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QCE Mathematical Methods · Year 12

QCE Mathematical Methods: what actually gets examined

Every question from 4 official QCAA papers, coded by unit, topic and marks — so you can decide what to revise from evidence rather than a feeling.

4 QCAA papers, 2022–2025 · 208 questions · 440 marks

8 of the 8 topics in QCE Mathematical Methods were examined in every paper on file, and the 2 units carry uneven weight. There is nothing here you can safely skip — the question is what order you revise in.

Counted from 4 official QCAA Mathematical Methods papers (2022–2025). 208 questions, 440 marks. Nothing estimated.

8 of 8topics in every paper on file
97marks in the single biggest topic
20multiple choice marks, every paper

The cognitive verbs that carry the paper

Share of written-response questions by QCAA cognitive verb, matched against QCAA's own Cognitive verb framework. Revising the content without revising the directive is how marks get lost. The lower / middle / higher grouping is ours — QCAA publishes the list but does not band it. Based on the 59% of written responses that open with a listed cognitive verb; the rest open with wording outside it, such as a direct question.

Determine70% · 53qmiddle order
Use17% · 13qlower order
Other8% · 6q
State5% · 4qlower order

Lower orderMiddle orderHigher order

Each tile is one key word; its size is that key word's share of written-response questions that open with one. The smallest 5 are grouped as Other: Compare 1% · 1q, Develop 1% · 1q, Express 1% · 1q, Solve 1% · 1q, Calculate 3% · 2q.

Where the marks sit

Each unit with its topics underneath. The bar is that topic's share of its own unit, and the chip says how many of the papers on file examined it.

Unit 3

200 marks
Integrals Every paper 97 marks

45 questions · 49% of this unit

The logarithmic function 2 Every paper 62 marks

29 questions · 31% of this unit

Further differentiation and applications 2 Every paper 41 marks

28 questions · 21% of this unit

Unit 4

241 marks
Further differentiation and applications 3 Every paper 50 marks

20 questions · 21% of this unit

Continuous random variables and the normal distribution Every paper 50 marks

20 questions · 21% of this unit

Discrete random variables 2 Every paper 48 marks

25 questions · 20% of this unit

Interval estimates for proportions Every paper 48 marks

26 questions · 20% of this unit

Trigonometric functions 2 Every paper 45 marks

20 questions · 19% of this unit

Across 4 papers the units carried 200, 241 marks.

How each topic gets asked

The 6 biggest topics, by the shape of the questions actually set on them. Revising the content without revising the directive is how marks get lost — the cognitive verbs below are QCAA's own, counted from the papers.

Integrals

Unit 3 · 97 marks across 45 questions

Asked as Multiple choice ×18 · Short answer ×22 · Extended response ×5

QCAA cognitive verbs Determine ×17 · Use ×4 · State ×2 · Calculate ×1

The logarithmic function 2

Unit 3 · 62 marks across 29 questions

Asked as Multiple choice ×9 · Short answer ×17 · Extended response ×3

QCAA cognitive verbs Determine ×15 · Solve ×3 · State ×1

Further differentiation and applications 3

Unit 4 · 50 marks across 20 questions

Asked as Multiple choice ×5 · Short answer ×11 · Extended response ×4

QCAA cognitive verbs Determine ×6 · Use ×3

Continuous random variables and the normal distribution

Unit 4 · 50 marks across 20 questions

Asked as Multiple choice ×10 · Short answer ×7 · Extended response ×3

QCAA cognitive verbs Determine ×3 · Calculate ×1

Discrete random variables 2

Unit 4 · 48 marks across 25 questions

Asked as Multiple choice ×7 · Short answer ×17 · Extended response ×1

QCAA cognitive verbs Determine ×7 · State ×2 · Calculate ×1 · Use ×1 · Compare ×1 · Consider ×1

Interval estimates for proportions

Unit 4 · 48 marks across 26 questions

Asked as Multiple choice ×10 · Short answer ×15 · Extended response ×1

QCAA cognitive verbs Determine ×5 · Use ×3

What the markers wanted

Queensland Curriculum and Assessment Authority publishes subject reports after each paper. This is our reading of the 2022–2025 feedback, in our words, grouped by unit and cited to the year and question it was seen in. It describes what markers rewarded in papers already sat; it does not predict the next one. The originals are linked below.

Across the paper

  • Technology-free algebra was the most frequently reported obstacle. Reports trace lost marks to expanding a squared bracket, simplifying the terms that result, and moving between fractions and decimals rather than to the calculus itself
  • Several of the hardest questions asked for a model to be built before it could be solved, and students who could start often stalled at the point of reducing the situation to a single variable
  • Where technology was allowed it was used well - solving equations, running statistical routines and evaluating rates of change - and the reports treat that as settled practice rather than a weakness
  • Estimation was a recurring gap in geometric problems: work that was progressing correctly stopped short because a value could not be brought to a sensible approximation
  • Setting out mattered on multi-step work. Reports link a clear, lined-up progression from formula to substitution to answer with both fewer errors and easier marking

Unit 3

Better responses

  • Differentiation of exponential, logarithmic and trigonometric expressions was handled confidently, including in the technology-free paper
  • The definite integral was used well for areas under and between curves, and integration was recognised as reversing differentiation
  • Qualitative work on logarithmic graphs went well - locating the vertical asymptote and reading a horizontal translation - and such equations were solved without technology
  • Modelling with exponential functions, and solving the equations that came out of it, was reported as secure across both familiar and more demanding contexts

Where marks were lost — and how to keep them

  • Clearing the algebra before integrating, since an error expanding or simplifying the integrand stops the calculus that follows
  • Applying several logarithmic rules in sequence and then handling the quadratic that results
  • Integrating a rate of change to recover the quantity itself, and combining two rates where a problem supplies both
  • Recovering velocity from a displacement model by differentiating and from an acceleration by integrating, keeping the two directions straight

Seen in 2025 Paper 1 Q18, 2024 Paper 1 Q13, 2024 Paper 2 Q18, 2022 Paper 2 Q17, 2022 Paper 2 Q19.

Unit 4

Better responses

  • Mean, variance and standard deviation for Bernoulli and binomial situations were computed reliably with and without technology
  • Confidence intervals for a population proportion, and the margin of error attached to them, were applied accurately
  • Sine and cosine rules and the triangle area formula were used soundly on problems mixing side lengths, angles and enclosed areas
  • Normal distribution probabilities were obtained confidently once the context had been translated into the right parameters

Where marks were lost — and how to keep them

  • Justifying an inflection point by showing concavity actually changes, rather than stopping at the second derivative being zero
  • Identifying which quantity a problem wants maximised, since maximising a rate is not the same as maximising the amount
  • Building a confidence interval without technology, and then using it to judge a claim rather than merely reporting it
  • Treating a probability from a density function as an integral to be set up and solved, not as a value to look up
  • Verifying an optimum with the second derivative test once the model has been reduced to one variable

Seen in 2025 Paper 1 Q12, 2025 Paper 1 Q13, 2025 Paper 2 Q18, 2024 Paper 1 Q19, 2023 Paper 1 Q17, 2022 Paper 2 Q16, 2022 Paper 1 Q18, 2022 Paper 1 Q19.

2025 QCAA subject report →2024 QCAA subject report →2023 QCAA subject report →2022 QCAA subject report →

How the paper is built

Marks by question format across the same 4 papers.

Multiple choice 8020 / 20 / 20 / 20 per paper
Short answer 24171 / 51 / 68 / 51 per paper
Extended response 11919 / 39 / 22 / 39 per paper

Multiple choice is exactly 20 marks in every paper. The rest moves around: short answer ran 71, 51, 68, 51 marks and extended response ran 19, 39, 22, 39 marks. 4 papers is not enough to call that a trend.

Every question, by topic

All 208 questions from the 4 papers, listed under the topic each was coded to — year, question number, marks as printed on the paper, cognitive verb and format — with QCAA's own copy of the paper linked on every row. The questions themselves are read there, not here. Marks here are as printed and every question is listed once, so these totals sit a little apart from “Where the marks sit” above, by design: there, a question coded to more than one topic has its marks split evenly. Open a unit to see its list.

Unit 3101 questions · 202 marks · show

Integrals · 44 questions, 94 marks

The logarithmic function 2 · 29 questions, 62 marks

Further differentiation and applications 2 · 28 questions, 46 marks

Unit 4107 questions · 238 marks · show

Further differentiation and applications 3 · 20 questions, 58 marks

Continuous random variables and the normal distribution · 20 questions, 50 marks

Discrete random variables 2 · 25 questions, 48 marks

Interval estimates for proportions · 26 questions, 48 marks

Trigonometric functions 2 · 16 questions, 34 marks

The papers this is counted from

Queensland Curriculum and Assessment Authority publishes every paper and its marking guidelines. These links go to QCAA's own copies — read the questions there. QCAA publishes each year in more than one booklet, and every one this page counted is linked.

2022 Paper 1 — multiple choice →2022 Paper 1 — question and response →2022 Paper 2 — multiple choice →2022 Paper 2 — question and response →2023 Paper 1 — multiple choice →2023 Paper 1 — question and response →2023 Paper 2 — multiple choice →2023 Paper 2 — question and response →2024 Paper 1 — multiple choice →2024 Paper 1 — question and response →2024 Paper 2 — multiple choice →2024 Paper 2 — question and response →2025 Paper 1 — multiple choice →2025 Paper 1 — question and response →2025 Paper 2 — multiple choice →2025 Paper 2 — question and response →

These are the external examination papers. They are not the whole subject: Mathematical Methods is also assessed by internal assessments set and marked by your school, which QCAA does not publish — so nothing on this page covers that part of your result.

Study Mathematical Methods on Revizi

QCE Mathematical Methods TopicsQCE Mathematical Methods PracticeQCE Mathematical Methods Past PapersQCE Past Exam PracticeQCE Exam PracticeQCE Flashcards HubAll QCE Questions by TopicQuestions by Topic — all curricula

Frequently Asked Questions

Which QCE Mathematical Methods topics come up every year?

8 of the 8. Every topic marked "Every paper" above was examined in all 4 papers on file. That describes the papers analysed, not a prediction — examiners set each paper fresh.

Which QCE Mathematical Methods unit is worth the most marks?

Unit 4 241, Unit 3 200 marks across the 4 papers analysed.

What is the biggest single topic in QCE Mathematical Methods?

Integrals, with 97 of the 440 marks counted across 4 papers.

How was this analysed?

Every question in 4 official QCAA QCE Mathematical Methods papers (2022–2025) was counted against the QCAA Mathematical Methods 2019 General Senior Syllabus, Units 3 and 4: its mark value, its format and its key word, and the unit and topic it assesses. Marks are reconciled against each paper's own stated total.

Are the exam questions reproduced here?

No. Queensland Curriculum and Assessment Authority owns the papers. This page publishes counts and links to QCAA's own copy of each paper so you can read the questions at the source. The analysis is ours; the papers stay with QCAA.

Does this predict what will be in my exam?

No, and it is not meant to. It describes what has been set. Examiners write each paper fresh and can weight a neglected topic heavily, which is why every topic is listed here, including the ones examined least.

Can I see which QCE Mathematical Methods questions were set on each topic?

Yes. Every question from the 4 papers is listed above under the topic it was coded to, with its year, question number, marks and cognitive verb, and a link to QCAA's copy of that paper. The question itself is read there, not here.

What did the QCAA markers say about QCE Mathematical Methods?

Queensland Curriculum and Assessment Authority publishes marker feedback after each paper. The "What the markers wanted" section above is our reading of it across 4 years, in our words, grouped by unit and cited to the year and question it was seen in, with the originals linked.

Coded against the QCAA Mathematical Methods 2019 General Senior Syllabus, Units 3 and 4. Where a question is coded to more than one topic its marks are split evenly, so topic totals within a unit can round a mark or two above the unit total. A topic is marked "Every paper" when it appears in all 4, "Most papers" when it is missing from one, and "Comes and goes" when it is missing from more — the one-paper tolerance absorbs a single coding miss rather than publishing it. Last updated 2026-09-01 · Exam papers © Queensland Curriculum and Assessment Authority, linked at source.