2019 PU3 MI H2 Math Prelim (with ans)

This document consists of 24 printed pages. [Turn over 2019 Preliminary Exams Pre-University 3 MATHEMATICS 9758/01 Paper 1 3 September 2019 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your admission number, name and class on all 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. Give your answers in the spaces provided in the question paper. 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. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless 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. Qn No. Q 1Q 2Q 3Q 4Q 5Q 6Q 7Q 8Q 9 Q 10 Q 11 * T otal Score Max Score 6 6 6 8 8 9 10 10 12 12 13 100 CANDIDATE NAME CLASS ADMISSION NUMBER www.KiasuExamPaper.com 376

2 © Millennia Institute 9758/01/PU3/Prelim/19 1 The nth term of a sequence 123, , , ...uuu is given by 2 1 ! nun n . (i) Show that 1 121 ! nn nuu n n     .[ 2] (ii) Hence find 2 2 121 ! n r rr r     .[ 3] (iii) State, with a reason, if the series in part (ii) converges. [1] 2 It is given that   2 3 for 0 2, f 1 2 for 2 4, 6 xx x xx        and that   ff 4xx  for all real values of x. (i) Sketch the graph of fyx for 31 0x  .[ 3] (ii) Find the volume of revolution when the region bounded by the graph of fyx , the lines 1x  , 2x  and the x-axis is rotated completely about the x-axis. [3] 3( i) Find  2d cosd xx .[ 2] (ii) Hence find 32sin dxx x .[ 4] 4( a) The curve C has equation fyx . (i) Given that  2 34f 1 xxx x   , sketch the curve C, showing the equations of the asymptotes and the coordinates of any turning points and an y points of intersection with the axes. [3] (ii) Hence, state the range of values of x where f0 x  .[ 2] (b) The curve with equation gyx is transformed by a stretch with scale factor 2 parallel to the x-axis, followed by a translation of 1 unit in the negative x-direction and followed by a translation of 1 unit in the positive y-direction. The resulting curve has equation 2 34 1 xxy x   . Find g x .[ 3] www.KiasuExamPaper.com 377

3 © Millennia Institute 9758/01/PU3/Prelim/19 [Turn over 5( i) On the same axes, sketch t