2019 J2 NYJC H2 Math Prelim (with ans)

This document consists of 6 printed pages. NANYANG JUNIOR COLLEGE Internal Examinations [Turn Over NANYANG JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 Candidate Name CT Class 1 8 Centre Number/ Index Number / MATHEMATICS 9758/01 Paper 1 2nd September 2019 3 Hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS Write your 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, highlighters, glue or correction fluid. Answer all the questions. Write 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. For examiner’s use only Question number Mark 1 2 3 4 5 6 7 8 9 10 11 12 Total www.KiasuExamPaper.com 529

2 NYJC 2019 JC2 Preliminary Examination 9758/01 1 The curve with equation 22 9yx  is transformed by a stretch with scale factor 2 parallel to th e x-axis, followed by a translation of 4 units in the negative x-direction, followed by a translation of 1 2 units in the positive y-direction. Find the equation of the new curve and state the equations of a ny asymptote(s). Sketch the new curve, indicating the coordinates of any turning points. [6] 2 The diagram shows a mechanism for converting rotational motion into linear motion. The point P, on the circumference of a disc of radius r, rotates about a fixed point O. The point Q moves along the line OX, and P and Q are connected by a rod of fixed length 3 r. As the disc rotates, the point Q is made to slide backwards and forwards along OX. At time t, angle POQ is  , measured anticlockwise from OX, and the distance OQ is x. (i) Show that   2cos 9 sinxr   .[ 2] (ii) State the maximum value of x.[ 1] (iii) Express x as a polynomial in  if  is sufficiently small for 3 and higher powers of  are to be neglected. [3] 3 Without using a calculato r, solve the inequality 2 34 212 xx xx   . Hence solve the inequality 2 34 212 xx x x aa aa   where 2.a  [6] 4 (i) Using double angle formula, prove that  4 1 34 c o s 2 o 4si c s 8n    . [2] (ii) By using the substitution 2cosx  , find the exact va