MJC_H2_MATH_P1_Question

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 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. MERIDIAN JUNIOR COLLEGE JC2 Preliminary Examination Higher 2 ___________________________________________________________________ H2 Mathematics 9740/01 Paper 1 15 September 2015 3 Hours Additional Materials: Writing paper List of Formulae (MF 15) ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST ___________________________________________________________________ This document consists of 6 printed pages. [Turn Over

2 MJC/2015 JC2 Preliminary Examinations/9740/01 1 In the quadrilateral OABC where O is the origin, the position vectors of the points A, B and C are a, b and c respectively. Given that AC is perpendicular to OB and OB bisects the angle AOC, express a in the form of k c , where k is a constant to be determined. [4] 2 It is given that     e for 0 1,f e 2 for 1 2, xxxx xx      and that    f f 2xx for all real values of x. (i) Sketch the graph of  fyx for 24 x   . [3] (ii) Find the exact value of   3 1 fd xx  . [4] 3 Consider the curve 2 2 49 4 xy x   . (i) Show, by differentiation, that there is only one stationary point. [3] (ii) Sketch the graph of 2 2 49 4 xy x   , stating the equations of any asymptotes, coordinates of any turning points and the coordinates of the points where the curve crosses the axes. [3] (iii) Hence find the range of values of p such that 2 22 2 49 4 x pxx   has no real roots. [2]

3 MJC/2015 JC2 Preliminary Examinations/9740/01 4 (a) Given that    2 1 1 2 16 n r nr n n     , find     1 2 2 2 2 n r r n r r     . (There is no need to express your answer as a single algebraic fraction.) [3]