Questions and Worked Solutions for C2 Edexcel Core Mathematics June 2012.

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Edexcel Core Mathematics C2 June 2012 Past Paper

Core 2 Mathematics Edexcel June 2012 Question 6

6. (a) Show that the equation tan 2x = 5 sin 2x

can be written in the form (1 – 5 cos 2x) sin 2x = 0

(b) Hence solve, for 0° ≤ x < 180°, tan 2x = 5 sin 2x

giving your answers to 1 decimal place where appropriate.

You must show clearly how you obtained your answers.

y = √(3x + x)

(a) Complete the table below, giving the values of y to 3 decimal places

(b) Use the trapezium rule with all the values of y from your table to find an approximation

You must show clearly how you obtained your answer.

A manufacturer produces pain relieving tablets. Each tablet is in the shape of a solid circular cylinder with base radius x mm and height h mm, as shown in Figure 3.

Given that the volume of each tablet has to be 60 mm^{3}

(a) express h in terms of x,

(b) show that the surface area, A mm^{2}, of a tablet is given by A = 2πx^{2} + 120/x

The manufacturer needs to minimise the surface area A mm^{2}

(c) Use calculus to find the value of x for which A is a minimum.

(d) Calculate the minimum value of A, giving your answer to the nearest integer.

(e) Show that this value of A is a minimum.

Core 2 Mathematics Edexcel June 2012 Question 9

A geometric series is a + ar + ar^{2} + ...

(a) Prove that the sum of the first n terms of this series is given by

The third and fifth terms of a geometric series are 5.4 and 1.944 respectively and all the terms in the series are positive.

For this series find,

(b) the common ratio,

(c) the first term,

(d) the sum to infinity.

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