ASRJC_9758_2024_Prelim P2

[Turn Over ANDERSON SERANGOON JUNIOR COLLEGE H2 MATHEMATICS JC2 Prelim Paper 2 (100 marks) 9758/2 16 Sept 2024 3 hours Additional Material(s): List of Formulae (MF26) CANDIDATE NAME CLASS / READ THESE INSTRUCTIONS FIRST Write your name and class in the boxes above. Please write clearly and use capital letters. Write in dark blue or black pen. HB pencil may be used for graphs and diagrams only. Do not use staples, paper clips, glue or correction fluid. Answer all the questions and write your answers in this booklet. Do not tear out any part of this booklet. 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. 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. All work must be handed in at the end of the examination. If you have used any additional paper, please insert them inside this booklet. The number of marks is given in brackets [ ] at the end of each question or part question. Question number Marks 1 2 3 4 5 6 7 8 9 10 11 Total This document consists of 22 printed pages and 6 blank pages.

2 Section A: Pure Mathematics [40 marks] 1 By using the substitution cot , for 0 , 4x=    find 22 1 d . 1 x xx + [4] 2 (a)(i) Find 2 d98 49 uu u − + . [3] (ii) The curve C is given by the parametric equations 2 1x u u= + + , 2 9 , where 0.49 uyu u= + Find the exact area bounded by C, the x-axis and the line 3.x= [4] (b) Find the volume of the solid formed when the shaded region bounded by the lines x = – 4, y = 2 and the ellipse 22( 2) 4( 1) 4xy+ + − = is rotated through 2π radians about the y-axis. Give your answer correct to 1 decimal place. [3] 3 With respect to the origin O, the points A, B, C, D and E have coordinates A ( )2,3, 4 , B ( )6,5,7 , C ( )8,9,6 , D ( )4,7,3 and ( )5,6,10E . (a) Show that the cartesian equation of the surface containing the points A, B and E is 5 2 5x y z− + =− . [2] A line passes through the point D and the midpoint M of the line segment EC. (b) Find the vector equation of the line DM. [3] (c) Find the exact coordinates of the foot of the perpendicular from the point M to the surface found in part (a). [3] (d) Hence find the exact shortest distance from the point M to the surface found in part (a). [2] (e) Verify the line DM intersects the surface found in part (a) at the point P with coordinates ( )9,8,13 . Hence find the vector equation of the reflection of the line DM about this slant surface. [4] y 1 x –4 –2 2