QCE Specialist Mathematics is Queensland's most advanced senior maths subject, and its external assessment is worth 50% of your final result. The 2025 exam tested motion with velocity as a function of position, a vector proof about a parallelepiped, overlapping confidence intervals and the length of a polar curve, and QCAA's subject report shows exactly where students gained and lost marks.
This guide breaks down the external assessment section of QCAA's 2025 Specialist Mathematics subject report. It covers how every multiple-choice question was answered across the state, the short-response questions QCAA singled out, what effective responses did and QCAA's advice for future students. For the school-based side of the subject, see our companion breakdown of the 2025 QCE Specialist Maths internal assessments.
Key Takeaways
- 4,722 students completed Units 3 and 4 in 2025, a 16.47% increase on 2024, and 95.68% received a C or higher.
- An A required a final mark of 86 or more out of 100, and 39.56% of students achieved one.
- Students averaged 62.5% on the Paper 1 multiple-choice questions and 67.2% on Paper 2.
- The hardest question was Paper 1, Question 10: only 21.05% chose the correct answer, while 42.06% chose the same wrong option.
- QCAA wants students to improve their notation (including brackets and dx), complex number algebra, trigonometric substitutions and understanding of X versus X̄.
The 2025 Cohort at a Glance
| Statistic | 2025 |
|---|---|
| Schools offering Specialist Mathematics | 314 |
| Students who completed Unit 1 | 5,328 |
| Students who completed Unit 2 | 5,078 |
| Students who completed Units 3 and 4 | 4,722 |
| Change in enrolment since 2024 | +16.47% |
| Students who received a C or higher | 95.68% |
Source: QCAA Specialist Mathematics subject report, 2025 cohort.
About 89% of the students who completed Unit 1 went on to complete Units 3 and 4, and only 7.4% received an Unsatisfactory result for Unit 2.
QCE Specialist Mathematics External Exam Structure
| Feature | Paper 1 | Paper 2 |
|---|---|---|
| Technology | Technology-free | Technology-active (graphics calculator allowed) |
| Section 1 | 10 multiple-choice questions (10 marks) | 10 multiple-choice questions (10 marks) |
| Section 2 | Short-response questions (50 marks) | Short-response questions (50 marks) |
| Total | 60 marks | 60 marks |
| Time | 5 minutes perusal + 90 minutes working | 5 minutes perusal + 90 minutes working |
The two papers are combined into a mark out of 50, which makes up 50% of your final result. The other 50% comes from your three internal assessments: IA1 (20%), IA2 (15%) and IA3 (15%). Subject matter from Mathematical Methods and from Units 1 and 2 can be assumed.
The most common external assessment results in 2025 fell between the high 30s and high 40s out of 50, peaking at about 46. Only a small number of students scored 49 or 50.
💡 Get ready for the exam with our step-by-step guide on how to prepare for QCE external exams.
2025 Grade Boundaries and Results
| Grade | Final Mark (out of 100) | Number of Students | Percentage of Students |
|---|---|---|---|
| A | 86–100 | 1,868 | 39.56% |
| B | 70–85 | 1,685 | 35.68% |
| C | 49–69 | 965 | 20.44% |
| D | 23–48 | 203 | 4.30% |
| E | 0–22 | 1 | 0.02% |
Source: QCAA Specialist Mathematics subject report, 2025 cohort.
Your final mark is your internal assessment total (out of 50) plus your external assessment mark (out of 50). Final marks peaked between about 85 and 95, right around the A cut-off of 86, so a few marks on the external exam can decide your grade.
Paper 1 (Technology-Free): Multiple-Choice Results
| Question | Correct Answer | % Correct | Most Common Wrong Answer |
|---|---|---|---|
| 1 | A | 81.78% | D (10.46%) |
| 2 | D | 67.40% | C (13.82%) |
| 3 | A | 43.15% | B (26.84%) |
| 4 | D | 57.21% | C (24.77%) |
| 5 | D | 73.43% | C (15.24%) |
| 6 | B | 80.97% | D (11.64%) |
| 7 | C | 65.18% | A (24.41%) |
| 8 | C | 83.27% | D (6.68%) |
| 9 | B | 51.47% | C (27.13%) |
| 10 | C | 21.05% | A (42.06%) |
Source: QCAA Specialist Mathematics subject report, 2025 cohort. Some students did not answer every question.
What the Paper 1 Results Show
- Question 10 was the hardest question on either paper. Twice as many students chose option A as chose the correct answer, C. When so many students pick the same wrong answer, it usually points to a common misconception.
- Questions 3 and 9 were answered correctly by only about half the cohort or less, and each had a wrong option chosen by more than a quarter of students.
- Questions 1, 6 and 8 were answered correctly by more than 80% of students.
- Paper 1's average (62.5%) was lower than Paper 2's. Without a calculator, small algebraic slips cost more.
Paper 2 (Technology-Active): Multiple-Choice Results
| Question | Correct Answer | % Correct | Most Common Wrong Answer |
|---|---|---|---|
| 1 | C | 80.92% | A (12.56%) |
| 2 | D | 46.91% | A (22.85%) |
| 3 | B | 75.50% | C (16.94%) |
| 4 | D | 84.18% | A (7.39%) |
| 5 | B | 94.44% | C (2.03%) |
| 6 | B | 66.82% | C (14.51%) |
| 7 | A | 29.73% | D (37.13%) |
| 8 | D | 39.68% | C (25.75%) |
| 9 | B | 79.11% | C (10.40%) |
| 10 | C | 74.74% | A (12.81%) |
Source: QCAA Specialist Mathematics subject report, 2025 cohort. Some students did not answer every question.
What the Paper 2 Results Show
- Question 7 was the hardest on Paper 2. More students chose D (37.13%) than the correct answer, A (29.73%), and C also drew almost a quarter of responses.
- Questions 2 and 8 were answered correctly by fewer than half of students.
- Question 5 was answered correctly by 94.44% of students, the easiest question across both papers.
A small group of students sat an alternative sequence (AS) version of the exam with the same structure. Their results are reported separately and are not included in the tables above.
💡 Check out why past papers are the best way to study for exams.
Short-Response Questions QCAA Highlighted
QCAA's report gave detailed feedback and sample responses for four short-response questions.
Paper 1, Question 13: Velocity as a Function of Position (Simple Familiar)
Students were given a velocity function in terms of position, v = 2cos⁻¹(x/3), for an object of mass 3 kg. They had to find (a) the momentum and (b) the acceleration at the origin.
Effective responses:
- used cos⁻¹(0) = π/2 to find the velocity at the origin: v = π m/s
- recalled that momentum = mass × velocity: p = 3π kg m/s
- differentiated the inverse cosine to find dv/dx = −2/√(9 − x²)
- used a = v dv/dx (or a = d/dx(½v²)) to find the acceleration: a = π × (−2/3) = −2π/3 m/s².
Key lesson: When velocity is given as a function of position, not time, you need a = v dv/dx. QCAA also accepted alternative notation such as arccos(x), as long as it was used correctly.
Paper 1, Question 16: Vector Proof With a Parallelepiped (Complex Familiar)
Students had to prove that two diagonals of a parallelepiped bisect each other.
Effective responses:
- defined both diagonals in terms of the given vectors a, b and c
- found the position vector of the midpoint of each diagonal
- showed that both midpoints were the same point, ½(a + b + c), so the diagonals bisect each other.
Key lesson: QCAA praised responses that used short statements to explain each key step, such as "let M be the midpoint of PR". A vector proof needs a clear conclusion that links the calculation back to what was being proved.
Paper 2, Question 17: Overlapping Confidence Intervals (Complex Unfamiliar)
Students were given a 90% confidence interval for a mean from one sample. They had to find the probability that a confidence interval from a second, smaller sample would overlap the first one.
Effective responses:
- used the given interval to find the sample mean and margin of error, then the size of the first sample (n = 75)
- found the size of the second sample (n = 15) and its margin of error
- recognised that the intervals overlap when the two sample means are closer than the sum of the two margins of error
- used the distribution of the sample mean to find the required probability (about 0.98 in the sample response).
Key lesson: QCAA highlighted the sample response for recognising that sample size must be a whole number and for setting out its statistical reasoning clearly.
Paper 2, Question 18: Length of a Polar Curve (Complex Unfamiliar)
Students used the formula for the length of a polar curve to find the length of part of the cardioid r = 1 + cos θ above the x-axis.
Effective responses:
- identified the bounds: 0 ≤ θ ≤ π
- found dr/dθ = −sin θ and substituted into L = ∫√(r² + (dr/dθ)²) dθ
- simplified using sin²θ + cos²θ = 1 to get √(2 + 2cos θ)
- used the double angle identity to rewrite this as 2cos(θ/2)
- integrated to find the length: L = 4 units.
Key lesson: This question rewarded a complete algebraic method and confident use of trigonometric identities, one of the areas QCAA wants students to practise more.
What Students Did Well
QCAA said the 2025 cohort responded well to:
- solving a system of equations using Gaussian elimination
- integration by parts
- simple familiar questions on both papers that tested practised procedures
- multiple-choice questions on both papers.
Areas QCAA Wants Students to Improve
1. X Versus X̄
Make sure you can tell the difference between the distribution of a random variable X and the distribution of the sample mean X̄, including their means, standard deviations and notation.
2. Notation
Use correct notation throughout, including brackets and dx in integrals. Missing or incorrect notation can cost marks in a subject where the working is as important as the answer.
3. Complex Numbers in Both Forms
Practise the algebra of complex numbers in both Cartesian and polar forms.
4. Trigonometric Substitutions
Practise integrals that need a trigonometric substitution or identity, as in the polar curve question.
5. Inverse vs Reciprocal Trig Functions
Know the difference between cos⁻¹(θ), the inverse cosine, and 1/cos(θ), the reciprocal (secant).
6. Your Graphics Calculator
QCAA encouraged students to learn the full capabilities of their graphics calculator for Paper 2.
💡 Not sure what "prove", "justify" or "evaluate" are asking for? Read our complete guide to QCE cognitive verbs.
Exam-Day Advice From QCAA
- Show your reasoning. Questions worth more than one mark need mathematical reasoning or working to support the answer.
- Use the right pages for extra working. Extra responses go on the pages labelled "Additional pages for student responses" at the back of the book, not on pages set aside for other questions.
- Fill in the multiple-choice bubbles. Work in the multiple-choice question book is not marked. Use a 2B pencil, fill each A, B, C or D bubble completely and answer every question.
How to Prepare for the QCE Specialist Maths External Exam
- Build technology-free fluency in complex numbers, vectors, matrices and integration techniques for Paper 1.
- Master your graphics calculator for statistics, matrices and numerical integration in Paper 2.
- Practise proofs with vectors and mathematical induction, writing a short statement for each step.
- Practise complex unfamiliar questions, such as polar curves and confidence interval problems, where you must choose the method yourself.
- Revise Mathematical Methods content, which is assumed knowledge for Specialist.
- Sit full past papers under timed conditions to practise managing 90 minutes per paper.
For more preparation:
- read our guide to getting an A in QCE Specialist Mathematics
- see our breakdown of the 2025 QCE Specialist Maths internal assessments
- read our 2025 QCE Maths Methods external assessment breakdown
- check the QCE exam timetable 2026 for this year's exam dates
- learn how QCE subject scaling works.
Need Help With QCE Specialist Maths?
Our QCE Specialist Mathematics tutors work one-on-one with students to master complex numbers, vectors, calculus and statistical inference, and to write the precise, well-reasoned responses QCAA markers look for.
Source: Queensland Curriculum & Assessment Authority, Specialist Mathematics subject report, 2025 cohort (January 2026).
