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The movement to mass upper secondary education (and now higher education).

Too true. Just look at a HSC Level 1 exam from the late 1960s. Many of the topics covered then are now only done at first-year university these days (infinite series, power series, coordinate geometry in space, matices, and modular arithmetic). And just look at the recent change in the format of...

Re: HSC 2015 4U Marathon $Let$\,\,u,v \in \mathbb{C}\,\,$be the roots of the equation$\\z + \frac{1}{z} = 2 (\cos \alpha + i \sin \alpha), \quad 0 < \alpha < \pi.\\$(a) Show that$\,\,u + i\,\,$and$\,\,v + i\,\,$have the same argument and that$\,\,u - i\,\,$and$\,\,v - i\,\,$have the same...

Re: HSC 2015 4U Marathon $That's correct. Next question. The system of equations$\\ \begin{align*}|z - 2 - 2i| &= \sqrt{23}\\|z - 8 - 5i| &= \sqrt{38},\end{align*}\\$has two solutions$\,\,z_1,z_2 \in \mathbb{C}.\,\,$Find$\,\, \displaystyle{\frac{z_1 + z_2}{2}}.

Re: HSC 2015 4U Marathon \noindent$Mmmm....What about if$\,\, z \in \mathbb{C}, z \neq 0,\,\,$such that$\\ \mbox{arg} \left (-\frac{1}{z} \right ) = - \frac{2\pi}{3} \quad \mbox{and} \quad \left |1 - \frac{2}{z} \right | = 1,\,\,$find$\,\,z.

Re: HSC 2015 4U Marathon $If$\,\ z \in \mathbb{C}\,\, $such that$\,\, \frac{1}{2} \leqslant |z| \leqslant 4, \,\,$find the sum of the greatest and least value of\,\,$ \left |z + \frac{1}{z} \right |.

Re: HSC 2015 4U Marathon $Here is another approach, though it is a little longer compared to other suggested solutions.$\\ \begin{align*}\frac{a}{1+ a} + \frac{b}{1 + b} &= \frac{1 + 2ab}{2 + ab}, \quad \mbox{since} \,\, a + b = 1\\&= \frac{2a^2 - 2a - 1}{a^2 - a - 2}, \quad \mbox{since} \,\...

Re: MX2 2015 Integration Marathon Correct! How about: \int \left (\frac{x}{x\sin x + \cos x} \right )^2\mbox{d}x

Re: MX2 2015 Integration Marathon $Okay. Sorry about that. How about$\\ \int^3_{\frac{1}{3}} \frac{\tan^{-1} x}{x^2 - x + 1} \mbox{d}x

Re: MX2 2015 Integration Marathon \int^1_0 \frac{\ln (1 + x)}{1 + x^2} \mbox{d}x