Which topic carries the most marks in the WACE Mathematics Specialist external exam?

Vectors in three dimensions carries 19.7% of the marks across the 12 SCSA papers from 2020 to 2025, ahead of Rates of change and differential equations on 18.9%.

How are marks split between question types in the WACE Mathematics Specialist exam?

Short answer carries 100.0% of the marks, measured across 12 papers and 817 marks from 2020 to 2025.

Has the topic balance changed in recent WACE Mathematics Specialist papers?

No. Comparing the 2020 to 2022 papers with the 2023 to 2025 papers, the largest movement in any topic's share was 1.7 percentage points, which is too small to plan revision around.

How many past papers is this WACE Mathematics Specialist analysis based on?

12 SCSA external papers from 2020 to 2025, covering 115 questions and 817 marks. 0.2% of those marks carry no dot-point mapping and sit outside the percentages.

WACE Mathematics Specialist most tested topics

Across the 12 SCSA Mathematics Specialist external papers from 2020 to 2025, Vectors in three dimensions carries 19.7% of the marks against 12.6% for Statistical inference, so the paper rewards Vectors in three dimensions more than any other topic. At dot-point level 4.2.7 carries 5.5% of paper marks, and zero of the 59 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 99.8% of marks that map to a syllabus dot point.

Computed from 12 SCSA Mathematics Specialist external papers, 2020 to 2025: 115 questions, 306 question parts and 817 marks.

Unit, topic and dot-point shares below are of the 815 marks that map to a dot point, so each of those tables adds to 100%. 98 of the 306 parts are assessed against more than one dot point, and their 280 marks are divided evenly between the dot points they cover.

What these papers are

Year	Paper	Questions	Marks
2025	Paper 1	7	45
2025	Paper 2	12	93
2024	Paper 1	8	47
2024	Paper 2	10	85
2023	Paper 1	8	48
2023	Paper 2	11	89
2022	Paper 1	7	48
2022	Paper 2	12	86
2021	Paper 1	8	49
2021	Paper 2	11	92
2020	Paper 1	8	49
2020	Paper 2	13	86

Marks by unit

Unit	Share of marks
Unit 3: Complex Numbers, Functions, and 3D Vectors	51.4%
Unit 4: Advanced Integration, Differential Equations, and Statistical Inference	48.6%

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Vectors in three dimensions	19.7%	11 of 12	6 of 6
Rates of change and differential equations	18.9%	10 of 12	6 of 6
Complex numbers	18.4%	12 of 12	6 of 6
Integration and applications of integration	17.1%	12 of 12	6 of 6
Functions and sketching graphs	13.3%	11 of 12	6 of 6
Statistical inference	12.6%	6 of 12	6 of 6

Marks by dot point

Dot-point numbers and wording are SCSA's own. Where a dot point is written as a list, its items run together here separated by semicolons.

Dot point	Content	Topic	Share of marks	Papers
4.2.7	4.2.7. consider and solve problems involving motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion and the use of expressions $\frac{dv}{dt}$ , $v\frac{dv}{dx}$ , and $\frac{d}{dx}\left(\frac{1}{2}v^2\right)$ for acceleration	Rates of change and differential equations	5.5%	6 of 12
4.3.5	4.3.5. use the approximate confidence interval $\left(\bar x-\frac{zs}{\sqrt{n}},\ \bar x+\frac{zs}{\sqrt{n}}\right)$ as an interval estimate for the population mean $\mu$ , where $z$ is the appropriate quantile for the standard normal distribution	Statistical inference	4.4%	6 of 12
3.2.8	3.2.8. sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree	Functions and sketching graphs	3.9%	7 of 12
3.1.10	3.1.10. identify subsets of the complex plane determined by relations such as $\\|z-3i\\|\le 4$ , $\frac{\pi}{4}\le \mathrm{Arg}(z)\le \frac{3\pi}{4}$ and $\\|z-1\\|=2\\|z-i\\|$	Complex numbers	3.9%	5 of 12
3.2.7	3.2.7. examine the relationship between the graph of $y=f(x)$ and the graphs of $y=\frac{1}{f(x)}$ , $y=\\|f(x)\\|$ and $y=f(\\|x\\|)$	Functions and sketching graphs	3.8%	8 of 12
4.1.6	4.1.6. determine volumes of solids of revolution about either axis	Integration and applications of integration	3.8%	6 of 12
4.1.2	4.1.2. use substitution $u=g(x)$ to integrate expressions of the form $f(g(x))\,g'(x)$	Integration and applications of integration	3.6%	5 of 12
4.3.2	4.3.2. simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of $\bar X$ across samples of a fixed size $n$ , including its mean $\mu$ its standard deviation $\frac{\sigma}{\sqrt{n}}$ (where $\mu$ and $\sigma$ are the mean and standard deviation of $X$ ), and its approximate normality if $n$ is large	Statistical inference	3.4%	5 of 12
3.1.4	3.1.4. use the modulus $\\|z\\|$ of a complex number $z$ and the argument $\mathrm{Arg}(z)$ of a non-zero complex number $z$ and prove basic identities involving modulus and argument	Complex numbers	3.1%	9 of 12
3.3.9	3.3.9. recognise the general form of a system of linear equations in several variables, and use elementary techniques of elimination to solve a system of linear equations	Vectors in three dimensions	3.0%	7 of 12
4.2.1	4.2.1. use implicit differentiation to determine the gradient of curves whose equations are given in implicit form	Rates of change and differential equations	3.0%	6 of 12
4.2.6	4.2.6. formulate differential equations, including the logistic equation that will arise in, for example, chemistry, biology and economics, in situations where rates are involved	Rates of change and differential equations	2.9%	4 of 12
3.1.6	3.1.6. define and use multiplication, division, and powers of complex numbers in polar form and the geometric interpretation of these	Complex numbers	2.8%	6 of 12
3.3.1	3.3.1. define the concept of a vector in three dimensions, using the unit vectors $\mathbf{i}$ , $\mathbf{j}$ and $\mathbf{k}$ , determining magnitude, scalar (dot) product and parallel and perpendicular vectors	Vectors in three dimensions	2.6%	9 of 12
4.1.5	4.1.5. calculate areas between curves defined by functions of the form $y=f(x)$ or $x=f(y)$	Integration and applications of integration	2.6%	9 of 12
3.3.13	3.3.13. differentiate and integrate a vector function with respect to time	Vectors in three dimensions	2.5%	6 of 12
4.1.4	4.1.4. use partial fractions where necessary for integration in simple cases	Integration and applications of integration	2.4%	5 of 12
4.2.2	4.2.2. examine related rates as instances of the chain rule: $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}$	Rates of change and differential equations	2.3%	5 of 12
4.2.4	4.2.4. solve simple first order differential equations of the form $\frac{dy}{dx}=f(x)$ ; differential equations of the form $\frac{dy}{dx}=g(y)$ ; and, in general, differential equations of the form $\frac{dy}{dx}=f(x)g(y)$ , using separation of variables	Rates of change and differential equations	2.3%	6 of 12

These 19 dot points carry 61.8% of the paper marks between them. Another 40 assessed dot points share the rest, and 0 of the 59 externally assessable dot points have not been assessed in any of these 12 papers. Content that has not appeared is still examinable.

What has moved between papers

No topic's share moved by more than 3.0 percentage points between the 2020 to 2022 papers and the 2023 to 2025 papers. The largest movement was 1.7 points, which is inside the range two papers a year produce by chance, so nothing here is a trend to revise around.

How the papers are built

Short answer carries 100.0% of the marks across these 12 papers.

Question type	Share of marks	Marks	Parts
Short answer	100.0%	817	306

Verb	Share of marks	Marks	Parts
determine	37.0%	302	111
calculate	11.9%	97	36
state	7.8%	64	29
show	7.6%	62	21
sketch	6.6%	54	19
justify	5.0%	41	17
evaluate	4.4%	36	8
solve	4.0%	33	11

What these percentages do not tell you

Where to practise

Every topic above links to its own page of real SCSA questions with marking criteria and average scores attached: Vectors in three dimensions, Rates of change and differential equations, Complex numbers, Integration and applications of integration, Functions and sketching graphs and Statistical inference. For how students actually score on this content, read WACE Mathematics Specialist hardest topics, and for the full question bank start at WACE Mathematics Specialist.

Syllabus and assessment material referenced in this guide is used under licence, © School Curriculum and Standards Authority. See our SCSA licensing notice. The School Curriculum and Standards Authority does not endorse this publication or product.

WACE Mathematics Specialist most tested topics

What these papers are

Marks by unit

Marks by topic

Marks by dot point

What has moved between papers

How the papers are built

What these percentages do not tell you

Where to practise

Frequently asked questions

Sources

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WACE Mathematics Specialist Hardest Topics: Where Students Lose the Most Marks

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