The 2012 STEP Results Discussion Thread

I feel addicted to all sorts of non-A-level related things, which reminds me that I have work to do.

Looks like there's a mistake on the TSR solution to STEP III 2004 Q5. Can anyone confirm?

http://www.thestudentroom.co.uk/showthread.php?t=828655&page=2&p=17914028#post17914028

His solution to part i) doesn't seem to work - $\frac{\pi}{2} - \omega$ doesn't seem right... according to my calculator at least

Show that [A] if and only if .
(Where A and B are statements)

To prove these type of questions, I usually show how [A] leads to , and then work backwards through the undertaken algebraic steps to show how leads back to [A], essentially repeating the method but in reverse... is this correct? How do you answer these type of questions?

My physics teachers are going to be so annoyed with me. I barely enjoy doing my A-levels maths work let alone opening a Physics textbook when I know there is a juicy STEP question to be hitting up. Anyone else feel addicted to STEP?

....

Show that [A] if and only if .
(Where A and B are statements)

To prove these type of questions, I usually show how [A] leads to , and then work backwards through the undertaken algebraic steps to show how leads back to [A], essentially repeating the method but in reverse... is this correct? How do you answer these type of questions?

It really depends. Say if it said prove x^4 + x^2 - 2 = 0 if and only if x^2 = 1, x being real.

Then I'd just factorise and show what would make it equal to zero. And say x^2 cannot equal -2.

Very simplistic example but yeah. Its definitely not necessary to go over everything both ways.

It really depends. Say if it said prove x^4 + x^2 - 2 = 0 if and only if x^2 = 1, x being real.

Then I'd just factorise and show what would make it equal to zero. And say x^2 cannot equal -2.

Very simplistic example but yeah. Its definitely not necessary to go over everything both ways.

I don't quite see how you've shown x^4 + x^2 - 2 = 0 if and only if x^2 = 1, x being real. You need to at least acknowledge the implication going in the other direction for it to be an iff.
As the Magic Man says, in STEP it's usually possible to just put $\iff$ without too much fallout (as long as you use common sense).

I have to put away the solution to the problem below, so before I forget I'm going to put up the solution spoilered because it is really nice

It seems to me like it is usually possible in STEP to just use double implications at every step

I feel the same, I'm worried that I spend too much time on STEP and as a result I will have difficulties with my school exams which are also very important...but so boring!

I guess it works out well that I took quite a few exams early and don't need much UMS in physics otherwise I would be very worried. Feel sorry for people without Jan exams...

Yeah, there's something wrong with $x=\dfrac{\pi}{2}-\omega$ although I haven't done the question/scrutinised the solution. The obvious reason being that $\cos x = 5+7\sin x$ and looking at the ranges of the LHS and RHS, we require $\sin x < -\dfrac{4}{7}$ for any hope of a solution i.e. $x$ must be greater than $\pi$.

Do you have a correct solution? If so feel free to post it up.

I don't have a correct solution (not one in terms of $\omega$ anyway), and his seems to make no sense! I'll try again tomorrow maybe.

EDIT: turns out giving up is a good motivator! One coming shortly I think...

In hindsight, I should have left it for you given that you had spotted it but I had half an hour free earlier so thought why not and posted one up here. I hope you don't mind - I did tag you in as credit for noticing the mistake.

That's fine, yours is way better than the one I had planned.

But for part (ii), did you solve the quadratic? Would it have been sufficient just to...

I did solve the quadratic. The only issue with your solution would be justifying the fact that there are only two values of $x$ which satisfy the quadratic in $\cos x$.