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GCE June 2007 : A2, C3: Core Mathematics 3

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ADVANCED General Certificate of Education 2007 Mathematics assessing Module C3: Core Mathematics 3 AMC31 Assessment Unit C3 [AMC31] TUESDAY 5 JUNE, 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. 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 AMC3S7 1993 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Use Simpson s Rule with 5 ordinates to find an approximate value for 3 e sin x dx x [6] 1 2 At time t seconds after a batsman has struck a cricket ball it has travelled a horizontal distance x metres and is y metres above the ground where x = 25t y = 1 + 15t 5t2 (i) Find the time taken for the ball to hit the ground and the horizontal distance it has travelled in this time. (ii) Find the Cartesian equation of the flight path of the cricket ball. 3 [4] [2] The graph of a function y = f(x) is sketched below in Fig. 1. y y = f(x) 3 A 2 x Fig. 1 On separate diagrams sketch the graphs of: (i) y = f(x) + 3 [2] (ii) y = f(2x 1) [2] indicating the coordinates of the images of point A. AMC3S7 1993 2 [Turn over 4 The curved top of an archway can be modelled by the equation y = 2 cos + 1 2 between = and = as shown in Fig. 2 below. y Fig. 2 Find the exact area of the opening. 5 [7] Integrate with respect to x: 3 (i) e4x + 6x 2 + 5x3 2x (ii) 2 sec x tan x sin x 1 6 [5] [4] (a) Find the equation of the tangent to the curve y = ln(x2 + 2x) at the point (1, ln 3) [6] (b) Differentiate with respect to x ex 1 + tan x AMC3S7 1993 3 [4] [Turn over 7 (a) Prove the identity 1 sin + 1 2 1 + tan cosec [5] (b) Solve the equation 2(3 cosec 2 ) = 7 cot for 0 8 360 [8] (i) Express x 2 (x + 2)(x + 1) in partial fractions. [6] (ii) Hence expand x 2 (x + 2)(x + 1) in ascending powers of x, as far as the term in x3, using the binomial theorem. (iii) Find the range of values of x for which the expansion is valid. S 1/06 0000 7-006-1 [11] [3] [Turn over

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Additional Info : Gce Mathematics June 2007 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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