MJC_JC2_H2_Maths_2012_Paper_2

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 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. MERIDIAN JUNIOR COLLEGE JC2 Preliminary Examination Higher 2 ___________________________________________________________________ H2 Mathematics 9740/02 Paper 2 17 September 2012 3 Hours Additional Materials: Writing paper List of Formulae (MF 15) ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST ___________________________________________________________________ This document consists of 7 printed pages and 1 blank page [Turn Over]

2 MJC/2012 JC2 Preliminary Examination/9740/01 BLANK PAGE

3 MJC/2012 JC2 Preliminary Examination/9740/02 Section A: Pure Mathematics [40 marks] 1 A lake in Pangaea has a population of 600 000 adult fish at the start of 2012 and it is increasing at a rate of approximately 5% per year. It is proposed that at the end of every year 40 000 adult fish should be harvested. Let nu denote the size of the population (in thousands) at the start of n years after 2012. (i) Write down a recurrence relation for nu , and show that  800 200 1.05 n nu  . [4] (ii) Hence find the predicted population of the adult fish at the start of 2020. State what happens to the population of the adult fish for large values of n. [2] (iii) If the population of adult fish is to be maintained at 600 000, what should be the proposed number of adult fish to be harvested at the end of every year? [1] 2 The functions f and g are defined by      f : 2 1 2 9 , , g : ln 2 , 2. x x x x x x x      (i) Given that -1f exist when domain is restricted to [ a, b] where a < 0 and b > 0, find the least value of a and greatest value of b. [1] Using the restricted domain found in part (i), (ii) find the domain of -1f and the expression for   1f x , [5] (iii) f