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# STEP maths I, II, III 1991 solutions Tweet

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1. Re: STEP maths I, II, III 1991 solutions
(Original post by DFranklin)
I think it comes out if you look at the real part of .
This type of trigonometric series came up again in the 1990 III paper, I encountered this example before in an outdated OCR maths textbook, so maybe it used to be in the syllabus? You then use a little trick to extract the real part if you don't know already.
2. Re: STEP maths I, II, III 1991 solutions
(Original post by khaixiang)
This type of trigonometric series came up again in the 1990 III paper, I encountered this example before in an outdated OCR maths textbook, so maybe it used to be in the syllabus? You then use a little trick to extract the real part if you don't know already.
Quickest way I see of getting the real part is to "assume the answer". i.e. show that . Which is very short, but a bit of a leap if you don't know it already.

Is there a way of finding this without too much work?
3. Re: STEP maths I, II, III 1991 solutions
(Original post by DFranklin)
Quickest way I see of getting the real part is to "assume the answer". i.e. show that . Which is very short, but a bit of a leap if you don't know it already.

Is there a way of finding this without too much work?
I've learnt from the old STEP booklet that they usually do the following factorisation, it can be very useful at times like this.

4. Re: STEP maths I, II, III 1991 solutions
(Original post by khaixiang)
I've learnt from the old STEP booklet that they usually do the following factorisation, it can be very useful at times like this.

Neat. I've been wondering: does it make sense to start a "useful tricks for STEP / AEA" thread? There are a few things like this that do seem to come up a lot.
5. Re: STEP maths I, II, III 1991 solutions
Khai, I don't quite understand the significance of that factorisation
Care to explain a little? I just woke up.... xD

Oh, that complex expansion works.
And (1+cos2T+isin2T)=(2cos²T+2isinT cosT) which is a one line proof! Thanks again.

(Original post by Franklin)
I've been wondering: does it make sense to start a "useful tricks for STEP / AEA" thread? There are a few things like this that do seem to come up a lot.
I would so benefit from that. I was sort of hoping there would be one around, but...no such luck.
I wonder how much one could really put in though, since STEP questions tend to be more or less unique. (Or do they?)
Last edited by Rabite; 05-06-2007 at 12:24.
6. Re: STEP maths I, II, III 1991 solutions
(Original post by Rabite)
I would so benefit from that. I was sort of hoping there would be one around, but...no such luck.
I wonder how much one could really put in though, since STEP questions tend to be more or less unique. (Or do they?)
I'm not sure how many formula you can give "exactly" (although if I were doing STEP, I think I would memorise the solutions to and ). But I think you can show enough "nice tricks" that (hopefully) in the exam you can think "I've seen something a bit like this before".

(In some senses, it's not that different from the solutions threads, but I think there are a lot of questions that really are "one-off" ideas that won't be repeated and so the stuff you really ought to make note of can get missed).
7. Re: STEP maths I, II, III 1991 solutions
(Original post by Rabite)
Khai, I don't quite understand the significance of that factorisation
Care to explain a little? I just woke up.... xD

Oh, that complex expansion works.
And (1+cos2T+isin2T)=(2cos²T+2isinT cosT) which is a one line proof! Thanks again.
For III/8 second part:

For the case of you can do similiar factorisation, which simplifies the algebra considerably.

This trick seems to be used quite often in the solutions provided by Siklos
8. Re: STEP maths I, II, III 1991 solutions
Ah hah, thanks for that. *sigh* I feel like I should be getting these things by now. :/

As for that little trick, I'll be hoping that they ask us to sum now
9. Re: STEP maths I, II, III 1991 solutions
(Original post by DFranklin)
Neat. I've been wondering: does it make sense to start a "useful tricks for STEP / AEA" thread? There are a few things like this that do seem to come up a lot.
I think it might, if you have any useful tricks. I've never seen many, but maybe that's just me...
10. Re: STEP maths I, II, III 1991 solutions
Are there a set of solutions for the STEP II specimen paper available online?
http://math.*you-can-guess-what-goes...I%20Sample.pdf
11. Re: STEP maths I, II, III 1991 solutions
(Original post by Speleo)
Are there a set of solutions for the STEP II specimen paper available online?
http://math.*you-can-guess-what-goes...I%20Sample.pdf
All the questions in this specimen paper are from real STEP II papers around 2000, 2001 and 2002. (or maybe you know this already?) So you can find the solutions in meikleriggs.
12. Re: STEP maths I, II, III 1991 solutions
Really? I only recognise a couple of them, which I assumed were from the Siklos book. Thanks
13. Re: STEP maths I, II, III 1991 solutions
(Original post by Speleo)
Really? I only recognise a couple of them, which I assumed were from the Siklos book. Thanks
LOL, after checking through, the specimen paper is STEP II 2002.
14. Re: STEP maths I, II, III 1991 solutions
So it is
Must have only glanced at that paper before (would explain why I hadn't done them but recognised a couple...).

That paper is very, very easy btw (got enough marks for an S with one hour's work unless my marking is very far out ), but the grade boundaries are as usual, must be because it's the first year of the specification
15. Re: STEP maths I, II, III 1991 solutions
III/6

God, this one took ages to type out.
No one's even gonna read it, but hey...

Could someone else at least try the question to see what the real answer is?
Attached Thumbnails

Attached Files
16. 1991 Q6.pdf (46.7 KB, 106 views)
17. Last edited by Rabite; 06-06-2007 at 02:06.
18. Re: STEP maths I, II, III 1991 solutions
(Original post by Rabite)
Could someone else at least try the question to see what the real answer is?
I've skimmed what you've done and I don't see a problem; the question seems a bit long and unpleasant, but in my experience every STEP question mentioning a hyperbolic function turns out to be a bit long and unpleasant! Any particular reason you think you didn't get the right answer?
19. Re: STEP maths I, II, III 1991 solutions
I've just never done a question with transformations before, and for some reason, I have this belief instilled in me that if a solution takes a ridiculous amount of algebra and multiple abbreviations, I'm probably doing it the wrong way
That's all though.
20. Re: STEP maths I, II, III 1991 solutions
(Original post by Rabite)
I've just never done a question with transformations before, and for some reason, I have this belief instilled in me that if a solution takes a ridiculous amount of algebra and multiple abbreviations, I'm probably doing it the wrong way
That's all though.
The thing is, I've never really had solutions other than ones I've done myself to compare to. So possibly there are some nice tricks I'm just not seeing. But in my experience, if a question involves conic sections, change of coordinates or hyperbolic functions, it will tend to be long and heavy on the algebra. As this Q had all 3 of those, I didn't think your answer was longer or more complicated than I'd expect.

In practical terms, this is the kind of question I'd look at, think "I don't see me getting that out in a hurry" and move on to something else. Of course, sometimes you have to pick the best question of a bad lot...
21. Re: STEP maths I, II, III 1991 solutions
I wouldn't have attempted it in an exam...
Also, is it too soon to start a 1990 thread? Or is there one...? I ran a search, but nothing came up, so I'm gussing not.
Then again, there are a lot of questions missing here.

I have mechanics phobia, so I won't be doing many more questions in this thread anyway, hehe...
22. Re: STEP maths I, II, III 1991 solutions
You are welcome to start a 1990 thread, at this stage we are doing the questions mostly for our own benefit, so it doesn't really matter if one or two are missing from each paper.