EJC_H2_2020_Prelim_P2

2020 JC2 H2 Mathematics Preliminary Examination [Turn over EUNOIA JUNIOR COLLEGE JC2 Preliminary Examinaton 2020 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CLASS INDEX NO. MATHEMATICS Paper 2 [100 marks] 9758/02 16 September 2020 3 hours Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civics group and question number 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 paper clips, highlighters, glue or correction fluid. Answer all 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 an approved graphing calculator. 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. This document consists of 28 printed pages (including this cover page) and 2 blank page. For markers’ use: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total

Section A: Pure Mathematics [40 marks] 1 The diagram above shows the curve  f.yx The curve cuts the x-axis at the point  1.5,0 and has a maximum point at  0,6 . The curve also has vertical asymptote 2x and horizontal asymptote 0.y Stating the equations of the asymptotes and coordinates of any turning points and points where the curves cross the axes, if it is possible to do so, sketch on separate diagrams, the curves (i)  1 f12yx , [3] (ii)   1 fy x . [3] 2 The curve 1C has equation 23 2 3 1 xxy x   . The curve 2C has equation     2 2 2 411 yx b    , where 0b . (i) Sketch 1C , stating the equations of any asymptotes and the coordinates of any turning points and points where the curve crosses the axes. [4] (ii) Hence, find the range of values of b such that there is no point of intersection between 1C and 2C . Using the maximum value of b found, sketch 2C on the same diagram as part (i). [3] y x O  0,6

2020 JC2 H2 Mathematics Preliminary Examination [Turn over 3 A curve C has parametric equations 1 cos ,x  sin 1,y    for 0 2  . (i) The point P on C has parameter p. Show that the normal to C at P crosses the y-axis at a point Q with coordinates  0, 1p . [5] (ii) The normal to C at P crosses the x-axis at point R. Given that point S is the midpoint of QR, find a cartesian equation of the curve