# Edexcel Core Mathematics C12 January 2015

Questions and Worked Solutions for C12 Edexcel Core Mathematics January 2015.

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Core 12 Mathematics Edexcel January 2015 Question 1

Simplify the following expressions fully.
(a) (x6)1/3

Core 12 Mathematics Edexcel January 2015 Question 2

Core 12 Mathematics Edexcel January 2015 Question 3

Figure 2 shows a sketch of part of the curve with equation y = f(x).
The curve crosses the coordinate axes at the points (2.5, 0) and (0, 9), has a stationary point at (1, 11), and has an asymptote y = 3.

On separate diagrams, sketch the curve with equation
(a) y = 3f(x)
(b) y = f(-x)

On each diagram show clearly the coordinates of the points of intersection of the curve with the two coordinate axes, the coordinates of the stationary point, and the equation of he asymptote.

Core 12 Mathematics Edexcel January 2015 Question 4

(a) Find the first 4 terms in ascending powers of x of the binomial expansion of
(2 + x/4)10
giving each term in its simplest form.

(b) Use your expansion to find an estimated value for 2.02510 stating the value of x which you have used and showing your working.

Core 12 Mathematics Edexcel January 2015 Question 5(b)

Find the sum of the integers which are divisible by 7 and lie between 1 and 500

Core 12 Mathematics Edexcel January 2015 Question 6

Given that
2log4(2x + 3) = 1 + log4x + log4(2x - 1), x > 1/2

(a) show that
4x2 - 16x - 9 = 0

(b) hence solve the equation
2log4(2x + 3) = 1 + log4x + log4(2x - 1), x > 1/2

Core 12 Mathematics Edexcel January 2015 Question 7

The circle C has equation
x2 + y2 + 10x – 6y + 18 = 0

Find
(a) the coordinates of the centre of C,

The circle C meets the line with equation x = –3 at two points.
(c) Find the exact values for the y coordinates of these two points, giving your answers as fully simplified surds.

Core 12 Mathematics Edexcel January 2015 Question 8

A sequence is defined by
u1 = k
un+1 = 3un – 12, n ≥ 1
where k is a constant.

(a) Write down fully simplified expressions for u2, u3 and u4 in terms of k.

Given that u4 = 15
(b) find the value of k

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