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GCE MAY 2008 : 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 2008 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 Assessment Unit C2 [AMC21] WEDNESDAY 21 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 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 AMC2S8 3157 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Integrate 3 2 2 +x x4 [4] A sequence is defined by un+1 = 2bun u1 = 6 (n = 1, 2, 3, 4 ...) (i) Find u2 and u3 in terms of b (ii) Find the range of values of b for which the sequence converges. 3 [3] [3] The lights in a street will remain lit for 16 hours during the night of 4th January 2009 Every subsequent night the time for which they will remain lit will be decreased by 200 seconds. (i) By using a suitable arithmetic progression show that they will remain lit for 52 000 seconds during the night of 1st February 2009 [6] (ii) Find the total number of hours for which the council needs to keep the street lights on during the month of February 2009 (night of 1st February up to and including the night of 28th February). [3] AMC2S8 3157 2 [Turn over 4 The equation of a circle is x2 + y2 6x + 12y 180 = 0 (i) Find the centre of this circle. [2] (ii) Find the radius of this circle. [2] AC is a diameter of this circle. The point B also lies on this circle. AB = 10 (iii) Find the length of BC. 5 [4] (i) Prove that 6 sin 2 x + 70 cos2 x 6 64 cos2 x [3] (ii) Hence or otherwise solve 6 sin 2 x + 70 cos2 x 6 = AMC2S8 3157 1 cos x 3 for 0 x 360 [5] [Turn over 6 Shown in Fig. 1 below is the javelin-throwing zone CAB in an athletics arena. CAB is a sector of a circle of radius 100 m and centre C. Angle ACB = 1.4 radians. A 100 J C 1.4 radians M 100 B Fig. 1 (i) Find the area of the zone. [2] A javelin is thrown from C and lands in the zone at point J. Angle JAC = 0.5 radians and AJ = 50 m. (ii) Find the distance of J from C. [3] (iii) Find in radians the angle CJ makes with the line CA. [3] Spectators stand all along the edge CB of the zone. The spectator standing at point M on CB is closest to J. (iv) Find the distance of M from J. AMC2S8 3157 [4] 4 [Turn over 7 Fig. 2 below shows the curve y = 4x 2x2 and the line y = x + 2 y A B 1 3 x Fig. 2 The curve and line intersect at points A and B. 1 (i) Verify that the x coordinates of A and B are and 2 2 (ii) Find the shaded area enclosed between this curve and line. AMC2S8 3157 5 [3] [10] [Turn over 8 (a) Express log3 6 log3 14 + 2 log3 7 as a single logarithm. [6] (b) Find x given that log4 x 2 logx 4 = 1 [9] THIS IS THE END OF THE QUESTION PAPER AMC2S8 3157 6 [Turn over S 11/06 529-044-1

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Additional Info : Gce Mathematics May 2008 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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