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# FP3

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1. http://pastpapers.download.wjec.co.uk/s15-0979-01.pdf
In 6ci, the mark scheme says x=2sintheta
Like how am i supposed to know that?
2. (Original post by Ayaz789)
http://pastpapers.download.wjec.co.uk/s15-0979-01.pdf
In 6ci, the mark scheme says x=2sintheta
Like how am i supposed to know that?
You want 4-x^2 to turn into a perfect square, so note that 1-sin^2x = cos^2x -> 4-4sin^2x=4cos^2x -> 4-(2sinx)^2=4cos^2x, so change x to 2sintheta as required so that you get 4cos^2theta under the square root, giving 2costheta.
3. It is quite a standard substitution.
4. (Original post by Ayaz789)
http://pastpapers.download.wjec.co.uk/s15-0979-01.pdf
In 6ci, the mark scheme says x=2sintheta
Like how am i supposed to know that?
The biggest hint is that the value of the integral is , so it MUST be a trig substitution, and once you know that the sub is very obvious.
5. This is not really related to FP3, but could someone please explain how to do this question?

"On a clear day, you are on an aeroplane which is at 38,000 ft above the middle of the Pacific ocean. Taking the radius of the earth as 6,400km, what is the approximate distance between you and the horizon of the earth? (1ft=0.3048m)"

Thank You
6. (Original post by SmithAmelia)
This is not really related to FP3, but could someone please explain how to do this question?

"On a clear day, you are on an aeroplane which is at 38,000 ft above the middle of the Pacific ocean. Taking the radius of the earth as 6,400km, what is the approximate distance between you and the horizon of the earth? (1ft=0.3048m)"

Thank You
**

it is a right angled triangle so you can use Pythagoras to find the missing side.*

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