2024 Y6 Timed Prac Rev Paper 4 (Qns)

This document consists of 24 printed pages and 2 blank pages.   RAFFLES INSTITUTION  RI2022  Mathematics Department  [Turn over               CANDIDATE NAME   CLASS 22     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. You may use the blank pages on page 2 and 26 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 100. For Examiner’s Use Only Sect A: Pure Math Q1 Q2 Q3 Q4 Q5 Q6 Q7 / 6 / 8 / 7 / 8 / 7 / 12 / 12 Sect B: Prob & Stats Q8 Q9 Q10 Q11 Q12 TOTAL / 6 / 6 / 8 / 8 / 12 / 100 RAFFLES INSTITUTION 2022 YEAR 6 COMMON TEST   2024 Y6 H2 Math Timed Practice Revision Paper 4:         The solution will be released in Ivy on 17 June (Monday)                                                **** Note that Qn 5 (Complex Numbers) will NOT be examined in the coming Timed Practice. So, you should complete this paper within 2 hrs 47 mins.

2   H2 MA 9758/2022 RI Year 6 Common Test BLANK PAGE You may continue your working on this page if necessary, indicating the question number(s) clearly.

3   H2 MA 9758/2022 RI Year 6 Common Test [Turn over Section A: Pure Mathematics [60 marks] 1 The curve C has equation 2 24 , xxyx b xb   . (i) Given that y cannot take values between 2 and 6, show that b = 2 using an algebraic method. [3]                           (ii) Describe a sequence of 2 transformations that transform the graph of C onto the graph of 2 54 , 0xxyx x  . [3]

4   H2 MA 9758/2022 RI Year 6 Common Test   2 The function g is defined by g: s i n ,x xx for ,x  .x  (i) Show that g0 x  for .x  Hence, or otherwise, show that g has an inverse. [2]                           (ii) Sketch on the same diagram the graphs of g( )y x  and 1g( )yx  . [3]

5   H2 MA 9758/2022 RI Year 6 Common Test [Turn over (iii) Show that the composite function 2g exists. [1]                   (iv) Find the exact solutions of the equation  2g. x x [2]

6   H2 MA 9758/2022 RI Year 6 Common Test 3 (i) Prove by the method of differences that   1 1 11 . 1 N r N rr    [3]

7   H2 MA 9758/2022 RI Year 6 Common Test [Turn over (ii) Find 1 4 1 1 N r rr    in terms of N. [2]                           (iii) Using part (i), show that  1 1 21 1 N r N r     [2]

8   H2 MA 9758/2022 RI Year 6 Common Test 4 A curve C has parametric equations ec o s,tx t es i n .tyt  (i) Find the equation of the tangent to C at the point with parameter p. Give your answer in the form ym x c . [5]

9   H2 MA 9758/2022 RI Year 6 Common Test [Turn over (ii) The tangent meets the x-axis at point A and the y-axis at point B. Find, in terms of p, the area of the triangle OAB, where O is the origin. [3]

10   H2 MA 9758/2022 RI Year 6 Common Test 5 The complex number z satisfies the equation f( ) 0z  , where   2f( ) 1 i 2 i 1 0 2 0 iza z z   and a is a real number. It is given that one root is of the form 1i b , where b is an integer . (i) Show that b satisfies the equation   43 2 21 2 4 2 9 0bb b b   . [3]