Search results

Re: HSC 2016 3U Marathon Don't need to waste time writing a long conclusion involving the 'if true for n = 1, then true for n = 2' etc. mantra (in fact, it's theoretically bad to). Just need to write something like 'hence the result is true by induction'.

$\noindent The Taylor series for $e^{-\frac{t^2}{2}}$ is $\sum _{k = 0}^{\infty} \frac{\left(-\frac{t^2}{2}\right)^k}{k!}$ (convergent for all $t\in \mathbb{R}$). Just integrate this term by term from $0$ to $z$ ($z\in \mathbb{R}$) to get the desired Taylor series. Truncate to $k=n$ to get the...

Re: HSC 2016 3U Marathon Those are binomial coefficients. You can read about them here: https://en.wikipedia.org/wiki/Binomial_coefficient .

Re: HSC 2016 3U Marathon Well so much for 3U methods. :p

Are you doing 3U/4U Maths next year? If so, your 2U mark would be essentially irrelevant.

Both thetas appear to be measuring the angle between the tilted diameter of the hemisphere and the horizontal.

For the convenience of those who want to see the Board of Studies' solutions, here is the link: https://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2010exams/pdf_doc/mathematics-sample-answers-10.pdf . The solution for that question is on the last page (which is page 19).

Re: HSC 2016 3U Marathon $\noindent There's no $O$ in the diagram (and it should be $S$ rather than $R$ to use that result). So what we could say is $PT^2 = PS \times PQ$.$ $\noindent Edit: oh, yeah, if we define $O$ as the foot of the wall, then that is true.$

Re: MATH1231/1241/1251 SOS Thread $\noindent Remember, the $ij$ entry of any matrix product is the $i$th row of the first matrix dotted with the $j$th column of the second matrix (by definition of matrix product). So for your question,$ $$\begin{align*}ij\text{ entry of }U^{T}U &=...

Note that in your answer both solutions are positive, so you would need to decide (with justification!) which solution is right.

$\noindent Alice drops a stone into a deep well and hears the sound of the stone hitting the bottom after a time $T$. Given that the speed of sound is $v_s$ and gravity is $g$, how deep is the well?$

What things constitute a Bachelor of Divinity?

For a constant speed of fluid (which it is here, namely 0.4 m/s), Volume flowing through in a time interval of length T = (speed of fluid)*(cross-sectional area)*T. So here, volume flowing through in 10 seconds = (0.4 m/s)*(cross-sectional area)*(10 seconds).

Re: MATH1231/1241/1251 SOS Thread With your first method, it's set up so that it always produces the normal vector that has 1 as its third component (because we're writing 1 in the third component from the outset). The second method isn't set up so that it'll guarantee the third component is...

Orbital radius.

Yeah a 100% would be cool, but I think there's usually just not enough time to do so (realistically speaking under exam pressure), even if you figure out how to do all the Q's (very easy to make silly mistakes too when rushing, and hard to finish everything in the time limit anyway (depends on...

Yeah that was my guess after writing the comment. My guess for the 'prize' would be either break the record (70) or just get highest mark this year.

There are several differences between HSC Physics projectile motion and HSC 3U. In HSC Physics, you are allowed to quote formulas like equations of motion and other relevant equations (at least ones on the Formula Sheet), whereas for 3U you need to derive them generally. For 3U, projectile...

What is the criterion for being awarded the special 'prize' now :p? Before it was get 70+, but since that was achieved last year (for the first time), would the criterion now be to break the record mark (which iirc is 70)?

What do you mean by "this is NOT intended to be an accurate reflection of the difficulty of the HSC. The questions are made to be as closely styled to HSC as possible."? Seems contradictory...did you mean to put a 'not' for the last sentence too (I probably misunderstood the intended meaning)?