CJC 2012 JC2 H2 Prelim Paper 2 Questions

9740/02/PRELIMS/2012 [Turn over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/02 Paper 2 29 AUGUST 2012 3 hours Additional Materials: List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your 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 signi ficant 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 a llowed 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, arrange your answers in NUMERICAL ORDER. Place this cover sheet in front and fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. Name: ___________________________ Class: ______ __________ Question 1 2 3 4 5 6 7 8 9 10 11 12 13 Total Marks Total 4 10 10 8 8 8 8 8 6 4 6 11 9 100 This document consists of 6 printed pages. Catholic Junior College

2 9740/02/PRELIMS/2012 [Turn over Section A: Pure Mathematics [40 marks] 1 Let f( x) be a cubic polynomial where 6) 2f( = and 15 ) 1f( =− . Also, f( x) takes on stationary values at 2−=x and 1=x . Find f( x). [4] 2 A line, l 1, and a plane p1, have equations ℜ∈           −+           − = λλ , 2 1 3 2 1 1 r and 4 2 0 1 =          − ⋅r respectively. (i) Find the intersection point of l1 and p1. [3] (ii) Find an equation, in scalar product form, for the plane p2 that contains l1 and the point B(0, -1, -2). [3] (iii) Find an equation for the line of intersection, l2, between p1 and p2. [2] (iv) A plane, p3, has an equation 3 1 =           ⋅ b ar . What is the relationship between a and b such that p3 is parallel to l2? [2] 3 The function f is defined as follows. 1 1: f 2 + −→ xx for ℜ∈x . (i) Sketch the graph of y = f( x). [1] (ii) If the domain of f is restricted to kx ≤ , state with a reason the greatest value of k for which the function )(f 1 x− exists. [2] (iii) With the restricted domain in (ii), find an express ion for )(f 1 x− and the real value of a such that )f( )(f 1 aa =− . [4] The function g is defined as follows. 3: g +→ xx for ℜ∈x . (iv) Find a restriction on the domai