RI 2023 MATH TP QP

 RI2023   [Turn over                 CANDIDATE NAME   CLASS 23     MATHEMATICS 9758 2 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (extracted from 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. You may use the blank page on page 18 if necessary and you are reminded to indicate the question number(s) clearly. 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 an approved graphing calculator. 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 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 65. For examiner’s use only Q1  Q2  Q3  Q4  Q5  Q6  Total    10    10    10    12    12    11           65      This document consists of 4 printed pages.   RAFFLES INSTITUTION Mathematics Department RAFFLES INSTITUTION 2023 YEAR 6 TIMED PRACTICE

2     H2 MA 9758/2023 RI Year 6 Timed Practice  1 (a) (i) Find 2sin dx x . [2] (ii) Hence or otherwise, show that    22 11 1sin d sin 2 cos 2 .44 8x xx x x x x c   [3] (b) (i) Sketch the graph of 2sinyx x   for 10 π2x , labelling the end points clearly. [2] (ii) Hence, find the exact area of the region bounded by the graph of 2sinyx x , the x-axis and the line 1 π2x . [3] 2 (a) A point R has position vector r = 1 24 35 a a        , where a is a real number. Describe geometrically the set of all possible positions of R as a varies. [2] (b) The angle between the vectors a and b is π 3 radians. (i) Given that the angle between the vectors b and  2ab is a right angle, show that 4ab . [3] (ii) Given also that 2b , find the exact length of projection of 2 ab onto  2ab . [5] 3 Do not use a calculator in answering this question. Two complex n