A level maths bag of tricks/useful things

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Angryification
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Report Thread starter 6 years ago
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So anyone who has done enough A level maths questions and/or does further maths will have found alternative/quicker routes around questions so I thought it'd be a good idea to post them here. Would also be nice if you could post an explanation or a link to one.


C4 - a lot of these cross over with FP2, but not everyone does FP2.
- Quick method of doing partial fractions - cover up method. I found about this while doing questions in the library. I thought I was special. http://www.sinclair.edu/centers/math...lFractions.pdf
- If you have a binomial expansion question where the index in an integer, it may be quicker to use Maclaurin's expansion. This is given on the FP2 section of the formula sheet for Edexcel and it's pretty straight forward.
- If a differential equation can be put into the form

 y'+Py=Q
You can multiply by  e^{\int P\ dx} and the left hand side is now the derivative of  ye^{\int P\ dx}

Now
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\frac{d}{dx} ye^{\int P\ dx} = Qe^{\int P\ dx




FP2
- If you have a differential equation in the form
 ay''+by'+cy=f(x) and you are given conditions at x=0, you can use a Laplace transform to solve it in a small number of steps. You have to be very good at using this and requires memorising a few transforms. I cannot find an explanation for why it works right now.

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m4ths/maths247
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Remembering the trapezium rule as 1/2 x h x (1st + last + 2 lots of the rest) rather than using the formula book could be an example.
Are you asking for 'cheats' or more efficient memory aids?
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Angryification
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Anything that will help people do the question correctly. My teacher said that any advanced method is valid [for Edexcel].
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user2020user
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Sometimes, expressing integrands in terms of complex exponentials can save a great deal of time. I've only seen this a few times however.
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