CJC_9758_2023_Prelim_P2

9758/01/J2Prelim/2023 [Turn Over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 9758/02 Paper 2 13 Sep 2023 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your class, index number and name on the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, 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 sp ecifically 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. Question 1 2 3 4 5 6 7 8 9 10 Total Marks Total 7 8 12 13 8 8 10 10 12 12 100 This document consists of 3 printed pages, including this cover page.

2 9758/02/J2PRELIM/2023 Section A: Pure Mathematics [40 marks] 1 Without using a calculator, solve the inequality 2 2 25 22 xx xx +− − . [4] Hence, solve the inequality 2 2 25 22 xx xx +− − . [3] 2 It is given that e sin 1xy x x −= + − . (a) Show that 2 2 d e cosd xy kxx −= , where k is a constant to be determined. [2] (b) By further differentiation of this result, find the Maclaurin series for y , up to and including the term in 3x . [3] (c) By using the result in part (b) and standard series from the List of Formulae (MF26), find the expansion of e sin 1 cos 2 x xx x − +− in ascending powers of x , up to and including the term in 3x , giving the coefficients in exact form. [3] 3 Following the popularity of the action role -playing game, Ginseng Im pact, three years ago, developers have developed a strategy game, Ginseng Impactful. The number of people who download Ginseng Impactful, P (in thousands), in a particular city, at time t months, can be modelled by the differential equation ( )d1 13 2d 26 P PPt =− . There were 2000 people who download Ginseng Impactful when it is launched. (a) Show that 1 2 26 9e 4 t P − = + . [6] (b) Determine, the time taken, in months, for the number of people who download Ginseng Impactful to double since the launch. [2] (c)