(6 marks) Section B (30 Answer the following questions on the lined paper provided. 1. [Maximum mark: 22] (a) Show that = 2 is a solution to the equation + 5p 2 = 0. p p3 p2 [2 marks] (b) Find the values of and such that + 5p 2 = (p 2)(p2 + + a b p3 p2 ap b). [4 marks] (c) Hence find the other two roots to the equation + 5p 2 = 0, writing your answer in the p3 p2 form where [3 marks] (d) An arithmetic sequence has as its common difference. Also, a geometric sequence has as p p its common ratio. Both sequences have 1 as their first term. (i) Write down, in terms of the first four terms of each sequence. p, [2 marks] (ii) If the sum of the third and fourth terms of the arithmetic sequence is equal to the sum of the third and fourth terms of the geometric sequence, find the three possible values of (Hint: use part c in this question) p.
(6 marks) Section B (30 Answer the following questions on the lined paper provided. 1. [Maximum mark: 22] (a) Show that p = 2 is a solution to the equation p3 + p2 5p 2 = 0. [2 marks] (b) Find the values of a and b such that p3 + p2 5p 2 = (p 2)(p2 + ap + b). [4 marks] (c) Hence find the other two roots to the equation p3 + p2 5p 2 = 0, writing your answer in the form where [3 marks] (d) An arithmetic sequence has p as its common difference. Also, a geometric sequence has p as its common ratio. Both sequences have 1 as their first term. (i) Write down, in terms of p, the first four terms of each sequence. [2 marks] (ii) If the sum of the third and fourth terms of the arithmetic sequence is equal to the sum of the third and fourth terms of the geometric sequence, find the three possible values of p. (Hint: use part c in this question)
2013-IBHL-Sem-1-Paper-11.docx