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Mr M's OCR (not OCR MEI) Further Pure 1 Answers May 2017

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Original post by eltree
if you forgot to rationalise the denominator would you still get full marks?


Yes
Reply 21
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eltree
also is there anyway to see what the diagram was mean to be for question 6i?
Reply 22
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ts241
2
Original post by Mr M
Mr M's OCR (not OCR MEI) Further Pure 1 answers May 2017


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


2. ±(35−i2)\pm (3\sqrt{5} - i \sqrt{2}) (5 marks)


3. (i) (628−147a−1)\begin{pmatrix} 6 & 28 \\-14 & 7a-1 \end{pmatrix} (2 marks)

(ii) (13a+28−95a+4)\begin{pmatrix} 1 & 3a+28 \\-9 & 5a+4 \end{pmatrix} (3 marks)


4. Proof (5 marks)


5. (i) Shear with x axis invariant taking (0, 1) to (5, 1) (3 marks)

(ii) (1004)\begin{pmatrix} 1 & 0 \\0 & 4 \end{pmatrix} (2 marks)

(iii) (1504)\begin{pmatrix} 1 & 5 \\0 & 4 \end{pmatrix} (2 marks)

(iv) 4 (2 marks)


6. (i) Sketch (3 marks)

(ii) 18\sqrt{18} and 7π20\frac{7\pi}{20} (5 marks)

(iii) Perpendicular bisector of line segment joining z1z_1 and z2z_2 (2 marks)


7 (i) Show (1 mark)

(ii) 0.629 (5 marks)

(iii) 71105\frac{71}{105} (1 mark)


8. a = -24, b = 45, c = -52 (7 marks)


9 (i) a = 2 (5 marks)

(ii) Any value other than a = 2 (1 mark)

(iii) p = -1 (3 marks)


10 (i) Show (4 marks)

(ii) b=±a33b=\pm \frac{a\sqrt{3}}{3} (6 marks)


Thanks to Mr K and Mr H for their work on this.


Mr M,
1)For 6iii I described the line using the angle above the x-axis (along with some other details) but didn't mention that it was the perpendicular bisector. Would I lose any marks?
2)For showing z1-z2 on the Argand diagram, how much labelling do you need? I drew it in the right place (I think), and drew it as part of a parallelogram with the origin and z1 and z2.
3) For 10ii, I left the whole thing under the square root, +-√(a^2/3). Is there any penalty for this?
Thanks!
Original post by eltree
also is there anyway to see what the diagram was mean to be for question 6i?


Mr H's artwork.
Mr H.jpg16.0KB
Original post by ts241
Mr M,
1)For 6iii I described the line using the angle above the x-axis (along with some other details) but didn't mention that it was the perpendicular bisector. Would I lose any marks?
2)For showing z1-z2 on the Argand diagram, how much labelling do you need? I drew it in the right place (I think), and drew it as part of a parallelogram with the origin and z1 and z2.
3) For 10ii, I left the whole thing under the square root, +-√(a^2/3). Is there any penalty for this?
Thanks!


1) Not enough for full marks

2) That sounds good

3) Probably still ok
Original post by Mr M
Mr H's artwork.


Hi Mr M,On 6i) I had the points in the right place and shower working to get the exact values but drew them as points instead of lines. How many marks will I lose?
Reply 26
Avatar for Hyih
Hyih
4
Minor point I know, but is - √2i fine rather than -i√2?
Original post by Mr M
Mr M's OCR (not OCR MEI) Further Pure 1 answers May 2017


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


2. ±(35−i2)\pm (3\sqrt{5} - i \sqrt{2}) (5 marks)


3. (i) (628−147a−1)\begin{pmatrix} 6 & 28 \\-14 & 7a-1 \end{pmatrix} (2 marks)

(ii) (13a+28−95a+4)\begin{pmatrix} 1 & 3a+28 \\-9 & 5a+4 \end{pmatrix} (3 marks)


4. Proof (5 marks)


5. (i) Shear with x axis invariant taking (0, 1) to (5, 1) (3 marks)

(ii) (1004)\begin{pmatrix} 1 & 0 \\0 & 4 \end{pmatrix} (2 marks)

(iii) (1504)\begin{pmatrix} 1 & 5 \\0 & 4 \end{pmatrix} (2 marks)

(iv) 4 (2 marks)


6. (i) Sketch (3 marks)

(ii) 18\sqrt{18} and 7π20\frac{7\pi}{20} (5 marks)

(iii) Perpendicular bisector of line segment joining z1z_1 and z2z_2 (2 marks)


7 (i) Show (1 mark)

(ii) 0.629 (5 marks)

(iii) 71105\frac{71}{105} (1 mark)


8. a = -24, b = 45, c = -52 (7 marks)


9 (i) a = 2 (5 marks)

(ii) Any value other than a = 2 (1 mark)

(iii) p = -1 (3 marks)


10 (i) Show (4 marks)

(ii) b=±a33b=\pm \frac{a\sqrt{3}}{3} (6 marks)


Thanks to Mr K and Mr H for their work on this.


Hi,
On 5i could you say "shear with x axis invariant by shear factor 4"?
Original post by Hyih
Minor point I know, but is - √2i fine rather than -i√2?


Depends if the i is inside the root or not.
Original post by Just sign in
Hi,
On 5i could you say "shear with x axis invariant by shear factor 4"?


Would it not be shear factor 5?
Reply 30
Avatar for Hyih
Hyih
4
Original post by britishtf2
Depends if the i is inside the root or not.


Outside
Original post by Just sign in
Hi Mr M,On 6i) I had the points in the right place and shower working to get the exact values but drew them as points instead of lines. How many marks will I lose?


Points should be fine.
Original post by Hyih
Outside


Multiplication of complex numbers is commutative, so it's fine.
Original post by Hyih
Minor point I know, but is - √2i fine rather than -i√2?


Yes so long as your square root symbol clearly doesn't extend above the i.
Original post by britishtf2
Would it not be shear factor 5?


Yeah sorry, I forgot what the q was. The matrix was of the form 1k01 and I said shear factor k. I've forgotten what number k was
Original post by Just sign in
Yeah sorry, I forgot what the q was. The matrix was of the form 1k01 and I said shear factor k. I've forgotten what number k was


As far as I understand, it is correct, if shear factor 5. Please don't quote me on it though xd
Original post by Just sign in
Hi,
On 5i could you say "shear with x axis invariant by shear factor 4"?


If you put shear factor 5 then yes.
Original post by britishtf2
As far as I understand, it is correct, if shear factor 5. Please don't quote me on it though xd


Yes that's ok.
Original post by Mr M
Yes that's ok.


Good to know I understand maths... outside of exams -.-
Has anyone done a walkthrough for question 10 ii).?

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