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# Edexcel A2 C4 Mathematics June 2016 - Official Thread watch

1. (Original post by Alby1234)
Am I being completely stupid here? I have no idea where the mark scheme is getting the limits in part b) as root 2 and 0, and also it seems they may be missing a t^2? either way I'm very confused about part b if anyone could help Attachment 555089 Attachment 555089555091
You integrate with the limits in t where the limits are the values of t at the two x values you want to find the area between. Because you're finding the area between x=0 and x=2, the limits are t=root2 for x=0 and t=0 for x=2.

Finding the area you would normally do the integral between two values of x of y dx. Using the chain rule we can turn this into the integral between two values of t of y multiplied by dx/dt with respect to t:

dx = dx/dt * dt

You don't need to square y, that would be the case for a volume of revolution though.
2. I am not worried about A* I am just trying my best to get a B :P
3. anyone else tend to make a lot of mistakes in c4?
4. (Original post by Yua)
anyone else tend to make a lot of mistakes in c4?
Yes I am prone to errors in C4. Very simple things really but I just need to take my time a bit i think. Idk what else i can do except papers to revise xD

Does anyone have some difficult Differential Equation questions?
5. Do we need to know how to derive the differentiation of y = ax
6. (Original post by BrainJuice)
Do we need to know how to derive the differentiation of y = ax
My revision book says we need to but I've seen it come up in past papers (not done that many tho)
7. (Original post by BrainJuice)
Do we need to know how to derive the differentiation of y = ax
I don't think we need to know how to derive it, but it's not too difficult anyway

y = ax
lny = lnax
lny = xln(a)
x = lny/lna (lna is a constant here)
dx/dy = 1/yln(a)
dy/dx = yln(a)
dy/dx = axln(a)

Something like this
8. (Original post by BrainJuice)
Do we need to know how to derive the differentiation of y = ax
It's really not that hard, if you look at the C3 formula sheet you can see that a^x=e^(xlna), then differentiate it in this form (giving lnae^(xlna)) and change e^(xlna) back to a^x
9. When integrating by parts does anyone have a list or any tips or rules on which part should be u and which part should be dv/dx? I think I saw a helpful list online somewhere that recommended the right way for lots of examples
10. (Original post by Yua)
anyone else tend to make a lot of mistakes in c4?
yes, this morning I did a gold paper.
- I wrote two cubed terms in the binomial expansion; accidentally writing the squared term as a cube.
- copied down dx/dt wrong when writing dy/dx. 4sint, instead of 4sin2t
- did something wrong in part (b)

If we are trying to find angle ACB aren't you supposed to use vectors CA and CB rather than AC and BC?

and I need 100%
11. (Original post by NotNotBatman)
yes, this morning I did a gold paper.
- I wrote two cubed terms in the binomial expansion; accidentally writing the squared term as a cube.
- copied down dx/dt wrong when writing dy/dx. 4sint, instead of 4sin2t
- did something wrong in part (b)

If we are trying to find angle ACB aren't you supposed to use vectors CA and CB rather than AC and BC?

and I need 100%
Same here, silly mistakes in binomials and integration - missing a negative sign and such

No you would AC and BC, you need the vectors moving away from the angle not towards it
12. (Original post by Ainsleyy)
When integrating by parts does anyone have a list or any tips or rules on which part should be u and which part should be dv/dx? I think I saw a helpful list online somewhere that recommended the right way for lots of examples
I'm sure stuff like that exists, but I would say, before integrating at all, look at which one would simplify or make the integral look nicer, so kind of plan it in your head if you want to look at it that way. This could be like seeing x differentiating to 1 so that you're integrating 1 * something else, or choosing to differentiate x^2 in x^2e^x^2 so that you're integrating 2xe^x^2 etc.
13. (Original post by Yua)
Same here, silly mistakes in binomials and integration - missing a negative sign and such

No you would AC and BC, you need the vectors moving away from the angle not towards it
AC and BC go towards C dont they? Or am I going crazy
14. (Original post by Ainsleyy)
When integrating by parts does anyone have a list or any tips or rules on which part should be u and which part should be dv/dx? I think I saw a helpful list online somewhere that recommended the right way for lots of examples
My teacher said use this order of preference for the u part that you differentiate:

(n is any integer)
lnx > x^n > e^x + trig functions

lnx you can't integrate so you have to do it by parts and differentiate it
15. (Original post by Ainsleyy)
AC and BC go towards C dont they? Or am I going crazy
(Original post by Yua)
Same here, silly mistakes in binomials and integration - missing a negative sign and such

No you would AC and BC, you need the vectors moving away from the angle not towards it
Just checked you do need CA and CB, although the mark scheme finds AC and BC for some reason, I just did
-5-(-1)=4 so I got the vector CB wrong.
16. (Original post by NotNotBatman)
Just checked you do need CA and CB, although the mark scheme finds AC and BC for some reason, I just did
-5-(-1)=4 so I got the vector CB wrong.
Surely it doesn't matter which set you get? AC and BC will give the opposite sign to CA and CB but when you calculate the angle you do cos(theta) = |blah| so it's positive anyway?
17. (Original post by Swifty139)
My teacher said use this order of preference for the u part that you differentiate:

(n is any integer)
lnx > x^n > e^x + trig functions

lnx you can't integrate so you have to do it by parts and differentiate it
Thanks alot man thats very helpful
18. Guys do we need to know how to integrate by substitution without them telling us what u is? e.g integrate (sinx)^5(cosx)
19. (Original post by Ainsleyy)
Guys do we need to know how to integrate by substitution without them telling us what u is? e.g integrate (sinx)^5(cosx)
You can achieve this using standard patterns. If we work backwards eg:

Let y = (sinx)^6 (notice how i've taken the (sinx)^5 and added one to the power)

dy/dx = (using the chain rule) 6(sinx)^5(cosx)

So that means if we integrate 6(sinx)^5(cosx) we get (sinx)^6

But we are trying to integrate (sinx)^5(cosx) without the 6, so we divide our answer by six so that the integral of (sinx)^5(cosx) = (1/6)(sinx)^6)

Sorry if this is unclear!
20. Hey so I'm a retaking student just trying to boost my UMS to next grade. Which past papers would be best to do to give me the broadest/hardest variety of questions which I can work through in one day? Thanks

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