Go for it.
UPDATE (08/11/25)
I have had epsilon chance to look at the exam(s), but the comments suggest that Q5(b) has caused enough concern to warrant it’s own post, which is now up, here.
UPDATE (08/11/25)
OK, I’ve looked at the exam. I don’t like it.
I won’t go through question by question. My feelings are similar to what people have written below, except my reaction seems to be stronger. With the insanities of the recent past not forgotten, there’s nothing that bad about the exam. But there is also nothing very good about it and it is continually clunky, both in content and format-wording. Q5 goes beyond clunkiness: that shouldn’t have happened.
Commenters seem to be of the opinion that the exam was not that “hard”, and they know SM students better than me, but I’m not convinced. There are a number of (too) easy questions but I think the novel aspects, the translated squares and the removable singularity and so forth, will catch many students. I don’t think such tricked-up questions are a good form of “separator”.
I am also very concerned about the way this exam may be graded. Given the clunkiness of the questions and their wording, given the number of “show that”s, not all of which are entirely clarified, and given last year’s SM assessors proved to be assholes, I am not convinced that this year’s students will not be screwed over.
UPDATE (15/11/25)
VCAA has now posted the exam, here.
Random thoughts:
Q1 – nice.
.
is an asymptote and … well, this has been discussed at length on this blog.
Q2 – nice, if a bit easier than Q1.
Q3 – reasonable, if a bit boring.
Q4 – reasonable. Partial fractions were easy enough. Part (b) could be done with the 68-95-99 rule.
Q5 – part (b) gave me pause as I got one value for a and one value for b. It took a moment to realise the b value could be converted into an a value given
Q6 – nice. I saw the substitution immediately, would have been difficult if I hadn’t seen it.
Q7 – nice. The algebra was a bit fiddly.
Q8 – easy.
Q9 – curious use of the plural asymptotes. This implies (perhaps) that
Thanks Red Five! I agree, it was another fairly safe exam.
Q1 – yep, I agree
Q2 – the numbers were a bit easy. I was expecting some fractions.
Q3 – To similar to Q5 – should have used another vector equation question
Q4 – I found the \sigma = 0.3 a bit ambiguous – but you progress a bit in the question and it’s obvious which interpretation they wanted.
Q5 – The stem for part b should have been inside the question part. Otherwise it seems to conflict with part c.
Q6 – straightforward
Q7 – Annoyed me – it’s just a shifted sum of squares. I wonder if they’d accept adding 1 to both sides…
Q8 – Too much space for part b and not enough for part c. I’m guessing some students might not notice part a!
Q9 – Part b was a nice surprise as removable singularities aren’t really part of the course. The oblique asymptote has always been part of SM – or am I missing something?
Now I’m going to go off make predictions for Exam II!
Mark allocation for 3a vs 4 vs 6 is a little hard to understand.
3a seems like a 2 mark question, given that almost all students will need to use a substitution for the integration – *unless* the examiners will allow you to observe that the general antiderivative of
is 
and then do a simple calculation to find C.
4 will cause some problems for students who may have forgotten how to calculate the mean of a continuous probability distribution. This brings back memories of a similar issue on an NHT exam a while back, which involved knowing formulas for a binomial probability distribution. That aside, 3 marks for doing the partial fractions, integrating and calculating seems ok.
6 seems pretty generous with the marks, given that the substitution is pretty clear and the calculation is easy.
Question 7: I like that the question stem spells out the meaning of the sigma notation. But I wonder if this is VCAA signalling that moving forward they will expect students to understand this notation, without it being spelled out?
Overall, a pretty straightforward and conceptually easy exam – but the fiddly algebra / arithmetic under time pressure is what will result in lost marks, which is disappointing.
I’m not sure the substitution is that obvious in Q6 as it is not exactly a common one. Requiring the answer in terms of
should give the game away, but that does not mean it will…
Q1: Having something like
is an old trick, I don’t like the trick here.
Q4: I have no issue with students having to find an expected value. Note the the Central Limit Theorem is implicitly on the course and its use in a question requires calculating a mean. I’d expect that calculating a mean is taught/reviewed/reinforced by any decent Specialist teacher.
Q6:
is irrational?)
I thought the substitution was obvious IF the derivative of arctan(x) was an automatic fact (which it should be).
Yet again, the required form is not unique. How hard is it to say a and c are co-prime (or relatively prime)? Surely the term is familiar from proof (how do you not use it to efficiently state the contradictaty statement when proving
Q7: Why use the sigma notation and then also define it? Clumsy. It’s in the course so I disagree with any ‘moving forward’ argument. Use one or the other but clumsy to use both.
Q3(a): Clearly the writing panel have become sensitive to the special meaning VCAA gives “Show”. I think the extra wording reinforces the special meaning – removing any ambiguity – and is not overly clumsy.
Q3(c): I dislike the first sentence and found it confusing. I’d prefer “… and moves along the same straight line as the first particle.
As a general point, I loathe “Show” questions. There are too many “Shows” (ditto Methods exams). For example, for Q3 I’d prefer something like:
(a) “Find …”
(b) Keep it.
(c) Preamble:
Particles 2 and 3 move along the same straight line as particle 1. Particle 2 has v = … and x = … relative to O.
“Three seconds …”
This structure gets rid of all the loathsome “Shows”.
Q8: When students give z = 1 – 2i as a solution (justification required for a mark?) in (b), does it need to be restated in (c)?
Q9 (b): I’d argue that removable singularities ARE part of the course. Of course, a decent syllabus would make this – and many other things – explicit.
The exam favoured fast students over slower students. I dislike a spread based on speed.
For Q8 (c) people seem to be fairly split over what counts as “all remaining solutions” and whether or not the conjugate is included. It feels a bit like a question that’s just designed to differentiate from ambiguity. We’ll have to wait and see how assessors decide to mark it.
At the moment I’m inclined to dislike it though.
Thanks, TN. By “people”, which people do you mean?
Students who sat the exam.
Ah. “Rabble”. Thanks, TN.
Question, JK – what do you mean by “old trick” in Q1.
Either I’m not old enough or I never learned the trick…
…and I like to learn tricks.
To ask for the derivative of something like
in maths methods and ‘trap’ students who write 
, 
etc. That is, trap students who don’t treat it as a constant (because they’re sucked in by the derivative of 
wrt x being equal to 
. I see students get trapped at the start of every year and I strongly suspect there will be some who get trapped on this exam.
I see… yeah, don’t like it.
Do you think it’s designed to be a trick? I guess students may be tricked in the manner you suggest, but the
doesn’t feel contrived.
No. Most likely an unintentional trick (especially since it’s Q1).
An experienced Maths Methods teacher would realise and point out the unintended consequence of using this value. Maybe it was pointed out and ignored.
I’d hope that if a student did make this mistake but the rest of their solution was logically correct means that they only lose 1 mark.
(For me the fact that it’s Q1 makes this mistake extra likely to occur – students are full of nervous energy and bolt from the blocks and some will trip over their shoe laces as a consequence).
OK, thanks, probably right. Dumb but not malicious.
Hello, has anyone had a go at question 5b.? Having sat the paper we are pretty sure 5b. is just wrong. One of the two values of a that let the dot product equal zero (a=-3/2) makes rp velocity vector a zero vector – which can’t be perpendicular to the rq velocity vector. Question also explicitly states there’s two solutions. Furthermore, the 5b. preamble that also applies to 5c. is incredibly confusing and just unnecessarily misleading – it could be stated much more explicitly. Thanks
By definition, a zero vector is orthogonal to all vectors, so it is not wrong
Yes, except crappy textbooks, such as Cambridge, can screw up the definition, and presumably the SD says bugger all.
The Cambridge textbook requires both vectors to be non-zero for their dot product being zero to imply they are perpendicular. Most students are using this textbook even if it is crap.
Also, plotting the paths of the two particles, the paths (and their tangents) are not perpendicular at their collision for a=-3/2. Though the velocity vectors may technically be perpendicular, this makes the intent behind the question even less clear.
Seems like a poor question as it only confuses students who think beyond bashing the algebra.
I’m not disagreeing unicorns, but Cambridge, and presumably VCAA to the extent they got off their asses to say anything, is entirely inconsistent. (For example, decompose 6i + 4j into bits parallel and perpendicular to 3i + 2j.)
The exact wording in the paper is “their velocities are at right angles to each other”. Certainly seems suspect.
Any way you cut it, and wherever the blame lies, it doesn’t sound good. I’ll look.
A very good point and I did puzzle over Q5b for a long time.
In the end I do believe
will be given as an answer and justified by the zero vector being orthogonal to all other vectors.
As to the follow-up question Marty posed, this deserves a WiTCH of its own.
What follow-up question is that? (Sorry, I’m getting drunk …)
Decomposing a vector.
SM-1 is not a difficult paper. Integration by parts and Chapter 5 (Vectors) are the new topics in the course, but there are no questions on integration by parts, and the vector question is too easy. The only question that requires some manipulation is the induction proof. You need to recognise that k+1 is a factor and know how to factorise a cubic in a SM exam. Alternatively, you can expand your target expression, which is 1/6 [2(k+1)^2+9(k+1)+13] , then match your n=k+1.
Interestingly, the last question in this paper is usually the first question of Exam 2. I’m curious to see what the first question of Exam 2 will be next Tuesday.
Was not a fan of the wording and structure of Question 5.
The statement above question 5B states ‘When the particles collide, their velocities are at right angles with each other’. It was unclear whether this applied to part 5C which wanted students to solve for the the values of a and b such that the magnitude of the accelerations are equal for both particles at t=1.
Should this statement have applied to part 5C, students would have had to reject one set of solutions (a=-5) as for this value of a, the velocity vectors are not at right angles.
I believe, VCAA should have either made clear in their wording in part C or used the i, ii, iii, etc. structure for this question (i.e bi = Q5B and bii = Q5C)
This could have also been made more clear if VCAA had worded question 5C as:
‘ALSO, when the particles collide at t=1, the magnitudes of their acceleration are equal’ where as the original statement neglected the word ‘also’.
I don’t believe it is reasonable for students who already under exam stress, should have to consider something so menial in a math exam.
I am reviewing this paper now, and I see the problem.
I think part b ‘s preamble could be a statement within part b, whereas part c be worded:
Find the value of ‘a’ if particles collide at t=1 , moving at right angle to one another AND the magnitudes of their accelerations are the same”
What are yours thoughts?
One of my better students produced both pairs a , b (so discounted preamble to part b
In the heat of the exam, you are supposed to have some sort of a “legal mind” ?
Thank you, zbl, and Banacek, and I’m sorry I overlooked specifically addressing this at the time. (Maybe I thought of it as being sufficiently addressed by having posted the WitCH.)
I agree with you both. Within the letter of the law, the preamble to (b) applies also to (c), which is how the thing has been graded. But the layout is obviosuly lazy and misleading, which adds to the bollocksedness of a thoroughly bollocksed question. These people are simply incompetent.
I will add a comment to the SM Error List.
Just another random thought about Q8b.
The question allows for ANY quadratic factor, surely, the way it is written, so
or 
should both be marked as correct…
Or is there something in the way VCAA likes to use words that invalidates one of these answers???
Probably of theoretical interest only, since it is difficult to see a student landing initially on the second quadratic. But, for what it is worth:
(1) There is no question that the second quadratic correctly answers the question.
(2) VCAA is capable of truly insane grading, but I think disallowing the second quadratic would be too insane even for them.
“It is difficult to see a student landing initially on the second quadratic” – I’m not sure. It’s not an error you’d expect many Specialist students to make, but (especially) under time / exam pressure, I can see some students “thinking” that if a quadratic has roots
, then the quadratic can be written 
…
Ah, yeah. Possibly.
I will freely admit that I assumed (wrongly, of course) when first working through the paper that the quadratic factor being asked was the one that did not have the first two linear factors as factors.
So unlikely interpretation it is, but it is exactly what I (wrongly) thought when first working through the paper.
That is very funny. So, not so non-sensical and hyper-pedantic a concern.
Indeed.
The question does say given 1+2i is a solution of f(z)=0, so in order to receive the mark for it either way, one would have to use that statement to work their way through it.
Again, like Marty, I believe this to be a completely theoretical (and non-sensically hyper-pedantic) debate
Yeah, but the question has other issues.
Since the coefficients of the requested quadratic are not defined to be real, there are actually four possible quadratics. (And of course, any of these quadratics could be multiplied through by any constant (real or non-real) to generate an infinite number of correct answers). But, to paraphrase Marty, it is difficult to see a student landing initially on any of the other three.
My main interest is how the marks will be allocated (in particular, will stating z = 1 – 2i is a solution require justification?)
Good nitpicks point about the nature of the quadratic (six possibilities?). But, yeah, the question of whether they’ll demand explicit statement of the conjugate is the active concern.
Indeed.
.
Aside from the point about other unintended answers, I have a more pedestrian concern, which is related to John Kermond’s point about the question not specifying the form in which the answer is to given.
is a quadratic factor of 
. Will writing that down be awarded full marks?
Of course writing
is more useful for answering c, but I don’t think that invalidates answering part b by writing the quadratic as a product of its linear factors.
Good point.
Great point. I think this illustrates why there should only have been one part after (a):
“Given ….”, find all remaining solutions of
. [4 marks]
That would have been a lot cleaner – an completely reasonable to expect of students. The hand holding was not necessary!
One more thought on an alternative approach Q8, which did occur to me as I read the question, but then I quickly realised that parts a and b are nudging me towards an easier method.
The quadratic
can be written as 
, and so the solutions to 
satisfy 
. Writing 
gives us the two equations 
and 
so 
and 
.
I guess the upshot is that writing down any one of the six possible quadratic factors of
may not be that far-fetched. It also adds to John’s point that the question was really over-scaffolded. Just asking students to solve 
even without part a could have been reasonable, especially for the second last question in the paper.