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# FP1 OCR - stuck on some questions

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1. I was doing some past papers for the FP1 exam tommorow and came across some questions that I didn't understand. And the mark scheme didn't help me understand it either, so just wondered if some on could explain the answers.

They are all from January 2009.
With this one I found the determinant of the matrix as 1/4K + 2 but I wasn't really sure where to go from there.

The next one Attachment 534693534697 was very frustrating for me because I am normally very good at these questions, but I must be missing something. First of all I found U(n+1) as 13^n+1 + 6^n, then I added U(n) and U(n+1) and the closest I can get to the answer is 6^n + 6^n+1 + 14(13^n).

The last one I think is just a lack of understand as I was ill when this part of the topic must have been taught.
Attachment 534693534697534700
I got the square roots for the first part as (+\-) (root10)/2 + (root2)/2 which the mark scheme says is correct, but I have no idea how the second part links to the first part or how to do it.

Thanks for your help, and good luck everyone!
Attached Images

2. (Original post by Nicksb158)
I was doing some past papers for the FP1 exam tommorow and came across some questions that I didn't understand. And the mark scheme didn't help me understand it either, so just wondered if some on could explain the answers.

They are all from January 2009.
With this one I found the determinant of the matrix as 1/4K + 2 but I wasn't really sure where to go from there.

The next one Attachment 534693534697 was very frustrating for me because I am normally very good at these questions, but I must be missing something. First of all I found U(n+1) as 13^n+1 + 6^n, then I added U(n) and U(n+1) and the closest I can get to the answer is 6^n + 6^n+1 + 14(13^n).

The last one I think is just a lack of understand as I was ill when this part of the topic must have been taught.
Attachment 534693534697534700
I got the square roots for the first part as (+\-) (root10)/2 + (root2)/2 which the mark scheme says is correct, but I have no idea how the second part links to the first part or how to do it.

Thanks for your help, and good luck everyone!
For the second one, assuming that your 6^(n+1) should be 6^(n-1), split the 6^n as 6 x 6^(n-1) then you can take a common factor of 6^(n-1) out of two of the terms then it should work.

For the last one, treat the equation in the second part as a quadratic about z^2 and solve it. You should then see the connection.
3. Thanks a lot, understand them both now. 😀 Got any clues on the first one?
4. (Original post by Nicksb158)
They are all from January 2009.
With this one I found the determinant of the matrix as 1/4K + 2 but I wasn't really sure where to go from there.
I get the determinant of the matrix formed from the LHS to be 4k - 4. There won't be a unique solution if this determinant = 0

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