ACJC_Question_Paper_1

ANGLO-CHINESE JUNIOR COLLEGE MATHEMATICS DEPARTMENT MATHEMATICS Higher 2 Paper 1 23 August 2012 JC 2 PRELIMINARY EXAMINATION Time allowed : 3 hours Additional Materials: List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your Index number, Form Class, graphic and/or scientific calculator model/s on the cover page. Write your Index number and full name on all the work you hand in. Write in dark blue or black pen on your answer scripts. You may use a soft pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 signi ficant 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 a graphic calculator. Unsupported answers from a graphic calculator are a llowed unless a question specifically states otherwise. Where unsupported answers from a graphic calculator are not allowed in the 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. At the end of the examination, fasten all your work securely together. This document consists of 5 printed pages. [Turn Over 9740 / 01

Anglo-Chinese Junior College H2 Mathematics 9740: 2012 JC 2 Preliminary Examination Paper 1 Page 2 of 5 ANGLO-CHINESE JUNIOR COLLEGE MATHEMATICS DEPARTMENT JC2 Preliminary Examination 2012 MATHEMATICS 9740 Higher 2 Paper 1 Calculator model : _____________________ Arrange your answers in the same numerical order. Place this cover sheet on top of them and tie them together with the string provided. Question No. Marks 1 /7 2 /4 3 /8 4 /8 5 /5 6 /8 7 /7 8 /7 9 /5 10 /7 11 /10 12 /7 13 /5 14 /12 / 100 Index No: Form Class: ___________ Name: _________________________

Anglo-Chinese Junior College H2 Mathematics 9740: 2012 JC 2 Preliminary Examination Paper 1 Page 3 of 5 1 (a) Find 2 d 4 7 x xx x + + ∫ . [3] (b) Find 0 d a x a x x −∫ by using integration by parts. [4] 2 The functions f and g are defined by 2 2 2f : 2 5 2 x x x x x + − + /arrowbarright, 1, , 2 2x x +∈ ≠ /Rbb , 2 3g : , 2 5 2 x x x − − + /arrowbarright1, , 2 2x x +∈ ≠ /Rbb . Without the use of the graphic calculator, find the subset of the domain for which the value of ( )f x is greater than or equal to the value of ( )g x . [4] 3 The function f is defined by ( ) 22f : ln ln , 0 x x x x − > /arrowbarright. Sketch the graph of f ( ) y x = , indicating clearly all points of intersection wit h the axes. Explain why the inverse function 1f − does not exist. [3] The function h is defined by ( ) 22h : ln ln ,