Is this case of D.E. included in the current SIII especification??

If so, how is it solved?

After differentiating the given expression and equating gradients I get four equations for a, b and n, which don't make sense altogether. Should I try to modify in some way the fraction of the D.E.?

Is using projective, inversive and advanced Euclidean geometry allowed on STEP? An example of what I mean:

10 S3 Q5
The vertices $A$, $B$, $C$ and $D$ of a square have coordinates $(0,0)$, $(a,0)$, $(a,a)$ and $(0,a)$, respectively. The points $P$ and $Q$ have coordinates $(an,0)$ and $(0,am)$ respectively, where $ 0 < m < n < 1$. The line $CP$ produced meets $DA$ produced at $R$ and the line $CQ$ produced meets $BA$ produced at $S$. The line $PQ$ produced meets the line $RS$ produced at $T$. Show that $TA$ is perpendicular to $AC$.

I have a basic understanding that the discs should both experience a force towards the centre of the line of centres. For a collision to occur, the initial elastic energy must be greater than the work done against friction to reach the centre.

The solution to this question is not given on the solutions sheet and I'm stuck. Letting the initial direction of travel of B be positive, I have -3mu=2mv_1+mv_2, where v_1 and v_2 are the velocities of A and B respectively, using conservation of momentum. I also have (v_1+v_2)/-u = e, which leads to v_1=(e-3)u and v_2=(3-2e)u. The problem is that I'm certain v_2 should be negative. But to reiterate my main point, the sheet gives no answers for this question

Hello,

I've only recently discovered STEP, and I'm somewhat surprised by the difficulty of some questions, given that they are designed for A level students.

The STEP III Statistics module has now been published here.

We are hoping to publish another 2 or 3 STEP III modules before the end of May.

Good luck with the exam prep!

The first part of the problem asks us to prove that
\[ \lvert e^{i\beta}-e^{i\alpha}\rvert = 2\sin\frac12(\beta-\alpha), \]
but as far as I can see, we have the identity
\[ 2\sin\frac12(\beta-\alpha) = \frac{e^{i\beta}-e^{i\alpha}}{ie^{i\frac12(\alpha+\beta)}}, \]
and the denominator of the RHS is generally not equal to $\pm 1$. Are we supposed to prove that the magnitude of the complex number $e^{i\beta}-e^{i\alpha}$ is equal to the RHS in the first equation instead?

I've been trying to get my head around the problem of the particle sliding down a moving wedge. I managed to get the required expression by using a pseudo force of $mA$ acting on the particle in the opposite direction to the motion of the wedge (where $A$ is the acceleration of the wedge), and then doing a horizontal force balance on both particle and wedge.

I'm looking at the ATS solutions

It says: "Now we can sum our series, it is: " ...

But I'm not sure how you get from the 2nd line to the third?

Thanks in advance!