2020 RI Y5 H2 Math Prelims

BP-462 RAFFLES INSTITUTION 2O2O YEAR 6 PRELIMINARY EXAMINATION CANDIDATE NAME CLASS ')i MATHEMAT]CS PAPER 1 Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) 97s8/01 3 hours READ THESE INSTRUCTIONS FIRST Write your name and class on all the wo* 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 conection fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers conect 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 ftom a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required lo 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 is 100. FOR EXAMINER'S USE l4 l4 ls l6 l7 ls lto Total lLo Ito ILL It2 It? lLOo This document consists of 28 printed pages and 0 blank page. RAFFLES INSTITUTION Mathematics Dgpartment PartnerlnLeaming 624 o Rt2020 [Tum over ax q2 03 Q4 Q5 Q5 Q7 QlZQ8 q9 Ql0 Q11

BP-463 2 I A particle is moving along the curve with equation 16xz +9yz =144. 9=Z" s-' -d I is positive when x=.r6.&& Find the rate of increase ofx at this instant. l4l 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 2Yo and 5%o accounts and gave the i.nterest eamed to his son. The amount in the 3% account, including interest, was re-invesled in the same account for another year. At the end ofthe second year, Mr. Li withdrew all the money out ofthe 3% account and gave t}re interest eamed to his son. The total interest received by the son from the tkee accounts was $1423.50 Given that the amount invested in the 2o/o ascovnt was $1000 more than the amount invested in the 5%o accotnt, find the amounts invested in each ofthe three accounts. t4l (ii) Hence find the general solution ofthe differential equation (dv v\ Id,-;.,] t3l(v-") =y2+2xzforx>0 (D Sketch the curve with equation x2 + yz - 6x =7 . l2l (ii) The region R is bouoded by the curve x'+y'- 6x=7,for x>3,andthe line x=3. Given that J" a"-x'dx= 2 'o , frod the exact volume of the solid of revolution4 formed when R is rotated completely about the]r-axis. H2 MA 9758/2020 Rl Year 6 Preliminary B€mination Paper 1 ParinerlnLeaming 625 3 (i) Prove that for x>0, the substitution y=r.s reduces the differential equation . ( d, ,\U-r