If you're having a go at the assignments but fancy a break, why not take a look at this video of a talk given by Dr Vicky Neale?

How do you neatly find the root of the equation for part 4)b)?

Can I give an age for the minister that I can guarantee will be above the second oldest member of the group? I have a list of ages for the other people and a range of values for the minister, so without knowing which list is correct can I just give an age from the smallest range? Or is there any way to narrow down my lists and find an exact age for the minister?

Hello,
I've been having a go at this question however can't get the first D.E out. I started off by saying $m(\frac {d^2y}{dt^2}) = m(g-f) - \frac {\lambda (a + y)}{l}$, with $\frac{\lambda a}{l}=mg$, however I'm not certain I've put $f$ in the right place? Even so when I expand the above I get very close to the answer except I'm missing the $g$ term. So i was wondering whether the question meant $y$ is the extension of the elastic band from it's natural length instead of equilibrium length, as this would make my equation work out?

For the last part,

I let $ T(x) = t(tan x) $ and I showed that $T(x) + T(y) = T(x+y) $

hence using the first part I concluded $ T(x) = Ax = t(tanx) $

to work out $t(u)$ I let $u=tanx$ and hence $x = arctanu + n\pi$

therefore $t(u) = Ax = A (arctan u +n\pi)$

But the solutions say $t(u) = A arctan u$ - to find the most general solution don't you need to add on the $n\pi$ ?

I would be grateful for a quick reply since the STEP exams are this week.

Thanks for all the help so far

I am sorry if this is off topics but as an old user of Ask Nrich I have recently discovered this forum and was wondering if, as well as STEP and MAT, this forum could be used to discuss BMO2 problems as well?

Thanks,

tridianprime

(June 15th 2015)
So anxious about having to take STEP 1!

I was able to find the general solution for $y_n $ in terms of $ \theta $:

$y_{n}(\theta)=A\cos n\theta+B\sin n\theta $

using the condition y(0) = 1 I found that A=1

However, I am not able to find the value of B by using the second condition - I have looked at the TSR solutions but I do not understand them.

The official STEP hints and solutions state $ cos (n(\theta + \pi)) = (-1)^{-n} cos (n\theta) $ - how does this help when you are actually substituting in $\theta = cos^{-1} x $ ?

Can you quote formulas from the formula book in STEP? E.g the section titled coordinate geometry in the formula book has useful formulas – in STEP 3 2014 Q3 you could use the perpendicular distance from point to line

Do you get penalised for bad notation? E.g. putting a single implication instead of a double implication

For part (i) I solution I have tried the following. Let $N$ be the number of balls drawn before and including the last white ball drawn. Using the hyper geometric distribution:

\[ P(N \leq n) = \frac{\binom{w}{w} \binom{b}{n-w}}{\binom{b+w}{n}} \]

Which simplifies to:

\[ P(N \leq n) = \frac{b! \times n!}{(b+w)! \times (n-w)!} \]

Also
\[ P(N = n) = P(N \leq n) - P(N \leq n-1) \]
\[ \therefore P(N = n) = \frac{b! \times n!}{(b+w)! \times (n-w)!} - \frac{b! \times (n-1)!}{(b+w)! \times (n-1-w)!} \]