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The big fat STEP megathread (NOT for getting help with maths questions)

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DFranklin

Anyone here agree with that? It seems to me that (a) the difference in difficulty between STEP I and STEP II is fairly marginal, and (b) STEP III is significantly more difficult than STEP II (slightly compensated by having lower grade boundaries). And how it could be claimed that Q1 STEP III 2008 was based on Further Mathematics is beyond me...

I think I and II are similar, with somewhat more emphasis on I being filled with questions requiring less algebra and maths knowledge, but more 'spotting the trick', so sometimes I do worse in I. (Although that was not true when I actually sat the exams as I wrote the worst II paper I have ever done when practising...)
My feeling is that III often requires 'harder' maths (i.e. largely only FM syllabus), but the actual questions are not too different from II. I tend to do better in II, so I guess that makes III harder.

Reply 201

DFranklin

Well, I may not be the best judge, coming at the questions somewhat 'overknowledged' and 'under practiced'. I also tend to judge a paper by "how bad was the worst question", not "how easy was the easiest one".
But my feelings on the difficulty:

The easier STEP I questions are the easiest questions on all 3 papers. But the more difficult questions can be just as hard as anything on STEP II/III. (For instance, I think the STEP I Q11 question this year is as hard as any mechanics question ever set on STEP III).
STEP II is less variable relative to STEP I. You don't find many absolute "gift" questions, but finding 6 questions that are doable isn't too bad.
There are some straightforward STEP III questions, but there are also often questions that are really very long and involved compared with STEP II. I also find you often get questions in STEP III that don't require any FM knowledge; the main reason for putting them in STEP III seems to be they are particularly long and tricky, or they involve looking at a problem in a very unusual manner.

Reply 202

harr

DFranklin

STEP II is less variable relative to STEP I. You don't find many absolute "gift" questions

There are still a reasonable number. I would say that 1, 3 and 12 were all gifts (though I made a minor error on Q1 due to not knowing the exact definition of "period 2"). Question 2 also looks easy, but when I tried doing it in the exam, I found I couldn't remember how to do partial fractions in that form, so as I haven't attempted it since then, I don't know how difficult it actually was.

Reply 203

DFranklin

harr

A question that "looks easy, but I couldn't get it out", is hardly a gift (unless you consider a Trojan horse a gift :p:

).

I consider a "gift" as a question where if I chose the right approach and don't waste time, I could reasonably get the question out in 15 minutes.

On that basis: Q1 isn't a gift question (it's straightforward, but the algebra is quite involved). Q2 certainly isn't a gift question (the examiners report says the average score on it was only 8/20). Q3 - somewhat a gift, but I bet a lot of people dropped marks because they didn't prove it in the way the examiner was wanting. Q12: sort of a gift. These probability questions don't usually take that long, but the chance of having made some dodgy assumption and losing half the marks is always quite high.

For STEP I, I'd say Q1 and Q5 qualify as "gift" questions. Q9 is also a gift to anyone who's done enough mechanics (i.e. the FM modules).

Reply 204

Kolya

There may be some truth in the suggestion that bringing STEP II closer to I may help avoid rejecting the people who simply have an "off day". Interestingly, Warwick didn't seem to be planning to make STEP compulsory: on the website, they said they were planning an offer of AAAA (with A's in all core modules, and 3 A's in further pure/mechanics modules), but that never happened. They've now also removed the requirement of A's in C1-C4 for all candidates, which suggests they would much rather have a decent grade at STEP than looking for high grades on all maths exams taken.

Reply 205

nota bene

harr

Question 2 also looks easy, but when I tried doing it in the exam, I found I couldn't remember how to do partial fractions in that form, so as I haven't attempted it since then, I don't know how difficult it actually was.

I had the same problem as you with the partial fractions - but after 20 minutes of fiddling with them I found the right one. I think this was the only question I got a really decent 'complete' solution to in the whole paper (but admittedly I wasted about 45 minutes on it, which is far too long) - but the second part of the question totally lacked guidance and was all about spotting/guessing to use 1/10 (or was it 9/10 or 1/9? I haven't looked at the question since June). So I'd not regard it as a complete gift.

Reply 206

harr

DFranklin

A question that "looks easy, but I couldn't get it out", is hardly a gift (unless you consider a Trojan horse a gift :p:

I failed to get in, let alone get it out. It just looks like a sort of question I found pretty easy in practice, but I couldn't tell as I couldn't even start the question (unless I wanted to spend ages working out how partial fractions work). Q1 on STEP III was the Trojan horse, couldn't-get-it-out question imo. If you spotted the right tricks, it was easy; if you didn't, you spent an hour going round in circles to get about five marks.

A low average mark suggests it wasn't that easy afterwards, but it may be that I wasn't alone in writing about three lines of working before realising that I couldn't do the partial fraction.

I consider a "gift" as a question where if I chose the right approach and don't waste time, I could reasonably get the question out in 15 minutes.

On that basis: Q1 isn't a gift question (it's straightforward, but the algebra is quite involved). ... Q3 - somewhat a gift, but I bet a lot of people dropped marks because they didn't prove it in the way the examiner was wanting. Q12: sort of a gift. These probability questions don't usually take that long, but the chance of having made some dodgy assumption and losing half the marks is always quite high."

I did each of those questions in under 15 minutes and I only scraped into Cambridge. I doubt a more intelligent and better prepared candidate would have much trouble with them.

Reply 207

DFranklin

harr

I did each of those questions in under 15 minutes and I only scraped into Cambridge. I doubt a more intelligent and better prepared candidate would have much trouble with them.

I doubt I'd get any of them out in under 15 minutes, and even in my rusty dotage, I'd be pretty disappointed to get < 110/120 on a STEP II paper.

Reply 208

harr

DFranklin

I doubt I'd get any of them out in under 15 minutes, and even in my rusty dotage, I'd be pretty disappointed to get < 110/120 on a STEP II paper.

I think I have a tendency to decide on an approach and push it through. If it works, I've almost finished the question when I start it. If it doesn't, I don't usually get an answer. This might explain me being quicker in these small stretches than you even if you'd beat me by 30 or 40 marks plus on average. I get a few questions quickly and struggle to pick up any marks on the rest.

Reply 209

psanghaLFC

I personally have seen a lot of STEP I questions that seem 'as' difficult as some STEP III questions though i do agree generally III is quite a bit harder. I would say II is harder than I but not my much. Personally i did only used paper III to practise whenever i occasionally did, even though i knew i would probably end up taking I,II (i was even contemplating all three at one point) and i must say while the questions are more difficult than II it's often only because they involve further Maths.

Reply 210

dave730

Where can I get hold of Stephen Siklos's 1996 booklet, Advanced Problems in Mathematics? Note that this is not the same as his 2002 booklet with 'Core' in the title before the word 'Mathematics'. The 2002 one is here

The Cambridge University maths reading list says the 1996 booklet is available from the OCR, but when I rang the OCR they said it wasn't.

Thanks in advance for any help with this!
Best,
Dave

Reply 211

psanghaLFC

I think it's the one on this site http://www.mathshelper.co.uk/STEPSiklos.pdf

Reply 212

harr

psanghaLFC

I think it's the one on this site http://www.mathshelper.co.uk/STEPSiklos.pdf

That's the core one. I have no idea where to get the other one though.

Reply 213

dave730

Could someone recommend a secondhand bookshop in Cambridge that might possibly have a copy or be able to source one? What's the best bookshop in Cambridge for secondhand maths books??

I tried the bookshops in Oxford today. They are cr*p!! Silly naive me was expecting that I could go into the secondhand section on the top floor of Blackwells and have a look at things like Gauss's Disquisitiones Arithmeticae, but the secondhand maths section there had about 10 books only!

Dave

Reply 214

nota bene

dave730

I tried the bookshops in Oxford today. They are cr*p!! Silly naive me was expecting that I could go into the secondhand section on the top floor of Blackwells and have a look at things like Gauss's Disquisitiones Arithmeticae, but the secondhand maths section there had about 10 books only!

Their selection of new books on the ground floor is much better (and more pricey of course...), all the second hand books that are good get nicked very quickly.

And nope, sorry I have no idea about that booklet.

Reply 215

wonderwall 124

psanghaLFC

I think it's the one on this site http://www.mathshelper.co.uk/STEPSiklos.pdf

This link is extremely helpful...Thanks :smile:

Reply 216

nuodai

I wonder if this answer's right. 2003 STEP I Question 2 Part 1 (I haven't done part 2 yet):

QUESTION:
The first question on an examination paper is:
Solve

x

for the equation

\frac{1}{x} = \frac{1}{a} + \frac{1}{b}.

where (in the question)

a

and

b

are given to be non-zero real numbers. One candidate writes

x=a+b

as the solution. Show that there are no values of

a

and

b

for which this will give the correct answer.

SOLUTION:
If

x = a + b

, then

\frac{1}{a+b} = \frac{1}{a} + \frac{1}{b}

\newline\therefore \frac{a+b}{a} + \frac{a+b}{b} - 1 = 0 \newline[br]\therefore \frac{a^2 + 2ab + b^2}{ab} - 1 = 0 \newline[br]\therefore a^2 + ab + b^2 = 0

This is a quadratic, so we can find its discriminant. We'll say first that

f(a) = g(b) = a^2 + ab + b^2

Discriminant for

f(a)

\sqrt{b^2 - 4b^2}

is not defined for real

b

, this is a contradiction, so

a

does not exist.
Discriminant for

g(b)

\sqrt{a^2 - 4a^2}

is not defined for real

a

, this is a contradiction, so

b

does not exist.

Q.E.D.

So

\frac{1}{x} = \frac{1}{a} + \frac{1}{b}

is not defined for

a,b \ne 0; a,b \in \mathbb{R}

Is this right or have I gone horribly wrong somewhere?

Reply 217

pyrolol

Yes, although you didn't really need to find the second discriminant, since x is real and if a is complex, b must be. Probably quicker your way, just observing^.

EDIT: Lol, I can't read. Yeah, you're signs got confused (see below).

Reply 218

harr

nuodai

You seem to have dropped a 2ab or got a sign wrong going from the first line to the second and you also dropped a negative sign going from the second to the third. These two mistakes (assuming that they are mistakes and I'm not being incredibly stupid) cancel each other out. It's quite possibly a typo anyway.