2007 SRJC Prelim Paper 2 Questions

# 2007 SRJC Prelim Paper 2 Questions - 1 SERANGOON JUNIOR...

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[Turn Over SERANGOON JUNIOR COLLEGE 2007 JC2 PRELIMINARY EXAMINATIONS MATHEMATICS Higher 2 9740/Paper 2 Tuesday 18 September 2007 Additional materials: Writing paper List of Formulae (MF15) TIME : 3 hours READ THESE INSTRUCTIONS FIRST Write your name and class on the cover page and on all the work you hand in. Write in dark 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 question paper consists of 8 printed pages and no blank pages.

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2 Section A: Pure Mathematics [40 marks] 1 The curve C is defined parametrically by sec xa and tan ya , where a is a fixed constant. It is known that the point P with coordinates ( sec , tan ) aa  lies on C . Show that the equation of the tangent at P is given by sin cos x y a  and the equation normal at P is given by sin 2 tan x y a  . The tangent and the normal at P cut the x -axis at T and N respectively. Prove that OT ON = 2 a 2 , where O is the origin. 2 (a) Find the modulus and argument of the complex number z , where 2 4 (1 ) 3 ) i z i , giving your answers in exact form.
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2007 SRJC Prelim Paper 2 Questions - 1 SERANGOON JUNIOR...

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