VJC_H2_MATH_P1_sharing

1 VICTORIA JUNIOR COLLEGE Preliminary Examination MATHEMATICS (Higher 2) 9740/01 Paper 1 September 2015 3 hours READ THESE INSTRUCTIONS FIRST Write your name and CT group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct t o 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 mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 5 printed pages © VJC 2015 VICTORIA JUNIOR COLLEGE [Turn over Additional Materials: Answer Paper Graph Paper List of Formulae (MF15)

2 1 A sequence 1 2 3, , , ...w w w is such that 1 1 [( 1) +1]nnw n w n   , where n  , and 1wa , where a is a constant. Use the method of mathematical induction to prove that ( 1)nw an n   . [5] 2 The function h is given by 32h : , x ax bx cx d x    , where , , and a b c d are real constants. The graph of h( )yx passes through the point (1,1) . Given that (2,2) is a stationary point, find three linear equations involving , , and a b c d . [3] By writing each of a, b and c in terms of d, find the exact set of values of d such that 0ab c „ . [3] 3 The curve C has equation 2 ,2 ax bx dy x   where a, b and d are constants. Given that the line 23yx is an asymptote to C, find the values of a and b. [3] Given further that 6d  , find the coordinates of any points of intersection with the x- and y- axes, lea ving your answer in terms of d. Hence sketch C, stating the equations of any asymptotes. [4] 4 The function g is defined by where  is a real constant. (i) Find the exact minimum value of  such that the inverse of g exists. [2] Using the value of  found in (i), (ii) find   1g1 , [2] (iii) sketch the graphs of  gyx ,   1gyx  and   1ggyx  on a single diagram. [3] g : e 7 , ,xx x x  

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