Edexcel A Level Maths C2 · Core Mathematics 2 June 2008 question paper 6664

₃₂

Use the factor theorem to show that (x + 4) is a factor of f (x).

Factorise f (x) completely.

y (5^x 2)

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

Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 + ax)¹⁰, where a is a non-zero constant. Give each term in its simplest form.

Given that, in this expansion, the coefficient of x³ is double the coefficient of x²,

find the value of a.

Find, to 3 significant figures, the value of x for which 5^x = 7.

Solve the equation.5^2x 12(5^x) 35 0

The circle C has centre (3, 1) and passes through the point P (8, 3).

Find an equation for C.

Find an equation for the tangent to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

A geometric series has first term 5 and common ratio . Calculate

the 20th term of the series, to 3 decimal places,

the sum to infinity of the series.

Given that the sum to k terms of the series is greater than 24.95,

find the smallest possible value of k.

the length of the arc BC,

the area of the sector ABC.

The point D is the mid-point of AC. The region R, shown shaded in Figure 1, is bounded by CD, DB and the arc BC. Find

the perimeter of R, giving your answer to 3 significant figures,

the area of R, giving your answer to 3 significant figures.

Figure 2 shows a sketch of part of the curve with equation.y 10 8x x² x³ The curve has a maximum turning point A.

Using calculus, show that the x-coordinate of A is 2.

The region R, shown shaded in Figure 2, is bounded by the curve, the y-axis and the line from O to A, where O is the origin.

Using calculus, find the exact area of R.

Solve, for 0 ≤ x < 360°,