CJC_H2_MATH_P2_QP

9740/02/Prelim/2015 [Turn over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/02 Paper 2 31 Aug 2015 3 hours Additional Materials: List of Formulae (MF15) Graph Paper Name: ___________________________ Class: ________________ READ THESE INSTRUCTIONS FIRST Write your name 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, arrange your answers in NUMERICAL ORDER. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages, including the cover page.

2 9740/02/Prelim/2015 [Turn over Section A: Pure Mathematics [40 marks] 1 A Singaporean tourist is visiting three countries, Denmark, Engl and and Russia and is planning to buy souvenirs back for her loved ones. She pl ans to spend SGD$84 on cheese, SGD$85 on chocolate, and SGD$77 on candy. She can only buy in souvenir packs consisting of 1kg cheese, 1kg chocolate and 1kg candy. The exchange rates to the three countries are as follows: SGD$1 – 5 Danish Krone SGD$1 – 0.5 British Pound SGD$1 – 35 Russian Ruble The prices of the commodities in the various countries’ currency are given in the following table. Cheese/kg Chocolate/kg Candy/kg Price in Danish Krone 20 30 30 Price in British Pound 4 5 2 Price in Russian Ruble 280 175 245 Find the total number of souvenir packs she s hould buy so that she spends all her money. [4] 2 The diagram below shows the graph of f( )yx . The curve has a minimum point at 11, 2   and crosses the x–axis at  2, 0 , 0, 0 and  2, 0 . The lines 1, 3 and 3xx y   are the asymptotes of the curve. (i) Sketch, on separate diagrams, the graphs of (a) 2 f( )yx  , [4] (b) f '( )yx , [3] stating clearly in each case the equations of as ymptotes, the coordinates of turning points and axial intercepts whenever possible. (ii) State the number of distinct real roots of the equation 1f( ) 0 2x 