RI_H2_2020_Prelim_P1

 RI2020 [Turn over CANDIDATE NAME CLASS 20 MATHEMATICS 9758/01 PAPER 1 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 quest ion specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, 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 Q6 Q7 /4 /4 /5 /6 /7 /9 /10 Q8 Q9 Q10 Q11 Q12 Total /10 /10 /11 /12 /12 /100 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 1 1 A particle is moving along the curve with equation 2216 9 144xy . 1d 2cm sd y t  and d d x t is positive when 5x . Find the rate of increase of x at this instant. [4] 2 Mr. Li invested a total of $30000 and divided this sum into three accounts, which paid 2%, 3% and 5% annual interest respectively. At the end of the first year, Mr . Li withdrew all the money out from the 2% and 5% accounts and gave the interest earned to his son. The amount in the 3% account, including interest, was re-invested in the same account for another year. At the end of the second year, Mr . Li withdrew all the money out of the 3% account and gave the interest earned to his son. The total interest received by the son from the three accounts was $1423.50. Given that the amount invested in the 2% account was $1000 more than the amount invested in the 5% account, find the amounts invested in each of the three accounts. [4] 3 (i) Prove that for 0x , the substitution y ux reduces the differen