STEP Prep Thread 2017

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    (Original post by Zacken)
    Yeah, I know you're trustworthy - was just warning him because he seemed to have very little reservation about sending it off to any person.
    oh sorry thought that since they were in year above it would be alright but is trustworthy as you said
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    (Original post by 11234)
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    That's a nice one ^.^ Don't overthink part iv!
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    Hey guys, im reapplying to uni this year, i have two quick questions.

    Can we talk about STEP in our personal statements (keep in mind im not applying to cambridge or anything) or does the referee do all that?

    also I got 1,3 in I and II. Is the 3 still worth mentioning since at least I tried it or will it hinder me too much as they'll think im not capable etc

    thanks
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    (Original post by DylanJ42)
    Hey guys, im reapplying to uni this year, i have two quick questions.

    Can we talk about STEP in our personal statements (keep in mind im not applying to cambridge or anything) or does the referee do all that?

    also I got 1,3 in I and II. Is the 3 still worth mentioning since at least I tried it or will it hinder me too much as they'll think im not capable etc

    thanks
    AKAIK, you must declare past STEP results; that being said, I'm sure there's no harm talking about it in your PS.


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    (Original post by ValerieKR)
    That's a nice one ^.^ Don't overthink part iv!
    finally solved part iv...didn't realise it would be like that cos I tried to use all the previous bits...oh well
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    (Original post by DylanJ42)
    Hey guys, im reapplying to uni this year, i have two quick questions.

    Can we talk about STEP in our personal statements (keep in mind im not applying to cambridge or anything) or does the referee do all that?

    also I got 1,3 in I and II. Is the 3 still worth mentioning since at least I tried it or will it hinder me too much as they'll think im not capable etc

    thanks
    Why don't you apply to Cambridge? Physicsmaths got an offer with 1,3. You'll need to declare both grades on UCAS (it's sufficiently iffy that you might get away with not declaring the 3, but I genuinely just wouldn't risk it, declare everything!) - you'll be fine.
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    (Original post by to4ka)
    AKAIK, you must declare past STEP results; that being said, I'm sure there's no harm talking about it in your PS.
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    okay thanks a lot
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    (Original post by Zacken)
    Why don't you apply to Cambridge? Physicsmaths got an offer with 1,3. You'll need to declare both grades on UCAS (it's sufficiently iffy that you might get away with not declaring the 3, but I genuinely just wouldn't risk it, declare everything!) - you'll be fine.
    applying for maths w/ compsci and as far as I can tell cambridge stops doing maths on that course after the first year & id rather have a split the whole way through

    congrats yourself on Camb, although i had no doubts about it
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    Hi guys, I've been using a resource that I don't think anyone has talked about (forgive me if it has). It's the Cambridge Step preparation modules:http://maths.org/step/assignments

    They're quite useful to set you up for a step question with warmup and preparation questions then Step question. There's also a fun warm down question at the end of each one. So far they have 3 modules up for the summer but I think in September they'll start releasing them each week. They're very good when you've no idea how to start doing step questions and to get you into the mindset of a question.

    BTW I'm actually in my second last year of secondary school this year but I'm a year ahead in maths. I'm considering doing step this year or next year. I'll probably end up doing it next year when I'll have more time and in search of more maths to do but I guess there's no harm in starting to prepare as early as possible. I'm in the Scottish system so am doing advanced higher maths this year. This course doesn't have any applied stuff, you have to do separate advanced highers for that. However my school doesn't offer these other courses so I might self-teach myself some of the applied maths next year, and then I'd also be able to try the applies step questions. I haven't decided which uni I want to go to yet (I might like to try for Oxbridge but then again going to a Scottish uni would be free for me) so I'm doing step mainly for extra maths and my own enjoyment.
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    (Original post by DylanJ42)
    applying for maths w/ compsci and as far as I can tell cambridge stops doing maths on that course after the first year & id rather have a split the whole way through

    congrats yourself on Camb, although i had no doubts about it
    are you applying to oxford then ? they have a math/s/compsci course
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    (Original post by Sherlock222)
    [...]
    It's a fairly well known resource, useful for beginners. I personally don't like it because the warm up questions spoils the question for you in the sense that it indicates what you should be thinking about and what sort of approach you need to try. But still, that's just my person opinion and many people benefit from that course.
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    (Original post by Sherlock222)
    Hi guys, I've been using a resource that I don't think anyone has talked about (forgive me if it has). It's the Cambridge Step preparation modules:http://maths.org/step/assignments

    They're quite useful to set you up for a step question with warmup and preparation questions then Step question. There's also a fun warm down question at the end of each one. So far they have 3 modules up for the summer but I think in September they'll start releasing them each week. They're very good when you've no idea how to start doing step questions and to get you into the mindset of a question.

    BTW I'm actually in my second last year of secondary school this year but I'm a year ahead in maths. I'm considering doing step this year or next year. I'll probably end up doing it next year when I'll have more time and in search of more maths to do but I guess there's no harm in starting to prepare as early as possible. I'm in the Scottish system so am doing advanced higher maths this year. This course doesn't have any applied stuff, you have to do separate advanced highers for that. However my school doesn't offer these other courses so I might self-teach myself some of the applied maths next year, and then I'd also be able to try the applies step questions. I haven't decided which uni I want to go to yet (I might like to try for Oxbridge but then again going to a Scottish uni would be free for me) so I'm doing step mainly for extra maths and my own enjoyment.
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    (Original post by Zacken)
    It's a fairly well known resource, useful for beginners. I personally don't like it because the warm up questions spoils the question for you in the sense that it indicates what you should be thinking about and what sort of approach you need to try. But still, that's just my person opinion and many people benefit from that course.
    the final warm down questions are quite interesting though
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    (Original post by gasfxekl)
    are you applying to oxford then ? they have a math/s/compsci course
    i am indeed
    Spoiler:
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    not the best thing to admit in a STEP thread :laugh:
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    (Original post by Sherlock222)
    Hi guys, I've been using a resource that I don't think anyone has talked about (forgive me if it has). It's the Cambridge Step preparation modules:http://maths.org/step/assignments

    They're quite useful to set you up for a step question with warmup and preparation questions then Step question. There's also a fun warm down question at the end of each one. So far they have 3 modules up for the summer but I think in September they'll start releasing them each week. They're very good when you've no idea how to start doing step questions and to get you into the mindset of a question.

    BTW I'm actually in my second last year of secondary school this year but I'm a year ahead in maths. I'm considering doing step this year or next year. I'll probably end up doing it next year when I'll have more time and in search of more maths to do but I guess there's no harm in starting to prepare as early as possible. I'm in the Scottish system so am doing advanced higher maths this year. This course doesn't have any applied stuff, you have to do separate advanced highers for that. However my school doesn't offer these other courses so I might self-teach myself some of the applied maths next year, and then I'd also be able to try the applies step questions. I haven't decided which uni I want to go to yet (I might like to try for Oxbridge but then again going to a Scottish uni would be free for me) so I'm doing step mainly for extra maths and my own enjoyment.
    I'm doing advanced higher maths and mechanics. Hope you get the grades you want, any thoughts on wher you fancy studying?
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    (Original post by DonAchille)
    I'm doing advanced higher maths and mechanics. Hope you get the grades you want, any thoughts on wher you fancy studying?
    I think maybe Edinburgh, St Andrews or Oxbridge (don't know which I like best between Oxford and Cambridge yet). But I'll go to some open days next year to see which unis I like the best. I know Edinburgh fairly well though and have been to the school of maths building there before which is quite nice.

    I'm still unsure about English universities since it is further away plus it's really expensive when I could just stay here in Scotland and get all my tuition fees paid for.
    However I've still got some time to make up my mind.

    What about you?


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    (Original post by Sherlock222)
    I think maybe Edinburgh, St Andrews or Oxbridge (don't know which I like best between Oxford and Cambridge yet). But I'll go to some open days next year to see which unis I like the best. I know Edinburgh fairly well though and have been to the school of maths building there before which is quite nice.

    I'm still unsure about English universities since it is further away plus it's really expensive when I could just stay here in Scotland and get all my tuition fees paid for.
    However I've still got some time to make up my mind.

    What about you?


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    You have!

    Cambridge, Edinburgh and St Andrews are all definites. I went to Oxford when I left school for 2 years and took classics, didn't like the course but the uni is amazing.

    Probably will apply to Durham and Warwick, but not 100% yet.

    The advanced higher course is really good. How you getting on with it?
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    (Original post by DonAchille)
    You have!

    Cambridge, Edinburgh and St Andrews are all definites. I went to Oxford when I left school for 2 years and took classics, didn't like the course but the uni is amazing.

    Probably will apply to Durham and Warwick, but not 100% yet.

    The advanced higher course is really good. How you getting on with it?
    Yeah it's a good course. We're onto differentiation now. It's been a little more challenging than higher but really quite interesting.


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    I've decided to have a go at some STEP questions before I start university. I'm not very good at them and pretty much struggle on all of them as I've never done STEP Q's before. I have a general idea of what to do on each question but begin to struggle sooner or later and end up spending too long and not getting anywhere, so I'm just trying to get better at them by practice.

    Here I've fully done a fairly simple question and I would like to know if my working is 'acceptable' or fully sufficient, so to speak. Whether it is more than enough or lacking in some areas, etc...

    Sorry in advance if this is the wrong thread to ask this question.

    The n positive numbers x_1,x_2,x_3,...,x_n, where n\geq3, satisfy:

    \displaystyle x_1=1+\frac{1}{x_2} , x_2=1+\frac{1}{x_3} , ... , x_{n-1}=1+\frac{1}{x_n}

    and also

    \displaystyle x_n=1+\frac{1}{x_1}

    Show that:

    (i) x_1,x_2,x_3,...,x_n > 1

    (ii) x_1-x_2=-\frac{x_2-x_3}{x_2x_3}

    (iii) x_1=x_2=x_3=...=x_n

    Hence find the value of x_1
    My solution:
    Spoiler:
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    (i) Here I can see that I can substitute the expression for x_n into x_{n-1}. This would give me:

    \displaystyle x_{n-1}=1+\frac{1}{1+\frac{1}{x_1}}=1  +\frac{x_1}{1+x_1}=\frac{2x_1+1}  {x_1+1}

    Now I am told that x_1 is a positive number, therefore I can deduce that x_{n-1}>1

    Therefore: 1+\frac{1}{x_n}>1 \longrightarrow \frac{1}{x_n}>0 for any n (though I get confused here because originally it says n is greater than or equal to 3. Maybe I should've used a different variable such as m where 1\leq m\leq n?)

    From here it is evident that x_1 , x_2 , ... , x_n > 1 as for each one you are adding something greater than 0 onto 1. So as far as I am concerned this is now shown?


    (ii) This just proved to be some simple algebraic manipulation. I knew I can express x_1 in terms of x_2, and x_2 in terms of x_3

    So;

    \displaystyle x_1-x_2=(1+\frac{1}{x_2})-(1+\frac{1}{x_3})

    \displaystyle =\frac{x_3-x_2}{x_2x_3}

    \displaystyle =-\frac{x_2-x_3}{x_2x_3}

    (iii) Here I use my answer to (ii) and rearrange it to get:

    x_1=x_2-\frac{x_2-x_3}{x_2x_3}

    and for what they're asking to hold true I must show that the numerator on the fraction is 0.

    Using the fact that x_n=1+\frac{1}{x_1} I know it should hold for some n_k and n_{k+1} where 1\leq k \leq n

    Since x_k and x_{k+1} equate to the same expression in terms of x_1 then they must be equal to one another.

    Therefore x_k=x_{k+1} \longrightarrow x_k-x_{k+1}=0

    If we set k=2 then our fraction will indeed be equal to 0 and we get x_1=x_2

    We can play the same game and say that k is any number from 1 to n and that would mean:

    x_1=x_2=x_3=...=x_n

    So I think this is now proven?


    (iiii) Solving for x_1 is quite straight forward as x_k=1+\frac{1}{x_1}

    Setting k=1 we find that (x_1)^2-x_1-1=0 which leads us to:

    x_1=\frac{1+\sqrt5}{2} after disregarding the negative root as that would make x_1 negative. Interestingly enough this whole question is about the golden ratio. Nice stuff.
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    Thanks a bunch for making this thread, gonna start working through the Siklos booklet next week i think. Hopefully i'll be comfortable with STEP 1 by around December.
    How difficult are the questions asked in interview compared to say STEP 1?
 
 
 
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