STEP Prep Thread 2017

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    Here is a tracker sheet I made last year for STEP if anyone is interested. It's basic but thought it may be helpful for some people.
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    Does anyone know what the marking is like for partial solutions? Since they don't show it I can't really tell how much each part of the question is worth

    This is the question I was doing
    https://gyazo.com/f5f40b6df07115a5857b2354da564df9
    I got up to the last part where I forgot to make one of the substitutions. Since it was only a 'deduce that' I assume that it wasn't worth the bulk of the marks, but around how many would that last part be?
    Thanks

    Edit: Just realised in the Siklos book there was so much more help... Probably wouldn't have been able to do it otherwise LOL
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    (Original post by solC)
    Does anyone know what the marking is like for partial solutions? Since they don't show it I can't really tell how much each part of the question is worth

    This is the question I was doing
    https://gyazo.com/f5f40b6df07115a5857b2354da564df9
    I got up to the last part where I forgot to make one of the substitutions. Since it was only a 'deduce that' I assume that it wasn't worth the bulk of the marks, but around how many would that last part be?
    Thanks
    I'd guess 4 or 5. I don't believe that final part wants you to use one of the t substitutions mentioned above though. Much more likely is this:

    Spoiler:
    Show


    Use the substitution  \theta \rightarrow \frac{\pi}{2} - \theta to get:

     \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\sin \alpha \cos \theta} = \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\sin \alpha \sin \theta}

     = \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\cos (\frac{\pi}{2} - \alpha ) \sin \theta}

     = \dfrac{\frac{\pi}{2}-\alpha}{\sin (\frac{\pi}{2}-\alpha )}

    Whilst they'll probably award some kind of marks for doing it using the substitutions again, it's unlikely to be the full ones and you should be very wary of ensuring you're fully deducing it.



    For the record the above solution I just posted (don't open the spoiler if you don't want it spoiled) demonstrates the sort of trick you should always have in mind whenever you see trig integrals within these limits on a STEP question.
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    (Original post by DJMayes)
    I'd guess 4 or 5. I don't believe that final part wants you to use one of the t substitutions mentioned above though. Much more likely is this:
    Spoiler:
    Show


    Use the substitution  \theta \rightarrow \frac{\pi}{2} - \theta to get:

     \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\sin \alpha \cos \theta} = \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\sin \alpha \sin \theta}

     = \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\cos (\frac{\pi}{2} - \alpha ) \sin \theta}

     = \dfrac{\frac{\pi}{2}-\alpha}{\sin (\frac{\pi}{2}-\alpha )}

    Whilst they'll probably award some kind of marks for doing it using the substitutions again, it's unlikely to be the full ones and you should be very wary of ensuring you're fully deducing it.



    For the record the above solution I just posted (don't open the spoiler if you don't want it spoiled) demonstrates the sort of trick you should always have in mind whenever you see trig integrals within these limits on a STEP question.
    Yeah, I actually got the first substitution right so I got up to
     \displaystyle\int_0^{\frac{\pi}{  2}} \dfrac{d\theta}{1+\sin \alpha \sin \theta}
    But then I forgot to change the  sin\alpha into a cosine.
    (It did take me a while to realise what to do though lol)
    Thanks, I wasn't really looking for that sort of sub so that's probably why it took so long to see it.
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    So, I'm doing my first STEP question
    1= 0+1
    2+3+4 = 1+8
    5+6+7+8+9 = 8+27
    10+11+12+13+14+15+16=27+64

    Guess a general law.

    So I've noted that

    1=0^3+1^3
    2+3+4 = 1^3+2^3
    5+6+7+8+9=2^3+3^3
    10+11+12+13+14+15+16 =3^3+4^3

    But I can't "guess the general law".
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    (Original post by NotNotBatman)
    So, I'm doing my first STEP question
    1= 0+1
    2+3+4 = 1+8
    5+6+7+8+9 = 8+27
    10+11+12+13+14+15+16=27+64

    Guess a general law.

    So I've noted that

    1=0^3+1^3
    2+3+4 = 1^3+2^3
    5+6+7+8+9=2^3+3^3
    10+11+12+13+14+15+16 =3^3+4^3

    But I can't "guess the general law".
    Ah I remember doing this one recently

    Observe the pattern. n^3+(n+1)^3=\sum r and just try to figure out the limits of the sum where n\geq 0

    For example, the first number of each result is always n^2+1 (the 1, 2, 5, 10, ...) to give you a hint. Can you express the last term of each summation of integers in terms of n?

    Once you have your limits, express the sum in terms of n; like you know that the sum of integers from 1 to n is \frac{1}{2}n(n+1). But I think a part previously to that should help you skip this step? Can't clearly remember that one.
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    (Original post by RDKGames)
    Ah I remember doing this one recently

    Observe the pattern. n^3+(n+1)^3=\sum r and just try to figure out the limits of the sum where n\geq 0

    For example, the first number of each result is always n^2+1 (the 1, 2, 5, 10, ...) to give you a hint. Can you express the last term of each summation of integers in terms of n?

    Once you have your limits, express the sum in terms of n; like you know that the sum of integers from 1 to n is \frac{1}{2}n(n+1)
    What I had was;

     (n^2+1) + (n^2+2) + (n^2+3) + \cdots + (n+1)^2 = n^3 + (n+1)^3

    I think the general law is \displaystyle \sum_{r=k}^{(k+1)^2}n=(n+1)^3+n^  3 , k \in \mathbb{N}
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    (Original post by NotNotBatman)
    What I had was;

     (n^2+1) + (n^2+2) + (n^2+3) + \cdots + (n+1)^2 = n^3 + (n+1)^3

    I think the general law is \displaystyle \sum_{r=n}^{(n+1)^2}n=(n+1)^3+n^  3 , k \in \mathbb{N}
    That's right, but the sum should read:  \displaystyle \sum_{r=n^2+1}^{(n+1)^2}r=(n+1)^  3+n^  3 , n \in \mathbb{N}

    To express it differently, try and use the part previous to that to help you. I think it fits perfectly for you when you have rewritten it as:

     (n^2+1) + (n^2+2) + (n^2+3) + \cdots + (n+1)^2 = n^3 + (n+1)^3
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    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
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    (Original post by Zacken)
    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
    Wow!


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    (Original post by Zacken)
    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
    Very convenient. Thanks.
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    (Original post by Zacken)
    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
    I swear I came across this site earlier this year, then couldnt find it again. is it possible it was released for a quick test and I happened to find it at the right time? :lol:
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    (Original post by EnglishMuon)
    I swear I came across this site earlier this year, then couldnt find it again. is it possible it was released for a quick test and I happened to find it at the right time? :lol:
    It's been out on Jesus's private-ish servers or something like that for a while, but it was public the entire time, just not listed anywhere. It's just been moved to a proper domain now. I do not know how you stumbled across it. :lol:
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    (Original post by Zacken)
    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
    Brilliant, cheers!
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    (Original post by Zacken)
    Check the end of Section 1 in the OP for a cool new addition!

    Dr. Siklos has released a cool new STEP database for looking up questions on specific topics/years/and various other filters you can think of at: http://stepdatabase.maths.org/index.html

    Knock yourselves out!
    Thank you
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    If I get an offer from Cambride I'll have 13 Maths exams. welp.
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    (Original post by Mitchb777dotcom)
    If I get an offer from Cambride I'll have 13 Maths exams. welp.
    You should do all three STEP papers anyway tbh; I did.
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    (Original post by IrrationalRoot)
    You should do all three STEP papers anyway tbh; I did.
    Yeah, time to get revising soon haha
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    Hi bit early as I am hoping to start step preparation in the new year. I do not have the best academic past so am planning to sit half my a levels this year and half the following my plan was to take step this year as well (academic year btw) step 1 and 2 and if i get very good module grades and 1 or better in step 1 and 2 then possibly step 3 the following year with intent of applying to Cambridge and having the option to take a year out and make a second bid in the highly likely event they reject me anyway.

    So could it hurt my uni application if i took step and flunked it as i know you have to declare exam history on ucas? my plan is to have at least c1-c4 done before end dec and hopefully the full maths A level (I mean done as in have the realistic view could get 90+ in exams I know i cant sit exams in jan) is it a terrible idea to sit them this academic year?

    also if i do go ahead and sit these papers what additional modules are a good idea to sit? since all my exams will be A level maths papers either maths further maths and statistics or maths further maths and additional maths. I might as well make sure i study the best modules this year for giving me the best chance at the step papers.

    from what I gather so far C1-C4 are essential and M1 and M2 really help with mechanics questions and S1 and S2 needed for statistics questions.

    I am planing on sitting 9-11 modules this academic year, at least half and an additional module or 2 if i can to take pressure off a bit for the following year.

    I am aware that whilst all I should need is C1-C4 and S1-2 plus M1-2 but have heard that other reading in maths can help or make the paper easier.

    so on top of these modules which I am sitting anyway which other 1-3 modules are good choice for helping me perform on the step papers?

    note I am aware if i do statistics A level it would make sense to sit S1-S3 so bank the AS, however I may do the additional further maths option with edexcel instead, still undecided and even if i do the AQA option I still hope to get 1-2 additional modules in as well.

    so advice would be much appreciated thanks.
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    (Original post by Luke7456)
    So could it hurt my uni application if i took step and flunked it as i know you have to declare exam history on ucas? my plan is to have at least c1-c4 done before end dec and hopefully the full maths A level (I mean done as in have the realistic view could get 90+ in exams I know i cant sit exams in jan) is it a terrible idea to sit them this academic year?

    [...]

    so advice would be much appreciated thanks.
    Yes, sitting and flunking the step exams is pretty much the best way to ensure that your application will be unsuccessful. Literally anything else would be better than doing that.

    Yes, in my opinion, it's a pretty terrible idea to be sitting STEP this year. Take your time, there's no rush, do it next academic year. STEP is not something to be trifled with.
 
 
 
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