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The marking criteria just says you need this for 2 marks: ''Correct proof''.

Haha. Yeah.

$A real number $a$ satisfies $a^2 < 1$ if and only if $-1<a<1$ (see the graph of $y=x^2$ for instance; $x^2$ is below $y=1$ when $-1<x<1$, and $not$ below it otherwise. In other words, $x^2 < 1$ if and only if $-1<x<1$).$

Maybe they could have made a "General" stream for the sciences, like they have for maths. Then, they could have kept the sciences as they were and not dumbed them down, so those who wanted a dumbed down version could do the General versions. I guess this was considered infeasible by the Board...

Re: HSC 2015 2U Marathon $Should be discriminant \textsl{less than} 0. For $both$ cases, the discriminant needs to be negative for the quadratic to be definite. If the discriminant is negative, then the quadratic is definite, and the sign of $a$ tells us whether it is positive definite, or...

I'm not entirely sure I get what you mean. Are you saying the students were beginning to find it hard to cope with the old difficulty, so they dumbed it down?

re: HSC Physics Marathon Archive I don't think so. Look at Q.21 on Page 13 of the HSC Physics paper from 2013: http://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-physics.pdf They implied there that you studied just one of the scientists, and they let you choose one.

What's the main reason most subjects have been dumbed down so much (both compared to 1960's, and also compared to pre-2001)?

I think it said on the HSC Timetable that borrowing materials is not permitted for HSC.

Well it's a 1-marker, so not much detail needed. You'd just need the right shape and right axial intercepts.

re: HSC Physics Marathon Archive Shouldn't be, since the syllabus dot point is: • identify data sources, gather, analyse and present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O’Neill or von...

Assuming the Q is just asking for a rough sketch: not much, generally just need things like general shape, easy-to-find axial intercepts and asymptotes. Don't need to waste time finding stationary points or inflexion points etc.

$If we sketch the graph of $y=\tan x$ for $0<x<2\pi$, we can see that the line $y=-2$ intersects the graph exactly twice.$ Sketch is here...

$Yes, that's valid: $\sin x = \int _0 ^x \cos t \text{ d}t < \int _0 ^x 1 \text{ d}t = x$, for $x>0$. In general, if $f(t) \leq g(t)$ for all $t$ in the interval $a\leq t \leq b$ (so $a\leq b$), we have $\int _a ^b f(t) \text{ d}t \leq \int _a ^b g(t) \text{ d}t$.$

Re: HSC 2015 2U Marathon There was a Trapezoidal and Simpson's Rule Q in 2013 HSC 2U. See Question 15(a) on page 13: http://www.boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf Edit: oh, you said multiple choice Q's.

$The limiting sum exists if and only if $-1<r<1$. In this case, $r=-\tan^2 \theta$, so $r$ is non-positive, so the limiting sum exists if and only if $r>-1$. So we just need to solve the inequation $-\tan^2 \theta > -1$. We have$ $$-\tan^2 \theta > -1 \Longleftrightarrow \tan^2 \theta < 1$$...

The words consist of five letters: _ _ _ _ _. Since in Case 1, we are having 2 I's, and I's are identical, we just choose the positions for them to go, which is done in 5C2 ways (from the 5 spaces, choose 2 for the I's to occupy).

Yeah that's a valid method.

$The answer is (D). We have $A=kB^3$, so $\sqrt[3]{A} = k_2 B$ for some constant $k_2 \equiv \sqrt[3]{k}$, so $\sqrt[3]{A}$ and $B$ have a linear relationship. This makes (D) the answer.$

In general for probability Q's, "times" corresponds to "and", and "plus" corresponds to "or".