2012_TJC_JC2_H2_Prelim_Paper_1

TEMASEK JUNIOR COLLEGE, SINGAPORE Preliminary Examination 2012 Higher 2 MATHEMATICS 9740/01 Paper 1 13 September 2012 Additional Materials: Answer paper 3 hours List of Formulae (MF15) 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. 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. © TJC 2012 [Turn over

TJC/MA 9740/Preliminary Exam 2012 2 1 An ellipse E has equation 229 16 144xy . (i) Find d d y x in term of x and y. [1] (ii) Show that the point P with coordinates ( 4cos, 3sin ) lies on E. [1] (iii) Find the equation of the normal to the ellipse E at the point P, in the form of y mx c where m and c are single trigonometric expressions of . [3] 2 Consider the equation     322 1 2i i 2 2i 0z z a b z       , where a and b are real. Given that 2 is a root of the equation, find the values of a and b. [3] Given also that 1i is another root, find the third root of the equation. [3] 3 HIMHEYS' Confectionery recently created three types of chocolate: Organic white, Organic milk and Organic dark, available in 250g bars. Cocoa butter, an essential ingredient in chocolate bars, make s up 25%, 20% and 15% of the mass of an Organic white, Organic milk and Organic dark chocolate bar respectively. To prepare for the official launch of the ir chocolate bars at an upcoming Food Expo, HIMHEYS' decides to manufacture a total of 300 bars for the event, with more th an 70 bars of each type. The confectionary intends to use 14kg of cocoa butter in the production of t he above batch of chocolate bars. I f the number of milk chocolate bars is to be smaller than the number of white chocolat e bars, d etermine how many organic chocolate ba rs of each type can be produced. [6] 4 Referred to an origin O, the position vectors of two points A and B are a and b respectively. The po