2007 PJC Prelims P2_questions

# 2007 PJC Prelims P2_questions - Candidate Name CT Group...

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Candidate Name : ____________________________ CT Group : ________ Index no : ________ PIONEER JUNIOR COLLEGE JC2 Preliminary Examinations MATHEMATICS Higher 2 9740 Tuesday 18 th Sept 2007 Additional material: Answer paper TIME 3 hours INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your full name, index number and CT group on all the work you hand in. Write in dark blue or black pen on both sides of the papers. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use a graphic calculator. Unsupported answers from a graphic calculator are allowed unless a question states otherwise. Where unsupported answers from a graphic calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notation and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. At the end of the examination, arrange your solutions in numerical order and fasten them securely together with the question paper. Marks Marks 1 8 2 9 3 10 4 11 5 12 6 13 7 Subtotal Subtotal Total ________________________________________________________________________ This question paper consists of 10 printed pages. PJC2007 [Turn over

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[Turn over 6 Section A: Pure Mathematics [40 marks] 1 The 3 rd , 4 th and 6 th term of a geometric progression are consecutive terms of an arithmetic progression. Find the sum to infinity of the geometric progression if the first term is 2, giving your answer in exact form. [5] 2 A sequence 0 1 2 , , , . . . u u u is defined by 01 2 and 1 2 where 0 nn u u u n   . Prove by induction that, for all n > 0,   1 1 5 2 3 n n u   . [4] State, with a reason, whether the sequence is convergent. [1] 3 Find, in i re form, where r and are exact, the roots of the equation 4 2 3 2i=0 w  . [4] Hence find, in similar form, the roots of the equation 44 1 2 3 2i =0 zz . [2] 4 A company manufactures three brands of instant coffee, namely Super, Top and Ace. The percentage composition of the mass of coffee, sugar and milk in each packet is shown in the following table.
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2007 PJC Prelims P2_questions - Candidate Name CT Group...

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