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GCE MAY 2007 : AS, C2 : Core Mathematics 2

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2007 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 Assessment Unit C2 [AMC21] THURSDAY 31 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. 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 AAMC2S7 2009 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 with respect to x 3 4 2x 3 + x 2 (i) Sketch the curve y = 2x [4] [2] The point P (b, 0.6) lies on this curve. (ii) Find b. [4] Point Q is the image of P when the curve y = 2x is transformed to the curve y = 2 x (iii) Write down the coordinates of Q. 3 [1] (i) Sketch the graph of the function f(x) = sin 3x for 0 x 360 and state the period of this function. [3] (ii) Hence write down the solutions of the equation sin 3x = 1 for 0 AAMC2S7 2009 x 360 [3] 2 [Turn over 4 A circle has equation x2 + y2 16x + ay + 20 = 0 and radius 45 (i) Show that a = 2 or a = 2 [3] When a = 2 the circle has equation x2 + y2 16x 2y + 20 = 0 (ii) Write down the coordinates of the centre of this circle. (iii) The line y = 2x is a tangent to this circle and touches it at the point (b, 2b). Find b. 5 [2] [5] Shown in Fig. 1 below are three stationary fishing boats A, B and C. AB = 400 m, BC = 300 m and AC = 600 m. B 400 m A 300 m 600 m C Fig. 1 (i) Find angle ABC, giving your answer in radians. [3] Because of fog, visibility is limited to 100 m. (ii) AAMC2S7 Find the area inside the triangle ABC which is not visible from boat B. 2009 3 [6] [Turn over 6 (a) A sequence is defined recursively by un = un 1 3 where u1 = 5 (i) Find u2 and u3 [2] (ii) Using the fact that the terms of this sequence form an arithmetic progression, find its 600th term. [4] (b) The time intervals t1, t2, t3, . . . between consecutive bounces of a ball, bouncing on the ground, form the terms of a geometric progression. The time interval t5 is an eighth of the time interval t2 (i) Find the common ratio. [4] The sum of the first 6 time intervals is 6.3 seconds. (ii) Find t1 AAMC2S7 2009 [3] 4 [Turn over 7 (a) Use the trapezium rule with 5 ordinates to find an approximate value for 0 4 x + 16 dx [6] 4 (b) Shown in Fig. 2 below is the curve y2 = 4x + 16 The curve crosses the y-axis at the points A and B. y A x B Fig. 2 (i) Find the coordinates of A. [1] (ii) Find the shaded area in Fig. 2 above by considering the integral x dy, evaluated between appropriate limits. [6] 8 (a) Solve the equation 3 tan x + 2 sin x = 0 log3 x log9 2x = 2 for 180 x [7] [6] 180 (b) Solve the equation AAMC2S7 2009 5 [Turn over THIS IS THE END OF THE QUESTION PAPER AAMC2S7 2009 6 [Turn over AAMC2S7 2009 7 [Turn over S 11/05 0000 7-001-1 [Turn over

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Additional Info : Gce Mathematics May 2007 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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