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    Zacken (or any admin),

    Is it worth reapplying to Cambridge to study maths, when I'm holding an unconditional from Imperial College?

    My STEP 2,3 marks were 63,62 respectively.
    A level grades were A* Maths, A* FM, A FAM (AS), B French, D3 Physics Pre U
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    (Original post by Superdjman1)
    Zacken (or any admin),

    Is it worth reapplying to Cambridge to study maths, when I'm holding an unconditional from Imperial College?

    My STEP 2,3 marks were 63,62 respectively.
    A level grades were A* Maths, A* FM, A FAM (AS), B French, D3 Physics Pre U
    I personally wouldn't, but it all depends on your position regarding taking a gap year: is it something you really actually want to do or is it something you're only doing to give you a shot at getting into Cambridge? If it's the latter, then I wouldn't recommend it, if the former then it becomes a viable option. Remember that Imperial is a perfectly good place to study maths, is having another shot (that is by no means guaranteed) at Cambridge worth a year of your life?
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    [Replying to watch thread]
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    (Original post by etothepiiplusone)
    [Replying to watch thread]
    This works too:
    Name:  Screen Shot 2017-09-03 at 23.29.07.jpg
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Size:  51.3 KB

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    (Original post by Doonesbury)
    This works too:
    (Original post by etothepiiplusone)
    [Replying to watch thread]
    Or this

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    (Original post by carpetguy)
    Also a biiiig shout out to the STEP Support Programme (link in Zacken's op).
    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". I look at the SSP daily :-)
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    (Original post by Drogo Baggins)
    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". I look at the SSP daily :-)
    If you don't post much but do makes posts with external links it's quite likely they will be "auto-reported" for approval. Such approval should usually be forthcoming but can take a little while

    Alternatively don't include links
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    (Original post by Drogo Baggins)
    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". 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" :')
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    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.
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    (Original post by tangotangopapa2)
    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.
    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.

    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.
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    (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.
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    (Original post by carpetguy)
    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" :'
    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!
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    TSR Community Team
    (Original post by Disregarded7017)
    When will the dates for STEP come out?
    The 2018 version is here

    https://www.thestudentroom.co.uk/sho....php?t=4844994
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    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).
    Name:  integration.png
Views: 105
Size:  4.7 KB
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    (Original post by tangotangopapa2)
    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).
    Name:  integration.png
Views: 105
Size:  4.7 KB
    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)
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    (Original post by Zacken)
    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)
    Thank you for the explanation. I almost forgot that the median of a trapezium is the average of the bases.
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    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
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    (Original post by 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
    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)
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    (Original post by 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
    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.
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    (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
 
 
 
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