Solve for xin the following inequality and give the integral values

(a) Let S= {1,2,3,4,5,6}, A= {1,3,5}, B= {4,6} and C= {1,4}. Compute the following set operations

(i) An B (1 mark)

(ii) B? C (1 mark)

(iii) An (B n C) (2 marks)

(iv) (A? B)C. (2 marks)

(b) Solve for xin the following inequality and give the integral values;

2(x– 1) >3(2x+ 3)

(2 marks)

(c) Solve the following equations simultaneously;

Y+ 2X= 3

X2+ Y2= 2

(3 marks)

(d) Compute the following limits

(2 marks)

(3 marks)

(e) The second, the fourth and the seventh terms of an Arithmetic Progression (AP) are the first three consecutive terms of a Geometric Progression (GP). The common difference of the AP is 2. Find

(i) The common ratio (3 marks)

(ii) The sum of the first eight terms of the GP. (3 marks)

(f) A customer deposited Ksh.48,000 at the beginning of a year in a bank account. The rate of interest is 8% p.a. compounded semi-annually for the first five years and 10 % p.a. compounded annually for the subsequent 5 years. Calculate the total amount of

money earned after the 10 years.

(g) Solve for xin the following equations.

(4 marks)

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