VJC_H2_MATH_P2

1 VICTORIA JUNIOR COLLEGE Preliminary Examination MATHEMATICS (Higher 2) 9740/02 Paper 2 September 2015 3 hours 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, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct t o 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 an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing 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 5 printed pages © VJC 2015 VICTORIA JUNIOR COLLEGE [Turn over Additional Materials: Answer Paper Graph Paper List of Formulae (MF15)

2 Section A: Pure Mathematics [40 marks] 1 It is given that 1e sin 22 y x . (i) Show that 22 2 dd 4 2edd yyy xx    . [2] (ii) By repeated differentiation of the result in part (i), find the first four non–zero terms of the Maclaurin series for y, giving the coefficients in exact form. [4] (iii) Show that the same result in part (ii) can be obtained using the standard results given in the List of Formulae (MF15). [3] 2 Relative to the origi n O , the points A , B and C have position vectors a , ac and c respectively. The point X is on AC produced such that :AC AX is 1: 4 and the point Y is such that AXYB is a parallelogram. (i) The lines AY and BX intersect at the point N. Find, in terms of a and c , the position vector of N . [2] (ii) Given that the area of triangle OAB is 2 square units, find the area of triangle AXB. [3] (iii) Give the geometrical interpretation of BXAX BX        . Using the results from part (ii), show that BXAX BX        k mn ca , where k, m and n are constants to be determined. [4] 3 The complex number z satisfies the equation 5 7i 6z   . (i) Show the locus of z on an Argand diagram. [2] (ii) If the locus in part (i) intersects the locus  arg z – – 2i 2a  at two distinct points, where a is a real number, find the set of values that a