STEP Prep Thread 2016

I remember trying it last year, I hadn't quite grasped M1 properly yet, so that question was wasted on me, let me know how it goes!

Then you're miles better than I was last year! Without trying to put a dampener on things, the last few papers have got a bit harder, so it may be worth checking out, say, 2011.

Step 2 seems like a good idea if you can hack it, but it is a big step up (no pun intended). Again, it's been getting quite tough over the last few years.

Posted from TSR Mobile

I get that too. Just a geometric series in the end. What I found odd was that the parts of the question were worth 6 marks, 8 marks and 6 marks (respectively). This seemed strangely high to me. For part (a), did you consider conservation of angular momentum? It's not common to see a problem where the collisions happen in a circle, which I found quite interesting

Well, it's an A Level question, and it is quite extended, so it deserves the marks, I think.
I didn't use conservation of momentum, just conservation of linear momentum during the collisions. I didn't actually justify my calculations when I did them, but I've thought about it a little and I think it's alright. It's tricky because the speed of separation becomes the speed of approach, and, looking from the side, the direction A approaches changes from one collision to the next.

I remember trying it last year, I hadn't quite grasped M1 properly yet, so that question was wasted on me, let me know how it goes!

Just finished this question. It wasn't too bad; the method was identical to the one needed in the previous question. The sign changes with multiple collisions can be a little tricky, so this was good practice.

Anyone link me to the A level thread, I can't find it?

In any case, totally lost at:

Coefficient of X^3 in

(1+x+x^2)^5

Without expanding it all, it then goes on to ask for x^5, which I could work out after I know the general method.

I know it's something with the general term but I can't get it.


Posted from TSR Mobile

Good job! How did you manage to come across those old A-Level questions?

Hint: $1+x+x^2$ is the sum of the first three terms of a geometric series.

I found them online a while ago. I'll post some more up later.

Textbook hasn't covered them yet, in Binomial Theorem topic


Posted from TSR Mobile

Well, essentially you can write $1+x+x^2$ as $\displaystyle \frac{1-x^3}{1-x}$ so that you get

$\displaystyle (1+x+x^2)^5 = (1-x^3)^5(1-x)^{-5}$, can you take it from here? Use the general term of each binomial.

I like that, but the book says its to be done by

((X+1)+x^2)^5


Posted from TSR Mobile

Anyone link me to the A level thread, I can't find it?

In any case, totally lost at:

Coefficient of X^3 in

(1+x+x^2)^5

Without expanding it all, it then goes on to ask for x^5, which I could work out after I know the general method.

I know it's something with the general term but I can't get it.


Posted from TSR Mobile

Anyone link me to the A level thread, I can't find it?

In any case, totally lost at:

Coefficient of X^3 in

(1+x+x^2)^5

Without expanding it all, it then goes on to ask for x^5, which I could work out after I know the general method.

I know it's something with the general term but I can't get it.


Posted from TSR Mobile

Well, I suppose that could work, but it's a little longer.

You have:

$\displaystyle \sum_{k=0}^{5} {n \choose k} (x+1)^{n-k}x^{2k}$

It may help to write y = x + x^2. This then gives (1+y)^5, which has the well-known series expansion 1 + 5y + 10y^2 + 10y^3 + 5y^4 + y^5. Then look at the different ways you can make up an x^3 term.

One approach