# QCAA Mathematical Methods source and partial crosswalk

**Official pin, checked 29 September 2026:** [QCAA Mathematical Methods landing page](https://www.qcaa.qld.edu.au/senior/senior-subjects/syllabuses/mathematics/mathematics-methods) links [Mathematical Methods 2025 v1.3, General senior syllabus](https://www.qcaa.qld.edu.au/downloads/senior-qce/syllabuses/snr_maths_methods_25_syll.pdf), January 2026, for students completing the course in 2026 or later. The current PDF cover and Unit 1 pages were inspected, rather than relying on an older v1.2 search cache. **Unit 1: Surds, algebra, functions and probability** begins at PDF p. 17 / printed p. 15. **Topic 1: Surds and quadratic functions** appears at PDF p. 18 / printed p. 16. No national Year 11 content code is invented; “M1–M10” below are local tracking labels, not QCAA codes.

The syllabus gives **Surds 4 notional hours**, **Quadratic functions 7 notional hours**, and Unit 1 **55 notional hours**. This pack uses eight 25-minute surd days (**200 minutes = 3 hours 20 minutes**) and two 25-minute quadratic introductions (**50 minutes**), **250 minutes = 4 hours 10 minutes** total. The sub-topic hours are guides within the school course. Our sequence leaves substantial surd consolidation and most quadratic work to follow; it does not claim to have “finished Topic 1” because it ran for two weeks.

| Local row | Official source position and scope, paraphrased | Pack evidence | Coverage limit |
|---|---|---|---|
| M1 | PDF p. 18 / printed p. 16, Surds bullet 1: interpret a surd as an irrational square-root/radical expression | Day 1, Card A, aid exact/approx | Only positive simple square roots; no general proof of irrationality |
| M2 | Same page, Surds bullet 2: simplify roots of natural numbers using perfect-square factors | Days 2–5, Cards B–E, Check A, square-factor explorer | Extensive examples but not all possible cases |
| M3 | Same page, Surds bullet 3: remove radicals from denominators of fractional expressions | Day 7, Card G, Day 8 audit, Check B | Single positive radical denominator; sums/conjugates not taught here |
| M4 | Same page, Surds bullet 4: simplify surds with addition, subtraction, multiplication and division | Days 3–8, Cards C–H, both checks | Initial fluency only; mixed extended problems and proof remain |
| M5 | Same page, Quadratic functions bullet 1: recognise parabolic graphs and find turning points, symmetry axes and intercepts in common forms | Days 9–10, Cards I–J, Check B | Only vertex and factor forms; general `ax²+bx+c` form not systematically covered |
| M6 | Same page, Quadratic functions bullet 2: solve equations by factorisation, quadratic formula, completing the square and technology | Day 10 uses factor-zero reasoning only | Quadratic formula, completing square, technology and varied equations remain |
| M7 | Same page, Quadratic functions bullet 3: sketch with/without technology | Days 9–10 point sketches | Introductory sketches only |
| M8 | Same page, Quadratic functions bullet 4: use discriminant to determine the number of solutions | Not taught | Required follow-up |
| M9 | Same page, Quadratic functions bullet 5: find turning points and zeros with/without technology | Days 9–10, simple forms | General cases and technology follow-up |
| M10 | Same page, Quadratic functions bullet 6: model and solve quadratic-function problems with/without technology | Fictional graph contexts are illustrative, not validated models | Required follow-up; no empirical fit is claimed |

**Unit objectives:** PDF p. 17 / printed p. 15 lists six Unit 1 objectives: recall, use, communicate, evaluate reasonableness, justify and solve problems. The cards ask for exact calculation, explanation, estimation and error diagnosis. They are small practice opportunities, not proof of full achievement of every objective. The assumed-knowledge list on PDF p. 9 / printed p. 7 includes prior algebra, solving simple quadratics and real numbers. Day 1 checks roots and Day 9 uses a square table to expose prerequisites. Teachers should adapt after seeing actual responses.

**Assessment boundary:** the QCAA syllabus sets school-designed assessment conditions for Units 1 and 2 (PDF p. 7 / printed p. 5). Checks A and B are **public formative feedback** with a public key. They are **not secure**, do not provide a Unit 1 reporting grade, and do not replace a school's assessment programme. The Year 11 Methods pathway is separate from General Mathematics and Essential Mathematics.