RI P1

RAFFLES INSTITUTION 2012 Year 6 Preliminary Examination MATHEMATICS 9740/01 Paper 1 12 September 2012 3 hours Additional materials: Answer Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and CT 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 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 test, fasten all your work securely together. This document consists of 5 printed pages. RAFFLES INSTITUTION  RI 2012 Math Department [Turn over

H2 MA 9740/ 2012 RI Year 6 Preliminary Examination [Turn Over 2 1 A study conducted by the Department of Health classified a population of size 21000 into three categories: underweight, normal and overweight. At the start of the study, it was found that x, y and z (in thousands) were the number of individuals in the population who were underweight, normal and overweight respect ively. At that time, the number of individuals who were overweight was three times the number of individuals who were underweight. Two years later, the Department found that 10% of the individuals who were underweight and 20% of the individuals who were overweight became normal but 5% of the individuals who were normal became overweight. The weight categories of the rest of the indivi duals remain unchanged. However, the number of individuals who were overweight was still three times the number of individuals who were underweight. Assuming that the population remains unchanged during the period of study, find the values of x, y and z. [3] 2 Expand 22 1 (1 2 )x as a series in ascending powers of x, up to and including the term in 6,x giving the coefficients in their simplest form. [2] Find the coefficient of 2rx and the range of values of x for the expansion to be valid. [3] 3 A graphic calculator is not to be used in answering this question. By writing i where , ,w a b a b   R solve the equation 2 5 12i.w  Hence find the roots of the equ