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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certifcate o± Education Advanced Level FURTHER MATHEMATICS 9231/02 Paper 2 October/November 2006 3 hours Additional Materials: Answer Booklet/Paper Graph paper List o± Formulae (MF10) READ THESE INSTRUCTIONS FIRST I± you have been given an Answer Booklet, ±ollow the instructions on the ±ront cover o± the Booklet. Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen on both sides o± the paper. You may use a so±t pencil ±or any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction ²uid. Answer all the questions. Give non-exact numerical answers correct to 3 signifcant fgures, or 1 decimal place in the case o± angles in degrees, unless a di±±erent level o± accuracy is specifed in the question. Where a numerical value is necessary, take the acceleration due to gravity to be 10 ms 2 . The use o± a calculator is expected, where appropriate. Results obtained solely ±rom a graphic calculator, without supporting working or reasoning, will not receive credit. You are reminded o± the need ±or clear presentation in your answers. The number o± marks is given in brackets [ ] at the end o± each question or part question. At the end o± the examination, ±asten all your work securely together. This document consists o± 6 printed pages and 2 blank pages. © UCLES 2006 [Turn over
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2 1 A uniform rod AB ,o fleng th2 a and mass m , has a particle of mass 1 2 m attached to B .T h er o di s smoothly hinged at A to a Fxed point and can rotate without resistance in a vertical plane. It is released from rest with AB horizontal. ±ind, in terms of a and g , the angular acceleration of the rod when it has rotated through an angle of 1 3 π .[ 5 ] 2 A light elastic string AB , of natural length 0.5 m and modulus of elasticity 12 N, has a particle of mass 0.3 kg attached to B .Th eend A is attached to a Fxed point at a distance of 0.7 m above a horizontal table. The coefFcient of restitution between the particle and the table is e . The particle is released from rest at A , hits the table and rebounds to a height of 0.22 m above the table. ±ind the value of e , assuming that there is no air resistance. [7] 3 The diagram shows a cross-section ABCD
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