IJC_JC2_H2_Maths_2012_Questions_Paper_1

INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION 2 in preparation for General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Additional Materials: Answer Paper Cover Page List of Formulae (MF15) 9740 /0 1 13 Sep 2012 3 hours READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on both sides of th e 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 signi ficant figures, or 1 decimal place in the case of angles in degrees, unless a different l evel of accuracy is specified in the question. You are expected to use a graphic calculator. Unsupported answers from a graphic calculator are a llowed 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 usin g 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. Innova Junior College [Turn over

IJC/2012/JC2 9740/01/S12 2 1 A renovation company wishes to obtain sand, stone a nd brick for construction work. The company sends its requirements for sand, stone and brick, measured in units, to three different suppliers, AngGui, BaBao and CaiTao. Their quotations are as follows: Price per unit ($) AngGui BaBao CaiTao Sand 15.00 11.00 12.00 Stone 10.50 17.30 13.00 Brick 8.10 7.00 10.00 Total price 205.2 229.4 208 (i) Find the number of units of sand, stone and brick required by the company. [3] (ii) Another supplier, DaoBi, charged 10% lower per uni t of sand, stone and brick than the company that charges the lowest for each of the materials. Find the total amount that the renovation company must pay i f all the materials were purchased from DaoBi, leaving your answers to the nearest cent. [2] 2 Find the general solution of the differential equa tion 2 2 dcosec d yx x x = . [3] Find the equation of the solution curve whose tange nt at the origin is parallel to the line 3 5 y x = − . [3] 3 (i) Prove by induction that 3 2 2 1 1 ( 1) . 4 n r r n n = = + ∑ [4] (ii) The th r term of a series