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GCE MAY 2009 : A2, C3: Core Mathematics 3

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1 2 3 4 5 6 ADVANCED General Certificate of Education 2009 7 8 9 Mathematics 10 Assessment Unit C3 12 assessing 13 Module C3: Core Mathematics 3 14 AMC31 11 [AMC31] 15 THURSDAY 28 MAY, AFTERNOON 16 17 18 19 20 21 TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES 22 Write your Centre Number and Candidate Number on the Answer Booklet provided. 23 Answer all eight questions. Show clearly the full development of your answers. 24 Answers should be given to three significant figures unless otherwise stated. 25 You are permitted to use a graphic or a scientific calculator in this paper. 26 27 INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each 29 question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. 30 Throughout the paper the logarithmic notation used is ln z where it is noted that ln z ; loge z 28 31 32 33 34 35 4147 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Differentiate: x (i) 4 x2 (ii) (x2 + 3)5 2 [4] [3] (a) Find the term in x3 in the binomial expansion of (1 + 2x) 1 6x 4 (b) Express in partial fractions. (2x 1)2 AMC3S9 4147 [4] [6] 2 [Turn over 3 (a) A slide in an adventure playground can be modelled by the curve y = 1 + 20e x between x = 1 and x = 10 as shown in Fig. 1 below. y 10 1 x Fig. 1 Find the shaded area. [6] (b) Find 4 3 x + sec 2 x tan 2 x + 7 dx x 5 [5] The graph of a function y = f(x) is sketched below in Fig. 2. y A 2 1 x Fig. 2 On separate diagrams sketch the graphs of: (i) y = 3f(1x) 2 [2] (ii) y = 4 f(x) [2] indicating the coordinates of the images of the point A. 4147 3 [Turn over 6 (i) Show that the equation 2 ln x = x2 has a solution between x = 1 and x = 2 [4] (ii) By taking x = 1 as a first approximation and using the Newton Raphson method twice, find a better approximation to the solution of the equation 2 ln x = x2 5 [5] A particle travels in a straight line in such a way that its distance x metres from a fixed point O at time t seconds can be given by the equation x = 4 + 3 sin 2t + cos 2t (i) Find the initial distance of the particle from O. (ii) Find the rate of change of the distance of the particle from O at time t. [3] (iii) Hence find the first time when the particle is at its greatest distance from O. 7 [1] [7] (a) Solve the equation 2 sec(2 30 ) = 3 for 180 , , 180 [7] (b) Prove the identity (cosec2 1)(tan2 + 1) cosec2 8 [7] Find the equation of the normal to the curve y = x2 ln(3x 2) + 5 at the point on the curve where x = 1 S 12/07 937-008-1 [9] 4 [Turn over

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Additional Info : Gce Mathematics May 2009 Assessment Unit C3 Module C3:Core Mathematics 3
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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