ASRJC_8865_2022_Prelim

1 ASRJC J2 H1 Mathematics Preliminary Examination ANDERSON SERANGOON JUNIOR COLLEGE Preliminary Examination H1 Mathematics Paper (100 marks) 8865/01 30 August 2022 3 hours Additional Material(s): List of Formulae (MF26) CANDIDATE NAME CLASS / READ THESE INSTRUCTIONS FIRST Write your name and class in the boxes above. Please write clearly and use capital letters. Write in dark blue or black pen. HB pencil may be used for graphs and diagrams only. Do not use staples, paper clips, glue or correction fluid. Answer all the questions and write your answers in this booklet. Do not tear out any part of this booklet. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a d ifferent level of accuracy is specified in the question. You are expected to use an approved graphing calculator. 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. All work must be handed in at the end of the examination. If you have used any additional paper, please insert them inside this booklet. The number of marks is given in brackets [ ] at the end of each que stion or part question. This document consists of 19 printed pages and 5 blank pages. Question number Marks 1 2 3 4 5 6 7 8 9 10 11 12 13 Total

2 ASRJC J2 H1 Mathematics Preliminary Examination Section A: Pure Mathematics [40 marks] 1 (i) Solve the inequality 22 3 2xx− . [2] (ii) Hence by means of the substitution exy= , find the range of values which will satisfy the inequality 22e 3e 2xx− . [2] 2 (a) Differentiate 2 2 23x x  − with respect to x. [2] (b) Find 3 2 d 54 x x− . [2] 3 The curve C has equation y = 8 – 2e1 – 4x . (a) Find the equation of the tangent to C at the point x = 1, giving your answer in the form y = mx + c, where m and c are exact. [4] (b) The finite area, A, between the curve C, the x – axis and the lines x = 1 4 and x = 1 is given by A = 3e qp+ where p and q are constants. Use integration to find the exact values of p and q. [3] 4 The curve C has equation y = x4 – 10x3 + 36x2 – 54x + 17 for 05 x . (i) Find d d y x . Hence find the coordinates of the stationary points on the curve. [4] (ii) Determine the nature of each of the stationary points. [2] (iii) Sketch the graph of C, stating the coordinates of any point (s) where the curve crosses the axes. [3] (iv) Determine the equation of a curve which, when used with the equation of C, will enable you to solve the equation x4 – 10x3 + 37x2 – 52x + 18 = 0. Sketch this curve on your diagram. [2] (v) Hence solve the equation