PJC_H2_MATH_P1

PJC2011 [Turn over] Candidate Name : ____________________________ CT Group : ________ Index no : ________ PIONEER JUNIOR COLLEGE JC 2 Preliminary Examination MATHEMATICS Higher 2 Paper 1 ( 9740 / 1 ) Wednesday 14 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 5 9 2 6 10 3 7 11 4 8 12 Sub-total Sub-total Total _________________________________________________________________________________ This question paper consists of 7 printed pages and 1 blank page.

PJC2011 [Turn over] 2

PJC2011 [Turn over] 3 1 (a) Find  12 tan 2 dx xx   . [ 3 ] (b) The region R is bounded by the curve 2 4y xx  , the line 29y x , and t h e y-axis. Find the volume of the solid when R is rotated completely about the x-axis, giving your answer correct to 2 decimal places. [3] 2 (i) Find the first three terms in the expansion of 2 1 4 x in ascending powers o f x . [ 3 ] (ii) Hence find the first four terms in the expansion of 2 1 4 x x   . [2] (iii) State the set of values of x for which this expansion is valid. [1] 3 Each time a ball falls vertically onto a horizontal floor, it rebounds to three - quarters of the height from which it fell. It is initially dropped from a point 4 m above the floor. (i) Show that the total distance the ball travels until it is about to touch the floor for the  1t hn time is given by 328 24 4 n   . [3] (ii) Find the least number of times the ball must bounce for it to trav