(a) the value of the common ratio of the series,
(b) the value of p,
(c) the sum of the first 15 terms of the series, giving your answer to 3 decimal places.
Give each term in its simplest form.
(b) Write down the expansion of (2 – 3x)4
in ascending powers of x, giving each term in its simplest form.
Given that (x – 3) is a factor of f(x),
(a) show that a = – 9
(b) factorise f(x) completely.
Given that g(y) = 2(33y) – 5(32y) – 9(3y) + 18
(c) find the values of y that satisfy g(y) = 0, giving your answers to 2 decimal places where appropriate.
(a) Complete the table below, giving the missing value of y to 3 decimal places.
Figure 1 shows the region R which is bounded by the curve with equation y = 5/(x2 + 1) the x-axis and the lines x = 0 and x = 3
(b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for the area of R.
(c) Use your answer to part (b) to find an approximate value for
giving your answer to 2 decimal places.
The plan of the garden ABCDEA consists of a triangle ABE joined to a sector BCDE of a circle with radius 12m and centre B.
The points A, B and C lie on a straight line with AB = 23m and BC = 12m.
Given that the size of angle ABE is exactly 0.64 radians, find
(a) the area of the garden, giving your answer in m2, to 1 decimal place,
(b) the perimeter of the garden, giving your answer in metres, to 1 decimal place.
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