JJC_H2_MATH_P2

JURONG JUNIOR COLLEGE J2 Preliminary Examination MATHEMATICS 9740/02 Higher 2 24 August 2009 Paper 2 3 hours Additional materials: Answer Paper List of Formulae (MF15) Cover Page READ THESE INSTRUCTIONS FIRST Write your name and civics 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 a graphic calculator. Unsupported answers from a graphic calculator ar e 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, fasten all your work securely together, with the cover page in front. This document consists of 7 printed pages and 1 blank page. [Turn over

2 8 1 , Section A: Pure Mathematics [40 marks] 1 Given that lines and where 1 15 :0 31 l         r 2 13 :0 30 l         r   , meet at point A. B is the poin 4) and lies on 1l while C is a point on 2l with non-negative coordinates. t (6, 8, (i) Given that AB and AC are of equal lengths, show that  . [3] 10 3 3 OC      (ii) A point D is such that ABDC is a parallelogram. Find the position vector of D. [2] (iii) Find the sine of the angle BAC exactly and hence find the exact area of the parallelogram ABDC. [3] 0 11n n  6 n 5 n 4 n 2 n 3 n 1 n y2 x The graph of 2 xyx e , for 01 x is shown in the diagram. Rectangles, each of width 1 n are drawn under the curve as shown. (a) Show that A, the total area of the rectangles may be expressed as 1 3 1 1 f( ) , n r rn    where f( is to be found. [2] )r Find, using integration by parts, the limiting value of A when n , giving your answer in exact form. [4]  (b) A region R in the first quadrant is bounded completely by the curve 2 xy xe , the line y e and the y-axis. Find the volume of revolution formed when R is rotated completely about the x-axis, giving your answer correct to 2 decimal places. [2]

3 3 (a) Expand 13 2 n x x      where n  , in ascending powers of x , up to and including the term in 2x . State the range of values of x for