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The 2012 STEP Results 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: The 2012 STEP Prep Thread!
(Original post by shamika)
One thing that is tangentially related to this is how mechanics questions are answered. There's two things from examiners reports that really baffle me:

- people aren't drawing (complete) diagrams as a matter of course
- people use a principle without stating it (I would clearly write down even 'using conservation of energy' or 'resolving forces tangentially to plane' since it makes it so much easier to see what you're doing if it unfortunately goes wrong).
Agreed on both. On TSR things get a bit 'biased' away from drawing diagrams because it's not really practical to do diagrams in LaTeX, but I would pretty much always draw a diagram in an actual exam (possibly not for a MofI type question where it's basically all about the integration).
2. Re: The 2012 STEP Prep Thread!
I just emailed stepinfo@cambridgeassessment.org .uk, confirming that we're allowed to do the exam in pencil.

She said no. Answers must be written in black or ball point pen.

I feel so heartbroken.
3. Re: The 2012 STEP Prep Thread!
(Original post by Ree69)
I just emailed stepinfo@cambridgeassessment.org .uk, confirming that we're allowed to do the exam in pencil.

She said no. Answers must be written in black or ball point pen.

I feel so heartbroken.
I hate pens. My pencil case consists of 5 HB Pencils, and a mechanical Parker pencil. 3 Hours with a pen, fml. *_*
4. Re: The 2012 STEP Prep Thread!
(Original post by Ree69)
OCR. I got battered by my teacher for writing stuff like:

Not only was I too lazy to write words (or even connectives/implication symbols), but it would've been incorrect unless I worded it very carefully.

So now I've become very careful when trying to introduce equality symbols in equations that have inequality symbols (which are meant to be solved). In all honesty though, I do find it a lot easier when doing so - especially for complicated inequalities.
Examiners' reports note that students don't like inequalities. Which is a shame because the logic you are following is nearly right. Just remember what you can and cannot do to an inequality and your method of 'critical values' is OK.
5. Re: The 2012 STEP Prep Thread!
Hello, sorry to jump in on this thread with a question.

I am currently in Year 11, and love Maths I am taking Maths and Further Maths at College, and aspire to study Maths at Cambridge. So it looks like I'm definitely going to encounter STEP Papers at some point.

Is there anything that I can do during college to prepare me for STEP papers? I want to be as prepared at possible, and I'm wondering if any of you could offer some tips? Or offer ideas that you wish you'd done to improve preparation?

Good luck with your STEP Papers!!
6. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Hello, sorry to jump in on this thread with a question.

I am currently in Year 11, and love Maths I am taking Maths and Further Maths at College, and aspire to study Maths at Cambridge. So it looks like I'm definitely going to encounter STEP Papers at some point.

Is there anything that I can do during college to prepare me for STEP papers? I want to be as prepared at possible, and I'm wondering if any of you could offer some tips? Or offer ideas that you wish you'd done to improve preparation?

Good luck with your STEP Papers!!
STEP papers need fluency with A level techniques and a high level of problem-solving. If you're starting early, I suggest you concentrate on problem-solving rather than trying to learn all the A level stuff early.

To show what I mean:

"Show n^3 - 7n + 3 is a multiple of 3 for all integers n"

A reasonable FM A level student would prove this by induction - an easy example. But a good Y11 student might reasonably find one of the two methods that do not depend on A level knowledge. Searching for that method even if it does not come easily builds the muscles that will be needed for STEP.

You could look at UKMT mentoring problem sheets for examples.
7. Re: The 2012 STEP Prep Thread!
(Original post by ian.slater)
STEP papers need fluency with A level techniques and a high level of problem-solving. If you're starting early, I suggest you concentrate on problem-solving rather than trying to learn all the A level stuff early.

To show what I mean:

"Show n^3 - 7n + 3 is a multiple of 3 for all integers n"

A reasonable FM A level student would prove this by induction - an easy example. But a good Y11 student might reasonably find one of the two methods that do not depend on A level knowledge. Searching for that method even if it does not come easily builds the muscles that will be needed for STEP.

You could look at UKMT mentoring problem sheets for examples.
That approach isn't necessarily open to everybody though. Having never completed a number theory/olympiad question like that in my life I think doing those sorts of problems would have put me off maths.
8. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Hello, sorry to jump in on this thread with a question.

I am currently in Year 11, and love Maths I am taking Maths and Further Maths at College, and aspire to study Maths at Cambridge. So it looks like I'm definitely going to encounter STEP Papers at some point.

Is there anything that I can do during college to prepare me for STEP papers? I want to be as prepared at possible, and I'm wondering if any of you could offer some tips? Or offer ideas that you wish you'd done to improve preparation?

Good luck with your STEP Papers!!
Practice STEP?
If you want to start now, I think your best bet is intermediate mentoring scheme, to boost you problem solving ability and improve your algebra skills. Assuming GCSE stuff is easy for you.

Again,
"Show n^3 - 7n + 3 is a multiple of 3 for all integers n"
Most of FM students would probably use induction, but modular arithmetic would save your time. They use this things on their schemes.
9. Re: The 2012 STEP Prep Thread!
(Original post by Dog4444)
Practice STEP?
If you want to start now, I think your best bet is intermediate mentoring scheme, to boost you problem solving ability and improve your algebra skills. Assuming GCSE stuff is easy for you.

Again,
"Show n^3 - 7n + 3 is a multiple of 3 for all integers n"
Most of FM students would probably use induction, but modular arithmetic would save your time. They use this things on their schemes.
Well I did my Maths GCSE last year, and yes, I found it very easy.. I am currently studying for the FSMQ, which covers a lot of C1&2, which introduces some new things, but is also quite easy..

How would I go about proving that n^3 - 7n + 3 is a multiple of 3 for all integers of n?
10. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Well I did my Maths GCSE last year, and yes, I found it very easy.. I am currently studying for the FSMQ, which covers a lot of C1&2, which introduces some new things, but is also quite easy..

How would I go about proving that n^3 - 7n + 3 is a multiple of 3 for all integers of n?
Assuming knowledge of the concept behind the method:
Induction way - let x_n = n^3 - 7n + 3. x_0 is a multiple of 3, then assume x_n is a multiple of 3, then write x_n+1 in terms of x_n and you should get x_n+1 = x_n + 3k for some integer k.

Modular arithmetic way - look at all the possible values of n^3 modulo 3, 7n modulo 3 then put it all together to get n^3 -7n + 3 = 0 modulo 3 always.
11. Re: The 2012 STEP Prep Thread!
(Original post by matt2k8)
Assuming knowledge of the concept behind the method:
Induction way - let x_n = n^3 - 7n + 3. x_0 is a multiple of 3, then assume x_n is a multiple of 3, then write x_n+1 in terms of x_n and you should get x_n+1 = x_n + 3k for some integer k.

Modular arithmetic way - look at all the possible values of n^3 modulo 3, 7n modulo 3 then put it all together to get n^3 -7n + 3 = 0 modulo 3 always.
I would think that ian.slater suggested the most basic of methods, which is indeed also nice.
Observe that if was a multiple of three, then you're done. However, what happens if it was not?
Last edited by gff; 04-04-2012 at 22:31.
12. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Well I did my Maths GCSE last year, and yes, I found it very easy.. I am currently studying for the FSMQ, which covers a lot of C1&2, which introduces some new things, but is also quite easy..

How would I go about proving that n^3 - 7n + 3 is a multiple of 3 for all integers of n?
If it has a lot of C1,2 you can try MAT papers, it assumes AS maths knowledge only.
How would you prove it? You tell me! Prove by induction is on the STEP1/2/3 syllabus, and it's covered (as far as I'm concerned) in FM only. So, it might be a good idea to learn it now (despite being in FM, it shouldn't be a problem, if you're good (what you seems to be).)
13. Re: The 2012 STEP Prep Thread!
(Original post by Dog4444)
If it has a lot of C1,2 you can try MAT papers, it assumes AS maths knowledge only.
How would you prove it? You tell me! Prove by induction is on the STEP1/2/3 syllabus, and it's covered (as far as I'm concerned) in FM only. So, it might be a good idea to learn it now (despite being in FM, it shouldn't be a problem, if you're good (what you seems to be).)
I'll check out some MAT Papers. I've tried some of the UKMT Papers, and I find them really fun and interesting! I've never entered officially, but my Maths teacher made me sit one in lesson, and I acquired enough points to qualify for the BMO he said.. So I think I will enter next time round.

I've been having a look at some induction examples, and it doesn't look too difficult when you compare to some of the other FM topics! I'll try and begin to teach it myself tomorrow after I've finished revising...
14. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
I'll check out some
I've been having a look at some induction examples, and it doesn't look too difficult when you compare to some of the other FM topics! I'll try and begin to teach it myself tomorrow after I've finished revising...
Depends on what you're trying to prove.
15. Re: The 2012 STEP Prep Thread!
Depends on what you're trying to prove.
Well yes, I suppose. I can't imagine I'm going to fully understand the more difficult concepts. But I'll have a go at understanding the basics.

Just out of curiosity, how do you all find A-Level Further Maths when compared to A-Level Maths?
16. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Just out of curiosity, how do you all find A-Level Further Maths when compared to A-Level Maths?
Not all that different.
17. Re: The 2012 STEP Prep Thread!
I was also curious, does STEP3 include all of FP1,2,3 material? If so, would it be a good idea to go through FP3 in summer?
18. Re: The 2012 STEP Prep Thread!
(Original post by Dog4444)
I was also curious, does STEP3 include all of FP1,2,3 material? If so, would it be a good idea to go through FP3 in summer?
I will also need to know this eventually, as at my college, we only do FP1&3. So I would have to self teach FP2.
19. Re: The 2012 STEP Prep Thread!
(Original post by CharlieBoardman)
Well I did my Maths GCSE last year, and yes, I found it very easy.. I am currently studying for the FSMQ, which covers a lot of C1&2, which introduces some new things, but is also quite easy..

How would I go about proving that n^3 - 7n + 3 is a multiple of 3 for all integers of n?
Sadly you've been given one of the methods already. If you are given a problem like this, a good way to start is to check that it works for small cases of n. And then you try to look for why it's true. Is there some pattern? Then you try to turn the pattern into a proof.

You are probably already familiar with two kinds of maths problem - those you know how to do and those you don't. There is a third kind - those you can figure out how to do if you work on them for long enough.

There is a more direct method than modular arithmetic.
20. Re: The 2012 STEP Prep Thread!
(Original post by Dog4444)
I was also curious, does STEP3 include all of FP1,2,3 material? If so, would it be a good idea to go through FP3 in summer?
I would practically say that none of the STEP III questions rely heavily on knowing anything from OCR MEI's FP3, with the exception of basic vectors. It is useful, however.