JPJC 2024 J2 H2 FM Prelim P2 Qn

Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC2 Preliminary Examination 2024 FURTHER MATHEMATICS 9649/02 Higher 2 16 September 2024 Paper 2 3 hours Additional materials: 12-page Answer Booklet (additional 4-page Answer Booklet(s), if applicable) List of Formulae (MF 26) READ THESE INSTRUCTIONS FIRST Write your name and civics class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, 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 8 printed pages. [Turn over

2 Section A: Pure Mathematics [50 marks] 1 (a) By considering 5 0 cos dxx   , use Simpson’s rule for two strips to show that cos10  is approximately a root of 2 2 2 21 1 0.30 15 15 xx          + + + − =                    [6] (b) Hence find an approximation to cos10  , giving your answer to 4 decimal places. [1] 2 A curve C has polar equation 4 3sinr k = + , where 0 2 and is a constant, 0.kk   (i) What can be said about the value of k in each of the cases • C is a parabola, • C is an ellipse, • C is a hyperbola. [3] (ii) Given that 2k = , find the equation of this curve in a standard cartesian form. [4] (iii) Determine the eccentricity of the curve and the coordinates of the two foci. [2]

3 3 (a) (i) The function f is such that f( a)f(b) < 0 where a < b. A student concludes that the equation f(x) = 0 has at least one root in the interval (a, b). Draw a sketch to illustrate why the student could be wrong. [1] (ii) The equation 2cosec 3ln 0xx−= has a root  in the interval [3, 4]. A student uses linear interpolation once on the interval to find an approximation to . Find the approximation to  given by this method and comment on the suitability of the method in