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GCE MAY 2006 : A2, C3: Core Mathematics 3

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ADVANCED General Certificate of Education 2006 Mathematics assessing Module C3: Core Mathematics 3 AMC31 Assessment Unit C3 [AMC31] WEDNESDAY 24 MAY, 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 a scientific calculator in this paper. 1 30.6.05BP 2 23.10.05HF 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 log e z AMC3S6 782 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Express as partial fractions 5x + 2 x2 4 2 [6] It is required to find the approximate area of parkland, bounded by a river and two roads. The course of the river can be modelled by the curve y = 2 sin x between x = 0 and x = and 2 as shown in Fig. 1 below. the roads as the straight lines y = 0 and x = 2 road y 2 0 er riv road 0 y=0 x= 2 Fig. 1 [6] 2 [Turn over 1 30.6.05BP 2 23.10.05HF Distances are measured in kilometres. Using calculus, estimate the area of parkland. AMC3S6 782 3 (i) On one diagram sketch the graphs of and y = ex and y = x2 [3] The x coordinate of the graphs only point of intersection can be found by solving the equation ex x2 = 0 [3] (iii) Taking x = 0.6 as a first approximation to this value of x, use the Newton-Raphson method twice to find a better approximation. [5] 1 30.6.05BP 2 23.10.05HF (ii) Verify that this value of x lies between x = 1 and x = 0 AMC3S6 782 3 [Turn over 4 (a) The graph of the function y = f(x) is sketched below in Fig. 2 y 3 x 4 Fig. 2 On separate diagrams sketch the graphs of: (i) y = 1f(x + 1); 3 [2] (ii) y = f( 2x). [2] (b) Fig. 3 below shows the graphs of y = | 2x 1| and y = 3 y = |2x 1| y y=3 x Fig. 3 [6] 1 30.6.05BP 2 23.10.05HF Find the coordinates of their points of intersection. AMC3S6 782 4 [Turn over 5 In a biology experiment it is assumed that the number, N, of micro-organisms in a substance at time T hours is given by N = abT where a and b are constants. (i) Given that N = 60 when T = 0 and N = 480 when T = 3, find the values of a and b. [3] (ii) Find the value of T when N = 1040 6 [6] Solve the equation 5 sec x 4 = sec x for 7 x [7] (a) Differentiate with respect to x x2 (i) 3+x [4] (ii) 2x ln x [3] (iii) sin3 4x [4] (b) Integrate with respect to x [5] 1 30.6.05BP 2 23.10.05HF 1 x2 + e3x + 2x AMC3S6 782 5 [Turn over 8 x2 9 (a) Simplify (x + 3) x2 5x + 6 [3] (b) Use the binomial theorem to expand in ascending powers of x 1+x 1 2 (1 x)2 up to and including the term in x2 [7] 1 30.6.05BP 2 23.10.05HF THIS IS THE END OF THE QUESTION PAPER AMC3S6 782 6AMC3S6 782 6[Turn over 1 30.6.05BP 2 23.10.05HF BLANK PAGE AMC3S6 7 [Turn over 2 23.10.05HF 1 30.6.05BP S 6/05 4000 302507(49) [Turn over

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Additional Info : Gce Mathematics May 2006 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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