PJC_H2_MATH_P2

PJC2011 [Turn over] Candidate Name : ____________________________ CT Group : ________ Index no : ________ PIONEER JUNIOR COLLEGE JC 2 Preliminary Examination MATHEMATICS Higher 2 Paper 2 ( 9740 / 2 ) Wednesday 21 Sept 2011 Additional material: Answer paper, List of Formulae MF15 TIME 3 hours INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your full name, index number and CT group 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 correc t 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 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. Attach this question paper with your answers, and arrange your answers in numerical order. For Examiner’s Use Qn Marks Qn Marks Qn Marks 1 7 13 2 8 14 3 9 4 10 5 11 6 12 Sub-total Sub-total Total _________________________________________________________________________________ This question paper consists of 6 printed pages and 2 blank pages.

PJC2011 [Turn Over] 2

PJC2011 [Turn Over] 3 Section A : Pure Mathematics [40 Marks] 1 The first four terms of a sequence are given by 1 2341, 2, 4, 8TT T T  . Given that rT is a cubic polynomial in r, find rT in terms of r. [4] 2 A sequence of positive real numbers 1x , 2x , 3x , ... satisfies the recurrence relation 1 3nnx x  for 1n . (i) If this sequence converges to , determine the exact value of . [2] (ii) By using a graphical method, prove that 1nnx x  if 0 x  . [2] 3 Without using a graphic calculator a nd showing your working clearly, solve the inequality 21 14 x x   . [ 3 ] Hence, solve the inequality 2e 114 e x x   , giving your answer in exact form. [3] 4 The diagram shows a pyramid with a square base OABC of side 4 cm. The vertex D is 6 cm vertically above M, the mid-point of AB. Taking O as the origin and unit vectors i, j and k as indicated, find (i) the position vector of L, the mid-point of CD, [2] (ii) the area of triangle OAL giving your answer in