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# STEP III 2012 Discussion Thread Tweet

Maths exam discussion - share revision tips in preparation for GCSE, A Level and other maths exams and discuss how they went afterwards.

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1. Re: STEP III 2012 Discussion Thread
(Original post by DFranklin)
Re Q2 being a gift; I got stuck for a long time on the start of (ii) thinking "I can't see how to get this from part (i)" before deciding there was no option but to try a similar argument to part (i).

To be fair, I hadn't actually bothered doing (i) because I could see how it worked, so I was thinking "they can't expect you to do that much work again". If I'd actually done it, I'd probably have realised that that was what they expected.

Meta: I guess it just stuck in my mind as a question where I got stuck because I was convinced the examiner couldn't mean you to do X, rather than because I couldn't actually do X!
I learnt a long time ago that you have to do STEP questions in the order intended, otherwise it's hard to spot the 'trick'!

Doing all (i), which isn't really that long at all makes it very obvious you had to do the same thing with another function. Its not like the algebra is hard in either part so its quick to confirm that the same method works.

I think you raise a very interesting point about a stumbling block in STEP questions, which is it's easy to become convinced that an examiner can't possibly be asking you do to X (when in reality they wanted X all along). I did it in 2012 STEP II Q2 - I was getting bored so didn't check my 'solutions' were all valid.

- I think someone's said they've done Q10
- I'm going to have to dig out my actuarial notes from that course over the weekend anyway so I'll be able to check whether the algebra is that bad. I remember it being long rather than complicated though...
2. Re: STEP III 2012 Discussion Thread
hey guys, did you all find STEP III incredibly hard when you first looked at it?
What would be the best strategy for a new-timer?
Many Thanks
3. Re: STEP III 2012 Discussion Thread
(Original post by jukebox123)
hey guys, did you all find STEP III incredibly hard when you first looked at it?
What would be the best strategy for a new-timer?
Many Thanks

Then the only thing you can do is to work through past papers. If you plan on applying to Cambridge and taking STEP be careful to save the latest papers (i.e. 2010, 2011, 2012) as mocks before the exam!
4. Re: STEP III 2012 Discussion Thread
(Original post by Lord of the Flies)

Then the only thing you can do is to work through past papers. If you plan on applying to Cambridge and taking STEP be careful to save the latest papers (i.e. 2010, 2011, 2012) as mocks before the exam!
What should I do if I get completely stuck on a question for like 3 hours?
5. Re: STEP III 2012 Discussion Thread
(Original post by jukebox123)
What should I do if I get completely stuck on a question for like 3 hours?
Don't worry about it. By all means don't go and take a peek at the solution if you get stuck. You are most likely to get a bit stuck on most of the questions at some point anyway (even during the exam): they are designed to take 45 minutes after all... You'll find that, with time and practice, the papers will seem less and less difficult (I don't want to say more and more easy...), and you will be able to complete STEP questions in a reasonable amount of time if you have some mathematical ability (which you will if Cambridge give you an offer).

I would suggest starting with STEP I papers since they are a bit easier than II and III.
6. Re: STEP III 2012 Discussion Thread
(Original post by Lord of the Flies)
Don't worry about it. By all means don't go and take a peek at the solution if you get stuck. You are most likely to get a bit stuck on most of the questions at some point anyway (even during the exam): they are designed to take 45 minutes after all... You'll find that, with time and practice, the papers will seem less and less difficult (I don't want to say more and more easy...), and you will be able to complete STEP questions in a reasonable amount of time if you have some mathematical ability (which you will if Cambridge give you an offer).

I would suggest starting with STEP I papers since they are a bit easier than II and III.
which papers did you sit, and what do you think you achieved in them?
7. Re: STEP III 2012 Discussion Thread
(Original post by jukebox123)
which papers did you sit, and what do you think you achieved in them?
I sat STEP I as a practice run this year (haven't applied to university yet). Didn't go as well as expected but it was alright - the paper was particularly dull too!
8. Re: STEP III 2012 Discussion Thread
(Original post by Lord of the Flies)
Solution to the second part of Question 3 (couldn't be bothered to the first part which only consists of sketches )
the sketches are tricky though. i think i would have been close to 120,120 were it not for failing to understand how 2 parobolas can touch in situation (d)

these 2 curves touch at x=1 and then cross at x=SQRT(6)-1 (about 1.45)

but i thought there was no touching point for (d) k>16, k/m<2 and said so on my sketch. Then in the last part i claimed that a could only take the negative value, since the other 2 possibilities gave case (d) and should be rejected
9. Re: STEP III 2012 Discussion Thread
(Original post by Lord of the Flies)
I sat STEP I as a practice run this year (haven't applied to university yet). Didn't go as well as expected but it was alright - the paper was particularly dull too!
yeah i sat it too...got 2 full solutions, 2 halfs and 2 partials...could've done better if i had prepared at least bit :/
I did near to no prep for it
10. Re: STEP III 2012 Discussion Thread
(Original post by jukebox123)
yeah i sat it too...got 2 full solutions, 2 halfs and 2 partials...could've done better if i had prepared at least bit :/
I did near to no prep for it
Yes, I barely remember what I did. I sort of panicked when I saw the overwhelming number of similar calculus-based questions (not my strong point for sure). How could they omit diophantine equations!
11. Re: STEP III 2012 Discussion Thread
(Original post by Lord of the Flies)
Yes, I barely remember what I did. I sort of panicked when I saw the overwhelming number of similar calculus-based questions (not my strong point for sure). How could they omit diophantine equations!
What do you think the boundaries will be?
12. Re: STEP III 2012 Discussion Thread
(Original post by shamika)
No, it's not. However arguably there were lots of other questions that were accessible on the paper so it's not a real loss. Another argument is that question choice is important in STEP - and it's not like that is a secret - so the smart thing to do is to move on to another question; in this scenario they may be able to justify not making many adjustments at all...

Before everyone gets the pitchforks out, it sounds like a lot of you did well. It may be possible to make equitable adjustments so no one is adversely affected. The wait may seem long but lets see what happens on results day. Hopefully no one will need further advice and you're all celebrating getting into the universities you want.
to your edit.....yh but this is question 1! If it was any other question what you said would make sense. I aint that bothered now.....busy moving on road
13. Re: STEP III 2012 Discussion Thread
Saw the paper so thought I'd have a go at typing a solution that is yet to be done. However, running out of battery so here is the first part of 6 - the following two parts seem to follow exactly the same method, but I haven't attempted them properly yet. Looks like it was a decent paper though.

Spoiler:
Show

Unparseable or potentially dangerous latex formula. Error 5: Image dimensions are out of bounds: 461x1054
Let $f(z) = z^2+pz+1$, then

\begin{align*}

f(x+iy) &= (x+iy)^2 + p(x+iy)+1

\\ &= x^2 + 2xyi - y^2 + px + pyi + 1

\\ &= x^2 - y^2 + px + 1 + (2xy+py)i = 0

\end{align*}

So we must have

\begin{align*}

x^2 - y^2 + px + 1 = 0 \mathrm{and} (2x+p)y = 0

\end{align*}

\\

\\

From the second condition above we must have either

\begin{align*}

p = -2x \mathrm{or} y=0

\end{align*}

Substituting $y=0$ into our first condition gives

\begin{align*}

x^2 + px + 1 &= 0

\\ p &= -\frac{x^2+1}{x}, x \neq 0

\end{align*}

\\

Now using the conditions on $p$, we get

\begin{align*}

x^2 - y^2 -2x^2 + 1 &= 0

\\ x^2 + y^2 &= 1

\end{align*}

and

\begin{align*}

x^2 - y^2 -x^2 -1 + 1 &= 0

\\ y^2 &= 0 \; \mathrm{\;and so\;} y=0

\end{align*}

Last edited by miml; 30-06-2012 at 00:21.
14. Re: STEP III 2012 Discussion Thread
(Original post by MrDD)
the sketches are tricky though. i think i would have been close to 120,120 were it not for failing to understand how 2 parobolas can touch in situation (d)

these 2 curves touch at x=1 and then cross at x=SQRT(6)-1 (about 1.45)

but i thought there was no touching point for (d) k>16, k/m<2 and said so on my sketch. Then in the last part i claimed that a could only take the negative value, since the other 2 possibilities gave case (d) and should be rejected
Yes they are a bit tricky. I uploaded them too now!
15. Re: STEP III 2012 Discussion Thread
(Original post by BabyMaths)
Q4 part i

All the required results can be put together from these pieces. The final result being
While I agree with all your sigmas should'nt the last result be 22e-1 cos when I cube 2n-1 I get 8n^3-12n^2+6n-1
16. Re: STEP III 2012 Discussion Thread
(Original post by mikelbird)
While I agree with all your sigmas should'nt the last result be 22e-1 cos when I cube 2n-1 I get 8n^3-12n^2+6n-1
The adding up at the end was the hardest part of the question.

Do you agree with my signature?
17. Re: STEP III 2012 Discussion Thread
my attempt at question 6
Attached Files
18. Step2012Paper3Question6.pdf (75.7 KB, 142 views)
19. Re: STEP III 2012 Discussion Thread
(Original post by DFranklin)
Given the nature of the mistake, I don't think this would be a fair solution. It may be what they end up doing nonetheless, of course.

It's very very hard to undo the can of worms once you've opened it - I don't think there's a particularly equitable solution here.
i agree there probably isn't a perfectly fair solution, but it is certainly interesting to speculate what the least unfair solution is.

one solution might be to take candidates 5 best solutions from questions 2-13 and multiply total by 1.2

anyone got any better ideas?
20. Re: STEP III 2012 Discussion Thread
(Original post by BabyMaths)
The adding up at the end was the hardest part of the question.

Do you agree with my signature?
I realised my mistake as I was typing this....I thought I backed out of it...clearly i did'nt!!!
21. Re: STEP III 2012 Discussion Thread
It really is difficult to know what to do about question 1. I'm fairly certain that if all the information was given for the question I'd have been able to complete it rather than attempt question 5 which I got stuck on at ii) B) and C). Thankfully I'm confident I've got a grade 1, but for anyone on the borderline of a grade 1 who cautiously did not attempt question 1, I think it would be unfair to give too many extra marks for those who did attempt the queston when those who didn't may have attempted it if there was some clarification as to what z was, and as a result got a critical few more marks to be comfortably over the grade 1 boundary
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