NJC_H2_MATHS_P2_Question

[Turn_over NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 PRELIMINARY EXAMINATION Higher 2 MATHEMATICS 9740/02 Paper 2 15 September 2015 3 hours Additional Materials: Answer Paper List of Formulae (MF15) Cover Sheet READ THESE INSTRUCTIONS FIRST Write your name, registration number, subject tutorial group, on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for diagrams or graphs. Do not use 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 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. At the end of the examination, fasten all your work securely together. The number of marks is given in the brackets [ ] at the end of each question or part question. This document consists of 6 printed pages. National Junior College

[Turn_over Section A: Pure Mathematics [40 marks] 1 (a) Use the substitution 3tanx  to find the exact value of 3 22 3 1 d 9 x xx    . [4] (b) Using integration by parts, find   2ln 4 dxx . [4] 2 (a) Joanne begins a monthly savings plan. In the first month, she puts $1000 into her savings, and for each subsequent month she puts 5% more than in the previous month. How many months would it take for Joanne’s total savings to first exceed $20000? [3] Jim starts a monthly savings plan two months later than Joanne with an initial savings of $2000, and for each subsequent month he puts $100 more than in the previous month. The table below shows the person whose total savings exceeds the other person’s total savings in the Nth month since Joanne started saving. Find the value of n. [4] (b) Suppose instead that Joanne puts a fixed amount of $1000 into her bank account on the first day of every month . The interest rate is r% per month, so that on the last day of each month the amount in the account on that day is increased by r%. At the end of 2 years, the total amount in her account will be at least $30000. Find the smallest value of r, correct to 1 decimal place. [3] N Person with more total savings in Nth month 1 Joanne 2 Joanne 3 Joanne 4 Joanne 5 Jim 6 Jim n – 1 Jim n Joanne

[Turn_over 3 The planes 1p and 2p have equations 1 10 1   r and 2 16 2     r respect