2012 H2 Math Prelims Paper 1 Qn Paper (final)

© DHS 2012 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) 9740/01 Paper 1 11 September 2012 3 hours Additional Materials: Answer 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 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. At the end of the examination, attach the question paper to the front of your answer script. 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 Q12 Total Score Max Score 3 4 5 7 8 9 9 10 11 11 11 12 100

2 DHS 2012 Year 6 H2 Math Preliminary Examination 1 By using the substitution ,yx solve the inequality 2 3 1. 1 x x    [3] 2 Obtain a formula for  1 2 21 2 tan 2 d14 n x xx   in terms of n, where 0.n Hence evaluate  1 2 21 2 tan 2 d14 x xx   exactly. [4] 3 Express 2 9 x x   as a series in ascending powers of x , up to and including the term in 2.x [3] By using only the first two terms in the series expansion above and substituting 1 9x , find an approximation for 5 in the form p q expressed in its lowest terms, where and pq are integers to be determined. [2] 4 Given f( ) (1 ) ! rr r  , show that 2 31f( 1) f( ) . (1 ) ! rrrr r     [2] (i) Hence find 2 2 31 (1 ) ! n r rr r   . [3] (ii) State the value of 2 2 31 (1 ) !r rr r      , justifying your answer. [2] 5 A function f is defined as f ( ) ln(5 ), 5.xx x  (a) Find the volume of revolution when the region bounded by the curve of f( )yx and the x- and y-axes is rotated completely about the y-axis. Give your answer correct to 2 decimal places. [2] (b) (i) State the set of values of x for which    f| | fx x . [1] (ii) Evaluate the value of   9 02 90 2 ,fd f | | dx xx x   giving your answer in the form ln 2,ab where a and b are constants to