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

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Simplify the following expressions fully.

(a) (x

Core 12 Mathematics Edexcel January 2015 Question 2

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)

giving each term in its simplest form.

(b) Use your expansion to find an estimated value for 2.025

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

2log

(a) show that

4x

(b) hence solve the equation

2log

Core 12 Mathematics Edexcel January 2015 Question 7

The circle C has equation

x

Find

(a) the coordinates of the centre of C,

(b) the radius 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

u

u

where k is a constant.

(a) Write down fully simplified expressions for u

Given that u

(b) find the value of k

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