2007 CJC Prelims Paper 2

2007 CJC Prelims Paper 2 - CATHOLIC JUNIOR COLLEGE...

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1 CATHOLIC JUNIOR COLLEGE PRELIMINARY EXAMINATIONS 2007 MATHEMATICS 9740/02 Higher 2 Paper 2 29 AUGUST 2007 3 hours Additional materials : Answer Paper Graph Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and HT 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 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. At the end of the paper, detach the cover page and attach it to the answer script with the cover page on top. Name :________________________________ HT : _______ Question Marks 1 2 3 4 5 6 7 8 9 10 Total Calculator Model: _____________ This document consists of 6 printed pages. [Turn over
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2 Section A: Pure Mathematics [40 marks] 1 . The variables x and u are related by x e dx du xe u u 4 (I) (i) By means of the substitution u xe y , obtain a differential equation relating y and x . [2] (ii) Hence show that the general solution of (I) is x k x u 2 ln , k is an arbitrary constant. [2] (iii) Sketch the solution curve for k = -1, stating clearly any asymptotes and axial intercepts. [2] 2. (a) (i) Find the fourth roots of the complex number -1 + i 3 , giving your answers exactly in the form r e i where r > 0 and < . [3] (ii) Deduce the solutions of the equation 0 4 2 4 8 z z , giving your answers exactly in the form
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2007 CJC Prelims Paper 2 - CATHOLIC JUNIOR COLLEGE...

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