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Re: HSC 2016 3U Marathon It does work; to see this, we can call the angles BOE and BDE instead, and then the angles are subtended by arc BE (and are essentially the same angles).

Those topics are important for computer science.

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Re: HSC 2016 4U Marathon Well he encouraged all current ones to participate – he didn't ban non-current ones from participating! :P

Re: HSC 2016 2U Marathon $In general, if $y=f(x)$ and $f$ is differentiable, with $f(x_0) = y_0$, we have the following: $y-y_0 = \int _{x_0}^{x} f^\prime (t) \text{ d}t$. The LHS here is just $\int _{y_0} ^y \mathrm{ d}\gamma$ (alternatively, view it via the Fundamental Theorem of Calculus...

Re: HSC 2016 2U Marathon $I realised what you meant by yours; but it should be this on the LHS: $\int _{y(0)} ^{y(x)} \mathrm{ d}y$ (that's why I said that was wrong; and this just simplifies to what I said to use). And yeah, I did that in the mechanics derivation of escape velocity on one of...

Re: HSC 2016 2U Marathon What do you mean by "not really"? The one I wrote is just a restatement of the fundamental theorem of calculus pretty much (since f(0) = 0).

Re: HSC 2016 2U Marathon $It should be: $y=f(x)=\int _0 ^x f^\prime (t) \text{ d}t$ (where $f^\prime (t) = t^2-4t+3$ is given).$

$You should know how to convert radians to degrees and vice-versa without a calculator. One reason for this is that you may get a variable in radians and be asked to convert this to radians, in which case a calculator won't help. Here is the rule. If $\theta$ is a real number, then...

Re: HSC 2016 2U Marathon $For your method, you need to write in the quotients that it's the limit as $\Delta x \to 0$. (And avoid using `d$x$' for that since $\mathrm{d}x$ has another meaning, use something else, like $\delta x$ or $h$ or $\Delta x$ etc.)$

Re: HSC 2016 2U Marathon $I didn't check the details of what you did (just glanced at the general method), but there is a faster method: just use the chain rule. If $f$ is even, then $f(x)=f(-x)$ for all $x$ in the domain. Differentiating both sides with respect to $x$, we have$...

Re: HSC 2016 2U Marathon $Basic percentages. Let the original price be $x$. Then we have $1.025 x = \$ 1600$. Therefore, $x=\frac{\$ 1600}{1.025}=\$ 1560.97561.... \approx \$ 1560.98$ (nearest cent). Hence the answer is (B).$

Sketch the graph of y = sin x between x = 0 and x = 2π. Also sketch in the horizontal lines y = √(2)/2 (dotted line since we want a strict inequality for this one) and y = -½. We want the values of x such that the sine wave is between these two horizontal lines. Refer to this graph...

Re: MX2 2015 Integration Marathon $\underline{Question (2)}$ $Given: $L=\lim_{n\to \infty} \frac{1}{n}\sum _{k=1}^n k \ln \left(\frac{n^2 + (k-1)^2}{n^2 + k^2}\right)$.$ $Let $S_n = \sum _{k=1}^n k \ln \left(\frac{n^2 + (k-1)^2}{n^2 + k^2} \right)$.$ $Note that in general,$...

No, just passing every test wouldn't necessarily imply a 70+ ATAR. You seem to be thinking if you get the average mark in everything, you'll get the average ATAR; but it depends on what subjects you did due to scaling of subjects, and moreover, it's not necessarily true that a "pass" is the...

Re: MX2 2015 Integration Marathon $OK well then if it was intended that $F(n)$ was a function of $x$, it would have been better to write it as $F_n (x)$. As it was written as $F(n)$, it looks like a function only dependent on $n$. Also, note that $F_n (x)$ is defined only up to a constant (as...

Re: HSC 2016 3U Marathon Out of '"Angle between the tangent AD and chord AC equal the angle in the alternate segment" or "Angle between the tangent AD and circle C2 and the chord equals the angle in the alternate segment"' the first one is OK to use, but I would avoid the second one...

Re: HSC 2016 3U Marathon You can just say ''alternate segment theorem''.

$If one did give the proof that there cannot exist two distinct rational points, wouldn't one be showing that $p_1 = p_2$ and $q_1 = q_2$? This would then make the equation quoted above say that $0=0$, and so there's no problem involving needing to know about the irrationality of $\pi+e$.$

Re: MX2 2015 Integration Marathon For Question (3), should there be limits on the integral for F(n)?