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Dr Pender was an excellent teacher. Mr Sadler was strict (and a touch scary) when I had him in junior maths but I never saw him teach senior maths. He wrote challenging exams, though. I only had one bad Maths teacher, who I won't be identifying, but he did not belong in a classroom.

I can add any integer multiple of 2\pi to a complex number and get the same complex number. So, \begin{align*} z = \cfrac{1+i\sqrt{3}}{2} &= \cos{\cfrac{\pi}{3}} + i\sin{\cfrac{\pi}{3}} \\ &= \cos{\left(2\pi + \cfrac{\pi}{3}\right)} + i\sin{\left(2\pi + \cfrac{\pi}{3}\right)} =...

No, because that equation suggests that there is hydrogen liquid present, which is not present in liquid air and would need a much lower temperature, and it sees oxygen just vanish and so is unbalanced.

"Awful" teachers can be a subjective standard. I had teachers who were competent but who I did not find great / inspiring, especially for subjects that I didn't like, but very few who I would describe as truly awful in the not competent sense.

No, they don't. Anyway, those pay bands define the standard for the public sector and comprise minimum rates. Private schools pay more, often much more. Even in institutions like universities, where there is again a grade and steps / levels within grades system, the rates can be higher...

And another thought... BoS works primarily on collaboration, recognising that the ability to explain to another is both beneficial to the other but can be valuable consolidation. Politics and Governance at a societal level functions through competition between two major parties... and looking...

Patriotic insistence on the primacy of work by one's one nation led the Soviets into the disaster of Lysenkoism in biology / genetics, too. Insisting on competing rather than collaborating can be beneficial so long as parties are willing to concede when a clearly superior notion is postulated...

Thank you and I agree. I have both tutored high achieving students and been one, and believe that an individualised approach that addresses individual needs and goals has significant advantages, as can a group-based approach.

Thank you for a very thoughtful response. The social aspects of the environment itself is less school-like formalised, at least for some centres, and I know that some students prefer a more structured environment. The social networking aspect for both collaborative support and friendship are...

Kindly refrain from making assumptions about me or the students who I have helped.

Alkyl group means a group like ethyl or methyl or propyl or decyl, Essentially, it is an alkane CnH2n+2 with one H replaced by a halogen.

All alkyl halides are halogenated organic compounds, but not all halogenated organic compounds are alkyl halides. For example, chloroethene (vinyl chloride, CH2=CHCl) is a halogenated organic compound, but it is not an alkyl halide as it does not have a saturated alkyl group. Similarly for...

s_n is defined in my first post in this thread, the number of distinct segments of a plane split by n all non-parallel lines.

Undeleted as I got an edit conflict in posting the solution.

The pattern of non-enclosed regions follows a simple pattern: 2, 4, 6, 8, 10, ... Imagine a 2D plane with some number of intersecting lines. Now, imagine yourself riding a new line in from infinity. The first line you meet will create a new non-enclosed region. The next will create a new...

@tito981, it is because you are trying to increase the amount of ammonia by adding nitrogen only, which means that you are decreasing the amount of hydrogen. As you need the equilibrium constant to be unchanged, you have two factors on the numerator, one increasing and one decreasing, to get...

Here is a related problem: The solution for part (i) is: Based on this solution, we hypothesise that the pattern is s_n = s_{n-1} + n,\ \text{for integers $n \geqslant 2$ with $s_1 = 2$. This can be shown to give s_n = \cfrac{1}{2}(n^2 + n + 2) by recognising that we can shown that s_n = 1...

@Life'sHard, my initial impression matches jazz's. However, I come at the exam having seen hundreds (maybe even into thousands) of chemistry exams over several HSC syllabi. This exam has questions that I see as part of the natural explorations of the theory that accumulate over years of HSC...

P(x) is a quadratic equation in x^2, so the solutions of P(x) = 0 are x^2 = \cfrac{-A \pm \sqrt{A^2 - 4(1)(B)}}{2} \text{and since}\ \sqrt{A^2 - 4B} < A\ \implies\ x^2 < 0 there are no real solutions.

I suspect we will develop over time to a situation akin to influenza, with routine vaccination being targeted to new variations over time. The US has done a fantastic job of illustrating what happens if we fail to respond rationally to emerging health challenges.