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GCE MAY 2008 : A2, C3: Core Mathematics 3

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ADVANCED General Certificate of Education 2008 Mathematics assessing Module C3: Core Mathematics 3 AMC11 AMC31 Assessment Unit C3 [AMC31] FRIDAY 23 MAY, MORNING 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 AMC3S8 3051 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 x+2 x2 9 x 3 2 + 5x + 6 x [4] (b) Use partial fractions to rewrite 3x 15 x(x + 3) 2 [6] A circle is defined by the parametric equations sin x = 2 cos + 4 y = 2 (i) Find the cartesian equation of this circle. (ii) Write down the centre and radius of this circle. 3 [4] [3] (i) Show that the equation x3 + 2x 1 = 0 has a root between x = 0 and x = 1 [3] (ii) Take the first approximation to this root to be 0.6 and use the Newton Raphson method twice to find a better approximation to this root. AMC3S8 3051 2 [5] [Turn over 4 A metal plate can be modelled by the area bounded by the curve y = 6 ln x, the x-axis and the line x = 5 as shown in Fig. 1 below. y y = 6 ln x x 0 1 5 Fig. 1 Find an approximate value for this area by using Simpson s Rule with 5 ordinates to estimate 5 1 6 ln x dx 1 + cot2 x cot2 x sec2 x 5 [6] [5] (a) Show that (b) Solve the equation sec2 tan = 1 AMC3S8 3051 3 0 2 [7] [Turn over 6 (a) Differentiate with respect to x : (i) x2 ln x [3] x (ii) sin x [3] (iii) tan5 x [4] (b) Integrate with respect to x 4 4 + sin 2x x2 3x 7 [6] Use the binomial theorem to expand (1 + x + x2) 1 in ascending powers of x up to and including the term in x3 8 [6] Sketched below in Fig. 2 is the graph of y = ex y y = ex x Fig. 2 (i) Sketch the graph of y = ex 1, marking on the horizontal asymptote. [2] (ii) Sketch the graph of y = |ex 1|, marking on the horizontal asymptote. [3] (iii) Find the exact values of x for which |ex 1| = 1 2 S 2/07 530-083-1 4 [5] [Turn over

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Additional Info : Gce Mathematics May 2008 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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