Discussion of the 2022 NHT Specialist Exams

This is our post for discussion of the 2022 NHT Specialist Mathematics exams, which have now been posted, here and here. (See also our corresponding 2022 NHT Methods exams post.) We’ve had a quick browse, and found plenty of irritants but no glaringly large errors. We don’t plan to look further or to post on the exams, except to follow up on whatever people find worthy of comment.

UPDATE (23/09/22)

The exam reports are now available, here and here.

26 Replies to “Discussion of the 2022 NHT Specialist Exams”

  1. Some quick thoughts on Exam 1 and with sentiments similar to Marty’s:

    Question 4 (a): Minor niggle – Would have preferred “*static* equilibrium” rather than simply “equilibrium”.

    Question 6: Minor niggle. “.. Find the magnitude of the resultant force, in newtons, after it has acted on the mass for four seconds, …” This sentence suggests that the resultant force is an old friend that has been introduced earlier. It wasn’t.

    Would have preferred that this resultant force was mentioned/introduced earlier:
    “A 2kg mass is moving under the action of a resultant force. Relative to a fixed origin, the position of the mass after t seconds is given by …”

    Question 7: The particle and its speed is approaching infinity after a finite time. I don’t like it. It’s sloppy and makes no physical sense. The time should have been restricted to something like \displaystyle \left[0, \frac{\pi}{3} \right] (But at least it’s not another stunt car with infinite initial acceleration).

    Question 8: Another wordy ‘real-life’ statistics question. I see from part (c) that students are now required to know z = 1.96 rather than z = 2. This is an under-handed change of policy.

    Given the relative irrelevance of the NHT exams, I think the writers get a pass mark for this one. There are no glaringly large errors (but I could argue a case for Question 7 – it could and should have been better with one simple change). But …. the continual shifting of the goal posts for the statistics content of Specialist Maths – given that we have this gratuitous content forced upon us – continues to greatly irritate me.

      1. I don’t have a problem with that.

        The exact answer is 34 and I’d hope that a student would give that answer without the specific instruction. However, what is NOT hilarious is the sort of unsimplified answer a student is likely to give if the instruction is not given …

        Asking for the answer as an integer is perhaps more a sad indictment on the standard of student than the exam.

          1. \displaystyle 15^2 = 225 is something that students should know. So a number a bit bigger than 15 whose square ends in 9 … Hmmm … What could it be …?

            (17 should be obvious, in my opinion. I don’t see the problem with this. Once upon a time students knew perfect squares up to 20^2 = 400, just like the times tables).

            But I agree that it might have been better (albeit introduce a greater chance of dumb arithmetic mistake) if the coefficient of \displaystyle t^2 had been \displaystyle \sqrt{6} rather than 6.

    1. Re: Question 8 and the required value of z. I see on the 2022 NHT Maths Methods Exam 1 Question 3 that the value z = 2 is explicitly given, with an expectation that this value is used. Clearly VCAA cannot make up its mind and establish a consistent expectation across all of its exams.

      1. In fact, I don’t understand why VCAA refuses to include critical values of z on the formula sheet. What is the point in requiring students to memorise 1.96?

    2. Thanks, John. Re Q6, yes, this is the kind of Not Quite Right wording that really gets up my nose. It’s not killingly wrong, but it’s plain bad writing.

  2. Regarding the z=1.96 or z=2 issue…

    1. Yes, it is an issue. Neither are exact for a 95% confidence interval. z=2 is correct to the nearest integer and z=1.96 is correct to 2 decimal places (or 3 significant figures for any IB teachers who may be reading this for ideas) but there is no reason why one should be chosen over the other. It is an arbitrary choice. As is the 95%… why not 94.7% just to be different…?

    2. The formula given for the two different exams is also a bit of an issue. It is the same formula, written differently. Why give two different versions of the same formula in different exams?

    Not an error in either case, but an ongoing frustration.

  3. Thoughts on SM1:
    – overall a balanced paper testing mainly outcome 1 and ocassionally outcome 2
    – no apparent conceptual error, although some questions could’ve been phrased with more conciseness and clarity as suggested by JF and RF
    – some questions from old exams were reinvented (i.e. Q7) but requirements should have been tightened compared to the similar one in 2013 SM1. Will be curious to see the assessment report later if students were expected to go on expressing y as a function of x and justifying y must be greater than or equal to zero, rather than just leaving it as a standard hyperbola form x^2/16 – y^2/4 =1
    – the styles and skills being tested look very similar to 2021 November exams (heard somewhere that these papers were developed together) with three vector calculus questions, though one may argue that Q7 is more of parametric differentiation nature rather than vector.
    On a side note I am not sure if the writers have assumed that students are expected to memorize the derivative of sec(x) is sec(x)tan(x), or d(csc(x))/dx = – csc(x)cot(x)…
    From 2013 SM reports I felt that…

    – The choice of 2 + 3 mark allocation for Q10 was again interesting. This makes the life easier for the students compared to Q10 in 2018 (straight 5 marks)
    – Reflection from Q5 in SM1 paper – a similar mcq was there in 2019 NHT SM2, suggesting potentials for tech-active questions to be suitably modified into tech-free questions, vice-versa. This can really test if the students understand and grasp the concepts and skills well rather than button-pressing. Also a warning bell to teachers and students – don’t underestimate the value of solid algebraic skills! If you know your concepts and algebra well, you will do well in Spesh…

    Thoughts on SM2:
    – MCQs are slightly easier compared to last Nov exam. Those who knew their buttons well should have done most questions faster
    – An interesting u-substitution question mcq1
    0. I am guessing if there would be a similar one in SM1 this November. Might be worthy to redo some exercises from Essential textbook – other substitutions.
    – mcq 6: interesting to see some crossovers between polynomial graphs and complex number. Usually SACE exams have questions set in similar manner.

    – Much easier than ERQ1 last year. Decent question.
    – modified based on 2015 SM1 question on complex number. Blended with similar ideas from previous exam questions involving perpendicular bisector
    – Not bad. Benign
    – 1998, 2005, 2011, 2016 all had similar inflow-outflow concentration problems. Every six or seven years, it appears. Are we expecting some logistic equations or population problem or predator-prey models in this November? Hopefully not chemical reaction rate problem…
    Very challenging. Very verbose, inevitably.
    Too many parameters to work with.
    Coefficient of friction is an essential part throughout the question. Some parts favored integration approaches over constant acceleration formulae.
    Interestingly, much easier than last year’s statistics question. The last part assessed binomial distribution, so students who did methods last year need to pick up their probability knowledge again this year before Nov exam…CRV, sample proportion, etc.
    If only students have access to some similar vector calculus questions around 1994-1997…Finally some vector integration questions appeared again. Last two parts were also very challenging. If this question were a November exam question I guess the percentage for students obtaining full marks would tend to be single digit, even decimals or close to zero. Hardly could some similar question to this be found in the mainstream textbooks…Again, this question, especially the last two parts, has proven that physics students are not necessarily advantaged. Specialist maths is far more than that.

    1. Thanks very much, Guardian. I’m sure that will be very helpful to teachers and students. I disagree on 5 versus 2 + 3, re Q10, but that’s a debate for another time.

    1. Hi Reef. I’ll look when home. Do you suspect an issue with the question, or just you’re not sure what is going on?

  4. Hello, All

    I don’t understand why the answer Maximum rate = 30.8 when t = 0.4.

    obviously, d2x/dt2 =0 then t=2.8 and rate =-4.2 gram / L is answer

    1. Hi Jack, I’ve been flat out but I’ll look tomorrow. Since no one has raised this earlier, I suspect you’ve made an error, but I’ll check.

    2. Hi Jack.

      The question asks for “the maximum rate at which the chemical flows \displaystyle from \displaystyle the \displaystyle tank” (my emphasis). That is, the maximum rate of outflow. The outflow rate is NOT dx/dt (dx/dt is the rate of change \displaystyle inside the tank). You’ve used the wrong rate in your calculation.

      1. Just to clarify:

        The rate of outflow is the rate of change of \displaystyle volume, it’s not the same as the rate of change of \displaystyle chemical leaving the tank. It’s a tricky question, containing several different rates that can easily lead to confusion!

    1. Nuts indeed. It’s funny what new crap you discover from an intelligent student who works carefully through a VCAA exam. Some crap (including in Exam Reports) lies dormant for several years. And then VCAA gets it knickers in a knot (or used to, the jury is still out now that there’s a new Maths Manager and Curriculum Manager) when the crap is pointed out.

      But I have issues beyond the picture.

      Questions like 8 are dumb. Not defective, just plain dumb. I’d love to know what the intent of the question is. Most students will simply use their CAS to draw the slope field (and in this case stop at option B). I don’t see the point. Just ask them to draw a slope field in Exam 1 if you want to see if they can. Or give them a slope field and ask about the behaviour of the solutions to the corresponding DE for different initial conditions. Or write a Study design that explicitly contains some worthwhile limit content.

      Students who try to find the correct option by eliminating wrong options with some mathematical analysis (which potentially makes such a question more worthwhile) get screwed over here. Sure, you can reasonably note that dy/dx = 0 when x = 0 and so eliminate A and C. This leaves B, D and E.

      But after this, you need to be very comfortable with limits. Because the only way I see to continue such an analysis is to argue dy/dx –> 0 as x –> -oo (eliminate D) and then dy/dx –> -oo as x –> 0 and y < 0 (eliminate E).

      I don't think many students would approach the question this way. They might eliminate A and C as above, but then would go to the CAS and get lucky with B.

      I consider these questions dumb and pathetic.

      1. I think that the elimination of D is quite easy. I would in fact eliminate E first, as the picture shows that dy/dx depends on both x and y which makes an easy elimination. It does not seem to me that those attempting an analysis strategy should be screwed over by this question any more than any other questions of a similar style.

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