NYJC_H2_2020_Prelim_P2

This document consists of 6 printed pages and 0 blank page. NANYANG JUNIOR COLLEGE Internal Examinations © NYJC 2020 [Turn Over NANYANG JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CT CLASS 1 9 Centre Number/ Index Number / MATHEMATICS 9758/02 Paper 2 15 September 2020 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and class on 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. 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. For examiner’s use only Question number Marks 1 2 3 4 5 6 7 8 9 10 11 Total

2 NYJC 2020 JC2 Preliminary examination 9758/02 Section A: Pure Mathematics [40 marks] 1 In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. It provides a method of rendering graphs and indicating the positions of points on a two-dimensional surface. The polar coordinate system is employed in mathematics, physics, engineering, navigation, robotics, and other sciences. The area of a region enclosed by a curve with polar equation f ( )r  where    , is given by the integral   21 f ( ) d2    . A curve C has polar equation  cos2 sinra  , where a is a positive constant and 26     . By using the formulae from the List of Formulae (MF26), show that the area of the region enclosed by C is given by   62 2 1 cos4 cos2 4cos2 sin 2 d4 a            . [2] Hence find, in terms of a, the exact area enclosed by C. [4] 2 The function f is given by 2f : 2x x kx  , for ,x x k  . (i) Find   1f x and state the domain of 1f  in terms of k. [3] For the rest of this question, let 2k  . (ii) The function g is given by   2 2 1g : 5 7 1 4 xx  , for x , 35 x  . If fg(x) = 32, find the exact value(s) of x. [4]