In an arithmetic progression the sum of the first five terms is 30 and the third term is equal to the sum of the first two terms. Write down the first five terms of the progression

QUESTION ONE (30 MARKS)

(a) Write down the sixth term of the expansion . Find the value of the constant term of the expansion.
[5 marks]

(b) By re-arranging the function y = 3×2 – 14x + 18 in the form

y = a(x + b)2 + c where a, b, and c are constants, find the

minimum value of y. State the value of x when y is a minimum.
[5 marks]

(c) Write down and evaluate in surd form an expression for

(i) Sin750 [3 marks]
(ii) Cos 1350 [2 marks]
(d) A bag contains 5 red balls and 7 white balls. Find the probability of drawing 2 white balls in the draws such that:

(i) The balls drawn are not being replaced. [2 marks]

(ii) The balls being replaced after each draw. [3 marks]

(e) Calculate the mean and the standard deviation of the following measurements in centimetres 2.25, 2.29, 2.36, 2.39, 2.31, 2.33
[5 marks]

(f) The second term of a geometric series is 1 and the fifth term is

. Find the first term and the common ratio of the series.

Determine the sum to infinity of the series. [5 marks]

QUESTION TWO (20 MARKS)

(a) A committee of six is to be formed from 9 women and 3 men. In how many ways can the members be chosen so as to include at least one man? [8 marks]

(b) Write down and simplify the term in y5 in the expansion of

[5 marks]

(c) Use Binomial theorem to find the value of (0.99)12 correct to three places of decimals. [7 marks]

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