RI_H2_2020_Prelim_P2

 RI2020 [Turn over CANDIDATE NAME CLASS 20 MATHEMATICS 9758/02 PAPER 2 3 hours Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. 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. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a ques tion, you are required to present the mathematical steps using mathematical notations 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. The total number of marks for this paper is 100. FOR EXAMINER’S USE Q1 Q2 Q3 Q4 Q5 Sub-Total Total /5 /5 /8 /10 /12 /40 Q6 Q7 Q8 Q9 Q10 Q11 Sub-Total /100 /7 /8 /9 /12 /12 /12 /60 This document consists of 28 printed pages and 0 blank page. RAFFLES INSTITUTION Mathematics Department RAFFLES INSTITUTION 2020 YEAR 6 PRELIMINARY EXAMINATION

2 H2 MA 9758/2020 RI Year 6 Preliminary Examination Paper 2 Section A: Pure Mathematics [40 marks] 1 An arithmetic series has first term 3 2 and fourth term 4.u A geometric series also has first term 3 2 and fourth term 4.u Given that the common ratio of the geometric series is non -negative and the sum of its first 3 terms is 21,2 find the sum of the first 10 odd -numbered terms of the arithmetic series. [5] 2 In a geometric series, the ratio of the sum of the first 8 terms to the sum of the first 4 terms is 17:16. Find the 2 possible values of the common ratio, 12,rr where 12 .rr The sum to infinity of the geometric series with first term a and common ratio 1r is denoted by 1S and the sum to infinity of the geometric series with first term b and common ratio 2r is denoted by 2 .S Find 12:SS in terms of a and b. [5] 3 The functions f and g are defined by       f 1 3e , , 0, g 1 3 , , where is a real constant. xx x x x x x x x c c          (i) Given that 4,c determine if