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(a) Given the functions ((x)=3x-x+10 and g(x)=1-5x. Solve the following operations: i. f(x)+3g(x) (3 marks) ii. g(x)-f(x) (3 marks) iii. f(x)g(x)-2f(x) (4 marks) (b) Given the functions f(x) =3x-2 and 2 3 3 i. gg(10) (5 marks) II. g f(x) (3 marks) value of K when f(k) 10 (3 marks) IV. the domain and range of g(x). (4 marks) 3. 1+,5 (a) Simplify in the form of a b/c where a,b,ce R -3-15 (5 marks) (b) N Given that Z= 2-71 Express in the standard form a +bi (5 marks) (c) l'a and B are the roots of the equation x² 3x T=0, form new quadratic equation with 0°8 and aB² as its roots (6 marks) (d) Solve the following inequalities i. x²<3x+10 (4 marks). ii. 12-3/25 (5 marks) 4. (a) Arithmetic sequence is given by 10,xy,z,2, find: i. values of and z. (5 marks) ii. 21t term of the sequence. (2 marks) iii. sum of the first 13 terms of the sequence. 3 marks) 8 (b) The second and fifth terms of a geometric sequence are 24 and 9 respectively. Calculate: i. common ratio. (5 marks) ii. first term. (2 marks) iii. sum to infinity. (3 marks) (c) Sum of the first four terms of a geometric series with the common ratio of .4 is 357. Find: common ratio. (3 marks) II. 8th term. (2 marks)

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