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,

(c) the sum of the first 15 terms of the series, giving your answer to 3 decimal places.

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

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.

3. f(x) = 2x

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

(c) find the values of y that satisfy g(y) = 0, giving your answers to 2 decimal places where appropriate.

y = 5/(x

(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/(x^{2} + 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.

(c) Use your answer to part (b) to find an approximate value for

giving your answer to 2 decimal places.

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 m^{2}, to 1 decimal place,

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

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