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    (Original post by tomahawker314)
    god damn this integral's a mess, just done the first of the 2 partial fractions and boy am i regretting this lol
    (Original post by Zacken)
    Yep, it's quite ugly.
    Just in terms of ugliness, the integral \displaystyle \int \frac{1}{x^4+4}\,dx requires exactly the same techniques but avoids having the pain of dealing with \sqrt{2} everywhere. (This is probably disproportionately beneficial when using LaTeX )
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    (Original post by tomahawker314)
    How hard do the integrals get in STEP 11 and 111. Are they as long, im guessing they need similar amounts of manipulation to be able to integrate, ie adding 0 to make it simpler.
    There have definitely been STEP questions where you end up finding \displaystyle \int \dfrac{1}{x^4+1}\,dx; the one I can remember has you solving an integral in terms of cosh and sinh, and then a x = e^t substitution gives you the x^4+1 integral.

    That was probably slightly on the short side for a STEP question (but then the integration questions are often on the shorter side, I think).
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    (Original post by DFranklin)
    There have definitely been STEP questions where you end up finding \displaystyle \int \dfrac{1}{x^4+1}\,dx; the one I can remember has you solving an integral in terms of cosh and sinh, and then a x = e^t substitution gives you the x^4+1 integral.

    That was probably slightly on the short side for a STEP question (but then the integration questions are often on the shorter side, I think).

    Oh my lord I have a long way to go then, that was such a struggle, no way could I do that in a reasonable time with my current integration skills (or lack of). I think a browse through the hard integral thread is in on my to-do list then.
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    (Original post by tomahawker314)
    Oh my lord I have a long way to go then, that was such a struggle, no way could I do that in a reasonable time with my current integration skills (or lack of). I think a browse through the hard integral thread is in on my to-do list then.
    Practice does make a big difference; I also think the method in the STEP question is perhaps a bit easier than the factorize the denominator into quadratics method.

    The question I had in mind, incidentally is STEP III, 2014, Q2.

    As far as the "hard integral" thread; be warned the difficulty is all over the place in that thread and most integrals are (IMHO) a lot harder than you'd be likely to see in STEP. I honestly don't believe it's going to be terribly helpful.

    FWIW, integration was definitely a weak point for me and the way I improved was going through literally hundreds of the examples in Bostock and Chandler (Pure Mathematics) - what's nice is that there's a progression in difficulty; you're not jumping straight into STEP level questions. Other books may also be good, but that one definitely worked well for me.
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    Guys, you know the Maths.org website set up by Cambridge? I'm doing the STEP foundation courses on that and I'm up to the 9th assignment. There're a few problems though: I use the hints too much. It's a problem and I feel like I can't get through the questions without them, since I've needed to use them for all but 2!

    Sometimes I'm just knee deep in algebra and I can't get out, sometimes the questions don't even make sense and the hints don't help either! There was this one time where I had to show that there were three distinct roots and thus had to have the maximum and minimum in the y positive and y negative. However, while I had one y co-ordinate sorted, the second was completely... well... you couldn't tell if it was positive or negative! It was something like (4/27)A^3 + B, where A was less than 0, B was more than 0. How are you supposed to know that that expression is less than 0? If A is -0.1 and B is 57, then it won't be less than 0 at all!

    I'm really really stressed out and I don't know what to do. I feel like I'm wasting valuable time, since I can't do the STEP questions at all. I don't think my parents will let me get a tutor, due to the cost. If I need to finish these 25 assignments by October but I have no idea how I can do this if I can't even do some of them without looking at the hints.

    Any thoughts? I'm seriously worried.
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    (Original post by Heirio)
    Guys, you know the Maths.org website set up by Cambridge? I'm doing the STEP foundation courses on that and I'm up to the 9th assignment. There're a few problems though: I use the hints too much. It's a problem and I feel like I can't get through the questions without them, since I've needed to use them for all but 2!

    Sometimes I'm just knee deep in algebra and I can't get out, sometimes the questions don't even make sense and the hints don't help either! There was this one time where I had to show that there were three distinct roots and thus had to have the maximum and minimum in the y positive and y negative. However, while I had one y co-ordinate sorted, the second was completely... well... you couldn't tell if it was positive or negative! It was something like (4/27)A^3 + B, where A was less than 0, B was more than 0. How are you supposed to know that that expression is less than 0? If A is -0.1 and B is 57, then it won't be less than 0 at all!

    I'm really really stressed out and I don't know what to do. I feel like I'm wasting valuable time, since I can't do the STEP questions at all. I don't think my parents will let me get a tutor, due to the cost. If I need to finish these 25 assignments by October but I have no idea how I can do this if I can't even do some of them without looking at the hints.

    Any thoughts? I'm seriously worried.

    How much time are you giving it before hints. If it's less than half an hour I don't think you're giving it enough time, that's the minimum you'll spend in the exam. Also what's the rush for October? STEP isn't until June and interviews aren't until December, which even then you don't need to be STEP ready I think.

    Right for that question, you treat \frac{4}{27} a^3 + b &lt;0 differently to &gt; 0. As you say there is no way of knowing from a<0 b>0. The next part requires manipulation into that form. It is the two turning points multiplied. If negative they are above and below y axis so have three roots, consider one positive and the other negative then switch, the graph is a bit differemt. The other 2 possibilities is that both turning points are negative or both are positive.

    DFranklin I'll look into that book.
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    What is the generally recommended advice for which applied modules to pick?

    I can do all 5 mechanics, or all 4 stats or a mix.
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    (Original post by mojos)
    What is the generally recommended advice for which applied modules to pick?

    I can do all 5 mechanics, or all 4 stats or a mix.
    I don't think there's generally recommended advice. It varies from person to person and what their strengths are. Personally I'd suggest a mix of the two and then learning specific topics from the higher numbered modules that come up in STEP often (e.g M1-3, S1-2 + moments of inertia, rotational stuff and equilibrium things, generating functions, plus one or two others I've undoubtedly forgot)
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    (Original post by Zacken)
    I don't think there's generally recommended advice. It varies from person to person and what their strengths are. Personally I'd suggest a mix of the two and then learning specific topics from the higher numbered modules that come up in STEP often (e.g M1-3, S1-2 + moments of inertia, rotational stuff and equilibrium things, generating functions, plus one or two others I've undoubtedly forgot)
    I was set on doing 5 mech modules was because I'm afraid the gaps from studying only specific topics instead of the whole module would make answering the applied questions very difficult.

    I read someone in this forum say that it would be better to focus on either mech or stats instead of getting a narrow understanding of both.

    As you are suggesting it, I assume this is not the case?
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    (Original post by mojos)
    As you are suggesting it, I assume this is not the case?
    Like I said, it varies from person to person. If you're set on doing all 5 mech modules, then go for that.

    [I would still suggest spending a few hours learning what a probability distribution is and what you can do with them along with basic probability theory things like expectation, conditioning and variance. That alone opens up a large choice of stats questions.]
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    (Original post by Zacken)
    Like I said, it varies from person to person. If you're set on doing all 5 mech modules, then go for that.

    [I would still suggest spending a few hours learning what a probability distribution is and what you can do with them along with basic probability theory things like expectation, conditioning and variance. That alone opens up a large choice of stats questions.]
    How about 'combinations of random variables' section in S3? I was told that's the only useful thing from S3 that would help.
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    (Original post by Student1914)
    How about 'combinations of random variables' section in S3? I was told that's the only useful thing from S3 that would help.
    That's veering towards the more advanced end of stats which isn't what I was going for in my previous answer; which was aimed at being able to do the stats questions that are just disguised pure integrals or require nothing more than knowing how to count and sum probabilities or draw tree diagrams.

    But yes - combinations of random variables, along with (M/P)GFs comes up not infrequently on STEP II(?) and III.
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    (Original post by Zacken)
    That's veering towards the more advanced end of stats which isn't what I was going for in my previous answer; which was aimed at being able to do the stats questions that are just disguised pure integrals or require nothing more than knowing how to count and sum probabilities or draw tree diagrams.

    But yes - combinations of random variables, along with (M/P)GFs comes up not infrequently on STEP II(?) and III.
    Had a quick look; the linearity of expectation operator doesn't seem to be anywhere on the Edexcel spec (there's the weaker result that E[aX+b] = aE[x] + b, but not E[X+Y] = E[X] + E[Y]); this is in the STEP (III) spec, and is something I'd expect to come up pretty often (I expect the Cambridge examiners consider it a key fundamental - I certainly do).

    It's not 100% clear looking at the STEP spec, but I don't think MGFs are on the syllabus anymore.
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    (Original post by DFranklin)
    Had a quick look; the linearity of expectation operator doesn't seem to be anywhere on the Edexcel spec (there's the weaker result that E[aX+b] = aE[x] + b, but not E[X+Y] = E[X] + E[Y]); this is in the STEP (III) spec, and is something I'd expect to come up pretty often (I expect the Cambridge examiners consider it a key fundamental - I certainly do).
    This was certainly in S3 on the old spec, I just opened up the new spec and I can't see a mention of it anywhere either, which is certainly surprising. I also had a look at the new formula booklet and whilst they mention (page 24) E(XY) = E(X)E(Y) for independent variables, I can't see linearity anywhere, whereas it used to be on the formula booklet in the old spec. All very bizarre.

    It's not 100% clear looking at the STEP spec, but I don't think MGFs are on the syllabus anymore.
    Just had a look at it, I can see what you mean. But STEP III 2008 (Q12) has a question dedicated to MGF's so I feel like it sort of is on spec, that said, I haven't seen a mention of it in any questions in 2008-2013 in a quick skim, so I'm not too sure what to think.
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    (Original post by Zacken)
    This was certainly in S3 on the old spec, I just opened up the new spec and I can't see a mention of it anywhere either, which is certainly surprising.
    Yes, why they have "two sample procedures" in the S4 spec, but linearity of expectiation is nowhere is, um, a strange declaration of prioritiies.

    Just had a look at it, I can see what you mean. But STEP III 2008 (Q12) has a question dedicated to MGF's so I feel like it sort of is on spec, that said, I haven't seen a mention of it in any questions in 2008-2013 in a quick skim, so I'm not too sure what to think.
    Yeah, it would actually be worth someone asking for clarification on this one (not that I'm going to bother).

    (Original post by Student1914)
    Quoting to draw your attention...
    (Original post by mojos)
    Ditto...
    When you look at the STEP spec, I think it's fairly clear that the most efficient way to cover what you need for STEP is to really to use the spec as a guideline rather than just think "So, I should do S3 and S4?" The examiners really do do a fair bit of picking and choosing and so you can narrow things down quite a lot.
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    1) Do I need to sit STEP 1, 2 AND 3 to get into Imperial/Cambridge? How many do I need to complete?
    2) Is it possible to get S by just doing the pure in a STEP paper?
    3) If one were to learn the new spec A Level Maths (C1/C2/C3/C4,Statistics, Mechanics) and the old spec FM (FP1, FP2, FP3, S2, M2, M3) be enough to get me S in STEP (1, 2, 3)? Of course, assuming that I learn the content well and do the past papers of STEP, practice papers, etc.
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    (Original post by thekidwhogames)
    1) Do I need to sit STEP 1, 2 AND 3 to get into Imperial/Cambridge? How many do I need to complete?
    Standard Cambridge offer requires taking STEP II and STEP III. Standard Imperial Offer requires the MAT (according to their website - and they may subsequently ask for STEP post interview).

    2) Is it possible to get S by just doing the pure in a STEP paper?
    Yes.

    3) If one were to learn the new spec A Level Maths (C1/C2/C3/C4,Statistics, Mechanics) and the old spec FM (FP1, FP2, FP3, S2, M2, M3) be enough to get me S in STEP (1, 2, 3)? Of course, assuming that I learn the content well and do the past papers of STEP, practice papers, etc.
    Yes.

    That said, I feel your questions show a lot of naivety about the entire process. There is a long and detailed post about STEP at the start of this thread, that has answers to *all * the questions you have just asked. You need to read it.
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    (Original post by DFranklin)
    Standard Cambridge offer requires taking STEP II and STEP III. Standard Imperial Offer requires the MAT (according to their website - and they may subsequently ask for STEP post interview).

    Yes.

    Yes.

    That said, I feel your questions show a lot of naivety about the entire process. There is a long and detailed post about STEP at the start of this thread, that has answers to *all * the questions you have just asked. You need to read it.
    Oh alright thanks! Yeah I just rushed to ask but I will read about it more. Again, thanks for the help!
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    (Original post by DFranklin)
    Standard Cambridge offer requires taking STEP II and STEP III. Standard Imperial Offer requires the MAT (according to their website - and they may subsequently ask for STEP post interview).
    Just FYI: Imperial don't do maths interviews (modulo special cases). They might ask for STEP post-MAT results or if you don't sit MAT but they still want to give you an offer.
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    fingers crossed I'll be applying for Cambridge Maths!
 
 
 
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