RI 9758/02 Prelim 2023

 RI2023   [Turn over                   CANDIDATE NAME   CLASS 23   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 signifi cant 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 an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calcul ator are not allowed in a question, you are required to present the mathematical steps usi ng 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 SECTION A: PURE MATHEMATICS  TOTAL  Q1 Q2 Q3 Q4 Total         9 9 11 11 40                100  SECTION B: PROBABILITY AND STATISTICS  Q5 Q6 Q7 Q8 Q9 Q10 Total  6   8  9 12 12 13 60    This document consists of 22 6 printed pages and 2 blank pages.   RAFFLES INSTITUTION Mathematics Department RAFFLES INSTITUTION 2023 YEAR 6 PRELIMINARY EXAMINATION

2 H2 MA 9758/2023 RI Year 6 Preliminary Examination Paper 2      Section A: Pure Mathematics [40 marks] 1 The curve C is defined by the parametric equations 2 ,3 2 w h e r e .xt t y t t    (a) Show algebraically that 1 4x for all values of t . [2] The line N is the normal to C at the point where 1t  . (b) Find the cartesian equation of N. [3] (c) Find the area of the finite region enclosed by C, N and 1 4x , correct to 3 decimal places. [4] 2 The terms of an arithmetic progression 1, 4, 7, 10, , are grouped into sets containing 1, 3, 5, 7,  integers, as indicated below, so that the number of integers in each set after the first is two more than the number of integers in the previous set.       1 , 4,7,10 , 13,16,19, 22, 25 , 28,31,34,37, 40, 43, 46 ,  .  (a) Find the total number of integers in the first n sets, in terms of n. [2] (b) Find the last integer in the nth set, in terms of n. Hence, find the value of k, given that the integer 2023 occur