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

4.2.7 (2.6 marks at risk per 100), 4.3.5 (2.0 marks at risk per 100) and 4.2.1 (2.0 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 Specialist figure based on?

17,474 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 Specialist hardest topics

Across 17,474 marked attempts on AusGrader, WACE Mathematics Specialist students average 59.2% on questions taken from board external papers. The lowest average of any command verb is evaluate on 37.7%, and the verb that costs the most marks is determine, which carries 37.0% of the paper against 4.4% 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 12 papers, 11 dot points and 14 verbs. Every figure shown carries its attempt count.
Scores cover questions mapped to the WACE Mathematics Specialist 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 Specialist performance stats, which count every attempt.

Score by question type

Question type	Average	Attempts
Short answer	57.8%	1,224
Multiple choice	59.5%	16,250

Score by unit

Unit	Average	Attempts
Unit 3: Complex Numbers, Functions, and 3D Vectors	59.2%	11,984
Unit 4: Advanced Integration, Differential Equations, and Statistical Inference	59.4%	6,732

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 17,474.

The priority list: heavy topics with low scores

Topic	Share of marks	Average	Attempts	Marks at risk
Vectors in three dimensions	19.7%	60.0%	6,838	7.9
Complex numbers	18.4%	57.5%	3,057	7.8
Rates of change and differential equations	18.9%	58.8%	4,763	7.8
Integration and applications of integration	17.1%	61.9%	1,478	6.5
Statistical inference	12.6%	56.0%	537	5.5
Functions and sketching graphs	13.3%	59.4%	2,092	5.4

The topic list is close: 7.9 against 7.8 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 dot-point level

Dot point	Content	Share of marks	Average	Attempts	Marks at risk
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	5.5%	52.7%	2,096	2.6
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	4.4%	54.1%	255	2.0
4.2.1	4.2.1. use implicit differentiation to determine the gradient of curves whose equations are given in implicit form	3.0%	34.1%	254	2.0
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 $y=f(\\|x\\|)$	3.8%	52.8%	615	1.8
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	2.8%	38.3%	293	1.7
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	3.1%	44.1%	925	1.7
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 $\\|z-1\\|=2\\|z-i\\|$	3.9%	56.2%	655	1.7
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	3.4%	54.8%	262	1.5
3.2.8	3.2.8. sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree	3.9%	62.2%	863	1.5
4.1.4	4.1.4. use partial fractions where necessary for integration in simple cases	2.4%	42.0%	265	1.4
4.1.6	4.1.6. determine volumes of solids of revolution about either axis	3.8%	67.0%	471	1.3
4.1.2	4.1.2. use substitution $u=g(x)$ to integrate expressions of the form $f(g(x))\,g'(x)$	3.6%	68.3%	692	1.1
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	2.6%	62.9%	3,216	1.0
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	3.0%	68.8%	465	0.9
3.3.13	3.3.13. differentiate and integrate a vector function with respect to time	2.5%	64.0%	693	0.9
4.1.1	4.1.1. integrate using the trigonometric identities $\sin^2 x=\frac{1}{2}(1-\cos 2x)$ , $\cos^2 x=\frac{1}{2}(1+\cos 2x)$ , and $1+\tan^2 x=\sec^2 x$	2.0%	58.3%	231	0.8
3.1.12	3.1.12. determine and examine the $n$ th roots of complex numbers and their location in the complex plane	1.5%	45.4%	68	0.8
3.3.15	3.3.15. apply vector calculus to motion in a plane, including projectile and circular motion	1.6%	48.8%	235	0.8
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	2.3%	64.7%	506	0.8
3.3.8	3.3.8. determine vector and Cartesian equations of a plane	2.1%	62.6%	686	0.8

Which command verbs cost the most marks

Verb	Share of marks	Average	Attempts	Marks at risk
determine	37.0%	57.0%	538	15.9
evaluate	4.4%	37.7%	52	2.7
state	7.8%	68.4%	50	2.5
show	7.6%	73.1%	73	2.0
express	1.5%	57.1%	58	0.6

Evaluate has the lowest average on the page at 37.7%, and it is not where the marks go. Determine averages 57.0% but carries 37.0% of the paper against 4.4%, so it puts 15.9 marks per 100 at risk against 2.7. Each verb above is practised in the WACE Mathematics Specialist 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: Vectors in three dimensions and Complex numbers 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 Specialist 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.

WACE Mathematics Specialist hardest topics

How to read these numbers

Score by question type

Score by unit

The priority list: heavy topics with low scores

The same cut at dot-point level

Which command verbs cost the most marks

What this does not measure

Where to practise

Frequently asked questions

Sources

Keep reading

WACE Mathematics Specialist Most Tested Topics: What the SCSA Exams Cover

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