QCE Mathematical Methods: Paper 1 without technology, Paper 2 with it, and what Units 3 and 4 cover

QCE Maths Methods assessment

Checked on 11 November 2026 against the QCAA Mathematical Methods syllabus (2025 version 1.3, January 2026).

The marks are added to give a total out of 100 and QCAA subject experts set the A to E cut-offs. The external exam does not scale your internal marks. For IA1 you have 3 hours of class time plus your own time, and technology must go beyond simple computation.

Paper 1 and Paper 2

Both papers assess Units 3 and 4, with assumed knowledge from Units 1 and 2, and both have 5 minutes perusal and 90 minutes working time. The QCAA gives you the Mathematical Methods formula book in each. Questions are short response and multiple choice, from "simple familiar" about 60% of marks, through "complex familiar" 20%, to "complex unfamiliar" 20%.

The 2026 external assessments run from Monday 26 October to Tuesday 17 November 2026. The 2027 timetable was not published when this page was checked.

What Units 3 and 4 cover, and what moved in 2026

• Unit 3, Further calculus and introduction to statistics. Differentiation of exponential and logarithmic functions, of trigonometric functions and the rules for combining them, further applications of differentiation, an introduction to integration, and discrete random variables.
• Unit 4, Further calculus, trigonometry and statistics. Further integration, trigonometry, continuous random variables and the normal distribution, sampling and proportions, and interval estimates for proportions.

For the 2025 syllabus the QCAA lists these changes: arithmetic and geometric progressions were removed, basic surd operations were added, logarithms were consolidated in Unit 2 except applications with base e, integration by recognition was removed, discrete random variables moved to Unit 3, and the formula book was updated.

Worked examples

Differentiating and finding stationary points

Take f(x) = x²e³ˣ. The product rule gives:

Since e³ˣ is never zero, the stationary points are at x = 0 and x = −2/3, and f(−2/3) = (4/9)e⁻² ≈ 0.060. Check a value of the derivative with the Derivative Calculator: at x = 1 it gives 5e³ ≈ 100.4.

Two integrals by hand

Paper 1 expects exact values. For a trigonometric integral and an area between curves:

A discrete random variable

A game pays 1, 2 or 3 points with probabilities 0.2, 0.5 and 0.3. The expected value is E(X) = 0.2 + 1.0 + 0.9 = 2.1. Next E(X²) = 0.2 + 2.0 + 2.7 = 4.9, so the variance is 4.9 − 2.1² = 0.49.

An interval estimate for a proportion

A sample of 200 shows 45% in favour. The standard error is √(0.45 × 0.55 ÷ 200) ≈ 0.0352, so an approximate 95% interval is 0.45 ± 1.96 × 0.0352, that is 0.381 to 0.519. Say what the interval means: about 95% of intervals built this way capture the true proportion.

Test the normal distribution from the Probability course, then press Mark:

Using the daily papers as a practice exam

Each daily paper has 8 original questions and 25 to 35 marks, so it is a short timed paper, not a QCAA exam. Queensland has no state trials; use the QCAA's published past papers for full-length practice.

• On the Year 12 calculus paper, sit the chain, product and quotient rule, stationary point, rates of change and area under a curve questions, without a calculator for Paper 1 practice.
• On the Year 11 paper, the exponentials and logarithms and functions and graphs questions give you the algebra that Unit 3 differentiation builds on.
• Skip parametric differentiation, differential equations, integration by substitution and by parts, first principles, partial fractions and sequence questions: they are not in the Methods subject matter. Daily papers do not cover the normal distribution in this track, so use the course for it.

Grades, results and ATAR

Results are reported as A to E with the mark out of 100. The 2026 results are released from 9:00 am on Wednesday 16 December 2026 and ATARs on 18 December 2026. A General and an Applied Mathematics subject cannot both count toward the ATAR.

Exam answers

Answers and a worked mark scheme for the daily paper come with today's paper once it's marked. We do not publish QCAA answers; the QCAA's marking guides sit with its past papers.

Common mistakes in QCE Maths Methods

• Losing the exact form. Paper 1 wants √3 ÷ 2, not 0.866, so keep surds and logarithms exact.
• Dropping the product rule. A function like x²e³ˣ needs both terms differentiated.
• Leaving out the interpretation. An interval or probability needs a sentence in context.
• Using CAS. Only graphics calculators without CAS functionality are allowed in Paper 2.

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Australia · QCEQCE Maths Methods formula sheet: what the QCAA book givesThe QCAA Mathematical Methods formula book for QCE external exams: what is in it, what is not, and how to use it in both papers.