the external assessment is 50% of your final result. The QCAA provides the formula book in both papers:

PaperWeightWorking timePerusalTechnology
Paper 125%90 minutes5 minutesNone: no calculator and no notes
Paper 225%90 minutes5 minutesQCAA-approved graphics calculator without CAS, or a scientific calculator; no notes

Both papers contain short response and multiple-choice questions on Units 3 and 4, and they may use assumed knowledge from Units 1 and 2. Because Paper 1 forbids technology, it tests whether you can find and apply the right line without a calculator. Our QCE Maths Methods guide covers the whole course.

What is not in the Methods formula book

  • The quadratic formula and the discriminant. The book gives graph equations, not how to solve them.
  • Trigonometric identities beyond sin² A + cos² A = 1. There are no double-angle formulas and no tan A = sin A ÷ cos A line.
  • Exact trigonometric values. The values at 0, π/6, π/4, π/3 and π/2 have to be remembered.
  • The derivatives of tan x and of ax. Only sin, cos, e and ln are given, with their chain rule forms.
  • The normal distribution and z-tables. The book has the sample proportion and confidence interval formulas but no z-score line and no table of critical values; z comes from your Paper 2 technology.
  • Sequences and finance. None are in the Methods book.
  • Differentiation from first principles beyond the definition. The book states the limit, but you do the algebra.

How to use the formula book in the exam

  1. Use the 5 minutes of perusal to find the page for calculus, statistics and mensuration so you do not search later.
  2. Write the line you are using first. Paper 1 awards method marks for the right formula even when arithmetic slips.
  3. Match your symbols to the book: the binomial lines use n, r and p; the confidence interval uses p-hat.
  4. In Paper 2, put values into the technology only after you have written the formula and the substituted numbers.

Example 1: the trapezoidal rule

Estimate\int_0^2x^2dxusing 4 strips. Then w = (2 − 0) ÷ 4 = 0.5, and the book's trapezoidal rule gives:

\frac{0.5}{2}\left[0+2\left(0.25+1+2.25\right)+4\right]=0.25\times11=2.75

The exact value is 8/3 = 2.667, so the rule overestimates for a curve that bends upward. Try the idea in the Calculus course.

Example 2: a binomial probability

A machine makes faulty parts with probability 0.2, and a batch has 10 parts. The probability of exactly 3 faulty parts uses the binomial line with n = 10, r = 3 and p = 0.2:

P(X=3)=\binom{10}{3}(0.2)^3(0.8)^7=120\times0.008\times0.2097152=0.2013

The book also gives the mean np = 2 and the variance np(1 − p) = 1.6 for the batch.

Example 3: a margin of error

A survey of 200 people finds a sample proportion of 0.4, and you are told to use z = 1.96. The margin of error line gives:

1.96\sqrt{\frac{0.4\times0.6}{200}}=0.068

so the interval runs from 0.332 to 0.468. The book gives both formulas, but you must remember that z = 1.96 belongs to a 95% interval.

Practise with the book 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 QCAA paper, but it is a good short mock for Paper 1 style working. Use the Year 11 paper for Unit 1 and 2 skills, and see how the other states handle sheets in our HSC maths formula sheet guide.

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 QCE Maths Methods?
Yes. The QCAA provides the Mathematical Methods formula book in both external papers, as the syllabus conditions state.
Is there a calculator in QCE Methods Paper 1?
No. Paper 1 is technology-free: no calculator, no technology and no notes. Paper 2 allows an approved graphics calculator without CAS.
Is the quadratic formula in the QCE Methods formula book?
No. Learn it, along with exact trigonometric values and the double-angle identities.
How long are the QCE Methods exams?
Each paper has 5 minutes of perusal time and 90 minutes of working time.
How much is the external exam worth?
External assessment is 50% of the final result, with each paper weighted at 25%.

Revision cards

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

Where to go next

  • Solve it

    Derivative Calculator

    Differentiate any function and see each rule applied

    Open the tool
  • Learn it

    Calculus

    Differentiation, integration and the mathematics that drives physics and engineering

    Start the course
  • Test it

    Year 11 Maths Advanced & Methods

    A new exam-style paper every day, with instant marking and a mark scheme

    Start today's paper
Read next
Australia · QCEQCE Maths Methods: Units 3 and 4, IAs and Exam PapersQCE Mathematical Methods explained: IA1 to IA3, technology-free Paper 1, technology-active Paper 2, Units 3 and 4 topics, 2026 changes, worked questions.