SAJC_H2_MATHS_P2

SAINT ANDREW’S JUNIOR COLLEGE Preliminary Examination MATHEMATICS Higher 2 9758/02 Wednesday 13 September 2017 3 hours Additional materials : Answer paper List of Formulae (MF 26) Cover Sheet READ THESE INSTRUCTIONS FIRST Write your name, civics group 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. Answer all the questions. Total marks : 100 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 including this page. [Turn over

2 [Turn Over] Section A: Pure Mathematics [40 marks] 1 Without the use of a calculator, find the complex numbers z and w which satisfy the simultaneous equations i3zw  2 63 i 0zw   [6] 2 (i) Show that 3 231 11 An B nn n n n    , where A and B are constants to be found. [2] (ii) Hence find 3 2 26n r r rr   . [3] (iii) Use your answer to part (ii) to find   2 21 0 123 n r r rr r    . [3] 3 The function f is defined by 2 1f : 1x x  , ,x 1x  . (i) Find 1f( ) x and write down the domain of 1f . [3] (ii) On the same diagram, sketch the graphs of f( )yx , 1f( )y x and 1ff ( )y x stating the equations of any asymptotes and showing the relationships between the graphs clearly. [4] (iii) State the set of values of x such that 11f f () f f ()x x  . [1] 4 Referred to the origin O, the point A has position vector −5i + 2j + 2k and the point B has position vector i + 3j − 2k. The plane  has equation: (1 2 ) (3 2 ) ( 2)     ri j k where ,  (i) Find the vector equation of plane  in scalar product form. [2] (ii) Find the position vector of th e foot of perpendicular, C, from A to . [3] The line l1 passes through the points A and B. (iii) The line l2 is the reflection of the line l1 about the plane . Find a vector equation of l2. [3]

3 [Turn Over] 5 It is given that DEFG is a square with fixed side 2 a cm and it is inscribed in th