Edexcel A Level Maths C2 · Core Mathematics 2 June 2012 question paper 6664

Find the first 3 terms, in ascending powers of x, of the binomial expansion of

giving each term in its simplest form.

Find the values of x such that

The circle C with centre T and radius r has equation

Find the coordinates of the centre of C.

Show that r = 5

The line L has equation x = 13 and crosses C at the points P and Q as shown in Figure 1.

Find the y coordinate of P and the y coordinate of Q.

Given that, to 3 decimal places, the angle PTQ is 1.855 radians,

find the perimeter of the sector PTQ.

f(x) = 2x³ – 7x² – 10x + 24

Use the factor theorem to show that (x + 2) is a factor of f(x).

Factorise f(x) completely.

Figure 2 shows the line with equation y = 10 – x and the curve with equation y = 10x – x² – 8 The line and the curve intersect at the points A and B, and O is the origin.

Calculate the coordinates of A and the coordinates of B.

The shaded area R is bounded by the line and the curve, as shown in Figure 2.

Calculate the exact area of R.

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

Hence solve, for 0 x 180°, tan 2 x = 5 sin 2 x giving your answers to 1 decimal place where appropriate. You must show clearly how you obtained your answers.

Complete the table below, giving the values of y to 3 decimal places.

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 mm³,

express h in terms of x,

show that the surface area, A mm², of a tablet is given by A = 2² + The manufacturer needs to minimise the surface area A mm², of a tablet.

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

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

Show that this value of A is a minimum.

A geometric series is a + ar + ar² +...

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,

the common ratio,

the first term,

the sum to infinity.