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

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


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


2. \pm (3\sqrt{5} - i \sqrt{2}) (5 marks)


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

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

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

(iv) 4 (2 marks)


6. (i) Sketch (3 marks)

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

(iii) Perpendicular bisector of line segment joining z_1 and z_2 (2 marks)


7 (i) Show (1 mark)

(ii) 0.629 (5 marks)

(iii) \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=\pm \frac{a\sqrt{3}}{3} (6 marks)


Thanks to Mr K and Mr H for their work on this.
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James2301
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I think Question 8 and 9 (iii) are incorrect. I think that 8 should be a=-24, b=45, c=-52 and 9 (iii) should be -1.

Also on Question 7 (i) and (ii) I got those answers, but I don't believe I did it with the intended method. I formed two simultaneous equations to find Z1 and Z2, then did Z1 - Z2 and found a complex number, I then typed the values into my Calculator and came out with those exact values. Will I still get the marks for this or will I lose some?

Finally, how would you compare the difficulty of this paper to previous years?
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Ucalyptas
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For q8, I don't think you need to divide through by 4.

a = -24
b= 45
c = -52

but thanks!!
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Mr M
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(Original post by James2301)
I think Question 8 and 9 (iii) are incorrect. I think that 8 should be a=-24, b=45, c=-52 and 9 (iii) should be -1.
Sorry fixed. Inability to read question and add.
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Ucalyptas
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Mr M,

What do you think the grade boundaries will be like? Some say that they found it very hard compared to previous years, and some thought it was easy.

Do you think about 68/72 for 100 UMS is probable?

Thanks again
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britishtf2
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(Original post by shreys)
Dear Mr M,

Thanks for this again.

Just a few questions:

1.On the Argand diagram drawing one I drew the correct angles for the first two (z1 and z2), however didn't include much of a scale. How many marks would I drop?

2. On the question for finding p, I made a simple arithmetic mistake and got p=-2, not p=-1. How many would I lose for this?

3. On the final question, I made a small mistake and got close to the answer, but not the actual answer. I got most of the working right, however and accidentally only put one b value, not plus or minus. How many marks would I lose for this?
1. Depends what you mean by "much of a scale". If you were to lose anything, I would say 1.

2. Depends where the error was; an error at the end would lose you 1 mark, earlier on it could lose you more.

3. I don't see why you would lose more than 1 mark for missing +/- when it is needed.
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James2301
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(Original post by Mr M)
Sorry fixed. Inability to read question and add.
On Question 7 (i) and (ii) I got those answers, but I don't believe I did it with the intended method. I formed two simultaneous equations to find Z1 and Z2, then did Z1 - Z2 and found a complex number, I then typed the values into my Calculator and came out with those exact values. Will I still get the marks for this or will I lose some?

Also how would you compare the difficulty of this paper to previous years?
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cfang99
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Mr M do you think the grade boundaries will be lower this year 9say compared to the 2016 one), or did you find this paper fairly standard
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Mr M
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(Original post by James2301)
Also on Question 7 (i) and (ii) I got those answers, but I don't believe I did it with the intended method. I formed two simultaneous equations to find Z1 and Z2, then did Z1 - Z2 and found a complex number, I then typed the values into my Calculator and came out with those exact values. Will I still get the marks for this or will I lose some?

Finally, how would you compare the difficulty of this paper to previous years?
Right answer = full marks.

I can't really compare difficulties.
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Mr M
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(Original post by shreys)
Dear Mr M,

Thanks for this again.

Just a few questions:

1.On the Argand diagram drawing one I drew the correct angles for the first two (z1 and z2), however didn't include much of a scale. How many marks would I drop?

2. On the question for finding p, I made a simple arithmetic mistake and got p=-2, not p=-1. How many would I lose for this?

3. On the final question, I made a small mistake and got close to the answer, but not the actual answer. I got most of the working right, however and accidentally only put one b value, not plus or minus. How many marks would I lose for this?
1. right quadrant and labelled = full marks

2. so did I! drop 1 mark

3. 1 mark for no plus or minus and possibly lose more if other stuff was wrong
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shreys
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(Original post by Mr M)
Right answer = full marks.

I can't really compare difficulties.
Dear Mr M,

Thanks for this again.

Just a few questions:

1.On the Argand diagram drawing one I drew the correct angles for the first two (z1 and z2), however didn't include a scale. How many marks would I drop?

2. On the question for finding p, I made a simple arithmetic mistake and got p=-2, not p=-1. How many would I lose for this?

3. On the final question, I made a small mistake and got close to the answer, but not the actual answer. I got most of the working right, however I accidentally also only put one b value, not plus or minus. How many marks would I lose for this?
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Mr M
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(Original post by Ucalyptas)
Mr M,

What do you think the grade boundaries will be like? Some say that they found it very hard compared to previous years, and some thought it was easy.

Do you think about 68/72 for 100 UMS is probable?

Thanks again
I don't guess boundaries - sorry!
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Mr M
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(Original post by cfang99)
Mr M do you think the grade boundaries will be lower this year 9say compared to the 2016 one), or did you find this paper fairly standard
Fairly standard but I have been doing this for a long time and can't really tell any more.
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yokitani
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Q10, if a=0 then b was independent of a, would that be in the mark scheme?
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Mr M
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(Original post by yokitani)
Q10, if a=0 then b was independent of a, would that be in the mark scheme?
No I don't think so. As it specifically asks for b in terms of a, it is safe to assume a is non-zero.
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britishtf2
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(Original post by jpb09)
10)ii) was +- a/(3)^0.5 i think
Same as given answer.
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Mr M
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(Original post by jpb09)
10)ii) was +- a/(3)^0.5 i think
I've just rationalised the denominator.
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joe421
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Why is it -√2i and not +√2i?
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eltree
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(Original post by Mr M)
I've just rationalised the denominator.
if you forgot to rationalise the denominator would you still get full marks?
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Mr M
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(Original post by joe421)
Why is it -√2i and not +√2i?
Try squaring it and see.
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