RI 2023 MATH CT QP

7 H2 MA 9758/2023 RI Year 6 Common Test                  CANDIDATE NAME   CLASS 23   MATHEMATICS 9758 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. 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 calculat or are not allowed in a question, you are required to present the mathematical steps us ing 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  Q5  Q6  Subtotal                                100  Section B: Statistics           Q7  Q8  Q9  Q10  Q11  Subtotal           5          7            7           8           13            40    This document consists of 26 7 printed pages.   RAFFLES INSTITUTION Mathematics Department RAFFLES INSTITUTION 2023 YEAR 6 COMMON TEST     4                10             10              11              12             13              60

2   H2 MA 9758/2023 RI Year 6 Common Test   Section A: Pure Mathematics [60 marks] 1 The points A, B and C have position vectors ,a b and c respectively. The points A and B are fixed while C varies. (a) Given that ,a b and c are non-zero vectors such that () ()ca b b ca , find the relationship between ()ca  and b . [2] (b) Hence describe geometrically the set of all possible positions of the point C. [2]   2 Complete the square for 229 5 .xx    [1] The function f is defined by 2f : 2 9 5 , for .xx x x       (a) Sketch the graph of f( ),y x stating the coordinates of any turning points and points of intersection with the axes. [2] (b) If the domain of f is further restricted to 1, x k state with a reason the largest value of k for