VJC 2023 JC1 MYE 9649

VICTORIA JUNIOR COLLEGE JC 1 WEIGHTED ASSESSMENT 1 2023 H2 Further Mathematics 9649/01 Paper 1 3 hours Additional Materials: Answer Paper Graph Paper List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name and CT group on 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 figur es, 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 us ing 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 5 printed pages [Turn over

2 1 The graph of the first derivative of a function f is shown in the diagram below. It is symmetrical about the origin O and approaches the lines 0.5y  and 0.5y for large values of x. Sketch the graph of f( )yx given that it has a pair of asymptotes that intersect at the origin. [3] 2 The terms in the sequence 01 2,,,uu u  satisfy the recurrence relation 21 1 () ,nn n nuur u u   where r is a non-zero constant. (i) Find the general solution of this recurrence relation. [2] (ii) Given that 0 0u  and the sequence converges to a finite value L, find an expression for nu in terms of L, n and r. State a necessary condition on r. [3] 3 A curve is defined parametrically by 2 3 2 ,, 1 txy t t t    where  is a positive constant. (i) Sketch the curve, stating the equation of its asymptote. [2] (ii) Find in terms of , the x-coordinate of the point P where the curve intersects itself. [1] (iii) Show that the area of the region bounded by the curve between P and the origin is given by an integral of the form 2 f( ) 0 4g ( ) d ,tt   where f( ) is a function of  and 2g( )t is a function of 2t to be determined. [5] 4 It is given that the equation 1c o s 2 0xx  has a root  in the interval [0, 1]. Use linear interpolation once on the interval [0, 1] to obtain an approximation x1 to . [2] Using x1 as an initial estimate, apply the Ne