DHS_H2_MATH_P2_QP

© DHS 2015 This question paper consists of 6 printed pages (including this cover page). Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 MATHEMATICS (Higher 2) 9740/02 Paper 2 23 September 2015 3 hours Additional Materials: Answer Paper Graph 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 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, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. For teachers’ use: Qn Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total Score Max Score 10 10 10 10 4 5 7 7 8 8 10 11 100

2 DHS 2015 Year 6 H2 Mathematics Preliminary Examination [Turn over Section A: Pure Mathematics [40 marks] 1 A sequence 12 3, , , ...uu u is such that 1 1 4u  and 1 22 4 , for all (1 ) (2 ) 1.nnuu n nn n     (i) Use the method of mathematical induction to prove that 22 1 .(1 ) nu nn  [4] (ii) Hence find 1 22 1 .(1 ) (2 ) N n nn n  [2] (iii) Give a reason why the series in part (ii) is convergent and state the sum to infinity. [2] (iv) Use your answer to part (ii) to find 2 22 1 .(1 ) N n nn  [2] 2 [It is given that a right circ ular cone with base radius r and height h has volume 21 3 π ,rh and the curved surface area is π ,rl where l is the slanted height of the cone.] The model of a silo is made up of three parts.  The roof is modelled by the cu rved surface of a right circular cone with base radius 12 x cm and height 5x cm.  The walls are modelled by the curved surface of a cylinder of radius 12x cm and height y cm.  The floor is modelled by a circular disc of radius 12x cm. The three parts are joined together as shown in the diagram. The model is made of material of negligible thickness. The curved surface of the c one is made of material A at the cost of $0.05 per cm 2. The curved surface of the cylinder and the base of the cylinder are