TJC_8865_Prelim_2022_Questions

1 TEMASEK JUNIOR COLLEGE 2022 JC2 Preliminary Examination Higher 1 CANDIDATE NAME CENTRE NUMBER S INDEX NUMBER MATHEMATICS 8865/01 Paper 1 26 August 2022 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name 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, 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. The total number of marks for this paper is 100. This document consists of 21 printed pages and 1 blank page. [Turn over For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 11 12 Total Marks

2 DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN @TJC 2022 8865 Section A: Pure Mathematics [40 marks] 1 Find algebraically the set of values of k for which ( ) 22 4 1 0kx x k− + +  for all real values of x. [4] 2 (a) Differentiate 31 23ln 9 2xx  − with respect to x. [3] (b) Find ( ) 2 23 dx x x −  . [3] 3 (i) Find the exact root of the equation 222e 1 3exx −−= . [3] (ii) Sketch on the same diagram, the graphs of 22e 1xy=− and 23e xy −= , showing clearly the equations of any asymptotes and the coordinates of the y-intercepts. [2] (iii) Use (i) and (ii) to deduce in exact form, the range of values of x that satisfy the inequality 222e 3e 1 0xx −− −  . [1] (iv) Deduce the range of values of p for which 2e 3e 1 0pp− − −  . [1] 4 A curve C satisfies the equation 2 d d ( 5) ya xx= − , where a is a constant. The equation of the