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Re: International Baccalaureate Marathon 2016 $\noindent If the speed travelled at is $v$, then the time taken is distance divided by speed, i.e. $\frac{50}{v}$. So the total cost (in terms of litres of fuel used) of the journey is the time multiplied by the rate of fuel usage, so it is $C =...

Why don't we have both? :cool: http://mathworld.wolfram.com/StandardNormalDistribution.html

It's (up to the inclusion of scale and location parameters) the equation of the famous "bell curve" that you often hear people talking about (as leehuan has alluded to above). I'm guessing when you said you don't 'get' it, you meant like you don't see why that one was there, because it's not...

Which doesn't work out?

$\noindent Have you tried using inverse square law? According to this law,$ $\noindent $I \equiv I\left(d\right) \propto \frac{1}{d^2}$,$ $\noindent where $I$ is the intensity in ($\text{W m}^{-2}$ here) and $d$ is the distance (in metres here).$ $\noindent We are given that $I(5) =...

The textbooks sometimes don't really go through the definition of cos and sin (I do think they are in the Year 11 3U Pender (Cambridge) Textbook though, so check that out if you have it). For HSC purposes, for a real number t, cos(t) and sin(t) are defined as follows: Draw the unit circle in...

By definition of cos and sin.

Re: HSC 2016 4U Marathon - Advanced Level I think you made a silly mistake in the computation of the integral at the end. (Also, we'd expect the final answer to only involve cubic terms in a as it's a volume. We can also see by inspection that the integral will result in only cubic terms in a.)

That's really good – averaging 100 means getting all 100's. :)

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread $\noindent Note $AD = AB = x$ (sides of isosceles triangle $BDA$, which is isosceles as it is similar to isosceles triangle $ABC$). You should be able to show from easy angle-chasing that $\triangle ADC$ is isosceles with...

Re: HSC 2016 2U Marathon NEW QUESTION $\noindent Suppose that a sequence of real numbers is both an A.P. and a G.P. Show that the sequence is a constant sequence.$

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread The area is positive. The signed area (which is the integral over that interval of the function) is negative. What is the question's wording?

Re: HSC 2016 4U Marathon $\noindent Draw a diagram with the fixed point $P$ $0.5$ m above the table, the mass on the table, and a string connecting the point and the mass. Note that the string is $1$ m in length, so using trigonometry, we can find all angles in the right-angled triangle formed...

English always counts to your ATAR. The rule is that your two best English units must count. Therefore, yes, English does matter (a lot).

No, that's irrelevant. E.g. The function g(x) = -e-x is increasing, yet always negative.

$\noindent Here's how to differentiate that function (I assume you know the quotient rule and how to differentiate exponentials). Let $f(x) =\frac{e^x}{1+e^x}$. Then $f^\prime (x) =\frac{e^x \left(1+e^x\right) - e^x \cdot e^x}{e^{2x}}$.$ Then just simplify that.

Which part are you referring to for this? The range? That's not sufficient to get the range.

That is the chain rule.

Well differentiating that is still just using the quotient rule. Have you tried using the quotient rule?

Yes, and show and state that they're of opposite sign.