Questions and Worked Solutions for C2 Edexcel Core Mathematics June 2011.

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Edexcel Core Mathematics C2 June 2011 Past Paper

C2 Mathematics Edexcel June 2011 Question 6

6. The second and third terms of a geometric series are 192 and 144 respectively.

For this series, find

(a) the common ratio,

(b) the first term,

(c) the sum to infinity,

(d) the smallest value of n for which the sum of the first n terms of the series exceeds 1000.

6 (a)(b) Geometric Series

7. (a) Solve for 0 ≤ x < 360°, giving your answers in degrees to 1 decimal place,

3sin(x + 45°) = 2

(b) Find, for 0 ≤ x 2π, all the solutions of

2sin^{2}x + 2 = 7cosx

giving your answers in radians.

You must show clearly how you obtained your answers.

A cuboid has a rectangular cross-section where the length of the rectangle is equal to twice its width, x cm, as shown in Figure 2.

The volume of the cuboid is 81 cubic centimetres.

(a) Show that the total length, L cm, of the twelve edges of the cuboid is given by

L = 12x + 162/x^{2}

(b) Use calculus to find the minimum value of L.

(c) Justify, by further differentiation, that the value of L that you have found is a minimum.

8 (b)

The straight line with equation y = x+ 4 cuts the curve with equation y = −x^{2} + 2x - 24 at the points A and B, as shown in Figure 3.

(a) Use algebra to find the coordinates of the points A and B.

The finite region R is bounded by the straight line and the curve and is shown shaded in Figure 3.

(b) Use calculus to find the exact area of R.

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