DHS P2

© DHS 2019 This question paper consists of 23 printed pages and 1 blank page. Name: Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 MATHEMATICS (Higher 2) 9758/02 Paper 2 September 2019 3 hours Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, index number and class on the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figur es, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unle ss 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 7 8 8 8 9 4 7 9 12 12 16 100 www.KiasuExamPaper.com 193

2 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 2 Section A: Pure Mathematics [40 marks] 1 Ryan has playing cards which he stacks into pyramids. He will begin by stacking up cards to form a pyramid with 1 level, followed by another pyramid with 2 levels and so forth. The pyramids with n levels for different values of n are shown below: Let nS denotes the number of cards in a pyramid with n levels. It is given that 2 nSa n b n c for some constants ,ab and c. (i) Give an expression of the number of additional cards needed to form a pyramid of thn level from (t h1)n level. Leave your expression in terms of a, b and n.[ 2] Commented [jo1]: APY www.KiasuExamPaper.com 194

3 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 2 [Turn over (ii) Find the values of a, b and c.[ 2 ] (iii) Hence prove that nS is the sum of an arithmetic progression and state the common difference. [2] (iv) One pyramid of each level from 1 to 23 is formed. Find the tota l number of cards required to form these 23 pyramids. [1] www.KiasuExamPaper.com 195

4 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 2 2 A curve C has equation 223251 4xx y y . (i) Show that d3 d5 yx y xx y .[ 2] (ii) Find the exact x-coordinates of the points on the curve C at which the tangent is parallel to the y-axis. [3] Commented [jo2]: CHC – new qn www.KiasuExamPaper.com 196

5 DHS 2019 Year 6 H2 Mathematics Preliminary Examination Paper 2 [Turn over