TJC_H2_MATHS_P1

TEMASEK JUNIOR COLLEGE, SINGAPORE JC 2 Preliminary Examination 2017 Higher 2 MATHEMATICS 9758/01 Paper 1 29 Aug 2017 Additional Materials: Answer paper 3 hours List of Formulae (MF26) 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 signifi cant 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 ar e 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. 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 7 printed pages and 1 blank page. © TJC 2017 [Turn over

2 TJC/MA 9758/Preliminary Exams 2017 1 The graph of f( )yx is shown below. (a) The graph of f( 2 )yx is obtained when the graph of f( )yx undergoes a sequence of transformations. Describe the sequence of transformations. [2] (b) Sketch the graph of f' ( )yx , stating the equations of any asymptotes and the coordinates of any points of intersection with the axes. [3] 2 The diagram shows two points at ground level, A and B. The distance in metres between A and B is denoted by x. The angle of elevation of C from B is twice the angle of elevation of C from A. The distance AC is 200 m and 3BAC    radians. Show that 200sin 2sin 3 x     . [ 2 ] It is given that  is a small angle such that  4 and higher powers of  are negligible. By using appropriate expansions from the List of Formulae (MF26), show that 22700 250 9x  . [ 4 ] A B 200 m C x m             •   •

3 TJC/MA 9758/Preliminary Exams 2017 3 The diagram above shows a circle C which passes through the origin O and the points A and B. It is given that 4OA units and 3OB units. (i) Show that the coordina tes of the centre of C is 32, 2   .   Hence write down the equation of C in the form  2 2 232 2x yr   , where r is a constant to be d e t e r m i n e d . [ 2 ] (ii) By adding a suitable line to the diagram above, find th e range of values of m for which the equat