JPJC_9758_2024_Promo_Question (JCMTC)

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC1 Year End Examination 2024 MATHEMATICS 9758/01 Higher 2 27 Sept 2024 Paper 1 3 hours Additional materials: Printed Answer Booklet List of Formulae and Results (MF27) READ THESE INSTRUCTIONS FIRST This document consists of 6 printed pages and 2 blank pages. [Turn over 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 co rrect 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 by [ ] at the end of each question or part question .

2 1 Differentiate each of the following expressions with respect to x. (a) ( ) 12cos 3 x− , [2] (b) 3 21ln x x  + . [3] 2 Water is poured at a rate of 0.1 m 3 per minute into a container in the form of an open cone. The semi-vertical angle of the cone is 30 o . At time t minutes after the start, the radius of the water surface is r m (see diagram). Find the rate of increase of the depth of water when the volume of the water is 3 m 3 . [5] [The volume of a cone of base radius r and height h is given by 21 3V r h = ] 3 A curve C has equation 2f ( ) ax bx cx= + + , where a, b and c are constants. It is given that C passes through the points ( )1, 4− and ( )2, 11− and the curve of 1 f ( )y x= has a vertical asymptote with equation 1x= . Find the equation of C. [4] 4 By writing ( )88x A x B= − + , where A and B are constants, find 1 2 0 d4 8 5 x xxx−+ , giving your answer in the form 1ln tanp q r s −+ , where p, q, r and s are values to be determined. [5] r m 30

3 5 The curve C has equation 2 1 x ax by x ++= + , where a and b are constants. It is given that C has a minimum point at ( )2,0 . (i) Show that 4a=− and 4b= . [3] (ii) Sketch the graph of C, indicating clearly the equations of any asymptotes and the coordinates of any turning points and axial intercepts. [3] (iii) By adding an appropriate graph to your sketch in (ii), deduce the number of re