Search results

Re: HSC 2016 4U Marathon Ah, Fitzpatrick made a mistake with his 'r'. He did the reciprocal of what it should be.

Re: HSC 2016 4U Marathon That's exactly what Fitzpatrick did. He then converted the argument to its principal argument value.

Re: HSC 2016 2U Marathon The period is halved though, they said. So the answer must be (A).

Re: HSC 2016 2U Marathon Yes

Maybe they thought it was too harsh to put into the HSC 3U course. There is some new theory, like inequalities, strong induction, etc.

Re: HSC 2016 2U Marathon $\noindent The answer can't just be $C$, because that would be equivalent to saying that the integrand is identically 0, but this is clearly not the case. One easy way to see that it is not the case is to sub. $x =0$ into the integrand.$

Re: HSC 2016 4U Marathon No, they got the RHS of that line by expanding the Cartesian forms of the numbers. The LHS came from consideration of the polar (aka 'mod-arg' in HSC) forms.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent It was a given fact $\Big{(}$recall that the value of $\frac{\mathrm{d}y}{\mathrm{d}x}$ at $x =a$ is the slope of the tangent at $x =a$$\Big{)}$.$

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent For (b), the $y$-intercept is $-3$, so $c =-3$. Since the slope here is $-2$, and $y^\prime = 2x +b \Rightarrow y^\prime (0) = b$, we must have $b=-2$.$ $\noindent For (c), the point $(5,0)$ is on the curve, so we...

Enclose in tex tags, i.e. [ tex] [ /tex] (Without any spaces in those brackets; I just put spaces there so the tags are visible.)

To write square roots like that without LaTeX, it is probably good to write it like this: y = sqrt(x) - 1.

$\noindent Is the curve $y=\sqrt{x-1}$? And they want the equation of the tangent at $x=t$?$

Re: HSC 2016 3U Marathon It's just proof by induction. There should be lots of videos about this online, though maybe not for the particular Q. you had in that post. Here's one example of a YouTube video on this: .

Re: HSC 2016 3U Marathon $\noindent To find the other roots, we can use polynomial long division (or synthetic division, or inspection) to find $\left(x^3 -5x^2 +4\right)\div \left(x-1\right)$. This will come out to be a quadratic (it should be $x^2 -4x-4$). Then we can find the roots of this...

$\noindent (a) Consider triangles $AEH$ and $ABD$. Angle $A$ is common and $AE:AB = AH:AD =\frac{1}{2}$, as $E$ and $H$ are midpoints. So $\triangle AEH$ is similar to $\triangle ABD $ (pair of sides in equal ratio and included angle is equal). So $\angle AEH = \angle ABD$ (corresponding angles...

$\noindent This is actually a mathematical theorem called the \textit{Infinite monkey theorem}. It isn't actually that surprising to me; if given enough time, it's pretty clear you'll eventually get a monkey to be able to write a Shakespearean piece, since there's a non-zero probability $p$ for...

Yeah the HSC Science courses got redesigned for the 2001 HSC so that they could be done with only General Maths level of maths. Before then, I believe that 2U maths was a requisite.

Yeah, logarithms is probably the only thing (and even then, it's only in the HSC course, not in Prelim., which is what OP asked).

Not much maths in Year 11 and 12 Chemistry.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread They are just a telescoping sum and product respectively. Like, write out the first few terms and you'll see most of the stuff will cancel. If you guess a formula using a calculator, you should prove it by induction or something...