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Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2016

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Original post by Mr M
Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2016


1. n(2n+3)(n−1)2\displaystyle \frac{n(2n+3)(n-1)}{2} (5 marks)


2. (i) 3−3i\sqrt{3}-3i (2 marks)

(ii) −1+43i49\displaystyle \frac{-1+4\sqrt{3} i}{49} (5 marks)


3. (i) α+β=−1k\displaystyle \alpha + \beta = -\frac{1}{k} and αβ=1\displaystyle \alpha \beta = 1 (1 mark)

(ii) 1k2\displaystyle \frac{1}{k^2} (5 marks)


4. (i) (5a−3b100)\begin{pmatrix} 5a-3b & 10 & 0 \end{pmatrix} (2 marks)

(ii) (6b−5)\begin{pmatrix} 6b-5 \end{pmatrix} (2 marks)

(iii) (6a12184a812−a−2−3)\begin{pmatrix} 6a & 12 & 18 \\4a & 8 & 12 \\-a & -2 & -3 \end{pmatrix} (2 marks)


5. Proof (4 marks)


6. (i) ∣z−3−3i∣=5\displaystyle |z-3-3i|=\sqrt 5 (4 marks)

(ii) Sketch (2 marks)

(iii) 2+5i2+5i and 4+i4+i (3 marks)


7. (i) Shear with x axis invariant taking the point (0, 1) to (3, 1) (2 marks)

(ii) (0−1−10)\begin{pmatrix} 0 & -1 \\-1 & 0 \\ \end{pmatrix}

Reflection in the line y=−xy=-x (6 marks)


8. (i) Show (1 mark)

(ii) n3(2n+3)\displaystyle \frac{n}{3(2n+3)} (6 marks)

(iii) 12(2n+1)\displaystyle \frac{1}{2(2n+1)} (3 marks)


9. (i) Show (3 marks)

(ii) Determinant = 0 when a = 3 so no unique solution. The equations are consistent because 3 x equation 3 - equation 1 = equation 2. (3 marks)


10. (i) 5+4i5+4i and −5−4i-5-4i (6 marks)

(ii) Show (1 mark)

(iii) ±541±4i41\displaystyle \pm \frac{5}{41} \pm \frac{4i}{41} (4 marks)


Just wondering how many marks I would lose in 2 ii) as I didn't see the conjugate parts so I used the part I got in part i) but I did everything else on that question right only used the non conjugate z how many marks would I lose?
Original post by deadroad
Thanks, also another question: For Question 8 iii.) if I stated the wrong evaluation of sum to infinity, and thus did not add a sixth to the answer, however stated the correct summation at the start (Sum of n to infinity = Sum of 1 to infinity - Sum of 1 to n-1). The only thing I missed was the sixth, so how many marks would I lose for this?


Probably just 1.
Original post by getjdhwgebrixow
Just wondering how many marks I would lose in 2 ii) as I didn't see the conjugate parts so I used the part I got in part i) but I did everything else on that question right only used the non conjugate z how many marks would I lose?


Either 1 or 2.
Original post by Mr M
Either 1 or 2.


Thank you
What was the last question?
Reply 85
Avatar for Kara_h
Kara_h
12
I know this post was a while ago, but I've been doing this paper as practice for next weeks exam. I was wondering how to get the answer to 7)ii) I've tried a lot of things but I'm still not sure! Thanks

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