Which topic carries the most marks in the QCE General Mathematics external exam?

Growth and decay in sequences carries 13.5% of the marks across the 12 QCAA papers from 2020 to 2025, ahead of Earth geometry and time zones on 12.5%.

How are marks split between question types in the QCE General Mathematics exam?

Short answer carries 84.3% of the marks and multiple choice carries 15.7% of the marks, measured across 12 papers and 575 marks from 2020 to 2025.

Has the topic balance changed in recent QCE General Mathematics papers?

Yes. Bivariate data analysis 2 moved down 4.5 percentage points, Graphs and networks moved up 8.5 percentage points, Networks and decision mathematics 2 moved down 4.3 percentage points and Loans, investments and annuities 2 moved down 3.2 percentage points between the 2020 to 2022 and 2023 to 2025 papers.

How many past papers is this QCE General Mathematics analysis based on?

12 QCAA external papers from 2020 to 2025, covering 193 questions and 575 marks. 0.0% of those marks carry no dot-point mapping and sit outside the percentages.

QCE General Mathematics most tested topics

Across the 12 QCAA General Mathematics external papers from 2020 to 2025, Growth and decay in sequences carries 13.5% of the marks against 4.6% for Loans, investments and annuities 2, so the paper rewards Growth and decay in sequences more than any other topic. At dot-point level 3.5.2.5 carries 4.4% of paper marks, and seven of the 86 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 100.0% of marks that map to a syllabus dot point.

Computed from 12 QCAA General Mathematics external papers, 2020 to 2025: 193 questions, 257 question parts and 575 marks.

Unit, topic and dot-point shares below are of the 575 marks that map to a dot point, so each of those tables adds to 100%. 74 of the 257 parts are assessed against more than one dot point, and their 263 marks are divided evenly between the dot points they cover.

What these papers are

Year	Paper	Questions	Marks
2025	Paper 1	25	57
2025	Paper 2	7	38
2024	Paper 1	25	57
2024	Paper 2	7	38
2023	Paper 1	25	57
2023	Paper 2	7	38
2022	Paper 1	25	57
2022	Paper 2	7	38
2021	Paper 1	25	57
2021	Paper 2	7	38
2020	Paper 1	26	60
2020	Paper 2	7	40

Marks by unit

Unit	Share of marks
Unit 3: Bivariate data and time series analysis, sequences and Earth geometry	56.1%
Unit 4: Investing and networking	43.9%

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Growth and decay in sequences	13.5%	12 of 12	6 of 6
Earth geometry and time zones	12.5%	9 of 12	6 of 6
Bivariate data analysis 1	11.4%	10 of 12	6 of 6
Bivariate data analysis 2	11.2%	12 of 12	6 of 6
Graphs and networks	10.8%	10 of 12	6 of 6
Loans, investments and annuities 1	10.5%	8 of 12	6 of 6
Networks and decision mathematics 1	10.4%	11 of 12	6 of 6
Networks and decision mathematics 2	7.6%	10 of 12	6 of 6
Time series analysis	7.5%	10 of 12	6 of 6
Loans, investments and annuities 2	4.6%	8 of 12	6 of 6

Marks by subtopic

Each topic above breaks into the subtopics below, in the same order.

Subtopic	Share of marks	Papers
The arithmetic sequence	8.2%	12 of 12
The geometric sequence	5.3%	9 of 12
Time zones	7.0%	9 of 12
Locations on the Earth	5.6%	7 of 12
Identifying and describing associations between two numerical variable	8.1%	9 of 12
Identifying and describing associations between two categorical variables	3.3%	6 of 12
Fitting a linear model to numerical data	9.8%	12 of 12
Association and causation	1.4%	6 of 12
Planar graphs, paths and cycles	6.5%	10 of 12
Graphs, associated terminology and the adjacency matrix	4.3%	9 of 12
Present value of ordinary annuities	5.7%	6 of 12
Compound interest loans and investments	4.8%	8 of 12
Project planning and scheduling using critical path analysis	5.9%	8 of 12
Trees and minimum connector problems	4.5%	8 of 12
Assigning order and the Hungarian algorithm	4.7%	8 of 12
Flow networks	2.9%	4 of 12
Analysing time series data	5.5%	10 of 12
Describing and interpreting patterns in time series data	2.0%	6 of 12
Perpetuities and future value of ordinary annuities	4.6%	8 of 12

Marks by dot point

Dot-point numbers and wording are QCAA's own. Where a dot point is written as a list, its items run together here separated by semicolons.

Dot point	Content	Topic	Share of marks	Papers
3.5.2.5	Solve practical problems involving time zones, making allowances for daylight saving where necessary, e.g. seasonal time systems used by Aboriginal peoples and Torres Strait Islander peoples, making phone calls, broadcasting events, travelling, preparing an itinerary	Earth geometry and time zones	4.4%	8 of 12
4.1.2.3	Solve practical problems involving the present value of an ordinary annuity, including determining the total amount of the annuity, periodic payment, total payments and total interest	Loans, investments and annuities 1	3.9%	6 of 12
3.2.1.6	Use the equation of the least-squares line to make predictions	Bivariate data analysis 2	3.9%	8 of 12
3.4.1.3	Use the rule for the $n^{\text{th}}$ term of an arithmetic sequence. * $t_n = t_1 + (n - 1)d$ where $t_n$ is $n^{\text{th}}$ term, $t_1$ is first term, $n$ is term number and $d$ is common difference	Growth and decay in sequences	3.8%	9 of 12
4.5.2.3	Use the Hungarian algorithm ( $3 \times 3$ up to $5 \times 5$ square matrices) to determine the optimum (minimum and maximum) assignment/s for larger practical problems	Networks and decision mathematics 2	3.7%	5 of 12
3.4.1.4	Use arithmetic sequences to model and analyse practical situations involving linear growth or decay, e.g. analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, calculating the value of an item using the straight-line method of depreciation	Growth and decay in sequences	3.4%	8 of 12
3.3.2.2	Deseasonalise a time series by calculating the seasonal indices using the average percentage method, including the use of spreadsheets	Time series analysis	3.1%	6 of 12
3.4.2.3	Use the rule for the $n^{\text{th}}$ term of a geometric sequence. * $t_n = t_1 r^{(n-1)}$ where $t_n$ is $n^{\text{th}}$ term, $t_1$ is first term, $n$ is term number and $r$ is common ratio	Growth and decay in sequences	2.8%	8 of 12
3.1.2.2	Construct and use a scatterplot to identify the association between two numerical variables	Bivariate data analysis 1	2.6%	6 of 12
4.1.1.3	Calculate the effective annual rate of interest, $i_{\text{effective}}$ , and use the results to compare interest on loans or investments when interest is paid or charged for different compounding periods, including daily, monthly, quarterly and six-monthly. * $i_{\text{effective}} = (1 + i)^k - 1$ where $i$ is interest rate per compounding period and $k$ is number of compounding periods per year	Loans, investments and annuities 1	2.4%	5 of 12
3.4.2.4	Use geometric sequences to model and analyse practical situations involving geometric growth and decay (use of logarithms not required), e.g. modelling the growth of a bacterial population that doubles in size each hour, calculating the value of an item using the diminishing-value method of depreciation	Growth and decay in sequences	2.3%	7 of 12
3.1.1.2	Construct two-way frequency tables and determine the associated row and column sums and percentages	Bivariate data analysis 1	2.3%	6 of 12
3.5.1.6	Calculate angular distance and distance between two places on Earth on the same parallel of latitude. * $D = 111.2 \cos \theta \times \text{angular distance}$ where $D$ is distance in kilometres and $\theta$ is latitude	Earth geometry and time zones	2.3%	4 of 12
3.2.1.2	Understand and use $m = r \frac{s_y}{s_x}$ and $c = \bar{y} - m\bar{x}$ to determine the equation of a least-squares line, where $m$ is slope (gradient), $r$ is correlation coefficient, $s_y$ is (sample) standard deviation of $y$ values, $s_x$ is (sample) standard deviation of $x$ values, $c$ is $y$ -intercept, $\bar{y}$ is mean of $y$ values and $\bar{x}$ is mean of $x$ values	Bivariate data analysis 2	2.2%	4 of 12
4.2.1.3	Solve practical problems involving the future value of an ordinary annuity, including determining the total amount of the annuity, periodic payment, total payments and total interest	Loans, investments and annuities 2	2.2%	5 of 12
4.4.1.2	Determine a minimum spanning tree in a weighted connected graph	Networks and decision mathematics 1	2.0%	6 of 12
4.5.1.4	Solve small-scale practical problems involving flow networks (up to 8 possible cuts), including determining the minimum cut and the maximum flow	Networks and decision mathematics 2	2.0%	4 of 12
3.1.2.3	Describe an association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)	Bivariate data analysis 1	1.8%	6 of 12
4.1.2.1	Use a recurrence relation to model the present value of an ordinary annuity, e.g. reducing balance loan or retirement pension with periodic payments where interest is calculated before the periodic payment is made. * $A_{n+1} = rA_n - d$ where $A_{n+1}$ is total amount at the beginning of the $(n + 1)^{\text{th}}$ period, $A_n$ is total amount at the beginning of the $n^{\text{th}}$ period, $d$ is periodic payment, and $r = 1 + i$ where $i$ is interest rate per compounding period	Loans, investments and annuities 1	1.8%	6 of 12
4.4.1.3	Solve practical problems involving minimum spanning trees, e.g. minimising the length of cable needed to provide power from a single power station to substations in several towns	Networks and decision mathematics 1	1.8%	5 of 12

These 20 dot points carry 54.7% of the paper marks between them. Another 59 assessed dot points share the rest, and 7 of the 86 externally assessable dot points have not been assessed in any of these 12 papers. Content that has not appeared is still examinable.

What has moved between papers

Comparing the 2020 to 2022 papers with the 2023 to 2025 papers, four topics have moved by more than 3.0 percentage points.

Topic	2020 to 2022 share	2023 to 2025 share	Movement
Bivariate data analysis 2	13.4%	8.9%	down 4.5 points
Graphs and networks	6.6%	15.1%	up 8.5 points
Networks and decision mathematics 2	9.7%	5.4%	down 4.3 points
Loans, investments and annuities 2	6.2%	3.0%	down 3.2 points

How the papers are built

Short answer carries 84.3% of the marks across these 12 papers.

Question type	Share of marks	Marks	Parts
Short answer	84.3%	485	167
Multiple choice	15.7%	90	90

Verb	Share of marks	Marks	Parts
determine	32.0%	184	50
calculate	11.0%	63	21
evaluate	10.1%	58	12
predict	5.7%	33	10
identify	5.4%	31	12
construct	4.3%	25	9
describe	2.4%	14	6
justify	2.4%	14	4

What these percentages do not tell you

Where to practise

Every topic above links to its own page of real QCAA questions with marking criteria and average scores attached: Growth and decay in sequences, Earth geometry and time zones, Bivariate data analysis 1, Bivariate data analysis 2, Graphs and networks, Loans, investments and annuities 1, Networks and decision mathematics 1, Networks and decision mathematics 2, Time series analysis and Loans, investments and annuities 2. For how students actually score on this content, read QCE General Mathematics hardest topics, and for the full question bank start at QCE General Mathematics.

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.