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

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The following are the solutions for the Edexcel Core Mathematics C2 June 2011 Past Paper

C2 Mathematics Edexcel June 2011 Question 1

1. f(x) = 2x

(a) Find the remainder when f(x) is divided by (x –1).

(b) Use the factor theorem to show that (x+1) is a factor of f(x).

(c) Factorise f(x) completely.

1 (a)

2. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of

(3 + bx)

where b is a non-zero constant. Give each term in its simplest form. Given that, in this expansion, the coefficient of x

(b) find the value of b

2 (a)

3. Find, giving your answer to 3 significant figures where appropriate, the value of x for which (a) 5

(b) log

3 (a)

3 (b)

4. The circle C has equation x

Find

(a) the coordinates of the centre of C,

(b) the radius of C,

(c) the coordinates of the points where C crosses the y-axis, giving your answers as simplified surds.

4(a)(b)

The shape shown in Figure 1 is a pattern for a pendant. It consists of a sector OAB of a circle centre O, of radius 6 cm, and angle AOB = π/3. The circle C, inside the sector, touches the two straight edges, OA and OB, and the arc AB as shown.

Find

(a) the area of the sector OAB,

(b) the radius of the circle C.

The region outside the circle C and inside the sector OAB is shown shaded in Figure 1.

(c) Find the area of the shaded region.

5 (a)

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