How should I go about preparing for the STEP Maths exam?

Original post by vnayak

I applied for Computer Science at Cambridge (rejection), Imperial (offer), Durham (still waiting on decision), Edinburgh (offer) and Manchester (offer).

Three days ago, I received an offer from Imperial at their standard requirements which I was chuffed about because it is the lowest requirements I can get since I am not eligible for contextual offers.

The A level requirement is A*AAA, which shouldn't be too much of a problem. I am predicted 5 A*s in Maths, Further Maths, CS, Chemistry and EPQ.

The bit of the offer I am worried about is the STEP condition. I have to attain a grade 2 in STEP II.

How should I go about preparing for the STEP? Any advice would be useful. I did some STEP I stuff as practice and I'm getting 4-5 questions right but I am worried about STEP II because obviously, it is going to be a huge step up (no pun intended). Any tips for the paper would also be much appreciated (e.g. sections I should avoid save time and sections I should focus on). Any links that would help in preparation for this paper would also be much appreciated.

I presume youve gone through the step 2 modules
https://maths.org/step/assignments-stepii
as they give some decent topic notes/exemplar questions with hints etc. If so, there isnt really a reason you couldnt have a decent attempt at past papers and ask about problems etc. If youre only doing step 2, then youve ~6 months to practice so Id just concentrate on hitting the papers (maybe a paper every week or so) and if thats the case Id not be thinking about sections to avoid at this stage. Last year, a level 2 was about 50/120 and about 1/3 of the people achieved it so its doable with a bit of practice.

(edited 4 months ago)

Reply 3

OP

Original post by normaw

I've moved your thread to the CS forum to help you get some replies. :smile:

Thank you!

Reply 4

OP

Original post by mqb2766

I presume youve gone through the step 2 modules
https://maths.org/step/assignments-stepii
as they give some decent topic notes/exemplar questions with hints etc. If so, there isnt really a reason you couldnt have a decent attempt at past papers and ask about problems etc. If youre only doing step 2, then youve ~6 months to practice so Id just concentrate on hitting the papers (maybe a paper every week or so) and if thats the case Id not be thinking about sections to avoid at this stage. Last year, a level 2 was about 50/120 and about 1/3 of the people achieved it so its doable with a bit of practice.

Yes, I've gone through the STEP I and II modules on the STEP support programme. I've done a few STEP I papers and 1 STEP II paper. After the time is up, I tend to go back through the questions on the paper (after marking it) and do them without any time so I can gauge my strengths and weaknesses.

Thank you for your advice!

Reply 5

Original post by vnayak

Yes, I've gone through the STEP I and II modules on the STEP support programme. I've done a few STEP I papers and 1 STEP II paper. After the time is up, I tend to go back through the questions on the paper (after marking it) and do them without any time so I can gauge my strengths and weaknesses.

Thank you for your advice!

If youre doing that, it sounds like youre made a reasonable start. Doing some elements of it timed, but attempting the whole paper for practice. Are there any particular problems youre having then?

(edited 4 months ago)

Reply 6

OP

Original post by mqb2766

If youre doing that, it sounds like youre made a reasonable start. Doing some elements of it timed, but attempting the whole paper for practice. Are there any particular problems youre having then?

I think the main problem is with the proof sort of stuff because some of the questions are a bit vague (in comparison to the A level Maths and Further Maths papers), which is as expected, so it takes some time to identify how to go about doing it. The other problem for me is that the solutions provide more of a report for how people did on each question rather than actually showing how you do it, which is the other problem I'm currently experiencing.

Reply 7

Original post by vnayak

I think the main problem is with the proof sort of stuff because some of the questions are a bit vague (in comparison to the A level Maths and Further Maths papers), which is as expected, so it takes some time to identify how to go about doing it. The other problem for me is that the solutions provide more of a report for how people did on each question rather than actually showing how you do it, which is the other problem I'm currently experiencing.

Why not post a typical question / your attempt here to get some specific advice.
Its hard to give advice without understanding what your problems are / what yove tried.

(edited 4 months ago)

Reply 8

OP

The 2022 STEP 2 paper - Question 3 (Fibonacci). It took me some time to realise that it was a proof by induction and then even more time to go about proving it.

Also, I just realised that I didn't scroll through the mark scheme document completely and I found the solutions to the questions. I thought it was just the reports initially.

Reply 9

OP

The 2014 STEP I paper - Question 3 part iii

I was able to do the first two parts without any problems (simple A level maths) but it was part 3 that had me confused.

I first went about establishing a general equation for the two limits "a" and “b” through integrating both sides to form the following equation:

We know that b>a so we can cancel (b-a) from both sides. This gets us:

And from this point, I’m unsure as to how I should approach the problem. I can obviously try to substitute p and q for the brackets on RHS but then I don’t know what I can do after that.

Reply 10

Original post by vnayak

The 2022 STEP 2 paper - Question 3 (Fibonacci). It took me some time to realise that it was a proof by induction and then even more time to go about proving it.

Also, I just realised that I didn't scroll through the mark scheme document completely and I found the solutions to the questions. I thought it was just the reports initially.

For some of the older papers, the cambridge solutions are not available (though there are some threads on here with solutions), but as you say, the later ones shoulld have solutions, even if theyre partial.

For this one, you could form the fibonacci position to term formula and it would grow at ~the golden ratio so about 1.6 < 2 though it would be a fair bit more work than required and step questions are reasonably prescriptive, so it would probably have asked you to derive it in a previous part if it was the way to go. So induction would be the prime candidate as you have the simple recurrence relationship (next term equals previous term ...) and youre interested in bounding the growth of a sequence with an infinite number of terms. It would help to spot that the "2" growth rate could only occur if the previous two terms were equal which only occurs when 1,1->2, otherwise the growth rate will always be <2. So again, a simple inductive argument would work.

You should be be able to make some arguments to yourself like that with a bit of experience. Similarly, working out the first few terms of the fibonacci sequence and understanding why they satisfy the property is often a good idea if youre a bit stuck.

(edited 4 months ago)

Reply 11

Original post by vnayak

The 2014 STEP I paper - Question 3 part iii

I was able to do the first two parts without any problems (simple A level maths) but it was part 3 that had me confused.

I first went about establishing a general equation for the two limits "a" and “b” through integrating both sides to form the following equation:

We know that b>a so we can cancel (b-a) from both sides. This gets us:

And from this point, I’m unsure as to how I should approach the problem. I can obviously try to substitute p and q for the brackets on RHS but then I don’t know what I can do after that.

Your images are not showing, but do you mean question 2 (step 1, 2014)?

Reply 12

baris22

4

STEP II can be a jump, but focus on nailing STEP I basics first. Practice past papers, manage your time well, and don't skip any section entirely.

Reply 13

OP

Original post by mqb2766

Your images are not showing, but do you mean question 2 (step 1, 2014)?

Yes

Reply 14

OP

Original post by baris22

STEP II can be a jump, but focus on nailing STEP I basics first. Practice past papers, manage your time well, and don't skip any section entirely.

Yeah, that's what I am doing currently... Trying to nail STEP I first. Currently getting 3-4 questions correct depending on the year but I want to get started with STEP II as soon as I can. 😊😊

Reply 15

Original post by vnayak

Yes

Can you try again uploading what you did? You need to put the images on another site, the enter the url as the usual image uploading isnt working.

Reply 16

OP

Original post by mqb2766

Can you try again uploading what you did? You need to put the images on another site, the enter the url as the usual image uploading isnt working.

general integration formula:

We can eliminate (b-a) since we know that b<a<0, which then leaves us with:

this is the STEP I question 3 from 2014.

Reply 17

OP

It's appearing fine for me and I have followed your instructions so if there are further issues, please let me know.. 🙂

Reply 18