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GCE MAY 2010 : AS, C2 : Core Mathematics 2

8 pages, 18 questions, 1 questions with responses, 1 total responses,

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2010 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 AMC21 Assessment Unit C2 [AMC21] THURSDAY 27 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 5213 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 (i) Write down the first 5 terms of the sequence defined by the recurrence relationship un +1 = 2 , where n > 0 and u1 = 3 1 + un (ii) State if the sequence diverges, converges and/or oscillates. 2 [3] [2] (i) Write down the centre of the circle whose equation is x2 + y2 + 4y 21 = 0 and find the circle s radius. [4] (ii) Find the gradient of the tangent to this circle at the point (3, 2). 5213 2 [3] [Turn over 3 A gold earring can be modelled as a sector of a circle with a triangle removed as shown in Fig. 1 below. Fig. 1 The sector has angle radians and is cut from a circle of radius 3 cm. 4 (i) Find the area of this sector. [2] The triangle is equilateral and of side 1 cm. The gold is 0.1 cm thick. (ii) Find the volume of gold in the earring. 4 [5] The first, second and third terms of a geometric series are 5, 3 and x. (i) Find x. (ii) State why a sum to infinity for this series exists. [1] (iii) Find the sum to infinity of this series. 5213 [3] [2] 3 [Turn over 5 (i) Find the first four terms in the binomial expansion, in ascending powers of x, of (1 + 3x)4 [4] The first three terms in the binomial expansion, in ascending powers of x, of (1 + x)12 are 1 + 12x + 66x2 For a certain value of x, where x 0, the sum of the first three terms in the binomial expansion of (1 + x)12 is equal to the sum of the first four terms in the binomial expansion in (i). (ii) Find x. 6 [3] (a) Find 3 x 3 dx [3] (b) Fig. 2 below shows a sketch of the graph of y = 4x2 x3 for 0 < x < a, where a > 4 y 0 4 a x Fig. 2 Given that the two shaded regions have equal areas, find a. 5213 4 [8] [Turn over 7 (a) Solve the equation 3 sin2 x + 8 cos x = 0 for < x < [7] (b) Two ships, C and D, leave harbour at 0900 hours. Ship D travels at a speed of 24 knots on a bearing of 030 Ship C travels at a speed of 15 knots on a bearing of 140 as shown in Fig. 3 below. N Ship D 30 Harbour 40 Ship C Fig. 3 [1 knot is a speed of 1 nautical mile per hour] Find the bearing and the distance, in nautical miles, of ship C from ship D at 1200 hours. 5213 5 [10] [Turn over 8 (a) Find x given that 32x = 7 [4] log x + log x2 + 2 log x3 = 1 [5] (b) Find x given that (c) Given that log2 x log2 y = 6 and that 1 23 = z show that y = z2x [6] THIS IS THE END OF THE QUESTION PAPER 5213 6 [Turn over 5213 [Turn over

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Additional Info : Gce Mathematics May 2010 Assessment Unit C2 Module C2 : Core Mathematics 2
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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