TJC_H2_Maths_P2

TEMASEK JUNIOR COLLEGE, SINGAPORE Preliminary Examination 2014 Higher 2 MATHEMATICS 9740/02 Paper 2 15 September 2014 Additional Materials: Answer Paper 3 hours List of Formulae (MF 15) READ THESE INSTRUCTIONS FIRST Write your Civics Group and Name on all the work that 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, highlighters, glue or correction fluid. Answer all the questions. 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 a graphic calculator. Unsupported answers from a graphic calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphic 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 7 printed pages. © TJC/Prelim Exam 2014/MA H2 9740 [ Turn over

TJC/Prelim Exam/2014/MA H2 9740/02 2 Section A: Pure Mathematics [40 marks] 1 It is given that 1f( ) 3 15 xx  . Find the roots  and  of the equation f( )x x , where   . [2] A sequence of real numbers 123,,, . . .x xx satisfies the recurrence relation given by 1 fnnx x  for 1n , and 1x is a value that lies between  and. The diagram shows how the graphs of f( )y x and y x are used to obtain 2x from 1x . (i) Copy the above diagram, and illustrate how 3x can be obtained. [1] (ii) Describe the behavior of the sequence in this case. [1] 2 A circle C1 has equation given by 22 43 0xx y   . Another curve C2 with equation   22 ax b y ca   is obtained from circle C1 after going through the following successive transformations:  Stretching with scale factor 3 parallel to the y-axis followed by  Translation of 1 unit in the negative y-axis direction. (i) Find the values of a, b and c. [3] (ii) Sketch, on the same diagram, the two curves, C1 and C2, indicating clearly the points of intersection of C1 and C2. [3] (iii)  1,x k and  2 ,x k are points on C1 and C2 respectively such that 2123 xx , where k is a real constant. State the range of values of k. [1]  fy x y x yx 1x  1f x 2x

TJC/Prelim Exam/2014/MA H2 9740/02 3 3 A curve has equation f( )y x , where  2 for 2,f 2 h( ) for 2. ax bx c xx x xx       The curve has a turning point at  3,5 . The only asymptotes are 1yx and 2x . (a) Fin