2024 Yr 6 RI H2 Math Timed Practice (Qn)

This document consists of 22 printed pages.   RAFFLES INSTITUTION  RI2024  Mathematics Department  [Turn over               CANDIDATE NAME   CLASS 24     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 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 / 7 / 6 / 9 / 10 / 10 / 12 / 11 Sect B: Prob & Stats Q8 Q9 Q10 Q11 TOTAL / 6 / 8 / 10 / 11 / 100 RAFFLES INSTITUTION 2024 YEAR 6 TIMED PRACTICE

2   H2 MA 9758/2024 RI Year 6 Timed Practice Section A: Pure Mathematics [65 marks] 1 Consider the second order differential equation 2 2 dd dd xx abtt  , where a and b are non-zero constants and d d x b ta . (a) By substituting d ,d xy t show that the above sec ond order differential equation can be written as d .d y ba yt  [2] (b) Find y in terms of t, and hence find x in terms of t. [5]

3   H2 MA 9758/2024 RI Year 6 Timed Practice [Turn over 1 [Continued]

4   H2 MA 9758/2024 RI Year 6 Timed Practice 2 Referred to an origin O, the position vectors of three points A, B and C are 325i j k , 42i j k and 2+ 4 i j k respectively. (a) Determine the value of  for which points O, A, B and C are coplanar. [2]

5   H2 MA 9758/2024 RI Year 6 Timed Practice [Turn over (b) Given that ,OD OA OB       find the value of  for which OD  is perpendicular to the y-axis. [2]                       (c) Hence, find the exact area of triangle OAD. [2]

6   H2 MA 9758/2024 RI Year 6 Timed Practice 3 (a) Write down constants A and B such that for all values of x, 1( 2 4 ).x Ax B   [1]           (b) By expressing 2 45x x in completed square form, find 2 1 d45 x xxx    . [4]

7   H2 MA 9758/2024 RI Year 6 Timed Practice [Turn over (c) Hence, without using a calculator, show that 2 1 2 2 1 1dl n t a n45 2 2 x px qxx q        , where p and q are exact real constants to be determined. [4]

8   H2 MA 9758/2024 RI Year 6 Timed Practice 4 The functions f and g are defined by 21 4 2f : , , , 32 3 sing: , , 0 . xxx x x xxx x x      (a) Find 1f( ) x and state its domain. [3]                           (b) Explain why  2024f x x for 2.3x [1]

9   H2 MA 9758/2024 RI Year 6 Timed Practice [Turn over (c) On the same diagram, sketch the graphs of fy x and   2024f,y x giving the equations of any asymptotes. [3]                         (d) Explain why the composite function gf exists. [1]             (e) Find the range of gf . [2]    x y

10   H2 MA 9758/2024 RI Year 6 Timed Practice 5 The curve C is defined by the parametric equations 2x t and 3 2,yt t where 11 t . (a) Sketch the graph of C. [2]                       (b) Without using a calculator, find the equation of the normal to C at the point where 1 2t . [4]          x y