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MATHS! How do you minimise careless mistakes? watch

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    I received my mock results today, and got harangued by my Add. Maths teacher because of this:

    Q12 a): It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 3 has no real roots. [5]

    What I saw: It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 0 has no real roots. :facepalm:

    Therefore, I slaughtered my entire 12-mark question by that one stupid mistake.

    Not only that ... what is so frustrating is that my '+' gets mutated to 'x' sometimes, and I muddle up my 'cot x' and 'cos x'! :rant:

    It's not that I don't know how to do these questions ... but it's just that these careless mistakes always seem to occur! I've done a lot of practice from past year papers, but even that doesn't seem to eliminate these stupid mistakes!

    Any ideas?
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    I used to make really silly mistakes all the time. I think it's just a practice thing -- you need to get good at spotting the difference between, say, f(x) = 0 and f(0) = x (I made this mistake on the last question of my first C1 exam, which cost me dearly :p:).

    As for the + getting mutated into a ×, there are two ways you can go about this really. First is to modify your handwriting for when you're doing maths -- things like crossing 7s and zs, putting flicks on vs (to distinguish them from us), writing lower-case x as curly and then × as rigid, etc. However frankly, I just avoid using '×' altogether -- it can usually be replaced by a dot or by brackets or something else.

    Muddling up cot x and cos x is an easy mistake (as is muddling up cos x and sin x) -- I do this kind of thing all the time. The way to reduce the amount that you do it really is to just be very careful when you're using any kind of trig function.

    You just have to get good at spotting what it is you often get wrong, and then forcing yourself to check what you're doing every time you do a problem to make sure you're not making the same mistakes.
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    some thoughs for what they are worth.

    Both your issues could be symptoms of rushing.

    As to reading the question; look at how you go about it. Do you just scan over picking out bits, and letting habit fill in the rest? If so, trying saying each word in your head, one word at a time as you go through the question. Try reading the question backwards (in addition to the normal way), it might force you to notice each item!

    With writing, just take more care and make sure your letters are clearly distinguishable. If you can confuse it, how's the person marking supposed to read it? Your brain can think what you are going to write far faster than you hand can actually do the writing, so engage part of it in writing clearly, and that might dissuade it from rushing ahead and being impatient.
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    Question: How do you minimise careless mistakes?

    Answer: Differentiate them and set them equal to zero.
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    (Original post by asparkyn)
    I received my mock results today, and got harangued by my Add. Maths teacher because of this:

    Q12 a): It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 3 has no real roots. [5]

    What I saw: It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 0 has no real roots. :facepalm:

    Therefore, I slaughtered my entire 12-mark question by that one stupid mistake.

    Not only that ... what is so frustrating is that my '+' gets mutated to 'x' sometimes, and I muddle up my 'cot x' and 'cos x'! :rant:

    It's not that I don't know how to do these questions ... but it's just that these careless mistakes always seem to occur! I've done a lot of practice from past year papers, but even that doesn't seem to eliminate these stupid mistakes!

    Any ideas?
    Start caring more?
    Or double check yourself, it's really the only way.
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    Quadruple check your answers at the end.

    I always find al least a fifth of them are wrong because I read the question wrong or left out a minus sign out or something.

    Which is also why I get everything wrong in class...
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    For a couple of weeks, be really pedantic with yourself trying to make sure your handwriting is perfect, after the couple of weeks your general writing will have vastly improved without you realising it, eliminating some of the more annoying mistakes. As for maths errors, they tend to occur with signs and trig functions, so make sure you carefully space these out where possible. As for the problem of reading the question wrong, its always worth reading twice or even doing ye olde underlining the important parts, even if it does seem a bit childish. If your main source of lost marks are errors/mistakes, then you will probably be completing questions fairly easily and so should easily have enough time in the exam to read each question twice and underline it before you do it.
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    For a start read all the questions before you start to get the feel for them but when you come to do each question make sure you have read the question at least twice. Being aware of your personal typical errors will also help you.
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    (Original post by Mr M)
    Question: How do you minimise careless mistakes?

    Answer: Differentiate them and set them equal to zero.
    Oh, sure ... and then find the second derivative and then determine its nature. :p:

    (Original post by Nuodai)
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    Thanks for the really helpful advice. I do flick my 7s and my zs, and it has been quite helpful to me. Sadly, no matter how many times I check my work through, I always seem to miss out these annoying errors.

    (Original post by ghostwalker)
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    You may be right. I do tend to do my work much faster than the ordinary person. Reading the question backwards sounds like a pretty cool trick to try, thank you! I don't actually think that my mixed-up signs are due to terrible handwriting though -- I can be quite quick and neat. Maybe my eyesight is just getting bad

    (Original post by perrytheplatypus)
    Quadruple check your answers at the end.

    I always find al least a fifth of them are wrong because I read the question wrong or left out a minus sign out or something.

    Which is also why I get everything wrong in class...
    I can relate to that, although on the rare occasion that I do actually quadruple check my answers, I always replace a previously-correct answer with something wrong, because I thought it wasn't right in the first place. Then the remainder of the time is spent cursing and crossing out everything again. The horror.

    (Original post by Rubgish)
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    Thank you! Unfortunately, with IGCSEs in a week or so I don't have time to perfect my handwriting. I shall make sure that I triple-read each question before doing it. That being said, the said mistake above was an anomaly (a terrible one, at that). The usual careless mistakes I make are not due to an error in reading the question, but rather, and error in the working itself. I get so eager to solve a question (I see the "final result") that I add an extra figure in my chain rule differentiation, or my integration gets weirded up (integrating sin to become cos etc.).

    Bleargh. I may still get my method marks, but it's not the full marks that I want :rant:

    (Original post by dotty_but_good)
    For a start read all the questions before you start to get the feel for them but when you come to do each question make sure you have read the question at least twice. Being aware of your personal typical errors will also help you.
    Ahh ... :yes: I do get lazy to read those long-paragraph questions, and that might have to be changed. I am quite aware of my personal typical errors -- but no matter how much I try to look out for them, it always seems like I've missed some!
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    All the above is useful. When I do maths, I always accept that every so often, there will be a mistake that I didn't spot. So I always (unless I'm stuck for time) go back over the questions and do them again but in a quicker way to get an estimate of the answer that I can check.

    For example, if I had to solve a quadratic or trigonometric equation, I might substitute in my value of x to see if it works.

    If I had to find the minimum point of a function, I could make a sketch graph (or plot it on a graphical calculator) and see if that matches.

    If I had to integrate something between two limits (you may not have covered this yet I'm not sure) then I would calculate it in a graphical calculator and see if the answer matches. Note that this is ok in an exam because the calculator will only give the answer as a decimal and won't show you any workings out.

    There are other methods I would use, but often I would just check if my answer 'looks reasonable' so I'd check if it's much larger or smaller than what I was expecting. I know if you're doing C1 then you won't be able to use a calculator, but I hope this is helpful for other modules as well.

    Edit: Sorry, I thought you were doing A-levels. I don't know much about IGCSEs but I hope this is useful. Oh and if you do discover an error and end up with a different answer, go through your two attempts and find where the mistake was, so you know what went wrong. Don't always assume that your second attempt is the right one.
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    (Original post by Mr M)
    Question: How do you minimise careless mistakes?

    Answer: Differentiate them and set them equal to zero.
    What if careless mistakes is not a differentiable function?
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    (Original post by ttoby)
    All the above is useful. When I do maths, I always accept that every so often, there will be a mistake that I didn't spot. So I always (unless I'm stuck for time) go back over the questions and do them again but in a quicker way to get an estimate of the answer that I can check.

    For example, if I had to solve a quadratic or trigonometric equation, I might substitute in my value of x to see if it works.

    If I had to find the minimum point of a function, I could make a sketch graph (or plot it on a graphical calculator) and see if that matches.

    If I had to integrate something between two limits (you may not have covered this yet I'm not sure) then I would calculate it in a graphical calculator and see if the answer matches. Note that this is ok in an exam because the calculator will only give the answer as a decimal and won't show you any workings out.

    There are other methods I would use, but often I would just check if my answer 'looks reasonable' so I'd check if it's much larger or smaller than what I was expecting. I know if you're doing C1 then you won't be able to use a calculator, but I hope this is helpful for other modules as well.
    Yes, I do this too. Sad to say, graphical calculators aren't allowed in our exam, so I won't be able to follow through with any of your suggestions. I check if my answer "looks reasonable" when it comes to questions involving coordinate geometry where a diagram is given and you can "see" if your coordinate fits. However, it isn't quite so in other questions :sad:

    Unfortunately for me, my syllabus covers integration involving exponential functions, trigonometry, simple algebra, areas under graphs and the whole shebang. What is C1?
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    http://www.calculatorsoftware.co.uk/...ke/gallery.htm

    http://mathforum.org/library/drmath/view/52382.html
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    (Original post by asparkyn)
    Any ideas?
    do what i did, practice practice practice. these are the very books i used to sail through my exams and yes i know your frustration you will overcome this with time, trust me. here are the books.

    http://cgi.ebay.co.uk/ws/eBayISAPI.d...STRK:MESELX:IT
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    (Original post by Peace0fM1nd)
    do what i did, practice practice practice. these are the very books i used to sail through my exams and yes i know your frustration you will overcome this with time, trust me. here are the books.

    http://cgi.ebay.co.uk/ws/eBayISAPI.d...STRK:MESELX:IT
    I don't have time to go through all those books :sad: And why does this sound like a marketing ploy to get me to buy? :p:
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    For your x and + problem, i always write an algebraic x like this: x. as a c next to a backwards c.
    I also had a similar problem of seeing something different or missing out a word which made the question different, go through the question and highlight the important bits such as the f(x) = 3 and then copy it down and make a list of the "important points", at least then if you do **** up the question with another misreading then the examiner might give you a mark for just a copying error
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    (Original post by asparkyn)
    I don't have time to go through all those books :sad: And why does this sound like a marketing ploy to get me to buy? :p:
    why i never. haha, in what sense am i a marketing ploy lol. i am only helping because ive been through it all and i know how frustrating it can be at times. hence, im sharing my own experience with you just in case it might help and yes they are the very books i used. if your intrested then fair enough dude :cool:
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    (Original post by asparkyn)
    I received my mock results today, and got harangued by my Add. Maths teacher because of this:

    Q12 a): It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 3 has no real roots. [5]

    What I saw: It is given that f(x) = 4x^2 + kx + k. Find the set of values of k for which the equation f(x) = 0 has no real roots. :facepalm:

    Therefore, I slaughtered my entire 12-mark question by that one stupid mistake.

    Not only that ... what is so frustrating is that my '+' gets mutated to 'x' sometimes, and I muddle up my 'cot x' and 'cos x'! :rant:

    It's not that I don't know how to do these questions ... but it's just that these careless mistakes always seem to occur! I've done a lot of practice from past year papers, but even that doesn't seem to eliminate these stupid mistakes!

    Any ideas?
    multiply like this (2)(3) = 6
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    (Original post by asparkyn)
    Yes, I do this too. Sad to say, graphical calculators aren't allowed in our exam, so I won't be able to follow through with any of your suggestions. I check if my answer "looks reasonable" when it comes to questions involving coordinate geometry where a diagram is given and you can "see" if your coordinate fits. However, it isn't quite so in other questions :sad:

    Unfortunately for me, my syllabus covers integration involving exponential functions, trigonometry, simple algebra, areas under graphs and the whole shebang. What is C1?
    C1 is Core 1, the first module of A-level maths which covers things like differentiation and coordinates. If you can't use a graphical calculator, you could always try and picture the graphs and get an approximation e.g. \displaystyle\int_0^1 x^2 dx will have an answer that's approximately the area of a right angled triangle going through (0,0), (1,0) and (1,1).
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    I make loads of mistakes when I'm tired. It might just be that simple. Sleep more! Or at least have some tea :p:
 
 
 
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