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Mr M's OCR (not OCR MEI) Core 1 answers May 2012

Mr M's OCR (not OCR MEI) Core 1 answers May 2012


1. x36x211x^3-6x^2-11 (3 marks)


2. (i) 7147^{\frac{1}{4}} (1 mark)

(ii) 7327^{-\frac{3}{2}} (2 marks)

(iii) 7247^{24} (2 marks)


3. (i) Gradient = 0.6 (1 mark)

(ii) (103,2)(\frac{10}{3}, -2) (4 marks)


4. (i) 2(x5)212(x-5)^2-1 (4 marks)

(ii) (5, -1) (2 marks)


5 (i) Sketch curve (only in first quadrant) (2 marks)

(ii) Translation in positive x direction by 4 units (2 marks)

(iii) y=x5y=\sqrt{\frac{x}{5}} (2 marks)


6. 4x6y29=04x-6y-29=0 (7 marks)


7. 16±6716\pm 6\sqrt7 (6 marks)


8 (i) (-2, -48) (5 marks)

(ii) Minimum (2 marks)

(iii) x2x \geq -2 (x > -2 will be marked right) (1 mark)


9 (i) 0<x<40<x<4 (6 marks)

(ii) 1.4y4.81.4 \leq y \leq 4.8 (5 marks)


10 (i) Centre (5, -2) Diameter 10 (3 marks)

(ii) y = 2x - 12 (4 marks)

(iii) 252 \sqrt 5 and inside (3 marks)

(iv) No (5 marks)


Original post by pzoDe
Full question paper:

1. Simplify (x5)(x2+3)(x+4)(x1)(x-5)(x^2+3)-(x+4)(x-1). [3]

2. Express each of the following in the form 7k7^k:
(i) 74\sqrt[4]{7}. [1]
(ii) 177\frac{1}{7\sqrt{7}}. [2]
(iii) 747^4 x 491049^{10}. [2]

3.
(i)
Find the gradient of the line ll which has equation 3x5y20=03x-5y-20=0. [1]
(ii) The line ll crosses the xx-axis at P and the yy-axis at Q. Find the coordinates of the mid-point of PQ. [4]

4.
(i)
Express 2x220x+492x^2-20x+49 in the form p(xq)2+rp(x-q)^2+r. [4]
(ii) State the coordinates of the vertex of the curve y=2x220x+49y=2x^2-20x+49. [2]

5.
(i)
Sketch the curve y=xy=\sqrt{x}. [2]
(ii) Describe the transformation that transforms the curve y=xy=\sqrt{x} to the curve y=x4y=\sqrt{x-4}. [2]
(iii) The curve y=xy=\sqrt{x} is stretched by a scale factor of 5 parallel to the xx-axis. State the equation of the transformed curve. [2]

6. Find the equation of the normal to the curve y=6x25y=\frac{6}{x^2}-5 at the point on the curve where x=2x=2. Give your answer in the form ax+by+c=0ax+by+c=0, where a, b and c are integers. [7]

7. Solve the equation x6x12+2=0x-6x^\frac{1}{2}+2=0, giving your answers in the form p±qrp\pm q\sqrt{r}, where p, q and r
are integers. [6]

8.
(i) Find the coordinates of the stationary point on the curve y=x4+32xy=x^4+32x. [5]
(ii) Determine whether this stationary point is a maximum or a minimum. [2]
(iii) For what values of xx does x4+32xx^4+32x increase as xx increases? [1]

9.
(i) A rectangular tile has length 4x4x cm and width (x+3)(x+3) cm. The area of the rectangle is less than 112cm2. By writing down and solving an inequality, determine the set of possible values of xx. [6]
(ii) A second rectangular tile of length 4y4y cm and width (y+3)(y+3) cm has a rectangle of length 2y2y cm and width yy cm removed from one corner as shown in the diagram.

MathsC19ii.png

Given that the perimeter of this tile is between 20cm and 54cm, determine the set of possible values of yy. [5]

10. A circle has equation (x5)2+(y+2)2=25(x-5)^2+(y+2)^2=25.
(i) Find the coordinates of the centre C and the length of the diameter. [3]
(ii) Find the equation of the line which passes through C and the point P (7,2). [4]
(iii) Calculate the length of CP and hence determine whether P lies inside or outside the circle. [3]
(iv) Determine algebraically whether the line with equation y=2xy=2x meets the circle. [5]
(edited 11 years ago)

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Have you got the questions? I'll try and remember them here if it will help anyone.
Also, thanks very much for doing this!
Original post by cleverslacker
Have you got the questions? I'll try and remember them here if it will help anyone.
Also, thanks very much for doing this!


Yes I have the questions. I don't have the time to type them all in though.
Reply 3
oooooo
Reply 4
Few questions

for question 6, i droped a sign and got 4x-6y+13..
How many marks would i lose?

for question 7 i got my values for x BUT totally forgot to sub it back in to get y..

how many would i lose there?

and finally, question 9

i did -7 < x < 4 and totally forgot about negative lengths.. how many would i lose there? :frown:

Sorry for all the questions
Original post by jameslad
Few questions

for question 6, i droped a sign and got 4x-6y+13..
How many marks would i lose?

for question 7 i got my values for x BUT totally forgot to sub it back in to get y..

how many would i lose there?

and finally, question 9

i did -7 < x < 4 and totally forgot about negative lengths.. how many would i lose there? :frown:

Sorry for all the questions


I also got -7<x<4 which would technically be right?
Reply 6
Original post by As_Dust_Dances_
I also got -7<x<4 which would technically be right?


LOL I hope so? What has MR M got to say about it?
Original post by As_Dust_Dances_
I also got -7<x<4 which would technically be right?


Drop one mark.
Reply 8
Hi Mr M, for 3(iii)

i put (40/3,-2) will i get any marks

i just divided it wrong.
How many marks do you think I would lose if I accidently put 2-6root7 for the other x value on qu7? 1 mark? Also if I got the perimeter wrong 9ii) and put 10y+3 instead of 10y+6 resulting in getting 1.7<x<5.1? 2 marks?
Original post by jameslad
Few questions

for question 6, i droped a sign and got 4x-6y+13..
How many marks would i lose?

for question 7 i got my values for x BUT totally forgot to sub it back in to get y..

how many would i lose there?

and finally, question 9

i did -7 < x < 4 and totally forgot about negative lengths.. how many would i lose there? :frown:

Sorry for all the questions


Q6 probably 4 or 5 marks

Q7 not really sure what you have done

Q9 already answered
Hi Mr M, if you had a guess what would you say will be the minimum for an A.
Reply 12
Original post by Mr M
Drop one mark.


Oh i see..

Question 6, i droped a sign and got 4x-6y+13..
How many marks would i lose?

for question 7 i got my values for x BUT totally forgot to sub it back in to get y..

how many would i lose there?
Original post by Kabelan1
Hi Mr M, for 3(iii)

i put (40/3,-2) will i get any marks

i just divided it wrong.


drop 1 mark
Original post by Mr M
Drop one mark.


HI for Q6 (normal one) I got the wrong gradient for the tangent but did the rest right I think, how many marks would I lose?thanks :smile:
Reply 15
Mr M, anychance of error carried forward for 4 ii)?
(edited 11 years ago)
Original post by mathsclown
Hi Mr M, if you had a guess what would you say will be the minimum for an A.


Not good at guessing these but I thought it was very straightforward.
I will be able to answer questions but I am teaching all afternoon and after school so it won't be until after 5 p.m.

I'll try and answer loads of queries then.
Reply 18
Original post by Mr M
Q6 probably 4 or 5 marks

Q7 not really sure what you have done

Q9 already answered


I'd lose 4/5 marks?! or did you men get lol?

and q7) basically i worked it all out and got my y value to be 3 +- root 7 .. i left it at that..

but i forgot to put it back into my equation and if i did then i would have got the right answer..

I think i'd lose 2 mark max?
68/72 will be above 90 ums right?

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