Edexcel Core Mathematics C2 June 2013

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

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Edexcel Core Mathematics C2 June 2013 Past Paper

Core 2 Mathematics Edexcel June 2013 Question 1

1. The first three terms of a geometric series are 18, 12 and p respectively, where p is a constant.

Find

(a) the value of the common ratio of the series,

(b) the value of p,

Core 2 Mathematics Edexcel June 2013 Question 2

2. (a) Use the binomial theorem to find all the terms of the expansion of (2 + 3x)⁴

Give each term in its simplest form.

(b) Write down the expansion of (2 – 3x)⁴

in ascending powers of x, giving each term in its simplest form.

Core 2 Mathematics Edexcel June 2013 Question 3

3. f(x) = 2x³ – 5x² + ax + 18 where a is a constant.

Given that (x – 3) is a factor of f(x),

(a) show that a = – 9

(b) factorise f(x) completely.

Given that g(y) = 2(3^3y) – 5(3^2y) – 9(3^y) + 18

Core 2 Mathematics Edexcel June 2013 Question 4

y = 5/(x² + 1)

(a) Complete the table below, giving the missing value of y to 3 decimal places.

Figure 1 shows the region R which is bounded by the curve with equation y = 5/(x² + 1) the x-axis and the lines x = 0 and x = 3

(b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for the area of R.

giving your answer to 2 decimal places.

Core 2 Mathematics Edexcel June 2013 Question 5

Figure 2 shows a plan view of a garden.

The plan of the garden ABCDEA consists of a triangle ABE joined to a sector BCDE of a circle with radius 12m and centre B.

The points A, B and C lie on a straight line with AB = 23m and BC = 12m.

Given that the size of angle ABE is exactly 0.64 radians, find

(a) the area of the garden, giving your answer in m², to 1 decimal place,

(b) the perimeter of the garden, giving your answer in metres, to 1 decimal place.