DHS_H2_MATHS_P2_QP

This document consists of 8 printed pages (including this cover page). Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 MATHEMATICS 9740/02 (Higher 2) 22 September 2014 Paper 2 3 hours Additional Materials: Answer Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your Name, Index Number 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 signi ficant 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, attach the question paper to the front of your answer script. The total number of marks for this paper is 100. For teachers’ use: Qn Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total Score Max Score 9 10 10 11 4 6 8 9 10 11 12 100

2 © DHS 2014 Year 6 H2 Mathematics Preliminary Examination [Turn over Section A: Pure Mathematics [40 marks] 1 (i) Prove by method of mathematical induction that           2231 3 3 7 1 1 1 2 ... 112 23 34 1 2 1 nn n n nn n         for all positive integral values of n. [4] (ii) Hence, by considering    2 11 1 rr rr    ,1 A Br rr   where A and B are constants to be determined, find an expression for 1 n r r   in terms of n. [5] 2 An event company builds a tent (as shown in the diagram) which has a uniform cross-sectional area consisting of an equilateral triangle of sides x metres and a rectangle of width x metres and height h metres. The length of the tent is 3x metres. (i) It is given that the tent has a fixed volume of k cubic metres and is fully covered (except the base) with canvas assumed to be of negligible thickness. Show that the area of the canvas used, A, in square metres, is given by 22 33 86. 23 kAx x x  Use differentiation to find, in terms of k, the value of x which gives a stationary value of A. Determine if A is minimum or maximum for this value of x. [7] (ii) It is given instead that th e tent has a volume of 360 cubi c metres and the area of canvas used is 300 square metres