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

for question 9i) i finished with x=-7 and x=4 would lose 1 or 2 marks for that?

It was a straightforward paper. That will be a very high mark but you will just have to wait to see your exact UMS.

does anyone have the paper , im resitting, i got a C

Full question paper:

1. Simplify $(x-5)(x^2+3)-(x+4)(x-1)$. [3]

2. Express each of the following in the form $7^k$:
(i) $\sqrt[4]{7}$. [1]
(ii) $\frac{1}{7\sqrt{7}}$. [2]
(iii) $7^4$ x $49^{10}$. [2]

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

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

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

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

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

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

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



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

10. A circle has equation $(x-5)^2+(y+2)^2=25$.
(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 $y=2x$ meets the circle. [5]

Could Mr M copy this to his first post for all to see? Thank you.

Here you go. I do apologise for any mistakes.

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


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


2. (i) $7^{\frac{1}{4}}$ (1 mark)

(ii) $7^{-\frac{3}{2}}$ (2 marks)

(iii) $7^{24}$ (2 marks)


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

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


4. (i) $2(x-5)^2-1$ (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) $y=\sqrt{\frac{x}{5}}$ (2 marks)


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


7. $16\pm 6\sqrt7$ (6 marks)


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

(ii) Minimum (2 marks)

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


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

(ii) $1.4 \leq y \leq 4.8$ (5 marks)


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

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

(iii) $2 \sqrt 5$ and inside (3 marks)

(iv) No (5 marks)

Hey i was wondering whether you could go through Q10, I'm having some difficulty with it and can't find any solutions online, especially part ii). Thank you

I can't remember this far back! Ask your teacher tomorrow?