JJC_H2_MATH_P1

JURONG JUNIOR COLLEGE J2 Preliminary Examination MATHEMATICS 9740/01 Higher 2 18 August 2009 Paper 1 3 hours Additional materials: Answer Paper List of Formulae (MF15) Cover Page READ THESE INSTRUCTIONS FIRST Write your name and civics class 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 signif icant 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, with the cover page in front. This document consists of 5 printed pages and 1 blank page. [Turn over

2 1 The diagram below shows the graph of f( )y x . Sketch, on separate diagrams, the following graphs, indicating clearly any asympt otes, axial intercepts and turning points, where possible. (i) , [2] f( ) 2yx  (ii) fy x , [1] (iii) f' ( )y x . [3] y f( )y x x 0 −2 A (2, −2) 2 The functions f and g are defined to be f: and 4 2 , , 0xxe x x    1g: 1 , , 0 , 1 . 1xx x x x    (i) Sketch the graph of f and state its range. [2] (ii) Prove that the composite function gf exists and define it giving its rule and domain. [3] (iii) Sketch the graph of g and hence find the range of gf. [2] 3 On the same Argand diagram, sketch the loci (i) 23 2 2zi  , [2] (ii) , [2] * 8zz i (iii) arg 3 3zi   . [2] The complex number w is represented by the point of in tersection of the loci in parts (i), (ii) and (iii). Find , in the form w x iy , giving the exact values of x and . [1] y

3 4 A student has $1000 in his savings account init ially. He decides to deposit $5 from his pocket money each week into the account, wh ich pays a compound interest rate of 1% per year. Taking a year to consist of 52 weeks and P to be the amount of money in the account after t years, show that the differential equation d 0.01 260d P Pt  may be used to model the balance in the student’s bank account. [1] (i) Exp