Questions and Worked Solutions for C2 Edexcel Core Mathematics January 2013.

Edexcel Core Mathematics C2 January 2013 Past Paper

Core 2 Mathematics Edexcel January 2013 Question 1

1. Find the first 3 terms, in ascending powers of x, in the binomial expansion of

(2 - 5x)^{6}

Give each term in its simplest form.

2. f(x) = ax

Given that (x – 1) is a factor of f(x),

(a) show that a + b = 7

Given also that, when f(x) is divided by (x + 2), the remainder is 9,

(b) find the value of a and the value of b, showing each step in your working.

3. A company predicts a yearly profit of £120 000 in the year 2013. The company predicts that the yearly profit will rise each year by 5%. The predicted yearly profit forms a geometric sequence with common ratio 1.05

(a) Show that the predicted profit in the year 2016 is £138 915

(b) Find the first year in which the yearly predicted profit exceeds £200 000

(c) Find the total predicted profit for the years 2013 to 2023 inclusive, giving your answer to the nearest pound.

4. Solve, for 0° ≤ x < 180°,

cos(3x - 10°) = -0.4

giving your answers to 1 decimal place. You should show each step in your working.

5. The circle C has equation

x^{2} + y^{2} -20x -24y + 195 = 0

The centre of C is at the point M.

(a) Find

(i) the coordinates of the point M,

(ii) the radius of the circle C.

N is the point with coordinates (25, 32).

(b) Find the length of the line MN.

The tangent to C at a point P on the circle passes through point N.

(c) Find the length of the line NP.

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