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2026 QCE Mathematical Methods exam: What to learn from last year's mistakes
Hi all, in preparation for the upcoming exam, here's what to learn from last year's mistakes.
2025 exam median and average: not stated in QCAA's report.
The exam was 110 raw marks, split evenly between two 55-mark papers, and worth 50% of the subject result.
I've gone through the report and both guides. A correct number wasn't always the whole answer. QCAA specifically called out missing justification for inflection points and unchecked logarithm solutions.
QCAA doesn't give written-question averages. The allocations below show what each question was worth, not the cohort's score.
Paper 1, Q12: Confidence interval without technology
4 marks.
Where an answer loses marks: Using the wrong sample proportion or leaving the interval unfinished.
What you needed: With 5 successes from 25 observations, p̂ = 1/5. Use the supplied z = 1, not an automatically memorised 1.96. The margin of error is √[(1/5)(4/5)/25] = 2/25. The interval is (3/25, 7/25), or (0.12, 0.28).
Paper 1, Q13: Point of inflection
4 marks.
Where students went wrong: Stopping at f″(3) = 0. The report says many responses didn't establish the change in concavity.
What they should have done: Here f″(x) = 2x − 6. Show f″(2) = −2 and f″(4) = 2. The function changes from concave down to concave up at x = 3, so it is an inflection point. Setting the second derivative to zero only found the candidate.
Paper 1, Q15: Logarithms
6 marks.
Where students went wrong: Finding solutions without checking them in the original equation.
What they should have done: Substitute y = log₂(x), giving y² − 2y − 8 = 0. That gives y = 4 or −2, so x = 16 or 1/4. The guide then allocates two marks to substituting a chosen solution back into the original equation and judging whether it works. For x = 16, both sides equal 16. Don't stop at the quadratic's roots.
Paper 2, Q18: Is the claim supported?
5 marks.
Where an answer loses marks: Calculating an interval without answering the claim about 75%.
What you needed: Use n = 500, lower endpoint 0.648 and z = 1.96. Solving p̂ − 1.96√[p̂(1 − p̂)/500] = 0.648 gives p̂ ≈ 0.6886. The upper endpoint is about 0.729. The claimed 0.75 lies outside (0.648, 0.729), so the survey does not support it at this confidence level. That comparison has its own mark.
For 2026, arithmetic and geometric progressions have been removed from the subject matter, and integration by recognition has been removed. Use the current syllabus and formula book to decide which old questions to prioritise.
Use the 2025 report alongside Paper 1 guide and Paper 2 guide. 2026 syllabus changes.
Figures and criteria: QCAA. Explanations paraphrased from its materials, © State of Queensland (QCAA) 2025–2026, CC BY 4.0.
Use the Mathematical Methods hub and past papers and marking guides alongside this.
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