2007 RJC Prelim H2MA P2 (Qns)


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RAFFLES JUNIOR COLLEGE JC2 Preliminary Examination 2007 MATHEMATICS 9740/02 Higher 2 Paper 2 19 September 2007 3 hours Additional materials : Answer Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and CT 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. This document consists of 6 printed pages. RAFFLES JUNIOR COLLEGE RJC IES 2007 Math Department [Turn over
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2 RJC 2007 9740 / 02 / S / 07 Section A: Pure Mathematics [40 marks] 1 (a) The complex numbers z and w are such that z = 3 5i 1 2i a and w = 1+13bi, where a and b are real. Given that z * = w , find the exact values of a and b . [3] (b) Show that    i i 2 e e cos n θ n θ n n w w w a θ w b , where a and b are real numbers to be determined. Hence find the roots of the equation 63 3 1 0 zz   in the form of θ r i e . [6] 2 The following system of linear equations is given: 2 2 4 -----------(1) 2 3 4 1 -----------(2) 4 3 2 -----------(3) x y z x y z x y z    (a) By solving the system of linear equations, comment on the solution of this set of equations and the geometrical representation of the equations. [3] (b) The Cartesian equations of planes 12 and  are given by equation (1) and (2) respectively. Find a vector perpendicular to both the normals of and . [2] Hence, find (i) a vector equation of l , the line of intersection of and . [2] (ii) in the form 1 .
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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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