Edexcel Core Mathematics C2 January 2013

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Edexcel Core Mathematics C2 January 2013 Past Paper
Core 2 Mathematics Edexcel January 2013 Question 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.

Core 2 Mathematics Edexcel January 2013 Question 2

f(x) = ax³ + bx²- 4x - 3, where a and b are constants.
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.

Core 2 Mathematics Edexcel January 2013 Question 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

Core 2 Mathematics Edexcel January 2013 Question 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.

Core 2 Mathematics Edexcel January 2013 Question 5

The circle C has equation

x² + y² -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.

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