Edexcel A Level Maths C2 · Core Mathematics 2 June 2017 question paper 6664

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

giving each term in its simplest form.

In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50 and angle BCA= x Find the two possible values for x, giving your answers to one decimal place.

y = 5^x + log₂(x + 1), 0 x ≤ 2 Complete the table below, by giving the value of y when x = 1

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

giving your answer to 2 decimal places.

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

giving your answer to 2 decimal places.

Figure 1 is a sketch representing the cross-section of a large tent ABCDEF. AB and DE are line segments of equal length. Angle FAB and angle DEF are equal. F is the midpoint of the straight line AE and FC is perpendicular to AE. BCD is an arc of a circle of radius 3.5 m with centre at F. It is given that AF = FE = 3.7 m BF = FD = 3.5 m angle BFD = 1.77 radians Find

the length of the arc BCD in metres to 2 decimal places,

the area of the sector FBCD in m² to 2 decimal places,

the total area of the cross-section of the tent in m² to 2 decimal places.

The circle C has equation

Find

the coordinates of the centre of C,

the radius of C,

the y coordinates of the points where the circle C crosses the line with equation x = 4, giving your answers as simplified surds.

f(x) = –6x³ – 7x² + 40x + 21

Use the factor theorem to show that (x + 3) is a factor of f(x)

Factorise f(x) completely.

Hence solve the equation

giving your answer to 2 decimal places.

2 log(x + a) = log(16a⁶), where a is a positive constant Find x in terms of a, giving your answer in its simplest form.

log₃(9y + b) – log₃(2y – b) = 2, where b is a positive constant Find y in terms of b, giving your answer in its simplest form.

Show that the equation

can be written in the form

Hence solve, for 0 ≤ x 360

giving your answers to 2 decimal places.

The first three terms of a geometric sequence are 7 k – 5, 5 k – 7, 2 k + 10 where k is a constant.

Show that 11k² – 130k + 99 = 0

Given that k is not an integer,

For this value of k,

evaluate the fourth term of the sequence, giving your answer as an exact fraction,

evaluate the sum of the first ten terms of the sequence.

Figure 2 shows a sketch of part of the curve with equation

The curve has a turning point at the point A.

Using calculus, show that the x coordinate of A is 1

The curve crosses the x-axis at the points B (2, 0) and C 0 The finite region R, shown shaded in Figure 2, is bounded by the curve, the line AB, and the x-axis.

Use integration to find the area of the finite region R, giving your answer to 2 decimal places.