# Edexcel Core Mathematics C2 January 2010

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### C2 Mathematics Edexcel January 2010 Question 1

1. Find the first 3 terms, in ascending powers of x, of the binomial expansion of
(3 - x)6 and simplify each term.

### C2 Mathematics Edexcel January 2010 Question 2

1. (a) Show that the equation
5 sin x = 1 + 2 cos2 x
can be written in the form
2 sin2 x + 5 sin x – 3 = 0
(b) Solve, for 0 ≤ x < 360°,
2 sin2 x + 5 sin x – 3 = 0

### C2 Mathematics Edexcel January 2010 Question 3

1. f(x) = 2x3 + ax2 + bx - 6
where a and b are constants.
When f(x) is divided by (2x – 1) the remainder is –5.
When f(x) is divided by (x + 2) there is no remainder.
(a) Find the value of a and the value of b.
(b) Factorise f(x) completely.

### C2 Mathematics Edexcel January 2010 Question 4

An emblem, as shown in Figure 1, consists of a triangle ABC joined to a sector CBD of a circle with radius 4 cm and centre B. The points A, B and D lie on a straight line with AB = 5 cm and BD = 4 cm. Angle BAC = 0.6 radians and AC is the longest side of the triangle ABC.
(a) Show that angle ABC = 1.76 radians, correct to 3 significant figures.
(b) Find the area of the emblem.

### C2 Mathematics Edexcel January 2010 Question 5

1. (a) Find the positive value of x such that
logx 64 = 2
(b) Solve for x
log2 (11 - 6x) = 2 log2 (x - 1) + 3

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