IJC_H2_MATH_P2_(9758)

INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION in preparation for General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CIVICS GROUP INDEX NUMBER Mathematics Paper 2 Additional materials: Answer Paper Cover Page List of Formulae (MF 26) 9758/02 12 September 2017 3 hours READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your name, class and index number 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. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages. Innova Junior College [Turn over

2 IJC/2017/JC2 9758/02/Sep/17 Section A: Pure Mathematics [40 marks] 1 The complex number z is such that 1z  and arg z  , where 0 4  . (i) Mark a possible point A representing z on an Argand diagram . Hence, mark the points B and C representing 2z and 2zz respectively on the same Argand diagram corresponding to point A. [2] (ii) State the geometrical shape of OACB. [1] (iii) Express 2zz in polar form,    cos cos i sinpq k k     , where p, q and k are constants to be determined. [2] 2 The function f is given by 1f : 3 2x x  for ,2xx  . (i) Find 1f ( ) x and state the domain of 1f  . [3] (ii) Explain why the composite function 2f exists. [1] (iii) Find the value of x for which 2f() x x . Explain why this value of x satisfies the equation 1f ( ) f ( )x x . [3] 3 It is given that a curve C has parametric equations 2 2 1, 1 xt t y t    for 22 t  . (i) Sketch C, indicating clearly the coordinates of the end points and the points where C cuts the y-axis. [4] (ii) Find the equation of the tangent to C that is parallel to the y-axis. [4] (iii) Express the area of the region bounded by C, the tangent found in part (ii) and both axes, in the form f( ) d b a tt , where the function f and the constants a and b are to be determined. Hence find this area, leaving your answer in exact form.