Which WACE Mathematics Methods past paper do students score lowest on?

The 2021 Paper 1, averaging 53.3% across 74 marked attempts on AusGrader. The 2025 Paper 1 is the highest on 74.0%.

Which WACE Mathematics Methods dot points give the best return on revision time?

4.2.2 (2.1 marks at risk per 100), 4.2.7 (2.0 marks at risk per 100) and 3.1.4 (1.7 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 WACE Mathematics Methods figure based on?

17,409 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 SCSA 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 SCSA publishes about this subject and do not replace it.

WACE Mathematics Methods hardest topics

Across 17,409 marked attempts on AusGrader, WACE Mathematics Methods students average 58.5% on questions taken from board external papers. The lowest average of any command verb is evaluate on 51.6%, and the verb that costs the most marks is determine, which carries 39.7% of the paper against 4.7% for evaluate. These are self-selected users practising when they chose to, not the SCSA cohort under exam conditions.

How to read these numbers

The figures are AusGrader users' marked attempts, not SCSA 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 3 papers, 27 dot points and 18 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the WACE Mathematics Methods syllabus from any board's external papers, which is why the sample is larger than the 12 SCSA papers alone. The paper table below is the exception and uses SCSA papers only.
Internal assessment and school-uploaded exams are excluded throughout, so these averages differ from the ones on WACE Mathematics Methods performance stats, which count every attempt.

Score by past paper

Year	Paper	Average	Attempts
2025	Paper 1	74.0%	164
2025	Paper 2	54.3%	113
2024	Paper 1	54.9%	89
2024	Paper 2	58.2%	71
2023	Paper 1	58.7%	95
2023	Paper 2	58.2%	50
2022	Paper 1	69.0%	116
2021	Paper 1	53.3%	74
2020	Paper 1	59.3%	90

The lowest average belongs to the 2021 Paper 1 on 53.3% from 74 attempts, and the highest to the 2025 Paper 1 on 74.0% from 164 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	57.2%	14,474
Short answer	61.2%	2,935

Score by unit

Unit	Average	Attempts
Unit 3: Differentiation, Integration, and Discrete Probability	57.7%	11,596
Unit 4: Logarithmic Calculus and Statistical Inference	59.7%	7,003

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 17,409.

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Further differentiation and applications	24.4%	56.5%	5,782	10.6
The logarithmic function	15.9%	56.8%	3,361	6.9
Continuous random variables and the normal distribution	15.9%	60.4%	2,698	6.3
Integrals	15.4%	61.0%	3,577	6.0
Discrete random variables	12.2%	56.0%	2,475	5.4
Interval estimates for proportions	16.1%	68.5%	977	5.1

Further differentiation and applications tops the list on 10.6 marks at risk per 100 paper marks, 3.7 ahead of The logarithmic function.

The same cut at dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
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	5.5%	62.0%	848	2.1
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	4.1%	51.4%	1,166	2.0
3.1.4	3.1.4 use exponential functions of the form $Ae^{kx}$ and their derivatives to solve practical problems	4.7%	63.8%	343	1.7
3.1.16	3.1.16 solve optimisation problems from a wide variety of fields using first and second derivatives	3.1%	47.2%	1,536	1.6
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	5.0%	68.7%	242	1.6
3.1.6	3.1.6 use trigonometric functions and their derivatives to solve practical problems	2.9%	53.9%	450	1.3
3.3.16	3.3.16 use binomial distributions and associated probabilities to solve practical problems	3.3%	62.2%	1,399	1.3
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	4.1%	72.5%	642	1.1
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	2.5%	60.4%	942	1.0
4.1.7	4.1.7 solve simple equations involving logarithmic functions algebraically and graphically	2.1%	53.2%	957	1.0
4.1.2	4.1.2 establish and use the algebraic properties of logarithms	3.4%	71.2%	473	1.0
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 $f(x)>0$	1.7%	44.2%	1,072	0.9
3.2.19	3.2.19 calculate the area under a curve	2.4%	61.5%	78	0.9
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 $f(ax-b)$	2.5%	63.6%	1,345	0.9
3.1.7	3.1.7 examine and use the product and quotient rules	1.5%	47.9%	482	0.8
3.1.12	3.1.12 identify acceleration as the second derivative of position with respect to time	1.6%	53.4%	66	0.8
3.3.1	3.3.1 develop the concepts of a discrete random variable and its associated probability function, and their use in modelling data	1.2%	39.9%	230	0.7
4.1.8	4.1.8 identify contexts suitable for modelling by logarithmic functions and use them to solve practical problems	1.5%	52.2%	67	0.7
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 $\hat p$	1.7%	59.7%	270	0.7
3.3.15	3.3.15 determine and use the probabilities $P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}$ associated with the binomial distribution with parameters $n$ and $p$ ; note the mean $np$ and variance $np(1-p)$ of a binomial distribution	1.4%	52.0%	1,452	0.7

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
determine	39.7%	59.2%	1,210	16.2
justify	5.4%	52.7%	86	2.5
evaluate	4.7%	51.6%	106	2.3
state	4.8%	66.8%	136	1.6
calculate	7.4%	78.8%	133	1.6
show	4.3%	78.5%	78	0.9
express	2.3%	62.2%	59	0.9

Evaluate has the lowest average on the page at 51.6%, and it is not where the marks go. Determine averages 59.2% but carries 39.7% of the paper against 4.7%, so it puts 16.2 marks per 100 at risk against 2.3. Each verb above is practised in the WACE Mathematics Methods question bank, where the marking criteria show what SCSA expects the answer to do.

What this does not measure

Where to practise

Work the priority list from the top: Further differentiation and applications and The logarithmic function first, then the dot points above. Each topic page holds real SCSA questions with marking criteria attached. For what the papers actually cover, read WACE Mathematics Methods most tested topics.

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.