TJC_H2_MATHS_P1_Questions

TEMASEK JUNIOR COLLEGE, SINGAPORE Preliminary Examination 2015 Higher 2 MATHEMATICS 9740/01 Paper 1 31 August 2015 Additional Materials: Answer paper 3 hours List of Formulae (MF15) 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. 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. © TJC 2015 [Turn over

TJC/MA 9740/Preliminary Exam 2015 2 1 The equation of a circle M is given by 22 0x y Ax By C     where A, B and C are real constants. The line y = 2(x + 1) passes through the centre of M and the graph of y = | x | intersects M at the points where x = 2 and x = 8. Find the equation of M. [4] 2 The diagram below shows the graph of y = g( x). The graph has a minimum point at (0, 2) and a maximum point at 13, 2   . The equations of the asymptotes are x = 1, y = 0 and y = 2x. On separate diagrams, sketch the graphs of (i) y = g(x), [2] (ii) 1 g( )y x , [2] showing clearly in each case, the equations of the asymptotes and the coordinates of the turning points and axial intercepts, where applicable. 3 Without using a calculator, solve the inequality 23 112 x x  . Hence solve 23 112 x x  . [5] 4 The sequence of real numbers 1 2 3, , , . . .u u u is defined by 11 2 and , where 1 and .4 nn nu u u a n an      (i) Prove by mathematical induction that for 1.12 ( 2)( 3)n nau nn   [4] (ii) Determine the limit of 1 ( 2) nunn u as .n [2] 5 The complex number z satisfies the equation 3 3 1 3 i1 z z   . Without the use of a graphing calculator, express z3 in the form rei where r  0 and  <   . Hence find the roots of the equation. [6] y = g(x) y x y = 2x x = 1 13, 2   2 (0, 2) 0

TJC/MA 9740/Preliminary Exam 2015 3 6 The figure below shows a rectangle OA