EJC_9649_2023_Prelim_P1

2023 JC2 H2 Further Mathematics Preliminary Examination Paper 1 [Turn over EUNOIA JUNIOR COLLEGE JC2 Preliminary Examination 2023 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CIVICS GROUP INDEX NO. FURTHER MATHEMATICS Paper 1 [100 marks] 9649/01 12 September 2023 3 hours Additional Materials: Answer Booklet List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civics group and index number on the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all 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 2023 JC2 H2 Further Mathematics Preliminary Examination Paper 1 1 A curve has parametric equations 42 4ln , 4 , 0.x t t y t t    The arc of the curve from 1t to tk , where 1k  , is rotated through one complete revolution about the x-axis. Express the surface area generated as a polynomial in k. Given that this surface area is 384 , find the value of k. [4] 2 The sequence  nx is given by 1 1x  and 1 1 1 14 1 2 for 2. n n nnnx x n n n        By multiplying the recurrence relation throughout by 1nn  , use a suitable substitution to determine nx as a function of n, simplifying your answer. [7] 3 The variables x and y are related by the differential equation 2 3 2 3d d yx y x x y yx    , (*) and it is given that 0xy . (a) Use the substitution y ux to find the general solution of the differential equation. [5] A particular solution of the differential equation (*) is such that 1y when 2x . (b) Use one step of the Euler method to calculate an approximate value of y when 2.5x . [2] (c) Given that the solution curve is concave downwards near the point (2, 1) , determine with a sketch whether the approximate value of y found in (b) is an over-estimate or under-estimate. [1] 4 The curve C has parametric equations ( sin ), (1 cos )x a t t y a t    where 3π0 2t and a is a positive constant. (i) The region R is bounded by the curve C, the x-axis and the line 3 12xa 