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It’s still early days of the new syllabus but here is a nice question (technically Ext1 level though) which uses that property of a cdf Let X be any continuous random variable with a cdf of F(x). Let Y = F(X). Show that the pdf of Y is that of a uniform distribution over [0,1].

All questions have to map to a section in the syllabus (see marking criteria document which shows this). It cannot map to a topic that doesn’t exist in the syllabus. In this example, it is mapped back to the dotpoint which says “apply these techniques of integration to practical and theoretical...

I was talking about the mechanics question lol

Interesting observation, they used "arctan" in the paper rather than the usual inverse tan notation. I think that's the first time I've ever seen a HSC paper use that notation...

Cheated a bit with using the 'otherwise' option, but still acceptable lol

The probability you are looking for is P(Z>0.4). The table only gives you P(0 < Z < 0.4), so you're missing half the entire normal curve. This means you need to do a bit of manipulation first P(Z > 0.4) = 1 - P(Z < 0.4) = 1 - [0.5 + P(0<Z<0.4)] ~ 0.5 - 0.1554 = 0.3446 The answer in the...

5^n = (2+3)^n \\\\= \sum_{k=0}^n\binom{n}{k}2^{n-k}3^{k}\\\\=2^n+\sum_{k=1}^{n-1}\binom{n}{k}2^{n-k}3^{k}+3^n The middle term is non-zero/positive provided n>1 as an integer so hence they cannot be equal.

https://www.smh.com.au/national/nsw/get-me-out-of-here-three-hours-of-hsc-exam-prove-the-real-test-20211115-p5991y.html

Look at the questions here - provided you know which parts are still relevant to the current syllabus (which would be most of the questions) https://www.boredofstudies.org/resources/bos-trials-mathematics-2013-2015-exams-and-solutions.17177/

Sorry, fixed the issue. Should be working now.

It's not, though I personally think it should be.

lolwut you do have to know the normal probability density equation. I'm surprised some of you here haven't been shown that given it's explicitly in the syllabus

Technically they’re not in this syllabus in the “explicit” sense. So it is unlikely you will find HSC questions in the current syllabus explicitly saying “use implicit differentiation...”. However, the idea of differentiating both sides and using the chain rule is not a concept outside the...

Cross products are not in the syllabus so it’s not worth spending time on that. Technically any modulus result of the cross product can be converted into an equivalent form of the dot product (the vector form not so much as you need to introduce the concept of the normal unit vector). Therefore...

Textbooks are written by private companies whereas the HSC is written by NESA. It is not surprising to have instances where textbooks have material that is outside the syllabus. If you look at the NESA topic guide for “Calculus” it explicitly says that relations “which involve more than one...

In one of the PDF attachments containing the results, check the results against your student number.

Recurrence relations with more than one index are generally outside the syllabus. There would have to be a lot of hand-holding if they ever ask that.

Thanks to everyone who participated and for your patience! Here are the solutions and student results for the 2021 Mathematics Extension 2 BoS trials. Thanks to CM_Tutor and Paradoxica for helping with solutions and marking! A reminder that whilst the questions are made to be as closely styled...

Given I have other priorities going on and this is not a straightforward task, I will not have time to look into this until later tonight. Please be patient. As mentioned already, access to the forum/resources is not being impacted with the account you are using now.

We will look into this. If you are the same person as that user, then it is clear you are still able to access this site with the current alt account so there is minimal impact. Your patience is appreciated.