Edexcel Core Mathematics C2 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) = 2x³ - 7x² -5x + 4
   (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)

1 (b)

1 (c)

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C2 Mathematics Edexcel June 2011 Question 2

2. (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of
   (3 + bx)⁵
   where b is a non-zero constant. Give each term in its simplest form. Given that, in this expansion, the coefficient of x² is twice the coefficient of x,
   (b) find the value of b
   

2 (a)

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2 (b)

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C2 Mathematics Edexcel June 2011 Question 3

3. Find, giving your answer to 3 significant figures where appropriate, the value of x for which
   (a) 5^x = 10,
   (b) log₃(x - 2) = -1.

3 (a)

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3 (b)

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C2 Mathematics Edexcel June 2011 Question 4

4. The circle C has equation x² + y² + 4x - 2y - 11 = 0
   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)

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4 (c)

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C2 Mathematics Edexcel June 2011 Question 5

5. 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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5(b)

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5 (c)

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