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August 17th, 2014, 08:59 AM   #1
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What books should people read to pass the Cambridge STEP papers?

The Cambridge STEP papers can be downloaded here:

Faculty of Mathematics MATHEMATICAL TRIPOS EXAMINATION PAPERS

What books should people read to pass these tough examination questions?
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August 17th, 2014, 09:41 AM   #2
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Originally Posted by wulgulmerang View Post
The Cambridge STEP papers can be downloaded here:

Faculty of Mathematics MATHEMATICAL TRIPOS EXAMINATION PAPERS

What books should people read to pass these tough examination questions?
For the 1st paper, I believe any textbook on linear algebra and calculus should do. Especially if it has exercises. I saw only 1 problem on complex analysis, so maybe that textbook too. Maybe Krantz-Calculus Revisited, or Yet another calculus textbook. I would generally recommend Lang-Complex Analysis, but that would be an overkill.

I'd like to solve some.

$z=2+2i$

$z^4={2(1+i)}^4=2^4{1+i}^4=16{{1+i}^2}^2=16{2i}^2= 64i^2=-64$

$e^{2z^2}-1=0
{e^{z^2}}^2=1
e^{z^2}=1$ or
$e^{z^2}=-1$
Putting $w=z^2$
$e^w=1
e^x(cos y + i sin y)=1
x=0
cos y + i sin y = 1
cos y = 1, sin y = 0
y=2k \pi
z= \sqrt {2k \pi}$

Last edited by raul21; August 17th, 2014 at 10:22 AM.
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August 17th, 2014, 10:25 AM   #3
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$z=2+2i$

$z^4={2(1+i)}^4=2^4{1+i}^4=16{{1+i}^2}^2=16{2i}^2= 64i^2=-64$

$e^{2z^2}-1=0
{e^{z^2}}^2=1
e^{z^2}=1$ or
$e^{z^2}=-1$
Putting $w=z^2$
$e^w=1
e^x(cos y + i sin y)=1
x=0
cos y + i sin y = 1
cos y = 1, sin y = 0
y=2k \pi
z= \sqrt {2k \pi}$
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August 17th, 2014, 11:39 AM   #4
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I'm glad you find those papers so tough, because they are past papers from the actual Mathematics course at Cambridge. If you manage to get a place, you'll be given a reading list to help you study for the exams.

The idea of the STEP papers is (or perhaps that should be was, because it's 20 years or more since I needed to worry about them) to use only material that you should have studied at 'A'-level, but to use it in imaginative ways.

Accordingly, you should probably focus on practising with past papers, rather than trying to acquire new knowledge.

Last edited by v8archie; August 17th, 2014 at 11:48 AM.
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August 17th, 2014, 11:57 AM   #5
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Here's some pages (referenced on the Cambridge website) that may be of help:
Pure Mathematics
Applied Mathematics
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April 14th, 2015, 10:19 PM   #6
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What books should people read to pass the Cambridge STEP papers?

I think People should Read that Books to Pass the Cambridge Step Papers, which will give them a great General Knowledge about these Papers as well as you should Check their Result in Last 3 or 4 Years.
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September 24th, 2015, 05:01 AM   #7
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I passed the STEP exams a couple of years ago, and my preparation was mostly using knowledge from A-level. There are over a thousand questions available, and my best advice is to spend as much time as possible, preferably over a time period of at least 6 months, doing those questions. They'll be very tricky at first, especially those on STEP III, but you *will* get the hang of it eventually.

I believe there are also some documents that were prepared by Stephen Siklos for the purpose of preparing for STEP, where he gives some general strategies and has lots of worked examples. TheStudentRoom is also an excellent resource for STEP stuff.
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November 10th, 2015, 08:24 AM   #8
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is there any online free lancer for maths and free quiz web for cambridge studies
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November 10th, 2015, 09:49 AM   #9
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You will not progress in maths at any level, just reading.

You must practise, practise, and practise again.

Or, as my old Nuffield Physics teacher used to say

Questions, questions, questions.
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