2007 SAJC Prelim Paper 2 questions

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

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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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## This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

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

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