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The 2012 STEP Results Discussion Thread

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    (Original post by number23)
    Are you allowed a formula booklet for STEP? Also, tips in preperaring for the exams?
    Yep. I've still got my three STEP formula books somewhere.
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    (Original post by Zuzuzu)
    Yep. I've still got my three STEP formula books somewhere.
    Out of interest, which uni are you at now?
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    (Original post by gff)
    Out of interest, which uni are you at now?
    I'm at UCL at the moment.
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    Guys could I have some advice on a solution I wrote.

    I know people have said you'd get full marks if you reach the right answer regardless of how you got there - but what if your working wasn't sufficient (or didn't consider all cases)? Surely you'd drop some marks..?

    Anyway, STEP I 2001 Q2ii: (And as it were, Q14 in Siklos' latest booklet)

    Solve the inequality:

     \sqrt{3x+10} > 2 + \sqrt{x+4}
    This reminds me of those C1 questions - where students were often penalised for randomly introducting an equality sign in order to quickly find the 'critical values' for an inequality equation to solve. Unfortunately I was one of them :sad:.

    Here's what I did:

    Spoiler:
    Show
    Consider the case where  \sqrt{3x+10} = 2 + \sqrt{x+4} . After squaring (twice) and rearranging, the expression becomes  (x+3)(x-5) = 0 and it becomes apparent that the 'critical' regions to consider for the question are -\frac{10}{3} \le x < -3, -3 < x < 5, and  x > 5. The restriction  x \ge -\frac{10}{3} is given in the question, but should probably be obvious anyway at first sight of the inital equation. Plugging in any value from each critical region will quickly show that the only one that works is  x > 5 - which is the only solution.


    Would that be sufficient for full marks? Bearing in mind this is only half a question - but to be honest no harder (or easier) than the first part. This looks considerably shorter than what's in the mark scheme...
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    Does anyone know what happens if you complete a whole STEP question but make one algebraic slip that causes you to get the wrong final answer given that you followed the correct method all the way through and demonstrated that you would have reached the right answer if you hadn't put a plus instead of a minus for example?
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    (Original post by Ree69)
    This reminds me of those C1 questions - where students were often penalised for randomly introducting an equality sign in order to quickly find the 'critical values' for an inequality equation to solve. Unfortunately I was one of them :sad:.
    Any solution that gets you the right answer (and, presumably, doesn't skip anything / involves an error) will get you full marks.

    I've never heard of this part of the C1 regime - when I took it, I forced equality as instructed by my teacher! What exam board are you on?

    ----------

    On a (kind of) related note, I found this nice tidbit from Silky McSilk:

    STEP questions are marked out of 20; no bonus marks, no alphas and betas, no extra credit for supposedly `neat' solutions. Borderlines are based on total marks and no other information from the scripts is used in the grading.

    The scripts of the Cambridge applicants are available for Directors of Studies to see in August, so that they can decide whether to accept an applicant who has not achieved the required conditions.


    Source. Any thoughts - does this change anything, or was it already common knowledge?

    Another interesting idea from a dozen or so years ago: STEP answers are weighted so that near-complete solutions are worth more than they should be. (Susan Langley's 9:15am post). I'm thinking this doesn't apply any more - STEP stopped saying "Extra credit is given for complete solutions" many years ago - but any thoughts?
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    (Original post by oh_1993)
    Does anyone know what happens if you complete a whole STEP question but make one algebraic slip that causes you to get the wrong final answer given that you followed the correct method all the way through and demonstrated that you would have reached the right answer if you hadn't put a plus instead of a minus for example?
    I think you just lose a few marks. Most of the marks in STEP are method marks, with a few "accuracy" marks too, but you wouldn't be left to die in a fiery pit just because you failed to appease the demons of sign...
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    (Original post by Ree69)
    Guys could I have some advice on a solution I wrote.
    I would think that you would get the marks for this question -- you've done the important bits and arrived at an answer.

    (Now I realised which sides are non-negative -- skim reading solutions isn't a good habit.)
    Spoiler:
    Show

    "If both sides are non-negative, that is if ``x > -1", we can square both sides again without changing the direction of the inequality. (Take x = -1/2, 1/2)
    But, if x < -1 , the inequality cannot be satisfied since the right hand side is always non-negative."

    It is certainly the case that squaring an inequality with non-negative sides is fine, but doing so if one of them isn't, or even both, is a dangerous tool.


    As a matter of fact, I would have done this question as follows.
    Spoiler:
    Show

    Observe that both of the sides are non-negative, and hence, squaring produces x + 1 > 2\sqrt{x + 4}.
    Now, we note that -4 \leq x and substitute v = x + 4, v \geq 0.

    Hence, we obtain v - 3 > 2\sqrt{v} \implies (\sqrt{v} + 1)(\sqrt{v} - 3) > 0, and it follows that x + 4 > 9.

    No spurious results, etc. However, I know why Siklos' emphasises on those things, and you'd need to understand them well.
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    (Original post by Ree69)
    ..
    Looks fine to me (I haven't checked the actual algebra). Might want to say something along the lines of "both sides are continuous, so the inequality can only change direction at the critical points".

    (Original post by oh_1993)
    ..
    For a single algebraic slip, I would expect you to lose 1-2 marks.
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    (Original post by Ree69)
    Guys could I have some advice on a solution I wrote.

    I know people have said you'd get full marks if you reach the right answer regardless of how you got there - but what if your working wasn't sufficient (or didn't consider all cases)? Surely you'd drop some marks..?
    Just to point out something which hopefully is obvious... you get full marks if you reach the right answer regardless of any correct method. You can't get lucky by randomly making things up and somehow getting the required solution
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    (Original post by shamika)
    Just to point out something which hopefully is obvious... you get full marks if you reach the right answer regardless of any correct method. You can't get lucky by randomly making things up and somehow getting the required solution
    So even if the question was find the sum to infinity of something and you just literally wrote down the answer e.g. 8 then you would get 20 marks if that was the entire question?
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    (Original post by oh_1993)
    So even if the question was find the sum to infinity of something and you just literally wrote down the answer e.g. 8 then you would get 20 marks if that was the entire question?
    Q1 1992 STEP I is a good example of this (it asks you to calculate the day of some date). There's plenty of ways to do this, but theoretically you can just do the calculation long hand until you reach the given date. But just writing 'Sunday' (say) is not sufficient, and would get you 0. You have to be able to convince the examiner that your method was correct.

    Note that this is particularly important when involving limits or sums to infinity, because as you'll see at university there's all sort of fun and games that could happen with such a sum. (You don't need to worry about trying to prove anything rigorously for STEP, as long as you use your A-Level methods and some intuition you should be fine.)
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    (Original post by shamika)
    Just to point out something which hopefully is obvious... you get full marks if you reach the right answer regardless of any correct method. You can't get lucky by randomly making things up and somehow getting the required solution
    Well I suppose not, but I've seen plenty of 'show that' questions - where it may be easy to fudge the working to get the required answer.

    But if you chose to tackle the question in an unexpected manner, but still managed to achieve the desired result - how sure could the marker be whether this is fudged or not?
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    (Original post by gff)
    It is certainly the case that squaring an inequality with non-negative sides is fine, but doing so if one of them isn't, or even both, is a dangerous tool.
    Yeah, which is why I introduced the equality sign into the question!

    Leaving the inequality sign in the question would force me to constantly think whether my algebraic manipulation is correct (well whether the direction of the inequality is correct). Such a pain that is...
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    (Original post by Ree69)
    Well I suppose not, but I've seen plenty of 'show that' questions - where it may be easy to fudge the working to get the required answer.

    But if you chose to tackle the question in an unexpected manner, but still managed to achieve the desired result - how sure could the marker be whether this is fudged or not?
    Because the examiner is experienced enough to follow a valid mathematical argument? (Was that what you meant?)

    Note that if a method is specified on the paper, you'll probably get no marks if you do it another way, particularly if your way is substantially easier than the method required on the paper.
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    (Original post by Xero Xenith)
    Any solution that gets you the right answer (and, presumably, doesn't skip anything / involves an error) will get you full marks.

    I've never heard of this part of the C1 regime - when I took it, I forced equality as instructed by my teacher! What exam board are you on?
    OCR. I got battered by my teacher for writing stuff like:

     x^2 - 3x + 2 > 0



(x-2)(x-1) = 0

    critical values = 1, 2
    Not only was I too lazy to write words (or even connectives/implication symbols), but it would've been incorrect unless I worded it very carefully.

    So now I've become very careful when trying to introduce equality symbols in equations that have inequality symbols (which are meant to be solved). In all honesty though, I do find it a lot easier when doing so - especially for complicated inequalities.
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    (Original post by shamika)
    Because the examiner is experienced enough to follow a valid mathematical argument? (Was that what you meant?)

    Note that if a method is specified on the paper, you'll probably get no marks if you do it another way, particularly if your way is substantially easier than the method required on the paper.
    I guess, but I was good at fudging answers last year (well, good enough to deceive my teacher!).

    Yeah I know, it's the ol' "hence..." versus "hence, or otherwise, ..."
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    (Original post by DFranklin)
    ...

    (Original post by shamika)
    ...
    +anyone else who knows university level maths.
    Are there any things that you can think of that at A level is not considered at all but would really annoy someone with knowledge of higher level maths like the people who mark our papers. For example: limits. I'm not sure how to express myself when regarding limits as I always have a sneaky feeling a pure mathematician would look at my work and go fuuuuuuuuuuuu. I try not to make my statements stronger than I need them by writing stuff like "sinx behaves like x for small x".
    Similarly with infinite sums.
    I guess my question is: Are there any things we should be careful of doing that probably wouldn't matter to an a level examiner but might really bother a postgrad marker?
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    I don't think the STEP markers will be particularly concerned about rigorous handling of limits etc.

    There are a couple of things that come to mind but I suspect you already know them.

    You're expected to be clear about how logical arguments work: the difference between "implies", "is implied by", "implies and is implied by". Things like proof using the contrapositive, what a counter example is, etc.

    When the STEP examiners say things like "hence" or "use this result to...", you really have to use the previous result or you'll be docked marks. To be honest I think they're pretty harsh on this one; I generally think I'm pretty good at understanding "this is what they want you to do" but even so there have been several questions where I'd probably have lost marks for not doing things the way they expected.

    --

    One that I don't think the examiners will mark you down for, but falls into "really annoy someone" (if that someone is me!): people writing down a load of lines of maths without anything connecting one line to the next. Actually having a logical connected argument will put you well ahead of the pack.
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    (Original post by DFranklin)
    I don't think the STEP markers will be particularly concerned about rigorous handling of limits etc.

    There are a couple of things that come to mind but I suspect you already know them.

    You're expected to be clear about how logical arguments work: the difference between "implies", "is implied by", "implies and is implied by". Things like proof using the contrapositive, what a counter example is, etc.

    When the STEP examiners say things like "hence" or "use this result to...", you really have to use the previous result or you'll be docked marks. To be honest I think they're pretty harsh on this one; I generally think I'm pretty good at understanding "this is what they want you to do" but even so there have been several questions where I'd probably have lost marks for not doing things the way they expected.

    --

    One that I don't think the examiners will mark you down for, but falls into "really annoy someone" (if that someone is me!): people writing down a load of lines of maths without anything connecting one line to the next. Actually having a logical connected argument will put you well ahead of the pack.
    Totally agree with all of this. I was going to write nearly exactly the same thing. DFranklin's point about not writing a logically connected argument would annoy me too, but its not necessarily something you would be expected to do perfectly for STEP. At university however, people were penalised harshly for it (note that there's plenty of time in your first year of university to practise writing your proofs logically and concisely). Anyone confidently using 'implies' and 'is implied by' would impress me and naturally portray themselves favourably.

    One thing that is tangentially related to this is how mechanics questions are answered. There's two things from examiners reports that really baffle me:

    - people aren't drawing (complete) diagrams as a matter of course
    - people use a principle without stating it (I would clearly write down even 'using conservation of energy' or 'resolving forces tangentially to plane' since it makes it so much easier to see what you're doing if it unfortunately goes wrong).

    If you've solved the problem then fair enough, you'll probably get the vast majority of the marks anyway. But surely for those who get halfway through and are stuck, drawing a diagram and explaining what you're doing can only help clarify thoughts? (There is an argument to say that if you can solve a problem without a diagram you're saving a few minutes by drawing one out by I would be shocked if that is a genuine time saving technique).

    The only other thing to note is that limits at STEP level are (necessarily) dealt with in a very wishy-washy way. As long as you get the idea and are able to explain in words what it is you're trying to do you should be fine. I think the point of those questions is to see whether you have that intuition, not whether you can deal with limits rigorously.

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