JPJC 2024 J2 Prelim Math P1 Qn paper

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC2 Preliminary Examination 2024 MATHEMATICS 9758/01 Higher 2 9 September 2024 Paper 1 3 hours Candidates answer on the Question Paper. Additional materials: List of Formulae (MF 26) READ THESE INSTRUCTIONS FIRST Write your name and civics 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. This document consists of 6 printed pages. [Turn over For Candidate’s Use For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 11 Total Marks / 100 Answer all the questions. 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 ans wers 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 by [ ] at the end of each question or part question.

2 1 The first four terms of a sequence are given by v1 =  9, v2 = 7, v3 = 47 and v4 = 141. It is given that vn is a cubic polynomial in n. Find vn in terms of n. [3] 2 Without using a calculator, solve the inequality 2 11 19 22 8 x x x    . [4] Hence solve 2 11e 19 2e 2e 8 x x x       , leaving your answer in the exact form. [2] 3 The region R is bounded by the lines 0y , 5 32y and the curve 2 2 25x y  . R is rotated about the y-axis through  radians. Using the substitution 5siny  , find the exact volume generated. [6] 4 (i) A curve C has equation    3 2 5 xy x x    . Sketch C, giving the equations of the asymptotes, the coordinates of the stationary point(s) and the point(s) where C crosses either axis. [4] (ii) Describe a sequence of transformations that maps C onto the graph of    2 3 1 2 5 xy x x    . [3] 5 The function f is defined by   2 f : e , , , 0. x c x x x k c      (i) Find the largest value of k in terms of c for which the function 1f  exists. [1] For the rest of the question, use the value of k found in part (i). (ii) Find 1f ( ) x and state the domain of 1f  .