QCE General Mathematics was completed by more than 21,000 Queensland students in 2025, and its external assessment is worth 50% of your final result. The 2025 exam covered seasonal indices, reducing balance loans, flow networks, Eulerian trails and least-squares models, and QCAA's subject report shows exactly where students gained and lost marks.
This guide breaks down the external assessment section of QCAA's 2025 General Mathematics subject report. It covers how every multiple-choice question was answered across the state, the short-response questions QCAA singled out, what effective responses did and QCAA's advice for future students. For the school-based side of the subject, see our companion breakdown of the 2025 QCE General Maths internal assessments.
Key Takeaways
- 21,188 students completed Units 3 and 4 in 2025, and 96.36% received a C or higher.
- An A required a final mark of 84 or more out of 100. Only 14.27% of students achieved an A, while 41.25% received a B.
- Students averaged 67.0% on the 15 multiple-choice questions. Four questions (8, 12, 13 and 14) were answered correctly by fewer than half the cohort.
- Students did well on Earth geometry, scatterplots, depreciation, perpetuities and critical paths.
- Marks were lost for stating rather than interpreting a slope, mixing up EST and LST when finding float time, calculating seasonal indices in the wrong order and not giving reasons to justify decisions.
The 2025 Cohort at a Glance
| Statistic | 2025 |
|---|---|
| Schools offering General Mathematics | 471 |
| Students who completed Unit 1 | 24,163 |
| Students who completed Unit 2 | 23,171 |
| Students who completed Units 3 and 4 | 21,188 |
| Students who received a C or higher | 96.36% |
Source: QCAA General Mathematics subject report, 2025 cohort.
About 88% of the students who completed Unit 1 went on to complete Units 3 and 4. Units 1 and 2 still caught some students out: about 13% received an Unsatisfactory result in each unit.
QCE General Mathematics External Exam Structure
| Feature | Paper 1 | Paper 2 |
|---|---|---|
| Question type | 15 multiple-choice questions + short-response questions | Short-response questions |
| Marks | 57 (15 multiple choice + 42 short response) | 38 |
| Focus | Simple familiar questions | Complex familiar and complex unfamiliar questions |
| Time | 5 minutes perusal + 90 minutes working | 5 minutes perusal + 90 minutes working |
The exam is worth 95 marks in total, which is converted to a mark out of 50 and makes up 50% of your final result. The other 50% comes from your three internal assessments: IA1 (20%), IA2 (15%) and IA3 (15%).
Paper 2 is where the harder problem-solving questions sit. Its 38 marks are all short response, and several questions asked students to make and justify a decision.
The most common external assessment results in 2025 fell between the low 30s and low 40s out of 50. Very few students scored above 47, so full marks are extremely rare.
💡 Get ready for the exam with our step-by-step guide on how to prepare for QCE external exams.
2025 Grade Boundaries and Results
| Grade | Final Mark (out of 100) | Number of Students | Percentage of Students |
|---|---|---|---|
| A | 84–100 | 3,024 | 14.27% |
| B | 68–83 | 8,740 | 41.25% |
| C | 45–67 | 8,653 | 40.84% |
| D | 22–44 | 759 | 3.58% |
| E | 0–21 | 12 | 0.06% |
Source: QCAA General Mathematics subject report, 2025 cohort.
Your final mark is your internal assessment total (out of 50) plus your external assessment mark (out of 50). Final marks clustered between about 60 and 80, so a few extra marks on the external exam can be the difference between a B and an A.
Paper 1: Multiple-Choice Results
| Question | Correct Answer | % Correct | Most Common Wrong Answer |
|---|---|---|---|
| 1 | D | 84.80% | A (10.90%) |
| 2 | A | 76.53% | D (12.59%) |
| 3 | B | 84.66% | C (12.13%) |
| 4 | A | 55.42% | D (24.80%) |
| 5 | C | 82.55% | B (7.68%) |
| 6 | B | 56.29% | C (25.68%) |
| 7 | B | 77.40% | D (13.59%) |
| 8 | B | 46.74% | C (29.53%) |
| 9 | C | 77.55% | B (10.02%) |
| 10 | C | 83.45% | B (6.47%) |
| 11 | A | 61.93% | B (20.86%) |
| 12 | D | 48.46% | B (29.44%) |
| 13 | B | 44.92% | C (20.77%) |
| 14 | D | 42.23% | B (19.71%) |
| 15 | D | 82.02% | C (6.54%) |
Source: QCAA General Mathematics subject report, 2025 cohort. Some students did not answer every question.
What the Multiple-Choice Results Show
- Question 14 was the hardest. Only 42.23% chose the correct answer, and the other three options were each chosen by about 18–20% of students. A spread like this usually means many students were guessing.
- Questions 8 and 12 each had one wrong option chosen by almost 30% of students, which points to a common misconception.
- Questions 1, 3, 5, 10 and 15 were answered correctly by more than 82% of students. These are marks you cannot afford to drop.
- Across the paper, students averaged 67.0%, so the typical student lost about 5 of the 15 multiple-choice marks.
💡 Check out why past papers are the best way to study for exams.
Short-Response Questions QCAA Highlighted
QCAA's report gave detailed feedback and sample responses for nine short-response questions. Here is what each one asked and what separated effective responses.
Paper 1, Question 17(b): Justifying an Association
Students used a two-way table of travel times to school to justify a suggested association between year level and travel time.
Effective responses:
- calculated the percentage of Year 6 students who travel less than 15 minutes (11/17 ≈ 64.7%)
- calculated the percentage of Year 10 students who do the same (3/12 = 25%)
- compared the percentages and described the difference as large, for example "significantly larger" or "more than double".
Key lesson: Saying the percentages are different is not enough. QCAA said you must state that the difference is large. Percentages that differ but are similar, such as 45% and 55%, suggest no association.
Paper 1, Question 19: Seasonal Index Across Two Years
Students were given a store's quarterly sales for 2023 and 2024, plus the 2023 quarterly average ($32,500). They had to find the 2024 average and the seasonal index for Quarter 3.
Effective responses:
- found the 2024 average: (7,500 + 23,500 + 82,000 + 12,500) ÷ 4 = $31,375
- divided each year's Q3 sales by that year's average: 94,000 ÷ 32,500 ≈ 2.89 and 82,000 ÷ 31,375 ≈ 2.61
- averaged the two ratios to get the Q3 seasonal index: ≈ 2.75.
Key lesson: QCAA asked teachers to make sure students do these steps in the correct order. Find the average for each year, not for each season or for all years combined. Then express each value as a ratio of its own year's average, then average the ratios for each season.
Paper 1, Question 20: Reducing Balance Loan
Students wrote a recurrence relation for a $24,000 loan at 5.4% p.a. compounding monthly, with monthly repayments of $557, then found the amount owing and the reduction in the balance after two months.
Effective responses:
- found r = 1 + 0.054/12 = 1.0045 and wrote Aₙ₊₁ = 1.0045Aₙ − 557, A₀ = 24,000
- applied the recurrence relation twice to show their working, giving $23,099.98 owing after two months
- found the reduction in the balance: 24,000 − 23,099.98 = $900.02.
Paper 1, Question 23(a): Why a Subgraph Is Not a Tree
Students identified why a given subgraph of a network was not a tree.
Effective responses stated that the subgraph contains a cycle and that a tree cannot contain a cycle. QCAA wants students to use the correct terms, linking a feature of the subgraph to the definition of a tree.
Paper 1, Question 24(b): Interpreting the Slope
Students were given a least-squares line for Australian average weekly earnings from 2013 to 2023 and asked to identify and interpret its slope.
Effective responses identified the slope as 49 and interpreted it in context: "for every year, average weekly earnings increase by $49".
Key lesson: QCAA wants students to interpret the slope, not just state it. An interpretation needs the direction, the size and the units of the change in context.
Paper 2, Question 3: Upgrading a Flow Network
Students built a flow network from a table of pipe capacities, found the maximum flow from source A to river E, and worked out which single pipe to upgrade to raise the maximum flow to 45 L/s.
Effective responses:
- drew the flow network with all vertices, edges and correct weights
- found every cut and its capacity to identify the original maximum flow (44 L/s)
- justified which pipe to upgrade: pipe C to E, from 24 L/s to 25 L/s, so the minimum cut became 45 L/s.
Paper 2, Question 5: Eulerian Trails and Walking Time
Students used a network of walkways to compare a usual walk (an open Eulerian trail taking 17 minutes) with a changed walk that had to finish where it started (a closed Eulerian trail).
Effective responses:
- used Pythagoras' theorem to find the missing walkway: √(105² + 208²) ≈ 233 m
- found the usual trail length (1,139 m) and the walking speed (1,139 ÷ 17 = 67 m/min)
- found the changed trail length (1,034 m) and its time (≈ 15.4 minutes)
- made a justified decision: the walk would not be completed in under 15 minutes.
Paper 2, Question 6: Two Hikers Meeting on a Track
Two people walked towards each other from opposite ends of a track. Their distances from the car park were given as rules (Fₙ = 2n and Gₙ = 12 − 3(n − 1)). After meeting and taking a 30-minute break, they walked back to the car park together, arriving at 4 pm.
Effective responses:
- found when and where they met by solving Fₙ = Gₙ: after 3 hours, 6 km from the car park
- found when the break ended (1:30 pm, after starting at 10 am)
- calculated the hiking speed: 6 km ÷ 2.5 h = 2.4 km/h.
QCAA's two sample responses used different but equally valid methods. One solved the equations algebraically, and the other listed terms from each rule until they matched.
Paper 2, Question 7: Evaluating a Profit Prediction
Students used four years of profit data for two businesses to evaluate a prediction about the annual profit of the merged company in 2040.
Effective responses:
- combined the profits of the two businesses and built a model, with variables clearly defined (the sample response built a linear model for each business and added the predictions)
- substituted 2040 to predict the merged company's profit (about $4.14 million in the sample response)
- compared their result with the prediction and made a justified decision about whether it was reasonable.
What Students Did Well
QCAA said the 2025 cohort responded well to:
- Earth geometry and time zones, including time differences, angular distance and distances in kilometres
- constructing scatterplots, including telling arithmetic and geometric sequences apart
- familiar financial situations, such as diminishing-value depreciation and fortnightly payments for a perpetuity
- networks, including drawing network graphs, minimum spanning trees, shortest walks and forward and backward scanning to find the critical path
- making predictions with a least-squares line or the rule for the nth term of a geometric sequence
- assumed knowledge and technology, such as Pythagoras' theorem, speed calculations, entering data and generating terms of a recurrence relation.
Areas QCAA Wants Students to Improve
1. Use the Correct Terminology
Use syllabus terms precisely, such as tree and cycle, and explain answers with them.
2. Interpret, Don't Just State
When asked to interpret a slope, describe what it means in context, including the units. Stating "the slope is 49" earns less than explaining what changes by 49 and per what.
3. Critical Path Analysis
Know the difference between the earliest starting time (EST) and the latest starting time (LST). Use the correct values from your forward and backward scans to calculate the float time of a non-critical activity.
4. Effective Annual Interest Rates
Use the effective annual rate formula for a perpetuity the same way you would for any other investment or loan. The effective rate lets you compare perpetuities with different compounding periods or payment frequencies.
5. Seasonal Indices
Follow the steps in order: average for each year, then the ratio of each value to its year's average, then the average of the ratios for each season.
6. Show Your Working the Way Markers Expect
- Define your variables when building a model or equation.
- Write the formula and identify each value before substituting.
- Give reasons to justify every decision.
- Re-read the question to check that you have answered every part.
💡 Not sure what "interpret", "justify" or "evaluate" are asking for? Read our complete guide to QCE cognitive verbs.
Exam-Day Advice From QCAA
- Use the marks as a guide. Any question worth more than one mark needs working or reasoning. A 5-mark answer must show evidence for five separate steps in the marking guide.
- Use pen, not highlighter, on network diagrams. Highlighter may not show up when your response is scanned. Draw a thicker or squiggly line in blue or black pen, or write the vertex sequence next to the diagram.
- Use the additional pages correctly. Continue long answers on the additional pages at the back of the book and write the question number clearly.
- Cross out work properly. If you start a new answer, rule a single diagonal line through the work you want cancelled. Otherwise your original response will be marked.
- Fill in the multiple-choice bubbles. Work in the multiple-choice question book is not marked. Use a 2B pencil, fill each A, B, C or D bubble completely and answer every question.
How to Prepare for the QCE General Maths External Exam
- Practise Paper 2-style questions. Complex familiar and complex unfamiliar questions make up 40% of the exam marks, and most ask for a justified decision.
- Learn the procedures step by step, especially seasonal indices, recurrence relations for loans, flow network cuts and forward and backward scanning.
- Practise interpreting results in context, including slopes, percentages and effective interest rates.
- Finish every decision question with a clear conclusion that refers back to your calculations.
- Revise assumed knowledge such as Pythagoras' theorem, speed, distance and time, and percentages.
- Sit full past papers under timed conditions to practise managing 90 minutes per paper.
For more preparation:
- read our guide to getting an A in QCE General Mathematics
- see our breakdown of the 2025 QCE General Maths internal assessments
- compare with our 2025 QCE Maths Methods external assessment breakdown
- check the QCE exam timetable 2026 for this year's exam dates
- learn how QCE subject scaling works.
Need Help With QCE General Maths?
Our QCE General Mathematics tutors work one-on-one with students to master finance, networks and data analysis, and to write the clear, justified responses QCAA markers look for.
Source: Queensland Curriculum & Assessment Authority, General Mathematics subject report, 2025 cohort (January 2026).
