CJC P2

9758/02/PRELIMS/2020 [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 16 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 all the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. 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 graphi ng 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. Question 1 2 3 4 5 6 7 8 9 10 11 Total Marks Total 5 6 7 12 10 8 8 8 9 13 14 100 This document consists of 28 printed pages.

2 9758/02/PRELIMS/2020 Section A: Pure Mathematics [40 marks] 1. The graph of a c urve C is a cubic polynomial and it passes through the origin, ( )2, 0 and ( )2.55, 0.0631− . Given that it has a turning point when 0.785x= , find the equation of C, giving its coefficients correct to 1 decimal place. [5] 2. (i) By means of the substitution cos ecx θ= , show that 2 3 2 322 63 1 d sin ( )d 1 x xx π π θθ= −∫∫ . You are to show all workings clearly. [3] (ii) Hence evaluate exactly 2 322 3 1 d 1 x xx −∫ . [3] 3. (i) By writing ( )( ) 3 3 13 4rr++ in partial fractions, find ( )( )1 3 3 13 4 n r rr= ++∑ in terms of n. [4] (ii) Hence find the exact value of 3 13 13 1 22 25 25 28 28 31×+×+×+ . [3] 4. Botanists are studying how excessive logging is affecting the population of forest trees in a country in South-East Asia. The population of trees in a forest after t years is denoted by x, in thousands. One simple model proposed is that the population increases at a rate proportional to its population size. It is known that t rees are chopped off at a constant rate of 3 thousand trees per year and the population stays constant when xp= . (i)