QCE General Mathematics21 October 2026

QCAA General Maths formula sheet and formula book explained (QCE)

The QCAA General Mathematics formula book is a two-page reference that every QCE General Maths student gets in the IA2 and IA3 examinations and in both external examination papers, with no notes allowed beside it. It prints its formulas under eight headings: Mensuration, Shape and measurement, Data, Sequences, Earth geometry, Graphs and networks, Trigonometry and Finance. This guide reproduces the whole book below, adds what the symbols mean, and lists the syllabus content the book leaves out.

This guide describes the General Mathematics 2025 v1.0 General senior syllabus, released in January 2024 with implementation starting in 2025 and current for Year 12 from 2026, and the Formula book, General Mathematics 2025, whose cover is dated June 2026 and carries no version number. For the rest of the subject, start at the General Mathematics question bank and the QCE hub.

What is the QCAA General Mathematics formula book?

It is a QCAA-issued reference that sits beside you in the exam room. The syllabus sets out who supplies it:

Assessment	Who provides the book	Notes allowed
IA2 examination (Unit 3)	Your teacher	No
IA3 examination (Unit 4)	Your teacher	No
External examination, Paper 1 and Paper 2	QCAA	No

The external papers allow a handheld QCAA-approved scientific calculator. The IA2 and IA3 conditions say you are required to use technology. Both are covered in the IA2 and IA3 examinations guide.

The book is a separate document from the syllabus. It is formulas and nothing else: no worked examples, no units except "(km)" for Earth geometry, and no statement of when each formula applies.

What formulas are in the QCAA General Mathematics formula book?

The tables below follow the book's own headings and order. The names and formulas are the book's. The right-hand column is our note, not part of the book: it gives the meaning of the symbols as the 2025 syllabus defines them where it does, and says so where the syllabus does not.

Modified from General Mathematics 2025: Formula book, QCAA, dated June 2026. © State of Queensland (QCAA) 2026, licensed under CC BY 4.0. The book sets two name and formula pairs per row; we have reset it as tables and added the notes column. QCAA's copyright notice lists the exceptions to the licence, and our QCAA licensing page records how we use its material.

Mensuration (page 1 of 2)

Name (as printed)	Formula	Symbols (our note)
circumference of a circle	$C = 2\pi r$	$r$ is the radius
area of a circle	$A = \pi r^2$	$r$ is the radius
area of a parallelogram	$A = bh$	$b$ is the base length, $h$ the perpendicular height
area of a trapezium	$A = \dfrac{1}{2}(a + b)h$	$a$ and $b$ are the parallel lengths, $h$ the perpendicular height
area of a triangle	$A = \dfrac{1}{2}bh$	$b$ is the base length, $h$ the perpendicular height
total surface area of a cone	$S = \pi rs + \pi r^2$	$r$ is the radius, $s$ the slant height
total surface area of a cylinder	$S = 2\pi rh + 2\pi r^2$	$r$ is the radius, $h$ the perpendicular height
surface area of a sphere	$S = 4\pi r^2$	$r$ is the radius
volume of a cone	$V = \dfrac{1}{3}\pi r^2 h$	$r$ is the radius, $h$ the perpendicular height
volume of a cylinder	$V = \pi r^2 h$	$r$ is the radius, $h$ the perpendicular height
volume of a prism	$V = Ah$	$A$ is the base area, $h$ the perpendicular height
volume of a pyramid	$V = \dfrac{1}{3}Ah$	$A$ is the base area, $h$ the perpendicular height
volume of a sphere	$V = \dfrac{4}{3}\pi r^3$	$r$ is the radius

Shape and measurement (page 1 of 2)

Name (as printed)	Formula	Symbols (our note)
perimeter of a sector	$P = 2r + \dfrac{\theta}{180}\pi r$	$r$ is the radius, $\theta$ the central angle. The book does not define $\theta$
area of a sector	$A = \dfrac{\theta}{360}\pi r^2$	$r$ is the radius, $\theta$ the central angle. The book does not define $\theta$
Heron's rule	$\text{area} = \sqrt{s(s-a)(s-b)(s-c)}$ , where $s = \dfrac{a+b+c}{2}$	$a$ , $b$ and $c$ are the three sides. This is the only formula where the book itself defines a symbol ( $s$ )

Data (page 1 of 2)

Name (as printed)	Formula	Symbols (our note)
mean	$\bar{x} = \dfrac{\sum x}{n}$	Neither the book nor the syllabus defines $n$ . Read it as the number of data values
median	$\left(\dfrac{n+1}{2}\right)^{\text{th}}$ data value	Neither the book nor the syllabus defines $n$ . Read it as the number of data values
linear equation	$y = mx + c$	$m$ is the slope (gradient), $c$ the $y$ -intercept
slope	$m = r\,\dfrac{s_y}{s_x}$	$r$ is the correlation coefficient, $s_y$ and $s_x$ the sample standard deviations of the $y$ and $x$ values
y-intercept	$c = \bar{y} - m\bar{x}$	$\bar{y}$ and $\bar{x}$ are the means of the $y$ and $x$ values
outliers (identifying)	$Q_1 - 1.5 \times \text{IQR} \le x \le Q_3 + 1.5 \times \text{IQR}$	$Q_1$ is the lower quartile, $Q_3$ the upper quartile. The book prints the interval a value lies inside when it is not flagged, so a value outside it is a possible outlier

Sequences (page 1 of 2)

Name (as printed)	Formula	Symbols (our note)
arithmetic sequence	$t_n = t_1 + (n-1)d$	$t_n$ is the $n$ th term, $t_1$ the first term, $n$ the term number, $d$ the common difference
geometric sequence	$t_n = t_1 r^{(n-1)}$	$t_n$ is the $n$ th term, $t_1$ the first term, $n$ the term number, $r$ the common ratio

Earth geometry (page 2 of 2)

The book prints one row labelled "distance (km)" with two formulas side by side and no label on either.

Formula	Symbols (our note)
$D = 111.2 \times \text{angular distance}$	The syllabus uses this for two places on the same meridian. $D$ is the distance in kilometres
$D = 111.2\cos\theta \times \text{angular distance}$	The syllabus uses this for two places on the same parallel of latitude. $D$ is the distance in kilometres, $\theta$ the latitude

Graphs and networks (page 2 of 2)

Name (as printed)	Formula	Symbols (our note)
Euler's formula	$v + f - e = 2$	$v$ is the number of vertices, $f$ faces, $e$ edges (planar graphs)

Trigonometry (page 2 of 2)

Name (as printed)	Formula	Symbols (our note)
Pythagoras' theorem	$c^2 = a^2 + b^2$	$c$ is the hypotenuse, $a$ and $b$ the other two sides
trigonometric ratios	$\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}$ , $\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$ , $\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}$	Right-angled triangle, $\theta$ an angle
cosine rule	$c^2 = a^2 + b^2 - 2ab\cos C$	$C$ is the angle opposite side $c$ . Printed in side form only
sine rule	$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$	The syllabus excludes the ambiguous case
area of a triangle	$\text{area} = \dfrac{1}{2}bc\sin A$	$b$ and $c$ are two sides, $A$ the included angle

Finance (page 2 of 2)

Name (as printed)	Formula	Symbols (our note)
dividend yield	$\dfrac{\text{dividend}}{\text{share price}} \times 100$	Printed as an expression with no "dividend yield =" in front
price-to-earnings ratio	$\text{P/E ratio} = \dfrac{\text{market price per share}}{\text{annual earnings per share}}$	Defined in words in the formula itself
simple interest	$I = Pin$	Defined in neither the book nor the syllabus. Read the symbols as in compound interest: $P$ the principal, $i$ the interest rate per period, $n$ the number of periods
compound interest	$A = P(1+i)^n$	$A$ is the total amount after $n$ compounding periods, $P$ the principal, $i$ the interest rate per compounding period
effective annual rate of interest	$i_{\text{effective}} = (1+i)^k - 1$	$i$ is the interest rate per compounding period, $k$ the number of compounding periods per year
recurrence relation for compound interest	$A_{n+1} = rA_n$	$A_n$ is the amount at the beginning of period $n$ . The syllabus gives $r = 1 + i$
recurrence relation for reducing balance loans	$A_{n+1} = rA_n - d$	$d$ is the periodic payment. The syllabus line for this recurrence prints $r = n + 1$ , while its compound interest and future value lines give $r = 1 + i$
recurrence relation for annuities	$A_{n+1} = rA_n + d$	$d$ is the periodic payment, $r = 1 + i$
annuity (present value)	$A_{PV} = d\left(\dfrac{1-(1+i)^{-n}}{i}\right)$	$d$ is the periodic payment, $i$ the interest rate per compounding period, $n$ the number of periods
annuity (future value)	$A_{FV} = d\left(\dfrac{(1+i)^n-1}{i}\right)$	$d$ is the periodic payment, $i$ the interest rate per compounding period, $n$ the number of periods
perpetuity	$A = \dfrac{d}{i}$	$A$ is the total amount, $d$ the periodic payment, $i$ the interest rate per compounding period

The book prints the two annuity formulas side by side under the single label "annuity", with subscripts $PV$ and $FV$ and no words for them. In the three recurrence relations the book never says how $r$ relates to $i$ , and elsewhere in the same book $r$ also stands for a radius, the correlation coefficient and the common ratio of a geometric sequence.

Topic pages for the Year 12 formulas: growth and decay in sequences, Earth geometry and time zones, bivariate data analysis 2, loans, investments and annuities 1, loans, investments and annuities 2 and graphs and networks.

What does the formula book not tell you?

The book states no conditions of use, so you carry these into the exam yourself:

Which Earth geometry formula to use. The two are unlabelled. The syllabus ties the first to two places on the same meridian and the second to two places on the same parallel of latitude.
What the symbols are. Only $s$ in Heron's rule is defined. $\theta$ in the sector formulas and the Earth geometry formula is left to you.
How $r$ relates to $i$ . The recurrence relations use $r$ , and the syllabus gives $r = 1 + i$ for the compound interest and future value recurrences.
Which way round the outlier rule runs. It prints the interval where a value is not flagged.
That $i$ is per compounding period. The syllabus defines $i$ that way in every compound interest and annuity formula.

What is not on the General Mathematics formula sheet?

The book has no formula for these. Each is in the 2025 syllabus, so you meet it in the course and in assessment, and the syllabus handles it as a procedure, a technology task or a skill.

Content	What the syllabus says
Sample standard deviation	Calculated using technology only. The book uses $s_x$ and $s_y$ only inside the slope formula
Pearson's correlation coefficient $r$ and the coefficient of determination $R^2$	Both are calculated from raw data using technology. You can also use $r$ to find $R^2$ and the reverse
Least-squares line	Fitted using technology. The book gives the slope and intercept formulas only
Percentage change, mark-ups, discounts, GST, inflation and the unit cost method	Applied as skills in Unit 1. The book prints no percentage formula
Scale factors for similar figures	A skill in Unit 1, with no formula in the book
Depreciation	Straight-line depreciation is modelled with arithmetic sequences and diminishing-value depreciation with geometric sequences. The book prints only the two sequence rules
Angles of elevation and depression, true bearings	Applied with right-angled and non-right-angled triangle trigonometry. The book prints the trigonometry rules and nothing on bearings
Matrix multiplication	Done manually up to 3×3 matrices, not limited to square matrices
Power of a matrix	Found using technology with matrix arithmetic capabilities when appropriate
Simple moving average	Smoothed using the mean or median for an odd number of data points
Seasonal indices	The average percentage method, no formula printed
Time zones	A sub-topic of Unit 3 Topic 5, with no formula in the book
Eulerian trails, Hamiltonian paths, shortest path, minimum spanning tree, flow networks	Procedures and definitions. The book's only network formula is Euler's formula
Earliest and latest starting times, float	Found by forward and backward scanning, no formula printed
Hungarian algorithm	A procedure for 3×3 up to 5×5 square matrices

Seasonal indices are the one most worth getting in the right order. QCAA's 2023, 2024 and 2025 reports each recommend the same sequence: average the data values for each year, express each data value as a percentage or ratio of the average for its year, then average the corresponding seasons' percentages across years. The 2024 and 2025 reports add that the first average is for each distinct year, not for each season and not for all years.

Because the book prints no depreciation, inflation or percentage change formula, you build those from the sequence rules and from percentage reasoning, not from a line in the book.

How do exam questions use the formula book?

QCAA's recommendations for the external examination are specific. The 2022 report asks teachers to familiarise students with the appropriate rules to select from the formula book, naming annuities, sequences and Earth geometry, and to encourage students to identify values for parameters before substitution. The 2023 report repeats the point, asking for support in spotting the cues in a question that tell you which rule to use, again naming annuity calculations and the distance between two places on Earth.

The 2023 report's annuity example shows what that looks like. The question asked for the monthly payment needed to pay off a reducing balance loan over 25 years, and the excerpt QCAA chose shows clearly labelled values for the amount borrowed, $i$ and $n$ , substituted into the correct annuity formula selected from the formula book.

If the question says	The rule to reach for
A lump sum grows with interest and you need the final amount	Compound interest, $A = P(1+i)^n$
Compare two investments that compound at different frequencies	Effective annual rate, $i_{\text{effective}} = (1+i)^k - 1$
A loan repaid by regular payments, or a regular payment that must fund a pension	Present value annuity
Regular deposits building up an investment	Future value annuity
Payments that continue indefinitely	Perpetuity, $A = \dfrac{d}{i}$
Two places on the same meridian (line of longitude)	$D = 111.2 \times \text{angular distance}$
Two places on the same parallel of latitude	$D = 111.2\cos\theta \times \text{angular distance}$
Each term is the previous term plus a constant	Arithmetic sequence
Each term is the previous term times a constant	Geometric sequence

QCAA's 2025 report adds that the effective annual rate formula applies to a perpetuity the same way as to any other compounding investment or loan, and can be used to compare perpetuities with different compounding periods.

Four short worked examples

These are our own illustrations of the formulas above, not QCAA questions.

Common mistakes with formulas

Practising with the formulas

The quickest way to learn which rule a question wants is to work unseen questions and mark them against the QCAA marking guide. The General Mathematics question bank holds marked past-paper questions you can answer and have graded, and the syllabus page shows where each formula sits in the course.

Frequently asked questions

Is it called the QCAA General Mathematics formula sheet or formula book?

Both names are in use. The 2019 syllabus said 'QCAA formula sheet' and the 2025 syllabus says 'QCAA General Mathematics formula book'. The document itself is titled 'Formula book, General Mathematics 2025'. Students search for either.

How long is the General Mathematics formula book?

Two numbered pages of formulas, plus a cover and a licence page. Page 1 of 2 holds Mensuration, Shape and measurement, Data and Sequences. Page 2 of 2 holds Earth geometry, Graphs and networks, Trigonometry and Finance.

Does the formula book explain what the variables mean?

Almost never. The only symbol the book defines is s in Heron's rule. It has no worked examples and does not say when each formula applies, including which of its two Earth geometry formulas suits which pair of places. The syllabus defines the symbols for most formulas, and this guide adds those as its own notes.

Is there a depreciation formula in the General Mathematics formula book?

No. The book prints the arithmetic and geometric sequence rules, and the syllabus uses those to model straight-line and diminishing-value depreciation. The book has no separate depreciation formula, and none for inflation or percentage change.

Which General Mathematics results come from technology rather than a formula?

Pearson's correlation coefficient, the coefficient of determination and the sample standard deviation are all calculated with technology in the 2025 syllabus, and the least-squares line is fitted with technology. The book prints no formula for any of them. The power of a matrix is also found with technology where appropriate.

Do I need to learn how to use the formula book, or just the formulas?

Both. QCAA's 2022 and 2023 reports recommend practising how to select the right rule from the book (2022 names annuities, sequences and Earth geometry; 2023 names annuities and distances on Earth), and how to identify the values to substitute before you substitute them.

Is there a formula for seasonal indices in General Mathematics?

Neither the syllabus nor the book prints one. The syllabus names the average percentage method, and QCAA's 2023, 2024 and 2025 reports describe the order of steps: average each distinct year, express each value as a percentage of its own year's average, then average the percentages for each season.

Sources

General Mathematics 2025: Formula book, QCAA, June 2026, pp. 1-2 of 2 (cover and licence page unnumbered). Every formula reproduced in the tables below, under the book's eight headings. The book defines no symbol except s in Heron's rule.
General Mathematics 2025 v1.0 General senior syllabus, QCAA, January 2024, pp. 14-21, 23-25, 27-30, 35, 38, 42, 45. The symbol definitions that go with each formula, the technology-only and technology-assisted dot points, the content with no formula, and the formula book provision for IA2, IA3 and both external papers.
General Mathematics 2019 v1.2 General Senior Syllabus, QCAA, July 2018, pp. 35, 43, 47. Superseded syllabus, cited only for its name for the resource, the QCAA formula sheet.
General Mathematics subject report, 2025 cohort, QCAA, January 2026, pp. 46-59. External assessment commentary on the effective annual rate formula applied to perpetuities and on seasonal indices.
General Mathematics subject report, 2024 cohort, QCAA, January 2025, pp. 35-52. External assessment commentary on seasonal indices and on rounding in annuity calculations.
General Mathematics subject report, 2023 cohort, QCAA, January 2024, pp. 35-44. Advice on selecting the appropriate rule from the formula book, and the annuity excerpt that shows labelled values for the amount borrowed, i and n.
General Mathematics subject report, 2022 cohort, QCAA, January 2023, pp. 27-38. Advice on selecting rules from the formula book for annuities, sequences and Earth geometry, and on identifying parameter values before substitution.

Syllabus and assessment material referenced in this guide is © State of Queensland (Queensland Curriculum and Assessment Authority), licensed under CC BY 4.0. See our QCAA licensing notice. AusGrader is an independent study tool and is not affiliated with, endorsed by, or operated by the QCAA.

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