Edexcel A2 C4 Mathematics June 2016 - Official Thread

Does anyone have an understandable proof for the integral of 2^x being (2^x)/ln2? Is it something we need to be able to prove?

Just use derivative of 2^x

2^x = e^(log(2^x)) = e^(xlog2)
Therefore derivative is log2e^(xlog2) = log2e^(log(2^x)) = log2(2^x)

hence the derivative of (2^x)/log2 is just log2(2^x)/log2 = 2^x

(note I mean the natural logarithm by log)

Does anyone have an understandable proof for the integral of 2^x being (2^x)/ln2? Is it something we need to be able to prove?

You mean Edexcel C4 June 15?

I did that paper last year and got 62/100 (c) ums.
I remember dropping marks everywhere.

Just make sure you work hard on all areas on C4 & that you've seen
literally everything, especially for that last question that threw everyone off.

In my opinion, only hardest bits on that paper are: last q on the vectors (if you drew a clear diagram its simple), that implicit differentiation question where you have to times on through on the left @y and that realise integrating 2^x = 2^x/ln(2)

Keep at it, don't let 1 paper performance stop you. Just realise where you dropped marks and your mistakes and move on.

prove
cot2x + cosec2x = cotx

in two simple steps

cot2x + cosec 2x = (cos2x)/sin2x +1/sin2x
=(2cos^(2)x)/2sinxcosx
=cosx/sinx
=cotx

prove
cot2x + cosec2x = cotx

in two simple steps

I have only just found out about the rule which stops you from having a mix of applied units in your normal maths alevel (eg: D1 in AS can't be followed by M2 in A2)

However is it possible to have this combination:

Maths- D1 in AS then M1 in A2
Further- S1 and S2 in AS then M2 and S3 in A2

??

cot 2x + cosec 2x = cos x / sin x = cot x

. Why is it every time I'm doing a seperating the variables question it seems like the side you take the constant to is guesswork?

e.g, dy/dx= KY.

From there you can either do:

the intergral of 1/Y = The intergral of K.

Or you can do:

The intergral of 1/KY= The intergral of 0

There are some questions where it doesn't matter at all and you'll easily get the same "C" + same final solution regardless of which way you did it. Yet there are other questions where it completely over complicates your answer if you do the one that Edexcel didn't want. It genuinely pisses me off. Am I missing something (or messing up an easy step)? Or is it that just how it is?

There's a problem if you think that dividing both sides by KY gives you 0...

if you have: dy/dx = ky

then this can be the same thing as integral of 1/(ky) dy = integral of 1 dx.

Oh that's what I meant. Not sure why I typed in 0. But the point stands, doing it either way vastly changed how difficult it it to get what's in the mark scheme.

Just have a guy feeling the vectors question next week will be tricky :/


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You're probably just missing an easy step, then. Post your working for an example.