Which QCE Specialist Mathematics past paper do students score lowest on?

The 2022 Paper 2, averaging 45.9% across 288 marked attempts on AusGrader. The 2024 Paper 1 is the highest on 75.5%.

Which QCE Specialist Mathematics dot points give the best return on revision time?

4.5.1.5 (1.6 marks at risk per 100), 4.5.2.7 (1.6 marks at risk per 100) and 3.5.2.1 (1.5 marks at risk per 100). Marks at risk combines a dot point's share of paper marks with the marks students drop on it, so it ranks by recoverable marks and not by score alone.

How many attempts is each QCE Specialist Mathematics figure based on?

15,578 marked attempts overall, with the per-row count shown in every table. Any cut below 50 attempts is withheld instead of published.

Do these averages show how the QCAA cohort performed?

No. They are AusGrader users' marked attempts, a self-selected group practising when they chose to and often without exam timing. They corroborate what QCAA publishes about this subject and do not replace it.

QCE Specialist Mathematics hardest topics

Across 15,578 marked attempts on AusGrader, QCE Specialist Mathematics students average 59.3% on questions taken from board external papers. The lowest average of any command verb is evaluate on 43.6%, and the verb that costs the most marks is determine, which carries 55.1% of the paper against 5.3% for evaluate. These are self-selected users practising when they chose to, not the QCAA cohort under exam conditions.

How to read these numbers

The figures are AusGrader users' marked attempts, not QCAA results. They corroborate what the board publishes about this subject and do not stand in for it.
Any cut with fewer than 50 attempts is withheld, which on this page is 1 subtopics, 26 dot points and 19 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the QCE Specialist Mathematics syllabus from any board's external papers, which is why the sample is larger than the 12 QCAA papers alone. The paper table below is the exception and uses QCAA papers only.
Internal assessment and school-uploaded exams are excluded throughout, so these averages differ from the ones on QCE Specialist Mathematics performance stats, which count every attempt.

Score by past paper

Year	Paper	Average	Attempts
2025	Paper 1	70.7%	191
2025	Paper 2	58.1%	219
2024	Paper 1	75.5%	333
2024	Paper 2	59.7%	210
2023	Paper 1	64.9%	252
2023	Paper 2	65.9%	165
2022	Paper 1	67.0%	171
2022	Paper 2	45.9%	288
2021	Paper 1	67.9%	272
2021	Paper 2	59.7%	247
2020	Paper 1	64.0%	348
2020	Paper 2	69.7%	235

The lowest average belongs to the 2022 Paper 2 on 45.9% from 288 attempts, and the highest to the 2024 Paper 1 on 75.5% from 333 attempts. A paper's average reflects both how hard it was and who chose to sit it, so treat the spread as a guide to which papers make demanding practice.

Score by question type

Question type	Average	Attempts
Multiple choice	58.9%	13,749
Short answer	60.5%	1,829

Score by unit

Unit	Average	Attempts
Unit 4: Further calculus and statistical inference	58.9%	8,107
Unit 3: Further complex numbers, proof, vectors and matrices	59.8%	7,938

An attempt counts once per unit, so a question assessed across two units appears in both rows and the column adds to slightly more than 15,578.

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Statistical inference	14.8%	56.2%	946	6.5
Vectors in two and three dimensions	13.8%	59.4%	4,606	5.6
Further complex numbers	13.1%	57.8%	2,152	5.5
Rates of change and differential equations	10.4%	61.5%	1,930	4.0
Vector calculus	10.2%	60.8%	1,098	4.0
Integration techniques	10.7%	65.8%	1,614	3.7
Applications of integral calculus	7.6%	65.0%	597	2.7
Further matrices	7.7%	65.6%	542	2.6
Modelling motion	5.5%	52.7%	3,357	2.6
Mathematical induction and trigonometric proofs	6.2%	63.1%	223	2.3

The topic list is close: 6.5 against 5.6 marks at risk separates first from second, so topic choice alone will not order revision. The dot-point list below spreads further.

The same cut at subtopic level

Subtopic	Share of marks	Average	Attempts	Marks at risk
Vector calculus	10.2%	60.8%	1,098	4.0
Integration techniques	10.7%	65.8%	1,614	3.7
Sample means	7.6%	55.4%	591	3.4
Confidence intervals for means	7.3%	57.2%	360	3.1
Vector and Cartesian equations	7.0%	59.8%	1,857	2.8
Applications of integral calculus	7.6%	65.0%	597	2.7
Complex arithmetic using polar form	5.6%	52.6%	1,303	2.6
Modelling motion	5.5%	52.7%	3,357	2.6
Rates of change	4.4%	47.1%	331	2.3
Differential equations	5.9%	65.8%	1,602	2.0
Mathematical induction	5.3%	62.6%	208	2.0
Algebra of vectors in three dimensions	4.3%	58.7%	3,291	1.8
Roots of complex numbers	3.6%	57.4%	237	1.5
Applications of matrices	3.4%	56.3%	141	1.5
Matrix algebra and systems of equations	4.3%	70.3%	410	1.3

The same cut at dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
4.5.1.5	Model and solve problems that involve sample means, with and without technology	3.5%	54.2%	506	1.6
4.5.2.7	Model and solve problems that involve interval estimates for sample means, with and without technology	3.2%	51.4%	80	1.6
3.5.2.1	Model and solve problems that involve real-life situations using matrices, including Dominance and Leslie matrices	3.4%	56.3%	141	1.5
3.1.1.2	Use De Moivre’s theorem for integral powers. $z^n = r^n \text{cis}(n\theta)$	2.8%	49.2%	603	1.4
3.1.1.1	Prove complex number identities involving modulus and argument, e.g. $z\bar{z} = \\|z\\|^2$ , $\\|z_1\\|\\|z_2\\| = \\|z_1 z_2\\|$ and $\text{arg}(z_1 z_2) = \text{arg}(z_1) + \text{arg}(z_2)$	2.9%	54.6%	905	1.3
3.4.1.3	Understand and use the position of two particles, each described as a vector function of time, and determine if their paths cross or if the particles meet	2.3%	49.6%	58	1.2
4.4.1.4	Model and solve problems that involve motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion, vertical motion under gravity with and without air resistance, and motion of a body in non-equilibrium situations on a smooth inclined plane (excluding situations with pulleys and connected bodies). If $\frac{d^2x}{dt^2} = -\omega^2 x$ then $x = A \sin(\omega t + \alpha)$ or $x = A \cos(\omega t + \beta)$ ; $v^2 = \omega^2(A^2 - x^2)$ ; $T = \frac{2\pi}{\omega}$ ; $f = \frac{1}{T}$	2.3%	50.2%	2,083	1.1
3.3.3.5	Use vector methods in applications, including areas of shapes and determining vector and Cartesian equations of a plane and of regions in a plane. vector equation of plane: $\boldsymbol{r} \cdot \boldsymbol{n} = \boldsymbol{a} \cdot \boldsymbol{n}$ ; Cartesian equation of plane: $ax + by + cz + d = 0$	2.8%	60.7%	756	1.1
4.3.2.1	Determine general and particular solutions of first-order differential equations of the form $\frac{dy}{dx} = f(x)$ , differential equations of the form $\frac{dy}{dx} = g(y)$ and differential equations of the form $\frac{dy}{dx} = f(x)g(y)$ using separation of variables	2.9%	64.0%	511	1.0
3.1.2.1	Determine and examine the $n$ th roots of unity and their location on the unit circle	2.4%	56.8%	68	1.0
3.4.1.4	Differentiate and integrate a vector function with respect to time	2.4%	60.1%	720	1.0
4.1.1.1	Integrate using the trigonometric identities $\sin^2(x) = \frac{1}{2}(1 - \cos(2x))$ , $\cos^2(x) = \frac{1}{2}(1 + \cos(2x))$ , $1 + \tan^2(x) = \sec^2(x)$ and $\cot^2(x) + 1 = \text{cosec}^2(x)$	2.3%	58.5%	243	0.9
4.5.2.2	Understand and use the approximate confidence interval $(\bar{x} - z \frac{s}{\sqrt{n}}, \bar{x} + z \frac{s}{\sqrt{n}})$ , as an interval estimate for $\mu$ , the population mean, where $z$ is the appropriate quantile for the standard normal distribution	2.1%	55.7%	295	0.9
3.2.1.1	Understand the nature of inductive proof including the use of initial statement, assumption statement, inductive step and conclusion	2.5%	63.4%	174	0.9
4.3.1.1	Use implicit differentiation to determine the gradient of curves whose equations are given in implicit form	1.4%	34.6%	275	0.9
3.3.3.3	Determine vector, parametric and Cartesian equations of straight lines and straight-line segments given the position of two points, or equivalent information, in both two and three dimensions. vector equation of line: $\boldsymbol{r} = \boldsymbol{a} + t\boldsymbol{d}$ ; parametric equations of line: $x = a_1 + t d_1, y = a_2 + t d_2, z = a_3 + t d_3$ ; Cartesian equation of line: $\frac{x - a_1}{d_1} = \frac{y - a_2}{d_2} = \frac{z - a_3}{d_3}$	2.2%	59.2%	728	0.9
4.3.1.2	Model and solve related rates problems as instances of the chain rule including situations that involve surface area and volume of cones, pyramids and spheres, with and without technology	3.0%	71.0%	60	0.9
4.4.1.3	Understand and use the expressions $\frac{dv}{dt}$ , $\frac{d^2x}{dt^2}$ , $v \frac{dv}{dx}$ and $\frac{d}{dx}(\frac{1}{2}v^2)$ to represent the acceleration of an object moving in a straight line	1.6%	51.7%	849	0.8
3.3.1.3	Calculate the magnitude of a vector $\\|\boldsymbol{a}\\| = \left\\| \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} \right\\| = \sqrt{a_1^2 + a_2^2 + a_3^2}$	1.5%	55.0%	60	0.7
3.1.3.1	Apply the factor theorem and the remainder theorem for polynomials	1.9%	64.4%	274	0.7

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
determine	55.1%	60.8%	922	21.6
evaluate	5.3%	43.6%	67	3.0
prove	7.0%	60.3%	114	2.8
show	5.8%	71.6%	106	1.6
state	1.6%	76.1%	80	0.4
express	0.8%	66.7%	71	0.3

Evaluate has the lowest average on the page at 43.6%, and it is not where the marks go. Determine averages 60.8% but carries 55.1% of the paper against 5.3%, so it puts 21.6 marks per 100 at risk against 3.0. For the plain ranking of verbs by score, and what QCAA has said about each, read the QCE Specialist Mathematics study guide.

What this does not measure

Where to practise

Work the priority list from the top: Statistical inference and Vectors in two and three dimensions first, then the dot points above. Each topic page holds real QCAA questions with marking criteria attached. For what the papers actually cover, read QCE Specialist Mathematics most tested topics.

Syllabus and assessment material referenced in this guide is © State of Queensland (Queensland Curriculum and Assessment Authority), licensed under CC BY 4.0. See our QCAA licensing notice. AusGrader is an independent study tool and is not affiliated with, endorsed by, or operated by the QCAA.