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# Edexcel Core 3 - 21st June 2016 AM watch

https://b3755649dbd1afe3db91a899c3b9...%20Edexcel.pdf

Solomon Paper H
Question 4(b)?
Any ideas? Thanks!
Simultaneous equations. They give you two x values and corresponding y values for f(x)
2. e^x+3e^-x=4.

Why can't I do:
x+ln(3)+ln(e^-x)=ln(4)
x-x=ln(4/3)

My x's keep cancelling out
3. (Original post by Anon_98)
Um, well personally I'm just doing a past paper + posting here everytime I get stuck/find the mark schemes aren't helpful enough.

Perhaps also use exam solutions if you really don't understand a topic/something?

Repeat until bedtime?
Thanks I've done every past paper, all the gold papers and really can't be bothered to do any of the past papers again.
4. 13 1 20 8 42 (sorry to keep bombarding you like this)

In this:

Attachment 553742553744 Attachment 553742553744553700 [attach]5.537425537445537e+23[/attach]

I understand that k lies between 11 and 5, but why is the 5 < k not 5 <= k?
Attached Images

5. (Original post by joodaa)
I'd use the points they have already given you to make two simultaneous equations
(Original post by -Bex-)
subbing the stationary points into formula (y = a+bcosecx) gives:

-1 = a+b(1)
-5 = a+b(-1)

as: cosec(π/2) = 1cosec(2π/3) = -1

then it's just a simultaneous equation
(Original post by Craig1998)
You are given some coordinates that lie on the graph.
Cheers guys!
6. (Original post by Don Pedro K.)
Can someone explain how their working gives the range? I understand the one where you use x = 0, but I don't get the second one. Do you sub in a massive value to find the asymptote, which is the min value for the range? 13 1 20 8 42

Attachment 553734
Yes, as x tends towards infinity, it will be (constant / twice that constant) so it is equal to half. I suggest trying to get a better understanding. Put x as 1000000 in that formula you will see you will get 0.500... the numbers won't make a big difference as x tends to 0.
7. (Original post by particlestudent)
e^x+3e^-x=4.

Why can't I do:
x+ln(3)+ln(e^-x)=ln(4)
x-x=ln(4/3)

My x's keep cancelling out
Have to bring ln to both sides not each term. Times each term by e^x and then its a quadratic answer ln3
8. (Original post by flylikeafly)
Thanks I've done every past paper, all the gold papers and really can't be bothered to do any of the past papers again.
Well... if you've done all that then uh your initial question was really misleading.

+ If you can't be bothered then I guess don't? There's no point overworking if you've done all you can.
9. (Original post by particlestudent)
e^x+3e^-x=4.

Why can't I do:
x+ln(3)+ln(e^-x)=ln(4)
x-x=ln(4/3)

My x's keep cancelling out
This is a quadratic in disguise.

Adjust it to make this: e^x + 3/e^x = 4
Then multiply by e^x
This will give you e^2x + 3 = 4e^x
Rearrange : e^2x - 4e^x +3

Now you should notice it is in the form of a quadratic.
I often set e^x = n --> this makes it easier to factorise
This would make it: n^2 - 4n +3

Then you can just factorise : (n-3)(n-1)
Thus n=3 and n=1
Then sub back in e^x :
e^x = 3 and e^x = 1
And i'm sure you know how to do the rest.

Hope this helps.
10. (Original post by particlestudent)
e^x+3e^-x=4.

Why can't I do:
x+ln(3)+ln(e^-x)=ln(4)
x-x=ln(4/3)

My x's keep cancelling out
You're using log rules wrong. Try this method

e^x + 3/e^x = 4
multiply by e^x
e^2x + 3 = 4e^x
subtract 4e^x
e^2x -4e^x +3 = 0

(e^x -3)(e^x -1) = 0
e^x = 3 e^x = 1
Use ln
x = ln(3) x = 0
11. (Original post by particlestudent)
e^x+3e^-x=4.

Why can't I do:
x+ln(3)+ln(e^-x)=ln(4)
x-x=ln(4/3)

My x's keep cancelling out
Because e^-x is 1/e^x, therefore In(e^-x) cannot equal -x.
12. Thanks guys!
13. In the formula booklet under trig identities, theres those for SinA+SInB =2Sin(A+b/2) cos(A-B/2) etc , what topic does this lie under? I remember something with P+Q method doing it in class but I haven't seen a edexcel question like that and Im confused on how you would apply or prove them.
14. Please could someone help with this question?
Spoiler:
Show
15. (Original post by Don Pedro K.)
13 1 20 8 42 (sorry to keep bombarding you like this)

In this:

Attachment 553742553744 Attachment 553742553744553700 [attach]5.537425537445537e+23[/attach]

I understand that k lies between 11 and 5, but why is the 5 < k not 5 <= k?
What paper is this?
16. It doesn't matter if you use f dash (x) or dy/dx right? Still gets the mark?
17. (Original post by ryanroks1)
Please could someone help with this question?
Spoiler:
Show
If theta = arcsin x then: sin (theta) = x

Thus cot theta which is cos theta/ sin theta
is cos theta/ x
Use identities from here.
18. (Original post by ryanroks1)
Please could someone help with this question?
Spoiler:
Show
As theta = arcsinx
You can simply say that sin(theta) = x
As sin(arcsinx) = x
Sub in for x and think of your trig identities
What paper is this?
Jan 14 (IAL)
20. (Original post by flylikeafly)
Does anyone know how to do 8b thanks
https://07a69ccf283966549a9350d1a669...%20Edexcel.pdf
It's essentially asking for the greatest value the equation could output.
You should know that as t tends to infinity, e^-t tends to 0

As proof, type e^-10000000 into your calculator, should give you 0

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