2020 J2 YIJC H2 Math Prelims P2

This document consists of 21 printed pages and 3 blank pages. YISHUN INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CG INDEX NO MATHEMATICS Paper 2 Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) 9758/02 14 September 2020 3 hours READ THESE INSTRUCTIONS FIRST Write your CG, index number and name on 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 Examiners’ Use Question 1 2 3 4 5 6 Marks Question 7 8 9 10 Marks Total marks 100

2 ©YIJC 9758/02/JC2 Prelim/20 BLANK PAGE

3 ©YIJC 9758/02/Prelim/20 [Turn over Section A: Pure Mathematics [40 marks] 1 (i) State the derivative of 3tan x . [1] (ii) Find 5 2 36 sec dx x x . [3]

4 ©YIJC 9758/02/JC2 Prelim/20 2 (a) Given that 4i,1 iz      and arg( )z  , find the value of z. [3] (b) Do not use a calculator in answering this question. The complex numbers z and w are given by 1 i 1 iz   and 2 1 iw  . (i) Express z and w in exact polar form ier  where 0r and      . [2]

5 ©YIJC 9758/02/Prelim/20 [Turn over (ii) On an Argand diagram, mark the points A, B and C representing z, w and z w respectively. State the shape of the quadrilateral OACB. [3] (iii) Hence by finding the argument of z w , show that tan 2 18   . [3]

6 ©YIJC 9758/02/JC2 Prelim/20 3 A curve C has parametric equations 3cos 2cos3 , 9sin sin 3 , x y         for 0 2   . (i) Sketch C and state the cartesian equations of its lines of symmetry. [2] (ii) Given that 3cos3 4cos 3cos    , find the exact values of  at the points where C meets the y-axis. [2]

7 ©YIJC 9758/02/Prelim/20 [Turn over (iii) Show that the area enclosed by the axes and the part of C in the first quadrant is given by 2 1 2 2(27cos 27 cos cos3 6cos 3 ) d         , where the values of 1 and 2 should be stated. [3] (iv) Hence find the exact total area enclosed by C. [5]

8 ©YIJC 9758/02/JC2 Prelim/20 4 The plane 1 has equation 2 5 11 1       r . The plane 2 passes through the points 1, 1, 2A  ,2, 3, 4B and 3, 4, 3 .C (i) Find a cartesian equation of 2 . [3] (ii) Find a vector equation of the line l where 1 and 2 meet. [2]

9 ©YIJC 9758/02/Prelim/20 [Turn over (iii) D is a general point on l. Find an expression for the square of the distance AD. Hence, or otherwise, find the coordinates of the point on l which is nearest to A. [5]

10 ©YIJC 9758/02/JC2 Prelim/20 4 [Continued] (iv) The plane 3 is parallel to 1 and contains the point 1, ,3E k . Given that the distance between 1 and 3 is 16 30, find the possible values of k. [3]