MJC_JC2_H2_Maths_2012_Paper_1

Write your name and civics 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, 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 notatio ns 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. MERIDIAN JUNIOR COLLEGE JC2 Preliminary Examination Higher 2 ___________________________________________________________________ H2 Mathematics 9740/01 Paper 1 11 September 2012 3 Hours Additional Materials: Writing paper List of Formulae (MF 15) ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST ___________________________________________________________________ This document consists of 7 printed pages and 1 blank page. [Turn Over]

2 MJC/2012 JC2 Preliminary Examination/9740/01 BLANK PAGE

3 MJC/2012 JC2 Preliminary Examination/9740/01 1 By using an algebraic method, solve the inequality 2 464 1 xx x   . [4] 2 The graph of a cubic polynomial passes through the origin and only has one stationary point at  1 ,3 . Find the cubic polynomial. [4] 3 (a) Given 2 ln 2x xy y    , find d d y x . [2] (b) (i) Find   2d 2d x x . [1] (ii) Hence find 22 ln 2 dxx x . [3] 4 The complex number z satisfies 2 4i 4z   and  0 arg 2 4z    . (i) On an Argand diagram, sketch the region in which the point repre senting z can lie. [3] (ii) Find the smallest value of  arg 2 4i .z [1] (iii) It is further given that the value of 2z is minimum at point P. Find the complex number w representing P in the form iab , giving the exact values of a and b. [2] 5 Relative to the origin O, t he point s A and B have position vectors 2i j k and 32  i j k respectively. (i) The point M lies on AB extended such that AB:AM = 4:5. Find the position vector of M. [2] (ii) Give a geometrical interpretation of OA OB OB  . [1] (iii) Find the shortest distance from the point (1,3,8)C