TJC 9758 2023 Prelim P1

1 TEMASEK JUNIOR COLLEGE 2023 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME CENTRE NUMBER S INDEX NUMBER MATHEMATICS 9758/01 Paper 1 24 August 2023 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, centre number and index number on 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 mathematica l 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 19 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 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 2023 9758 1 (a) Find 1tan dx xx − ∫ . [3] (b) Find sin 2 cos5 dx xx∫ . [2] 2 A curve C has equation 4x2 − 24x + 9y2 = 0. (a) Sketch C, giving the exact coordinates of points where the curve meets the axes.[2] (b) Describe a sequence of transformations that transform the graph of C onto the graph of ( ) 22 1 194 yx α −+= where α is a positive constant. [3] (c) State the value of α for which the resulting curve takes on the shape of a circle. [1] 3 The function g is defined by ( )g 4 xx x = − , , 0 4.xx∈ << It is given that ( ) 23f x ax bx cx= ++ is the binomial expansion of ( )g 4 xx x = − in ascending powers of x up to and including terms in 3x . (a) Find the exact value of a, b and c. [4] (b) Find the range of values of x such that the percentage error in using ( )f x to approximate ( )g x is less than 4%. [2] 4 A curve C has equation ( ) 23 85 3 xxy kx − +−= − where k is a positive real constant and x ≠