Integration by substitution
Select a response · Section Multiple choice
QCE Specialist Mathematics · Free interactive sample
Find official questions, understand lost marks and choose what to practise next.
Historical evidence and practice priorities. Future exam questions are not guaranteed. Independent of QCAA.
2024–2025 complete General question corpus · 121 indexed questions, separately marked subparts or printed essay alternatives. Official option-response percentages joined to answer keys for all 40 multiple-choice items. Two complete General examinations, each with separate technology-free and technology-active papers. The 2026 syllabus changes paper duration and some subject matter. Complex-plane region questions moved to assumed knowledge; two uncertain mappings are withheld. Some mathematical notation is absent from the source text capture, so the linked official PDF is required to attempt the question. Showing 6 sample entries; trend percentages use this sample only. Official result percentages describe the published exam cohort.
Choose a topic, open the official question, then check your answer against examiner feedback.
Official averages are unavailable for these entries. 5 questions have sourced incorrect-answer percentages. Fewer marks means a smaller question, not an easier question.
Use your current filters to choose a set, then time your practice or print a worksheet.
6 matching questions
Select a response · Section Multiple choice
Select a response · Section Multiple choice
Select a response · Section Multiple choice
Select a response · Section Multiple choice
Determine · Section Short response
Select a response · Section Multiple choice
Compare the share of marks, then open the exact questions behind each figure.
Sample only: Main examinations only. Percentages show the share of known printed marks in the selected section and year. These describe the indexed historical papers, not probabilities for 2026.
| Topic | 2025 | Years present |
|---|---|---|
| Further complex numbers | 1/1 | |
| Integration techniques | 1/1 | |
| Mathematical induction and trigonometric proofs | 1/1 | |
| Modelling motion | 1/1 | |
| Statistical inference | 1/1 | |
| Vector calculus | 1/1 |
Present in 1 of 1 year shown
Present in 1 of 1 year shown
Present in 1 of 1 year shown
Present in 1 of 1 year shown
Present in 1 of 1 year shown
Present in 1 of 1 year shown
All printed alternatives are counted in these historical shares; candidates follow the paper’s instructions to choose which questions to answer. Mixed-topic items are kept together, and each indexed question contributes its marks once.
Topic and skill labels are original ATARMAxxing analysis, not official question wording. Historical marks describe the indexed printed corpus, not the probability of future examination content. Multiple-topic items can contribute to more than one topic. Missing results remain missing, and no means are inferred from response percentages. © State of Queensland (QCAA); source publications are linked under their stated CC BY 4.0 terms and exceptions.
Use these patterns alongside your own lost marks to choose practice. Keep covering the full syllabus: repeated topics are not guaranteed to appear again.
Topic and skill labels are original ATARMAxxing analysis, not official question wording. Historical marks describe the indexed printed corpus, not the probability of future examination content. Multiple-topic items can contribute to more than one topic. Missing results remain missing, and no means are inferred from response percentages. © State of Queensland (QCAA); source publications are linked under their stated CC BY 4.0 terms and exceptions.
Classification: Historical 2024–2025 General papers; item-level mapping to the 2025 syllabus and official text/topic changes for 2026 assessment. Each question is counted at the separately marked subpart level. The source questions and stimuli remain in the authority's original documents.