ACJC 9758 2023 Prelim P2

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME TUTORIAL/ INDEX FORM CLASS NUMBER MATHEMATICS 9758/02 Paper 2 29 August 2023 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your index number, class and name on all 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. The use of an approved graphing calculator is ex pected, where appropriate. 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 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 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 26 printed pages and 2 blank pages. [Turn over Question Marks 1 /5 2 /8 3 /8 4 /9 5 /10 6 /7 7 /10 8 /9 9 /9 10 /12 11 /13 /100

2 ANGLO-CHINESE JUNIOR COLLEGE 2023 H2 MATHEMATICS 9758/02 Section A: Pure Mathematics [40 marks] 1 Using the substitution cosux= , find 2 sin2 dcos cos 2 x xxx++∫ , giving your answer in terms of x . [5] 2 It is given that ( )coty xa= + for some constant a. (i) Show that ( ) 2d 1d y yx = −+ and hence find 2 2 d d y x and 3 3 d d y x in terms of y. [3] (ii) Explain why the Maclaurin series of y cannot be found when 0a= . [1] In the case where π 2a= , (iii) use your answers in (i) to find the series expansion of y in ascending powers of x, up to and including the term in 3x . [2] (iv) Using your answer in (iii) and the standard series from the List of Formulae (MF26), find the series expansion of 2 y x+ in ascending powers of x , up to and including the term in 3x . [2] 3 The Stoke’s Law states that when a spherical object of radius R is falling at velocity v in a fluid, the resistance force F acting on the sphere is given by 6πF Rv η=− , where η is the coefficient of viscosity of the fluid. The following table shows the coefficients of viscosity of various fluids at 25 C° . Fluid Coefficient of viscosity η, 11kgm s−− Acetone 43.06 10 −× Benzene 51.81 10 −× Castor Oil 0.985 Corn Syrup 1.3806 Ethanol 31.074 10 −× Methanol 45.44 10 −× Olive Oil 28.1 10 −×

3 ANGLO-CHINESE JUNIOR COLLEGE 2023