2007 IJC Prelims Paper 2 Question

# 2007 IJC Prelims Paper 2 Question - 2 Section A: Pure...

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9740/2/2007 [Turn over 2 Section A: Pure Mathematics [40 marks] 1 Find the 4 th roots of the complex number 3i + . Give your answers exactly, in the form i e r θ . [4] Hence solve the equation ( 29 84 23 40 zz - += . Give your answers exactly, in the form i e r θ . [4] 2 The diagram shows the graph of y = f( x ) with stationary points at ( - 3, 3) and (1.5, - 4). The curve cuts the axes at ( - 4, 0), ( - 1, 0), (3, 0) and (0, - 2). On separate diagrams, sketch the graphs of (i) 2f ( 3) yx =- , [2] (ii) 2 f () , [3] (iii) 1 f y x = . [3] y = f( x ) ( - 3, 3) 0 - 4 - 1 3 (1 .5 , -4 ) - 2

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9740/2/2007 [Turn over 3 3 (a) In a geometric progression, the first term is 2007 and its common ratio is 7 9 - . (i) Find, correct to 2 decimal places, the value of the sum of all the negative terms of the progression. [3] (ii) Find the least value n such that 1 2007 n U < , where n U denotes the n th term of the progression. [4] (b) An arithmetic progression has first term 2 and common difference d , where d is non-zero. The second, fifth and tenth terms of the progression are consecutive terms of a geometric progression. Find the sum of the first 15 terms of the arithmetic progression. [5] 4 (i) Prove that 1 2 d1 (tan ) d 1 x x x - = + . Find 12 d tan ( 1) d x x -  -   given that 1 x . [4] (ii) By means of the substitution sec x θ = , find the exact value of 2 2 1 1 d 1 x x - . [5] (iii) Find the exact value of 2 1 tan ( 1 )d xx - - . [3]
9740/2/2007 [Turn over 4 Section B: Statistics [60 marks] 5 A kindergarten has nine Year One classes and six Year Two classes with different class sizes. An education ministry official wishes to call on the kindergarten to visit five of the classes. Describe how he could make a random selection of the classes using (i) simple random sampling, [1] (ii) stratified sampling. [2]

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## This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

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2007 IJC Prelims Paper 2 Question - 2 Section A: Pure...

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