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GCE JAN 2010 : A2, C3: Core Mathematics 3

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ADVANCED General Certificate of Education January 2010 Mathematics assessing Module C3: Core Mathematics 3 AMC31 Assessment Unit C3 [AMC31] FRIDAY 15 JANUARY, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. 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 question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z 5214 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 (a) Simplify as far as possible x 2 + x 12 x 3 2 x 2 16 x 4x [5] (b) Express 3x + 3 ( x 1)( x + 2) in partial fractions. 2 [6] Use Simpson s rule with 5 ordinates to find an approximation for 4 1 dx 1 + x3 0 3 [6] (a) Find the binomial expansion of 1 x2 up to and including the term in x4 [6] (b) Find the exact values of x for which | ln x | = 3 5214 2 [5] [ 4 Fig. 1 below shows a sketch of the graph of the function y = f (x). y A 1 2 x 1 1 2 1 Fig. 1 On separate diagrams sketch the graphs of: (i) y = f(x + 2); [2] 1 (ii) y = 3f( x) 2 [2] marking clearly the image of the point A on each sketch. 5 (a) Differentiate (i) (3x2 4)6 (ii) [3] ln x x2 1 [4] (b) Find x cos 2x + cosec x 2x dx 5 5214 2 3 [5] [Turn over 6 The temperature, H centigrade, of the heating element in an electric heater, t seconds after it has been switched off, is given by H = 10 + 60e kt where k is a constant. (i) Find the initial temperature of the element. [2] The heating element takes 30 seconds to reach 20 C. (ii) Show that k = 0.0597 to 3 significant figures. (iii) Find the rate at which the temperature of the element is changing after 1 minute. 7 [4] [4] (a) Prove the identity: cosec2 + sec2 cosec2 sec2 [6] (b) Find the exact values of x given that 3 tan2 x 5 sec x + 1 = 0 where < x 5214 [7] 4 [ 8 Fig. 2 below shows a drawing of a capstan. Fig. 2 Fig. 3 below shows the cross-section through a vertical plane containing the centre of the capstan. y L A x Fig. 3 The outline of the cross-section can be modelled by the parametric equations x = 3 1 , sin y = 2 cos (i) Find a corresponding Cartesian equation. [4] (ii) Hence or otherwise, find the coordinates of the point A at which the curve crosses the x-axis and write down the equation of the asymptote L. [4] THIS IS THE END OF THE QUESTION PAPER 5214 5 [ 1312-004-1

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Additional Info : Gce Mathematics January 2010 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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