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I was quite surprised matrices was put into 2U only; I was expecting it'd be in MX2. But the words 'matrix' or 'matrices' don't appear to be in the MX2 document anywhere (or even MX1). Will matrices be assumed knowledge for MX1/2 and will there be Q's involving them in their exams?

Here's the link to the Year 11-12 2U/3U Maths syllabus: https://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths23u_syl.pdf . Here's the HSC 4U Maths syllabus: https://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf .

Some proofs/derivations get asked very often in exams (e.g. 4U deriving equation of tangent to conics), which you'll probably end up remembering just by practising past papers enough. Which ones did you have in mind? Things like proofs of compound angle formulas, calculus rules (like product...

I think it's unlikely they'd get you to derive the perpendicular distance formula.

Re: HSC 2016 4U Marathon Is there any story behind the naming of this 'guitar method' (like there was for the 'burning lady log law' thing)?

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent (b) Without loss of generality, let the circles have radius $2$. Note that the edges $AO,AP,BO,BP,PO$ all have length $2$ as each is a radius of $\mathcal{C}$ or $\mathcal{D}$. So $\triangle AOP$ is equilateral. So...

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent Do you mean how did I arrive at $180 = Vt$ at the time of collision? This was done by equating the two equations of motion and cancelling common terms from each side.$

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread There is no motion in the horizontal direction.

Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent (a) Note the motions are just in the vertical direction, so the trajectories aren't actually parabolas of course (as they're just either dropped or thrown straight up). Let $y=0$ be the ground level. The stone's...

Re: HSC 2016 4U Marathon $\noindent Let $n$ be a positive integer. For integers $k$, let $\omega_k =\mathrm{c}i\mathrm{s} \left(\frac{\left(2k+1\right)\pi}{n}\right)$ (this is a complex $n^{\text{th}}$ root of $-1$). Show that $\omega_{j}=\overline{\omega_k}$, where $j=n-k-1$.$

Re: International Baccalaureate Marathon 2016 That's still pretty close to 2, isn't it?

Ah yeah, that solution is much nicer. The product of roots is greater than 1. Since the roots are each positive numbers (as they are tan of something that is acute), at least one of them must be greater than 1 (otherwise both would be less than 1, and then their product would have been less...

$\noindent Here's one way to do it.$ $\noindent Note that the range of the projectile is $R=\frac{V^2 \sin 2\theta}{g}$ (left as exercise for the reader, it's quite a standard thing to prove). So any point above the ground that is reachable by the projectile has $x$ value less than $R$, and...

$\noindent Basically it's saying to show that no point above the ground can be hit by firing the projectile at two different smaller-than-$45^\circ$ angles. E.g. it's impossible to hit the same point with a projection angle of $30^\circ$ and also with an angle $15^\circ$ (assuming $V$ is held...

$\noindent That $a$ is just the focal length (in absolute value). The latus rectum is defined here, along with a picture (the blue chord in the picture in this link):$ http://mathworld.wolfram.com/LatusRectum.html .

$\noindent The equation is of the form $\left(x-2\right)^2 = 4a \left(y-5\right)$, where $|a|$ is the focal length (the sign of $a$ here will dictate which way the parabola faces). To find $a$, sub. in $x=0$ and $y=9$, since the curve cuts the $y$-axis here. Once you've found $a$, you can draw a...

Re: HSC 2016 3U Marathon If we said alternate angles as the reason for the equality, that'd mean we already know the lines are parallel, but this is what we're trying to show (we don't know it yet). We use corresponding angles in congruent triangles (proof of congruence done in first part of...

This question is quite a poor one. (Like in terms of the options provided.)

You would also need to know 4U Integration to do those topics. (A lot of the questions in those topics are just applications of integration, requiring 4U Integration methods like Integration By Parts, partial fractions, etc.)

$\noindent 1) Let $x$ be the depth in metres at time $t$ hours after 12 noon on $19^{\text{th}}$ June. The extreme positions are $x =11$ and $x=15$, so the amplitude is clearly $2$. The centre of motion is at $x = 13$. It takes 8 hours to go from the peak to the trough, which is a half-period...