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

Further differentiation and applications carries 24.4% of the marks across the 12 SCSA papers from 2020 to 2025, ahead of Interval estimates for proportions on 16.1%.

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

Short answer carries 100.0% of the marks, measured across 12 papers and 897 marks from 2020 to 2025.

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

Yes. Further differentiation and applications moved down 3.0 percentage points and The logarithmic function moved up 3.7 percentage points between the 2020 to 2022 and 2023 to 2025 papers.

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

12 SCSA external papers from 2020 to 2025, covering 97 questions and 897 marks. 1.3% of those marks carry no dot-point mapping and sit outside the percentages.

WACE Mathematics Methods most tested topics

Across the 12 SCSA Mathematics Methods external papers from 2020 to 2025, Further differentiation and applications carries 24.4% of the marks against 12.2% for Discrete random variables, so the paper rewards Further differentiation and applications more than any other topic. At dot-point level 4.2.2 carries 5.5% of paper marks, and 12 of the 85 dot points that the board assesses externally have not appeared in one of these papers. Every percentage below covers the 98.7% of marks that map to a syllabus dot point.

Computed from 12 SCSA Mathematics Methods external papers, 2020 to 2025: 97 questions, 390 question parts and 897 marks.

Unit, topic and dot-point shares below are of the 885 marks that map to a dot point, so each of those tables adds to 100%. 150 of the 390 parts are assessed against more than one dot point, and their 395 marks are divided evenly between the dot points they cover.

What these papers are

Year	Paper	Questions	Marks
2025	Paper 1	7	47
2025	Paper 2	10	97
2024	Paper 1	7	51
2024	Paper 2	10	100
2023	Paper 1	5	53
2023	Paper 2	9	96
2022	Paper 1	6	54
2022	Paper 2	9	100
2021	Paper 1	7	51
2021	Paper 2	10	100
2020	Paper 1	7	51
2020	Paper 2	10	97

Marks by unit

Unit	Share of marks
Unit 3: Differentiation, Integration, and Discrete Probability	52.1%
Unit 4: Logarithmic Calculus and Statistical Inference	47.9%

Marks by topic

Topic	Share of marks	Papers it appears in	Years
Further differentiation and applications	24.4%	12 of 12	6 of 6
Interval estimates for proportions	16.1%	6 of 12	6 of 6
Continuous random variables and the normal distribution	15.9%	12 of 12	6 of 6
The logarithmic function	15.9%	12 of 12	6 of 6
Integrals	15.4%	11 of 12	6 of 6
Discrete random variables	12.2%	11 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
4.2.2	4.2.2 examine the concepts of a probability density function, cumulative distribution function, and probabilities associated with a continuous random variable given by integrals; examine simple types of continuous random variables and use them in appropriate contexts	Continuous random variables and the normal distribution	5.5%	9 of 12
4.3.9	4.3.9 define the approximate margin of error $E=z\sqrt{\frac{\hat p(1-\hat p)}{n}}$ and understand the trade-off between margin of error and level of confidence	Interval estimates for proportions	5.0%	6 of 12
3.1.4	3.1.4 use exponential functions of the form $Ae^{kx}$ and their derivatives to solve practical problems	Further differentiation and applications	4.7%	6 of 12
4.2.7	4.2.7 calculate probabilities and quantiles associated with a given normal distribution using technology, and use these to solve practical problems	Continuous random variables and the normal distribution	4.1%	6 of 12
4.3.8	4.3.8 use the approximate confidence interval $\left(\hat p- z\sqrt{\frac{\hat p(1-\hat p)}{n}}\ ,\ \hat p+ z\sqrt{\frac{\hat p(1-\hat p)}{n}}\right)$ as an interval estimate for $p$ , where $z$ is the appropriate quantile for the standard normal distribution	Interval estimates for proportions	4.1%	6 of 12
4.1.2	4.1.2 establish and use the algebraic properties of logarithms	The logarithmic function	3.4%	9 of 12
3.3.16	3.3.16 use binomial distributions and associated probabilities to solve practical problems	Discrete random variables	3.3%	9 of 12
3.1.16	3.1.16 solve optimisation problems from a wide variety of fields using first and second derivatives	Further differentiation and applications	3.1%	6 of 12
3.1.6	3.1.6 use trigonometric functions and their derivatives to solve practical problems	Further differentiation and applications	2.9%	6 of 12
3.1.15	3.1.15 sketch the graph of a function using first and second derivatives to locate stationary points and points of inflection	Further differentiation and applications	2.5%	5 of 12
4.2.3	4.2.3 define the expected value, variance and standard deviation of a continuous random variable and evaluate them in simple cases, using technology where required	Continuous random variables and the normal distribution	2.5%	8 of 12
3.1.9	3.1.9 apply the product, quotient and chain rule to differentiate functions such as $xe^x$ , $\tan x$ , $\frac{1}{x^n}$ , $x\sin x$ , $e^{-x}\sin x$ and $f(ax-b)$	Further differentiation and applications	2.5%	10 of 12
3.2.19	3.2.19 calculate the area under a curve	Integrals	2.4%	5 of 12
3.2.20	3.2.20 calculate the area between curves determined by functions of the form $y=f(x)$	Integrals	2.1%	5 of 12
4.1.7	4.1.7 solve simple equations involving logarithmic functions algebraically and graphically	The logarithmic function	2.1%	8 of 12
4.3.2	4.3.2 discuss sources of bias in samples, and procedures to ensure randomness	Interval estimates for proportions	1.9%	5 of 12
4.1.13	4.1.13 determine derivatives of the form $\frac{d}{dx}(\ln f(x))$ and integrals of the form $\int \frac{f'(x)}{f(x)}\,dx$ for $f(x)>0$	The logarithmic function	1.7%	7 of 12
4.3.4	4.3.4 examine the concept of the sample proportion $\hat p$ as a random variable whose value varies between samples, and the formulas for the mean $p$ and standard deviation $\sqrt{\frac{p(1-p)}{n}}$ of the sample proportion $\hat p$	Interval estimates for proportions	1.7%	5 of 12
3.1.10	3.1.10 use the increments formula: $\delta y \approx \frac{dy}{dx}\times \delta x$ to estimate the change in the dependent variable $y$ resulting from changes in the independent variable $x$	Further differentiation and applications	1.6%	6 of 12
4.1.6	4.1.6 identify the qualitative features of the graph of $y=\log_a x$ ( $a>1$ ), including asymptotes, and of its translations $y=\log_a x+b$ and $y=\log_a(x-c)$	The logarithmic function	1.6%	5 of 12

These 20 dot points carry 58.7% of the paper marks between them. Another 53 assessed dot points share the rest, and 12 of the 85 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

Comparing the 2020 to 2022 papers with the 2023 to 2025 papers, two topics have moved by more than 3.0 percentage points.

Topic	2020 to 2022 share	2023 to 2025 share	Movement
Further differentiation and applications	25.9%	22.9%	down 3.0 points
The logarithmic function	14.1%	17.8%	up 3.7 points

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%	897	390

Verb	Share of marks	Marks	Parts
determine	39.7%	356	149
calculate	7.4%	66	30
explain	5.7%	51	20
justify	5.4%	48	24
state	4.8%	43	18
evaluate	4.7%	42	17
show	4.3%	39	15
sketch	2.9%	26	8

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: Further differentiation and applications, Interval estimates for proportions, Continuous random variables and the normal distribution, The logarithmic function, Integrals and Discrete random variables. For how students actually score on this content, read WACE Mathematics Methods hardest topics, and for the full question bank start at WACE Mathematics Methods.

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 Methods 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 Methods Hardest Topics: Where Students Lose the Most Marks

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