2007 SAJC Prelim Paper 2 questions

2007 SAJC Prelim Paper 2 questions - SAINT ANDREW'S JUNIOR...

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SAINT ANDREW’S JUNIOR COLLEGE PRELIMINARY EXAMINATION MATHEMATICS Higher 2 9740/02 Paper 2 Wednesday 12 Sep 2007 3 hours Additional materials : Answer paper List of Formulae(MF15) Cover Sheet READ THESE INSTRUCTIONS FIRST Write your name, civics group and index number 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 any diagrams or graphs. 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 state otherwise. Where unsupported answers from a graphic calculator are not allowed in a question, you are required to present the mathematic 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 including this page. [Turn over
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[Turn over 2 Section A (40 marks) 1 Find the three complex numbers, 0 1 2 , z z z that satisfy the equation 0 2 4 2 4 3 i z . Give your answers in the form θ i re , where θ is in terms of π . [4] Hence show that w = 6 2 6 1 6 0 z z z is an imaginary number. Find Im( w ). [3] 2 When Mrs Wong retired in 2006, she put a sum of $5000 into a fund that has a constant rate of return of 5 % per annum. Starting in 2006, she withdraws $400 each year and gives the money to her granddaughter as a birthday gift. Denote the amount of money Mrs Wong has at time t years by $ x . (i) The differential equation relating x and t is in the form d dt x kx c  . State the values of k and c . . [1] (ii) Solve the differential equation and find the amount of money Mrs Wong has after 15 years. Give your answer to the nearest integer. [4] (iii) In which year will the granddaughter receive her last $400? [2] Comment on whether the model can be regarded as a good model of the situation in the real world. [1] 3 The parametric equations of a curve are given by secθ xa , tanθ ya where a is a real constant.
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2007 SAJC Prelim Paper 2 questions - SAINT ANDREW'S JUNIOR...

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