PJC_H2_MATHS_P2

Candidate Name: ________________________ Class: _____________ JC2 PRELIMINARY EXAM Higher 2 MATHEMATICS 9740/02 Paper 2 21 Sept 2015 3 hours Additional Materials: Cover page Answer papers List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your full name and class 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, 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 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 6 printed pages.

2 @PJC 2015 [Turn Over] Section A : Pure Mathematics [40 marks] 1 The function f is defined by 2f : , , , 2x x x x x     where 2 . (i) Find, in terms of  ,   1f x , stating the domain of 1f  . [4] (ii) On the same diagram, sketch the graphs of  fyx and   1fyx  , showing their graphical relationship clearly. [2] (iii) Find, in terms of  , the solution of the equation     1ff xx  . [3] 2 By sketching the graphs of 3 1y x  and yx , solve the inequality 3 1 xx  . [2] Hence, without using a calculator, evaluate 4 1 34 1 dxx x  . [4] The area bounded by the curves 3 1y x  , yx , the line 2x and the x-axis is rotated completely about the y-axis to form a solid of revolution of volume V. Find the numerical value of V, giving your answer correct to 3 decimal places. [3]

3 @PJC 2015 [Turn Over] 3 Sketch, on a single Argand diagram , the set of points representing all complex numbers satisfying both of the following inequalities: 3 1 3 i2 2 2z    and arg( 2i) 03 z    . [4] Hence find (i) the minimum value of i2 z , [3] (ii) the exact value of the complex number z such that arg( )z is minimum. [3] 4 The parametric equations of a curve are 2xt , 2y t t . (i) The point P on the curve has parameter p. Show that the equation of the tangent at P is   22 2 1py p x p   . [3] (ii) The tangent at