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Trigonometry is a key part of the Mathematics Extension 1 Course. Inverses and three-dimensional trig problems are often tricky to navigate for 3 unit students. However, most of the time these seemingly mystical problems aren't actually that difficult once you've encountered a wide variety of...

Here are the 3U problems on Trigonometry.

Re: HSC 2014 4U Marathon - Advanced Level Yep, that's the way to do it. You consider the four cases in which you don't get a red triangle, which are 1) No reds, 2) One red, 3) Two reds, 4) Three reds in a line. $Prove that $\\...

Re: HSC 2014 4U Marathon - Advanced Level Yeah, a proof of that result about the primes (I believe it's called Wilson's Theorem) in all probability will involve modular arithmetic, which isn't included in the syllabus. But, if you do happen to know how that works, it is possible to understand a...

Re: HSC 2014 4U Marathon Yep, that's correct, Dunjaaa. There is a slightly faster solution in which you make the substitution u=1/x. But all the deft moves are in your solution. First, the use of a substitution to equate the integral with a similar looking integral. Then the use of some basic...

Re: HSC 2014 4U Marathon Prove that \int_\frac{1}{b}^b \frac{\tan^{-1}(x)}{x} = \frac{\pi \cdot \mathrm{ln}(b)}{2}.

Here's a nice set of problems about complex numbers and polynomials. In my view, questions that combine the two areas are probably the most tricky out of the MX2 course and have a reasonable likelihood of popping up in the last few questions. But, regardless of whether or not they'll come up in...

Re: HSC 2014 4U Marathon - Advanced Level Sorry, I should have been more clear when I said 'confines of the syllabus'. While I don't think it's explicitly mentioned in the syllabus, it is a technique that comes up in HSC 4u exams (generally in the harder questions, for instance in 2011)...

Re: HSC 2013 3U Marathon Thread This is a nice little problem about binomial coefficients. \\$a) Prove that $\binom{n}{k}=\binom{n-1}{k}+\binom{n-1}{k-1}\\$b) Prove that$ \binom{2^n-1}{k} $ is odd for all integers $ k $ such that $ 0 \leq k \leq 2^n-1 \\$c) Prove that$ \binom{2^n}{k} $ is even...

Re: HSC 2014 4U Marathon - Advanced Level With regards to the circle geometry problem above, there are a number of ways to solve the problem. If you want a hint, just highlight the following text: Proof by contradiction is very helpful in existence problems like these. For instance, you could...

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