DHS_H2_MATH_P1 with ans

© DHS 2015 This question paper consists of 6 printed pages (including this cover page). Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 MATHEMATICS (Higher 2) 9740/01 Paper 1 17 September 2015 3 hours Additional Materials: Answer Paper Graph paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your Name, Index Number and Class 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 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. For teachers’ use: Qn Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total Score Max Score 5 6 6 6 6 8 8 9 9 11 13 13 100

2 DHS 2015 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over 1 A graphic calculator is not to be used in answering this question. (i) Find the value of 2(1 4i) , showing clearly how you obtain your answer. [1] (ii) Given that 12 i  is a root of the equation 2 (i ) 0 ,zza b   find the values of the real numbers a and b. [2] (iii) For these values of a and b, solve the equation in part (ii). [2] 2 Using partial fractions, find 2 2 62 d.(1 2 )( 1) xx xxx   [6] 3 A curve C has parametric equations cos , sin , for 0 π.xy       (i) Sketch the curve .C [2] (ii) The point P on the curve C has parameter p and the point Q has coordinates ( π,0). The origin is denoted by O. Given that p is increasing at a constant ra te of 0.1 units per second, find the rate of decr ease of the area of triangle OPQ when 3 4 π.p [4] 4 The complex number z is given by 1 6 πi e.)3   (i) Given that (1 i) ,wz find w and arg w in exact form. [2] (ii) Without using a calculator, find the smallest positive integer n such that nw is purely imaginary. State the modulus of nw when n takes this value. [4]

3 DHS 2015 Year 6 H2 Mathematics Preliminary Examination Paper 1 [Turn over 5 The dia