TMJC 9758 2023 Prelim P2

Tampines Meridian Junior College 2023 JC2 Preliminary Examination H2 Mathematics CANDIDATE NAME: ___________________________________________________ CIVICS GROUP: _______________________________________________________ __________________________________________________________________________________ H2 MATHEMATICS 9758/02 Paper 2 19 SEPTEMBER 2023 3 hours Candidates answer on the question paper. Additional material: List of Formulae (MF26) ________________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name and Civics Group 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. _________________________________________________________________________________ This document consists of 6 printed pages and 0 blank pages. TAMPINES MERIDIAN JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION For Examiners’ Use 1 2 3 4 5 6 7 8 9 10 Total [Turn Over

2 Section A: Pure Mathematics [40 marks] 1 The position vectors of points A, B and P with respect to an origin O are a, b and p respectively, where 3 2.= −pab (a) Show that A, B and P are collinear and hence find the ratio :.BP AP [4] (b) It is given that b is a unit vector, 4 3=a and the angle between a and b is π .3 The point N is a point on li ne BP which is closest to the origin . Find the value of BN BA . [5] 2 (a) Logarithmic functions are useful as measurement units for phenomena with large scale of values, such as decibels (for sound) or Richter scale (for earthquakes). Logarithmic functions make the measurement units smaller and easier to work with. An example of a logarithmic function is given as ( ) 2ln 1 2 3 .y xx= ++ (i) By using differentiation, find the Maclaurin series for y , up to and including the term in 2.x [4] (ii) By using the standard series in MF26, verify that the answer obtained in part (i) is correct. [2] (b) Find the series expansion of , 4 x x+