TJC_H2_MATHS_P2_Questions

TEMASEK JUNIOR COLLEGE, SINGAPORE Preliminary Examination 2015 Higher 2 MATHEMATICS 9740/02 Paper 2 16 September 2015 Additional Materials: Answer paper 3 hours List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your Civics group and name on all the work that you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. 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 a graphic calculator. Unsupported answers from a graphic calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphic 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. At the end of the examination, fasten all your work securely together. This document consists of 6 printed pages. © TJC 2015 [Turn over

2 © TJC 2015 TJC/MA 9740/Preliminary Exam 2015 Section A: Pure Mathematics [40 marks] 1 Sketch, on an Argand diagram , the locus of the point representing the complex number z such that 5πarg( 3 i) . 6z   [2] Give a geometrical description of the locus of the point representing the complex number w such that i,wk where k is real. [1] (i) Given that the two loci intersect at e xactly one point, show that k = a or kb where a and b are real constants to be determined. [3] (ii) In the case when k takes the value of a, find the complex number representing the point of intersection, in the form x + iy, where x and y are exact. [3] 2 (a) Given that the sequence 5, 11, 17, , x is arithmetic, solve the equation 5 11 17 2760 x     . [4] (b) Mr Tan set aside $80,000 for his two sons . On the first day of the year that his sons turned 7 and 17 years old, he deposited $ x into the younger son’s bank account and the remaining sum of money into the elder son’s bank account. Mr Tan adds a further $1000 into the younger son’s account on the first day of each subseq uent year. The bank pays a compound interest at a rate of 2% per annum on the last day of each year. Each son will withdraw the full sum of money from his account (after interest had been added) on the last day of the year that he turns 21 years old. (i) Find the amount of money the elder son will withdraw in terms of x. [1] (ii) Show that the