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QCE General Mathematics formula book: finance, data, trigonometry and what is missing

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Formula sheet

The card below opens today's Year 12 Statistics paper with the sheet in a drawer. 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 General Mathematics page before you rely on it.

Formula sheet

Year 12 Statistics (Standard & General Maths)

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

Shape and measurement

P=2r+\frac{\theta}{180}\pi rperimeter of a sector
A=\frac{\theta}{360}\pi r^2area of a sector
\text{area}=\sqrt{s(s-a)(s-b)(s-c)}Heron's rule, where s = (a + b + c)/2

Data

\overline{x}=\frac{\sum x}{n}mean
\left(\frac{n+1}{2}\right)^{th}\ \text{data value}median
y=mx+clinear equation
m=r\frac{s_y}{s_x}slope
c=\overline{y}-m\overline{x}y-intercept
Q_1-1.5\times IQR\le x\le Q_3+1.5\times IQRidentifying outliers

Sequences

t_n=t_1+(n-1)darithmetic sequence
t_n=t_1r^{(n-1)}geometric sequence

Earth geometry

D=111.2\times\text{angular distance}distance in kilometres along a meridian
D=111.2\cos\theta\times\text{angular distance}distance along a parallel of latitude θ

Graphs and networks

v+f-e=2Euler's formula

Trigonometry

c^2=a^2+b^2Pythagoras' theorem
\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}cosine ratio
\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}sine ratio
\tan\theta=\frac{\text{opposite}}{\text{adjacent}}tangent ratio
c^2=a^2+b^2-2ab\cos Ccosine rule
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sine rule
\text{area}=\frac{1}{2}bc\sin Aarea of a triangle

Finance

\frac{\text{dividend}}{\text{share price}}\times100dividend yield
\text{P/E ratio}=\frac{\text{market price per share}}{\text{annual earnings per share}}price-to-earnings ratio
I=Pinsimple interest
A=P(1+i)^ncompound interest
i_{effective}=(1+i)^k-1effective annual rate of interest
A_{n+1}=rA_nrecurrence relation for compound interest
A_{n+1}=rA_n-drecurrence relation for reducing balance loans
A_{n+1}=rA_n+drecurrence relation for annuities
A_{PV}=d\left(\frac{1-(1+i)^{-n}}{i}\right)annuity, present value
A_{FV}=d\left(\frac{(1+i)^n-1}{i}\right)annuity, future value
A=\frac{d}{i}perpetuity

When you get the book

General Mathematics has a combination-response external examination worth 50% of your final result. It has two papers, and the QCAA provides the formula book in each:

PaperWeightWorking timePerusalQuestions
Paper 130%90 minutes5 minutesShort response and multiple choice, simple familiar
Paper 220%90 minutes5 minutesShort response, complex familiar and complex unfamiliar

You may use a handheld QCAA-approved scientific calculator in both papers, and you must not bring notes or other resources. Our QCE General Maths guide covers the course content.

What is not in the General Maths book

  • Statistics beyond the mean and median. The book has no standard deviation formula, no correlation coefficient formula and no z-score line, although it uses r and the standard deviations in the slope formula.
  • Probability. There are no probability rules at all.
  • Time series and seasonal indices. No formula for moving averages or deseasonalising data.
  • Matrices. No matrix operations, no inverse and no transition matrices.
  • Network algorithms. Euler's formula is given, but nothing about shortest path, minimum spanning tree or critical path methods.
  • The meaning of the symbols. The book never says that i is the rate per period, that d is the payment or that r in the recurrence lines is 1 + i, so learn those.

How to use the formula book in the exam

  1. During perusal, find the finance page. Interest, annuity and loan questions use it more than any other.
  2. Write the formula and the substitution before you press the calculator, so a slip still earns method marks.
  3. Write i as the rate per period, not per year. A monthly rate is the annual rate divided by 12.
  4. Check the units: the Earth geometry line gives kilometres and the area lines give square units.

Example 1: compound interest

$5,000 earns 4.8% a year, compounded monthly, for 3 years. The monthly rate is i = 0.048 ÷ 12 = 0.004 and n = 36, so:

A=P(1+i)^n=5000\times1.004^{36}=5772.76\ \text{dollars}

The interest earned is $772.76. The effective annual rate line then gives (1.004)¹² − 1 = 0.0491, or 4.91%, which is higher than the 4.8% quoted.

Example 2: Heron's rule

A triangle has sides 5, 6 and 7. The semi-perimeter is s = 9, so the area from Heron's rule is:

\text{area}=\sqrt{9(9-5)(9-6)(9-7)}=\sqrt{216}=14.7\ \text{square units}

Heron's rule saves you finding a height, which you could not do from the sides without the cosine rule.

Example 3: distance along a parallel

Two towns are on the 30° S line of latitude, 20° of longitude apart. The parallel line gives:

D=111.2\cos30^\circ\times20=1926\ \text{km}

Along a meridian the same 20° would be 2,224 km, so latitude shortens the east-west distance by the factor cos 30°.

Example 4: a reducing balance loan

A $10,000 loan has a monthly interest rate of 0.5%, so r = 1.005, with repayments of $300. The recurrence line gives the balance after one payment and two:

A_1=1.005\times10000-300=9750,\qquad A_2=1.005\times9750-300=9498.75

Each month the interest is added and then the repayment is taken off.

Practise with the book open

Our Year 12 Statistics (Standard and General Maths) daily paper is a short timed paper of 8 questions worth 25 to 35 marks, not a QCAA paper. Use it as a short mock with the book open and a scientific calculator. For triangle sums, try our Trigonometry course.

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 General Maths?
Yes. The QCAA provides the General Mathematics formula book in both external papers, as the syllabus states.
Can I use a calculator in the QCE General Maths exam?
Yes. A handheld QCAA-approved scientific calculator is allowed in both papers. Notes are not.
What finance formulas are in the book?
Simple and compound interest, effective rate, three recurrence relations, annuities, perpetuities, dividend yield and the price-to-earnings ratio.
Is probability in the General Maths formula book?
No. There are no probability rules in it.
How are the two papers weighted?
Paper 1 is 30% and Paper 2 is 20% of the final result.

Revision cards

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

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