# Edexcel Core Mathematics C2 June 2009

Questions and Video Solutions for C2 Edexcel Core Mathematics June 2009

Edexcel Core Mathematics C2 June 2009 Past Paper

### C2 Mathematics Edexcel June 2009 Question 6

6. The circle C has equation

x^{2} + y^{2} - 6x + 4y = 12

(a) Find the centre and the radius of C.

The point P(–1, 1) and the point Q(7, –5) both lie on C.

(b) Show that PQ is a diameter of C.

The point R lies on the positive y-axis and the angle PRQ = 90°.

(c) Find the coordinates of R.

### C2 Mathematics Edexcel June 2009 Question 7

7. (i) Solve, for –180° ≤ θ < 180°,

(1 + tanθ)(5 sinθ - 2) = 0

(ii) Solve, for 0 ≤ x < 360°,

4sin x = 3tan x.

### C2 Mathematics Edexcel June 2009 Question 8

8. (a) Find the value of y such that

log_{2} y = –3

(b) Find the values of x such that

(log_{2} 32 + log_{2} 16)/log_{2} x = log_{2} x

### C2 Mathematics Edexcel June 2009 Question 9

Figure 2 shows a closed box used by a shop for packing pieces of cake. The box is a right
prism of height h cm. The cross section is a sector of a circle. The sector has radius r cm
and angle 1 radian.

The volume of the box is 300 cm^{3}

(a) Show that the surface area of the box, S cm^{2} , is given by
S = r^{2} + 1800/r

(b) Use calculus to find the value of r for which S is stationary.

(c) Prove that this value of r gives a minimum value of S.

(d) Find, to the nearest cm^{2}, this minimum value of S.

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