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GCE JUN 2006 : AS, C2 : Core Mathematics 2

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2006 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 Assessment Unit C2 [AMC21] THURSDAY 1 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. 1 27/6/05EA 2 27/10/05HF 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 AAMC2S6 1572 1 27/6/05EA 2 27/10/05HF BLANK PAGE AAMC2S6 1572 2 [Turn over Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 1 The first term of a Geometric Series is 4 and its common ratio is 2 Find: (i) the fifth term of the series; (ii) the sum to infinity of the series. 2 [2] [2] (a) Evaluate 3 x 2 + 3 x dx [4] 1 (b) The graph of y = 2 + x 2 is shown in Fig. 1 below. y x Fig. 1 Use the Trapezium Rule with 6 ordinates to find an approximation for the area bounded by the curve the x-axis and the lines x = 0 and x = 5 [6] 1 27/6/05EA 2 27/10/05HF y = 2 + x2 AAMC2S6 1572 3 [Turn over 3 (a) For each of the sequences defined below find if the sequence converges or diverges. (i) un = 2n [2] 1 (ii) un = n+2 [2] (b) A sequence is defined by u1 = a un = 3un 1 + 2 (n = 2, 3, 4 . . .) (i) Find u2 and u3 in terms of a. (ii) Find the value of a given that u2 = u3 4 [3] [2] (i) Find the centre and radius of the circle whose equation is x2 + y2 4x + 6y = 12 [5] 1 27/6/05EA 2 27/10/05HF (ii) Find the equation of the tangent to this circle at the point (6, 0) [3] AAMC2S6 1572 4 [Turn over 5 A front door is to be made for a new house. It consists of a sector of a circle and two congruent right-angled triangles as shown in Fig. 2 below. A B E C D Fig. 2 AB = 2 m BD = 1.5 m Find [2] ^ (ii) ACB in radians, [2] (iii) the perimeter of the door, [4] (iv) the area of the door. [4] 1 27/6/05EA 2 27/10/05HF (i) AC, AAMC2S6 1572 5 [Turn over 6 An angling club has designed a new logo by reflecting the curve y= 1 x ( x 4)2 2 in the x-axis between the lines x = 0 and x = 6 as shown in Fig. 3 below. y 1 y = x(x 4)2 2 0 4 6 x Fig. 3 (i) Find the total area enclosed by the curve y= 1 x ( x 4)2 2 and the x-axis between x = 0 and x = 6 [8] [1] 1 27/6/05EA 2 27/10/05HF (ii) Hence find the total area of the logo. AAMC2S6 1572 6 [Turn over 7 Solve the equations cos 2 = 0.7 (i) for 0 < 360 [6] tan = 2 cos (ii) for 0 < 8 180 [8] (i) Find the value of xy, given that log2 x + 2 log4 y = 4 [4] (ii) Hence solve the simultaneous equations log2 x + 2 log4 y = 4 and [5] 1 27/6/05EA 2 27/10/05HF x + y = 10 AAMC2S6 1572 7 [Turn over 2 27/10/05HF 1 27/6/05EA S 6/05 4000 302507(65) [Turn over

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Additional Info : Gce Mathematics June 2006 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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