Edexcel A Level Maths C2 · Core Mathematics 2 June 2013 question paper 6664R

Using calculus, find the coordinates of the stationary point on the curve with equation

Complete the table below with the value of y corresponding to x = 1.3, giving your answer to 4 decimal places.

Use the trapezium rule, with all the values of y in the completed table, to obtain an approximate value for

giving your answer to 3 decimal places. You must show clearly each stage of your working.

Find the first 4 terms, in ascending powers of x, of the binomial expansion of

giving each term in its simplest form.

f(x) = ax³ – 11x² + bx + 4, where a and b are constants. When f(x) is divided by (x – 3) the remainder is 55 When f(x) is divided by (x + 1) the remainder is –9

Find the value of a and the value of b.

Given that (3 x + 2) is a factor of f(x),

factorise f(x) completely.

The first three terms of a geometric series are 4 p, (3 p + 15) and (5 p + 20) respectively, where p is a positive constant.

Show that 11p² – 10p – 225 = 0

Hence show that p = 5

Find the common ratio of this series.

Find the sum of the first ten terms of the series, giving your answer to the nearest integer.

Given that log₃ x = a, find in terms of a,

giving each answer in its simplest form.

Solve, for x,

giving your answer to 4 significant figures.

The line with equation y = 10 cuts the curve with equation y = x² + 2x + 2 at the points A and B as shown in Figure 1. The figure is not drawn to scale.

Find by calculation the x-coordinate of A and the x-coordinate of B.

The shaded region R is bounded by the line with equation y = 10 and the curve as shown in Figure 1.

Use calculus to find the exact area of R.

Figure 2 shows the design for a triangular garden ABC where AB = 7 m, AC = 13 m and BC = 10 m. Given that angle BAC = radians,

show that, to 3 decimal places, = 0.865

The point D lies on AC such that BD is an arc of the circle centre A, radius 7 m. The shaded region S is bounded by the arc BD and the lines BC and DC. The shaded region S will be sown with grass seed, to make a lawned area. Given that 50 g of grass seed are needed for each square metre of lawn,

find the amount of grass seed needed, giving your answer to the nearest 10 g.

Solve, for 0 180

giving your answers to 1 decimal place.

Find all the values of x, in the interval 0 x 360, for which

giving your answers to 1 decimal place.

You must show clearly how you obtained your answers.