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STEP Prep Thread 2018

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Cheers! On the STEP Support Programme website I am "Hypatia"

I do occasionally look at this thread (and sometimes post, but sometimes my posts are not approved - I assume because of "advertising" :wink:

. I look at the SSP daily :-)

Oh I see.
I was wondering btw who writes the modules. I really enjoyed the fractals - great frozen references. "Perhaps with the popularity of frozen fractals will become well known again". This was brilliant after the "you may have heard Elsa singing frozen fractals" :')

(edited 6 years ago)

Reply 201

username2452153

I have already completed year 13 and I am planning to do STEPs next year. My question is about the books that will be helpful for the exams. I don't dislike Stephen Silko's books but I was looking for something slightly advanced/ higher level, yet useful for STEP.

Are the olympiad style books on algebra, geometry, combinatorics or number theory particularly useful for the STEP?
At first glance, it looks like you won't really use any of the inequalities you need for the olympiad. And you won't be seeing integration by parts/ reduction formulae in olympiad books which STEP seems to heavily contain.

Would undergraduate level books (for eg. analysis) give you any advantage?
I was about to start Spivak's calculus but not sure if it would be highly helpful.

Reply 202

Zacken

Original post by tangotangopapa2

Are the olympiad style books on algebra, geometry, combinatorics or number theory particularly useful for the STEP?

I don't personally think so, no. They're quite different things. Problem solving from Olympiad will often be helpful for STEP, but in terms of the actual content, not really.

At first glance, it looks like you won't really use any of the inequalities you need for the olympiad. And you won't be seeing integration by parts/ reduction formulae in olympiad books which STEP seems to heavily contain

Yep.

Would undergraduate level books (for eg. analysis) give you any advantage?
I was about to start Spivak's calculus but not sure if it would be highly helpful.

Not at all, not apart from one or two very specific STEP questions that are clearly torn out from an Analysis problem and suitably derigourised.

At the end of the day, the most useful thing for learning how to do STEP is doing STEP, which is why Siklos's book, which is just a collection of STEP problems is probably the most effective way apart from past papers. If you want to read up on more advanced things that still helps reasonably with STEP, then a methods book is the best thing that fits that criteria in my opinion.

Reply 203

Superdjman1

Original post by Zacken

Something advanced/higher level but useful for STEP would be a few popular methods books, stuff like advanced mathematics for engineers or the like. I think the Mathematical Methods course has some book recommendations in the Cambridge schedule. I've forgotten the exact names of the books, but I've seen them recommended on here before.

I don't personally think so, no. They're quite different things. Problem solving from Olympiad will often be helpful for STEP, but in terms of the actual content, not really.

Yep.

Not at all, not apart from one or two very specific STEP questions that are clearly torn out from an Analysis problem and suitably derigourised.

At the end of the day, the most useful thing for learning how to do STEP is doing STEP, which is why Siklos's book, which is just a collection of STEP problems is probably the most effective way apart from past papers. If you want to read up on more advanced things that still helps reasonably with STEP, then a methods book is the best thing that fits that criteria in my opinion.

One thing I have definitely learnt from STEP, is just because your competent at solving BMO1 problems, it doesn't necessarily mean you'll ace STEP. STEP is as much about getting used to the format of questions and knowing which questions you should pick above anything else. Olympiad skills alone in STEP will not get you very far. Practising problems from STEP itself seems to me to be the most important thing.

Reply 204

Drogo Baggins

Original post by carpetguy

No prob! The "foundation assignments" were written by Stephen Siklos and myself, as part of the (no longer operational) STEP Correspondence Course. We wrote different bits (the fractals bit was all mine though :-) ).

The other modules were written by myself and someone else from the NRICH team, and we also extended the "hints and solutions" for the foundation modules quite a lot (this is still ongoing this year). We are always grateful for suggestions on how we can take things further!

Reply 205

She-Ra

Universities Forum Helper

Original post by Disregarded7017

When will the dates for STEP come out?

The 2018 version is here

https://www.thestudentroom.co.uk/showthread.php?t=4844994

Reply 206

username2452153

I am assuming this thread is also for posting questions and solutions to STEP questions.

Let f(x) be a curve with f '' (x) > 0 in the interval (a,b). With the help of a sketch, show that trapezoidal approximation for

\int_{a}^{b}f(x)

is an overestimate and the rectangular approximation (mid-point rule) is an underestimate of the area.

It is quite easy to show that trapezoidal approximation is an overestimate as the area of the integral would be totally inside the area of the trapezium/trapezia (for multiple partitions). It is the second part of the question that is giving me serious trouble. I can see that the area of the rectangle looks smaller than the area of integral but I don't know how to explain this. Any suggestion would be highly appreciated.

This question was asked in 2004 in STEP 3 (Question 3).

(edited 6 years ago)

Reply 207

Zacken

Original post by tangotangopapa2

\int_{a}^{b}f(x)

It's not a rectangle. It's another trapezium. Draw the tangent to f at the point (a+b)/2 and the lines x = a, x =b then you get a trapezium.

The quantity f((a+b)/2) is the average height of the two sides (the tangent intersecting the lines x = a and x =b along with the x-axis forms a trapezium)

Reply 208

username2452153

Original post by Zacken

Thank you for the explanation. I almost forgot that the median of a trapezium is the average of the bases.

Reply 209

Slewis99

Can anyone help me with this? It's a foundation module question.
I have found the least value of the function, but I'm not sure how to get the greatest value.
I'm not sure how I sketch the function either, without using a specific value of k

Reply 210

123Master321

Original post by Slewis99

Use your graph and mark on the endpoints on the bounds for x, you notice that the maximum value isn't a stationary point, so you just need to see where the highest point on the curve will be noting how 'k' is bounded(the values are chosen very cleverly)

Reply 211

username2452153

Original post by Slewis99

Complete the square to get the upward facing parabola. Minimum value is the local minimum but the max value is one of the two boundary values depending on k<0 or k>=0. When k>2 the local minimum would be out of range, so both min and max are boundary values.

Reply 212

etothepiiplusone

Original post by Slewis99

I'm not sure how I sketch the function either, without using a specific value of k

Hint: all you need to know is where the curve intersects the axes

Reply 213

iMacJack

Hey guys, any idea how to go about sketching functions such as f(x) = ln(x) divided by x? ( ln(x)/x )
Obviously I know how to draw ln(x), and I know how to draw 1/x, but how do I draw the combined result? Thanks!

Reply 214

Deranging

Original post by iMacJack

The kind of questions you need to ask yourself with sketch questions are:
Where do I expect the function to be defined?
Are there any roots? Are there any stationary points - if yes what kind?
What happens when

x \to 0

x \to \pm \infty

?

Then at the end connect the dots essentially (with a tiny bit of thought so that the slopes aren't horribly wrong).

(edited 6 years ago)

Reply 215

pink.lemonade

Hi, I've just started looking into maths admissions tests and was after some help! I'm looking at using it to boost my application (as I don't study further maths) for MORSE at Warwick and/or Southampton.

1) When are the STEP papers taken? On the website it looks as if they are sat June time....

2) If this is the only time they are taken are they done pre- or post- application? I'm in yr13 just going through the UCAS process - or am I too late?

3) Would a TMUA have a similar value?

Thank you x

(edited 6 years ago)

Reply 216

Zacken

Original post by pink.lemonade

1) They are taken in June of Year 13 when you are taking all your A-Level exams.

2) Yes, this is the only time they are taken. They are done post application. It is usually a condition of an offer.

3) For MORSE? Probably.

Reply 217

pink.lemonade

Original post by Zacken

Thank you so much!!!

Reply 218

Zacken

Original post by pink.lemonade

Thank you so much!!!

No problem.

Reply 219

Bangz

STEP
This question refers to the 1994 STEP1 paper question 8. I have done the first two parts but I dont know how they relate to the last part.

so far I have tried manipulating (1+sinx)/(1+cosx) to get 1 + tan(x). I tried splitting the integral, using the property of logarithms, and I have gotten nowhere.

what am I not seeing?

p.s. please can you nudge and not give the whole question away.

thanks