QCE General Mathematics study guide

General Mathematics is assessed on four instruments across Units 3 and 4: an IA1 problem-solving and modelling task worth 20%, two internal examinations worth 15% each, and a 50% external examination in two papers. Your school writes and marks the three internal assessments, with QCAA approving each task before it is sat (endorsement) and checking a sample of the marking afterwards (confirmation); QCAA writes and marks the exam. Units 1 and 2 are reported satisfactory or unsatisfactory and do not feed your final mark out of 100.

This guide describes the General Mathematics 2025 v1.0 General senior syllabus, current for Year 12 from 2026. Every subject report QCAA has published so far, covering the 2022 to 2025 cohorts, describes students assessed under the superseded 2019 v1.2 rules, so each figure below carries its cohort year. No published report yet describes marking under the current criteria.

How the marks add up

Half your result is internal and half is external, and the internal half is split 20/15/15, so the modelling task alone outweighs either internal exam. The weightings are unchanged from the 2019 syllabus.

The two internal exams and the external exam are all built to the same question specification, within ±2%: 60% simple familiar, 20% complex familiar, 20% complex unfamiliar. A simple familiar question is one where the procedure is clear from the wording or the context has been a focus of prior learning, and three fifths of everything you sit is that.

The exam is half of your result

Two papers, sat on the same day under the same conditions.

All four reports from 2022 to 2025 describe the same mark split as sat: Paper 1 carried 15 multiple-choice marks and 42 short-response marks, Paper 2 carried 38 short-response marks, for a raw total of 95. Paper 2 has no multiple-choice section.

QCAA publishes the full per-option response percentage table for all 15 multiple-choice items every year. Reading across the 2025 table, four items drew under half the cohort onto the correct option, with Q14 at 42.23% correct and the three wrong options within about 1.5 percentage points of each other. That reading of the spread is ours, not QCAA's: the reports print the table and do not rank or flag any item.

What QCAA keeps saying, four years running

The reports' "practices to strengthen" sections repeat themselves. Ranked by how many of the four cohorts named each one:

Constructing scatterplots was named a weakness in 2022, 2023 and 2024, and in 2025 it moved into the list of things students did well. It is the only item in the four-year set to cross from one list to the other.

Interpret the value, do not just state it

The external exam is the only assessment where QCAA reproduces enough student prose to compare wordings. The same gap shows up every year.

On that last one QCAA states the rule itself, in the 2025 report: "Stating there is a difference in percentages is not the same as stating there is a large difference in percentages. Percentages that differ but are similar (e.g. 45% and 55%) suggest no association."

Where the marks are actually lost

QCAA does not publish performance per syllabus dot point. Our own marking data does, at the cost of covering a self-selected group of students practising when they chose to, so read these as resolution on top of QCAA's findings and never as a substitute for them.

Across 16,959 marked attempts on 392 General Mathematics questions on AusGrader, almost all of them from the 2020 to 2025 external papers, these are the weakest outcomes with a publishable sample:

Two of those independently corroborate something QCAA already asks for above: deseasonalising in the correct order, and setting the Hungarian algorithm out step by step. Where our figures disagree with a QCAA finding, they are left off this page entirely, which is why three outcomes with weak-looking averages are missing from the table.

The strongest outcomes with a publishable sample sit above 80%: semi-Eulerian and Eulerian graph problems (83.2%, 216 attempts), constructing a graph or digraph from an adjacency matrix (80.9%, 419), walk, trail, path, circuit and cycle terminology (80.3%, 666) and describing time series plots (80.5%, 295). Describing a time series plot is one of our strongest outcomes, at 80.5%, and constructing one is our weakest, at 39.6%, on the same topic.

By cognitive verb

QCAA publishes nothing at this granularity. Across the same 16,959 attempts, our per-verb averages with 50 or more attempts, weakest first:

Calculate is our weakest verb by a wide margin, and it is the most straightforwardly mathematical of them. QCAA defines it as determining a numerical value or quantity through mathematical operations. Every verb below 50 attempts, including describe, interpret, justify and evaluate, has too small a sample to publish. By question format, our multiple-choice average is 61.0% across 15,429 attempts and our short-answer average 54.7% across 1,293. The investigate figure above and our assignment-format figure come from the same 237 attempts, so they are one finding.

Do not chase a fixed grade boundary

QCAA sets boundaries each year against the reporting standards, so the number moves.

The A boundary rose from 82 to 84 across those four cohorts and the B boundary from 64 to 68, while the C boundary sat at exactly 45 in all four. So the drift has been upward, and only at the top two standards.

In the 2025 cohort, 21,188 students from 471 schools completed Units 3 and 4, and 96.36% earned a C or higher: 14.27% at A, 41.25% at B and 40.84% at C.

Where to start

If you are in Year 12 now, the two internal examinations arrive first and are the cheapest marks in the course to protect, because the mark is arithmetic once the paper is written. Read how IA2 and IA3 are marked before your first one, particularly the part about the cut-off being strictly greater than.

The IA1 problem-solving and modelling task is the largest single internal instrument at 20% and the one where preparation actually changes the mark, because you can read the descriptors before you write a word.

For content, the outcomes table above says where to spend revision time. Time series analysis and networks and decision mathematics carry most of our weakest outcomes; graphs and networks and bivariate data analysis carry most of our strongest. Work through unseen questions on the General Mathematics question bank, or see what else the QCE hub covers.