Use Binomial theorem to find the value of (0.99)12 correct to three places of decimals

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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