NYJC_9758_2024_Promo_Qns

This document consists of 4 printed pages and 0 blank page. NANYANG JUNIOR COLLEGE Internal Examinations © NYJC 2024 [Turn Over NANYANG JUNIOR COLLEGE JC1 END-OF-YEAR EXAMINATION Higher 2 CANDIDATE NAME CT CLASS 2 4 MATHEMATICS 9758/01 Paper 1 2 October 2024 2.5 hours Additional Materials: Printed Answer Booklet List of Formulae and Results (MF27) READ THESE INSTRUCTIONS FIRST Answer all questions. Write your answers on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. 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 must present the mathematical steps using mathematical notations and not calculator commands. You must show all necessary working clearly. 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 80.

2 NYJC 2024 JC1 End-of-Year Examination 9758/01 1 A curve C has equation 2 2 e xayb c x   , where a, b and c are constants. It is given that C passes through the point with coordinates  21, 2e 1 . When C undergoes a scaling of factor 2 parallel to the x-axis, the transformed curve passes through the point with coordinates 21, 8 e  . When C undergoes a translation by negativ e 1 unit in the direction of the y-axis, the transformed curve passes through the point with coordinates   233,2e 4  . Find the values of a, b and c. [4] 2 (a) Show that 2 49xx  is always positive for all real values of x. [2] (b) Hence, without using a calculator, solve   22 2 49 2 0 67 xx x xx     . [3] 3 The curve D has equation 2 25 23 xy xx   . (a) Sketch the graph of D, stating the equations of any asymptotes, the coordinates of the points where the curve crosses the axes and the stationary point(s). [3] (b) By considering a suitable curve, hence, find the exact range of values of k, where 0k  , such that the equation  2 2 2 2 253 23 xx k xx     has at least one positive real root. [3] 4 During a clinical trial, the concentration U, of a specific blood agent is measured at one-hour intervals following the initial ad ministration of the trial drug to a patient. The following readings were obtained 34 5 88, 76 and 70,UU U  where tU denotes the reading t hours after the drug was first administered. It is believed that U satisfies the relationship 1 , 0 ,ttUp q U t   where p and q are constants. (a) Find the values of p and q. [2] (b) Determine the initi