SRJC_H2_MATH_P1

1 [TURN OVER] SERANGOON JUNIOR COLLEGE 2018 JC2 PRELIMINARY EXAMINATION MATHEMATICS Higher 2 9758/1 11 Sept 2018 3 hours Additional materials: Writing paper List of Formulae (MF 26) TIME : 3 hours READ THESE INSTRUCTIONS FIRST Write your name and class on the cover page and on all the work you hand in. Write in 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 calcul ator are not allowed in a question, you are required to present the mathematical steps us ing mathematical notatio ns 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. Total marks for this paper is 100 marks. This question paper consists of 6 printed pages (inclusive of this page) and 2 blank pages.

2 Answer all questions [100 marks]. 1 Find 2 2 d25 x xxx++ . [3] 2 The complex numbers z and w satisfy the equations *2 1 5 izw z+= and 23 1 1wz+= . Find the complex numbers z and w. [6] 3 Without the use of a graphing calculator, find the range of values of x for which 218 492 xxx ≥++− . [3] Hence find the exact range of values of x for which 218 e4 e 92e xx x ≥+ +− . [3] (i) The curve with equation 2 2 19 y x−= undergoes a two-step transformations to become curve C with equation () 22 1 194 xy −−= . State the two transformations involved for the curve 2 2 19 y x−= . [2] (ii) Draw a sketch of the curve C, labelling clearly the equation(s) of its asymptote(s), intersection with the axes and the coordinates of any turning points. [3] (iii) Show that the point () 1, 3−− lies on the line 3ym x m=+ − for all real values of m. [1] (iv) Hence using the diagram drawn in (ii), find the range of values of k such that the equation () () 22 31 194 kx k x+− − −= has 2 negative real roots. [2] 4

3 [TURN OVER] 5 (i) Find ()ln 1 dxx+ for 1x >− . Show your working clearly. [2] (ii) The curve C is defined by the parametric equations () ()22 l n 12 , 22 l n 11xt t y t t=− + + = − − + + where 1t >− . Another curve L is defined by the equation () 2 21 6xy=+ − . The graphs