Which QCE General Mathematics past paper do students score lowest on?

The 2021 Paper 1, averaging 53.5% across 146 marked attempts on AusGrader. The 2023 Paper 1 is the highest on 69.2%.

Which QCE General Mathematics dot points give the best return on revision time?

4.5.2.3 (1.8 marks at risk per 100), 3.4.1.3 (1.7 marks at risk per 100) and 4.1.2.3 (1.7 marks at risk per 100). Marks at risk combines a dot point's share of paper marks with the marks students drop on it, so it ranks by recoverable marks and not by score alone.

How many attempts is each QCE General Mathematics figure based on?

17,109 marked attempts overall, with the per-row count shown in every table. Any cut below 50 attempts is withheld instead of published.

Do these averages show how the QCAA cohort performed?

No. They are AusGrader users' marked attempts, a self-selected group practising when they chose to and often without exam timing. They corroborate what QCAA publishes about this subject and do not replace it.

QCE General Mathematics hardest topics

Across 17,109 marked attempts on AusGrader, QCE General Mathematics students average 60.1% on questions taken from board external papers. The lowest average of any command verb is calculate on 41.0%, and the verb that costs the most marks is determine, which carries 32.0% of the paper against 11.0% for calculate. These are self-selected users practising when they chose to, not the QCAA cohort under exam conditions.

How to read these numbers

The figures are AusGrader users' marked attempts, not QCAA results. They corroborate what the board publishes about this subject and do not stand in for it.
Any cut with fewer than 50 attempts is withheld, which on this page is 6 papers, 1 subtopics, 36 dot points and 29 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the QCE General Mathematics syllabus from any board's external papers, which is why the sample is larger than the 12 QCAA papers alone. The paper table below is the exception and uses QCAA papers only.
Internal assessment and school-uploaded exams are excluded throughout, so these averages differ from the ones on QCE General Mathematics performance stats, which count every attempt.

Score by past paper

Year	Paper	Average	Attempts
2025	Paper 1	62.5%	265
2024	Paper 1	55.5%	256
2023	Paper 1	69.2%	191
2022	Paper 1	66.2%	163
2021	Paper 1	53.5%	146
2020	Paper 1	62.7%	126

The lowest average belongs to the 2021 Paper 1 on 53.5% from 146 attempts, and the highest to the 2023 Paper 1 on 69.2% from 191 attempts. A paper's average reflects both how hard it was and who chose to sit it, so treat the spread as a guide to which papers make demanding practice.

Score by question type

Question type	Average	Attempts
Short answer	53.8%	1,466
Multiple choice	61.2%	15,643

Score by unit

Unit	Average	Attempts
Unit 4: Investing and networking	58.6%	8,294
Unit 3: Bivariate data and time series analysis, sequences and Earth geometry	61.4%	8,831

An attempt counts once per unit, so a question assessed across two units appears in both rows and the column adds to slightly more than 17,109.

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Growth and decay in sequences	13.5%	56.9%	2,596	5.8
Earth geometry and time zones	12.5%	56.5%	158	5.4
Loans, investments and annuities 1	10.5%	54.2%	2,521	4.8
Bivariate data analysis 2	11.2%	62.9%	2,406	4.2
Graphs and networks	10.8%	62.8%	2,628	4.0
Bivariate data analysis 1	11.4%	65.2%	1,125	4.0
Networks and decision mathematics 1	10.4%	62.6%	1,307	3.9
Networks and decision mathematics 2	7.6%	56.3%	1,514	3.3
Time series analysis	7.5%	63.3%	2,565	2.8
Loans, investments and annuities 2	4.6%	57.5%	948	1.9

The topic list is close: 5.8 against 5.4 marks at risk separates first from second, so topic choice alone will not order revision. The dot-point list below spreads further.

The same cut at subtopic level

Subtopic	Share of marks	Average	Attempts	Marks at risk
Fitting a linear model to numerical data	9.8%	63.1%	2,381	3.6
Identifying and describing associations between two numerical variable	8.1%	59.6%	585	3.3
The arithmetic sequence	8.2%	61.8%	1,451	3.1
Time zones	7.0%	55.5%	65	3.1
Project planning and scheduling using critical path analysis	5.9%	49.5%	477	3.0
The geometric sequence	5.3%	51.6%	1,372	2.6
Present value of ordinary annuities	5.7%	55.8%	1,932	2.5
Planar graphs, paths and cycles	6.5%	62.5%	2,297	2.4
Locations on the Earth	5.6%	57.3%	93	2.4
Compound interest loans and investments	4.8%	50.6%	817	2.4
Analysing time series data	5.5%	63.3%	2,065	2.0
Assigning order and the Hungarian algorithm	4.7%	57.5%	848	2.0
Perpetuities and future value of ordinary annuities	4.6%	57.5%	948	1.9
Graphs, associated terminology and the adjacency matrix	4.3%	63.6%	1,186	1.6
Flow networks	2.9%	55.0%	666	1.3

The same cut at dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
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	3.7%	51.5%	621	1.8
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	3.8%	55.5%	313	1.7
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	3.9%	56.7%	1,633	1.7
3.3.2.2	Deseasonalise a time series by calculating the seasonal indices using the average percentage method, including the use of spreadsheets	3.1%	50.6%	750	1.5
3.2.1.6	Use the equation of the least-squares line to make predictions	3.9%	63.5%	856	1.4
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	2.8%	50.7%	57	1.4
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	3.4%	62.3%	1,370	1.3
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	2.4%	50.5%	534	1.2
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	2.2%	52.7%	205	1.0
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	2.0%	47.9%	641	1.0
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	2.3%	55.4%	700	1.0
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	2.2%	56.7%	455	0.9
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	1.8%	54.0%	1,168	0.8
4.2.1.5	Solve practical problems involving perpetuities, including determining the total amount of the perpetuity, periodic payment and interest rate per compounding period	1.6%	52.1%	486	0.8
3.1.1.2	Construct two-way frequency tables and determine the associated row and column sums and percentages	2.3%	67.4%	304	0.8
4.1.1.4	Solve practical problems involving compound interest loans or investments, including determining the total amount of the loan or investment, total interest, principal, interest rate per year and per compounding period, and the effect of the interest rate and number of compounding periods on the total amount	1.4%	49.7%	504	0.7
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)	1.8%	62.9%	253	0.7
3.1.2.4	Calculate Pearson’s correlation coefficient, $r$ , from raw data using technology, and interpret it to quantify the strength of a linear association	1.8%	63.7%	247	0.7
4.4.1.2	Determine a minimum spanning tree in a weighted connected graph	2.0%	72.9%	616	0.5
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	1.8%	72.1%	412	0.5

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
determine	32.0%	45.1%	362	17.6
calculate	11.0%	41.0%	163	6.5
identify	5.4%	57.5%	87	2.3
explain	1.7%	68.2%	55	0.5
state	1.4%	62.2%	93	0.5
write	0.9%	75.9%	64	0.2

Calculate has the lowest average on the page at 41.0%, and it is not where the marks go. Determine averages 45.1% but carries 32.0% of the paper against 11.0%, so it puts 17.6 marks per 100 at risk against 6.5. For the plain ranking of verbs by score, and what QCAA has said about each, read the QCE General Mathematics study guide.

What this does not measure

Where to practise

Work the priority list from the top: Growth and decay in sequences and Earth geometry and time zones first, then the dot points above. Each topic page holds real QCAA questions with marking criteria attached. For what the papers actually cover, read QCE General Mathematics most tested topics.

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.