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2013 STEP thread mark II

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How concise are we allowed to be, do you think? For instance, would I lose marks for writing

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{\pi}{ \sqrt{2}}\,?

Or, (inspired by the mock I did today) say a question asks to show that a polynomial has no rational roots, something simple such as

p(x)=x^3-x+3

, and I've managed to show that the only possibilities are -3, -1, 1, 3. Can I simply say "clearly these are not roots", or would they expect me to write out the specific values of p(-1), p(1) etc., making it explicit that they are not 0?

These are details I suppose, but I'd like to know people's opinions.

Reply 41

bananarama2

Original post by Lord of the Flies

How concise are we allowed to be, do you think? For instance, would I lose marks for writing

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{\pi}{ \sqrt{2}}\,?

Or, (inspired by the mock I did today) say a question asks to show that a polynomial has no rational roots, something simple such as

p(x)=x^3-x+3

I know I don't do STEP but from a-levels I can say that first integral definitely needs more working. You want your working to be as clear and easy to follow as possible. It's all very well if you get it right, but if it goes tits up you don't want to be losing more marks than is necessary. Ultimately your just encouraging the examiner to give you the marks.

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Reply 42

bogstandardname

Original post by Lord of the Flies

How concise are we allowed to be, do you think? For instance, would I lose marks for writing

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{\pi}{ \sqrt{2}}\,?

Or, (inspired by the mock I did today) say a question asks to show that a polynomial has no rational roots, something simple such as

p(x)=x^3-x+3

Surely just slip in

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{1}{\sqrt{2}}\arctan \left(\frac{1}{\sqrt{2}}\right)_{-\infty}^{\infty}=\frac{\pi}{ \sqrt{2}}\,

Reply 43

Lord of the Flies

Original post by bananarama2

Original post by bogstandardname

Surely just slip in

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{1}{\sqrt{2}}\arctan \left(\frac{x}{\sqrt{2}}\right) \Big|_{-\infty}^{\infty}=\frac{\pi}{ \sqrt{2}}\,

Ok I'll do that, thanks for the advice.

Reply 44

Sketch

Original post by bananarama2

Spoiler

I understand now, but I'm still having problems:

Spoiler

Original post by bogstandardname

Surely just slip in

\int_{-\infty}^{\infty} \frac{dx}{2+x^2}=\frac{1}{\sqrt{2}}\arctan \left(\frac{1}{\sqrt{2}}\right)_{-\infty}^{\infty}=\frac{\pi}{ \sqrt{2}}\,

To be honest I'd write

\lim_{(a,b) \to \infty} \left[ \frac{1}{\sqrt{2}}\arctan \left(\frac{x}{\sqrt{2}}\right)_{-b}^{a} \right]

Just to be safe :colone:

(edited 10 years ago)

Reply 45

bananarama2

Original post by Sketch

I understand now, but I'm still having problems:

Spoiler

To be honest I'd write

\lim_{(a,b) \to \infty} \left[ \frac{1}{\sqrt{2}}\arctan \left(\frac{x}{\sqrt{2}}\right)_{-b}^{a} \right]

Just to be safe :colone:

Spoiler

Reply 46

bogstandardname

Original post by Sketch

I understand now, but I'm still having problems:

Spoiler

To be honest I'd write

\lim_{(a,b) \to \infty} \left[ \frac{1}{\sqrt{2}}\arctan \left(\frac{x}{\sqrt{2}}\right)_{-b}^{a} \right]

Just to be safe :colone:

Certainly you are correct, but I get the feeling STEP examiners are very lenient when it comes to dealing with limits of infinity.

Reply 47

Femto

Wow, this is a fantastic thread! I wish all of you taking STEP the very, very best of luck!

Provided you've worked as hard as you can for this exam, you'll be fine :wink:

Reply 48

Sketch

Original post by bananarama2

Spoiler

Reply 49

TheMagicMan

Original post by Sketch

I understand now, but I'm still having problems:

Spoiler

To be honest I'd write

\lim_{(a,b) \to \infty} \left[ \frac{1}{\sqrt{2}}\arctan \left(\frac{x}{\sqrt{2}}\right)_{-b}^{a} \right]

Just to be safe :colone:

I wouldn't bother with the limits. It's implicit in STEP that all infinite sums/integrals etc. converge

Reply 50

tilal6991

Hey all. I've lurked a long time on this thread and TBH been very comforted by it :P

I was just wondering whether someone could take a look at how many marks I would get in the 2011 STEP 2 paper. Just sat it as a mock under strict time conditions. BTW I need a 2 for my offer to Imperial.

Spoiler

Thanks to anyone who takes a look!

(edited 10 years ago)

Reply 51

TheMagicMan

Original post by tilal6991

Spoiler

Thanks to anyone who takes a look!

I wouldn't only attempt 4 questions...I would find 2 questions with easy beginnings and spend 10 minutes on them to get 10 marks. This will give you a lot more leeway with the other 4.

Reply 52

tilal6991

Original post by TheMagicMan

I wouldn't only attempt 4 questions...I would find 2 questions with easy beginnings and spend 10 minutes on them to get 10 marks. This will give you a lot more leeway with the other 4.

That's what I've been doing until this paper. In this paper though these were the only questions which I really thought I could do any of the parts convincingly. Since I'm from Scotland I haven't actually done any of the mechanics or stats so my range in this paper was quite limited considering for the pure questions only 1-3 had a mean mark above 7.

Sounds like good advice for the paper next Wednesday though!

(edited 10 years ago)

Reply 53

Sketch

Original post by TheMagicMan

I wouldn't bother with the limits. It's implicit in STEP that all infinite sums/integrals etc. converge

Original post by bogstandardname

Certainly you are correct, but I get the feeling STEP examiners are very lenient when it comes to dealing with limits of infinity.

Ahh fair enough, cheers :smile:

Reply 54

Llewellyn

Original post by tilal6991

But can you see why, for example, Q4 may have been a good idea? You wouldn't even have to finish the first part but you could definitely pick up 3+ marks for some pretty basic stuff. (Keeping this vague because not everyone has sat the exam).

Likewise Q5 and Q7 have relatively simple openings (either of which could be on a standard Higher Level/ A Level paper).

Reply 55

tilal6991

Original post by Llewellyn

Yeah I guess so. I did have a quick look at 6 and 7 as they caqught my eye as being easy but I just could not get my head round them :/

Reply 56

ian.slater

Original post by Lord of the Flies

Or, (inspired by the mock I did today) say a question asks to show that a polynomial has no rational roots, something simple such as

p(x)=x^3-x+3

If you're looking for rational roots you might normally start by saying 'suppose x = p/q for integers p,q (often helps to specify coprime)' and work to a contradiction. Did you mean integer roots?

Reply 57

shamika

Original post by ian.slater

If you're looking for rational roots you might normally start by saying 'suppose x = p/q for integers p,q (often helps to specify coprime)' and work to a contradiction. Did you mean integer roots?

Rational root theorem?

Reply 58

sa6opopov

I have read that since 2008 there has been a change in the curriculum.Can someone explain what exactly is that change?

Reply 59

Dog4444

Hi guys, I noticed I struggle with STEP integration and vector/geometry related problems, are there any other questions out there that I can practice or any advice/tips/tricls on how to do them, dunno?