Search results

It says 2U will be made a prerequisite, but will there be any minimum mark requirement (e.g. Band 5 required)? If not, someone could do 2U just for the sake of keeping USyd open as an option and do 10 other units. These 10 other units would be their 'serious' units that would count for their...

What do you mean by calculus being everything in maths?

Correct! In fact, many topics have been removed from the NSW high school maths curriculum over the past 100 years (including things like group theory and the Riemann Zeta function it seems). Here's a post that lists these:

The NSW maths HSC (or equivalent) papers from 30-50 or so years ago had linear algebra in them as well as calculus (and more calculus than now). From memory, for linear algebra, the old HSC 4U papers had Q's on things like matrices operations and calculations, linear transformations (like...

Both of these use the intermediate value theorem (IVT). For 7), note that g(0) = f(0) – 0 = f(0), which is in [0, 1], since the range of f is in [0, 1]. If f(0) = 0, we have a suitable c of c = 0. So suppose g(0) = f(0) is strictly positive instead (this is the only other possibility...

$\noindent Here's the idea for showing that if $p$ and $q$ are polynomial functions, then $p\circ q$ is a polynomial function.$ $\noindent If either $p$ or $q$ is a constant polynomial, then so is $p\circ q$, so it is also a polynomial. Suppose that neither $p$ are constant polynomial...

I think he was referring to the the general curriculums / system overall, rather than school-specific things, as he said ''as a result we have the watered down HSC we have today. The education system right now caters to the lowest common denominator''.

Harare is the capital city of Zimbabwe.

I don't think it's the existence of a formula sheet that makes some people say notes for maths aren't useful, because people have said this before this year too, when formula sheets were not implemented (other than the standard integrals sheet).

$\noindent There are 1200 students in total, so the teacher needs to survey $120$ students (since this is $10\%$). Since she did the same number of students in each year group, she surveyed $20$ students from each year group (as there are six year groups).$ $\noindent Under the stratified...

I guess in this case, rote would be repeating something over and over (e.g. a formula or practice questions) until you get used to something without understanding in any way (even intuitively) why it's true or how it could be proved (or at least know that where it comes from). For example, some...

Even though many formulae are on the sheet now, people will probably still memorise at least some of them. It's like how all the standard integrals were always given, yet most people knew them all (or most) anyway.

Quite a bit of it rote learnt by some people. For example, some people rote learn complex number loci, general solutions to trig. equations, lots of formulas (which are now going to be on a formula sheet but weren't before), etc.

Yep :). If the points P and Q had coordinates such that they were not just reflections of each other about a coordinate axis (or the same point), it turns out that such a tangential circle would not exist in the first place; the interested HSC 4U student may like to try and prove this.

Yeah, all the reflection thing is really saying is that if we flip the entire diagram of the ellipse about the horizontal axis, the picture remains the same because the ellipse is symmetric about the x-axis. Since the two points of interest are also reflections of each other about the x-axis...

$\noindent There are a few ways to argue that $y=0$ by symmetry. The first is to draw in the circle with centre $(h,k)$ and the ellipse $E$, with the two points $P$ and $Q$ labelled. Then note that if we applied a reflection transformation $\mathcal{R}$ to the plane so that everything is...

Oh sorry, I meant normal in all instances above, not tangent.

What was your method? Finding both normals and solving them simultaneously? (By the way, I realised now that getting the equation of one of the normals was an earlier part of the question.)

There was a BOS thread about this I think. It was called "Extension 3 Maths" or something, but I can't find it right now. Edit: It's here: http://community.boredofstudies.org/10/maths/327388/extension-3-maths.html .

For that ellipse question, the y-value of the circle's centre is clearly 0 by symmetry (specifically it must be equidistant from the two given points on the ellipse, which means it lies on the perpendicular bisector to the line segment joining those two points, which is the x-axis). A way to...