TJC_H2_Maths_P1

TEMASEK JUNIOR COLLEGE, SINGAPORE Preliminary Examination 2014 Higher 2 MATHEMATICS 9740/01 Paper 1 1 September 2014 Additional Materials: Answer Paper 3 hours List of Formulae (MF 15) READ THESE INSTRUCTIONS FIRST Write your Civics Group and Name on all the work that 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 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 6 printed pages. © TJC/Prelim Exam 2014/MA H2 9740 [ Turn over

TJC/Prelim Exam/2014/MA H2 9740/01 2 1 (i) Find the derivative of 24 x with respect to x. [1] (ii) Given the differential equation 2 2 2 d41 d yx x  , find y in terms of x. [4] 2 (a) The point A has coordinates (3, a, b) where ,ab  . Given that A lies on the xy-plane and the magnitude of the position vector of A is 5, find the values of a and b. [ 3 ] (b) The real numbers c and d are such that the vectors dc mi j k and cdni j k are perpendicular to each other. Show that  2 1cmn . [3] 3 Given  2f zp z q z r  where p, q and r are complex numbers such that f1 2 i . The equation  f0 z  has roots 1i and 12 i . Find p, q and r. [6] 4 Without the use of a graphic calculator, solve the inequality 1025 2x x  . [3] Hence find the solution to the inequality 102cos 5 2c o s   , where 02   . [3] 5 A souvenir company received an order to produce a souvenir that must satisfy all of the following conditions: (1) The souvenir is a solid cuboid with a square base. (2) The souvenir is made using 1m3 of superior clay. (3) The external surface of the souvenir must be coated with a special-mixed glow paint. Find the dimensions of the souvenir, in m, such that the amount of special paint needed i s t h e m i n i m u m . [ 7 ] [Turn over

TJC/Prelim Exam/2014/MA H2 9740/01 3 6 A contagious disease was found to infect a village with a population of 10000 people. Let P, i