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GCE MAY 2009 : AS, C2 : Core Mathematics 2

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2009 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 Assessment Unit C2 [AMC21] FRIDAY 22 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 4189 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 (a) (i) Simplify x(3x2 + 2 + 4x 3) [1] (ii) Hence, integrate with respect to x x(3x2 + 2 + 4x 3) [4] (b) Using the trapezium rule with 6 ordinates, find an approximate value for 1 4 dx 0 (1 + x 2 ) 2 [6] (i) A sequence is defined recursively by un+1 = 2 un 3 where u1 = 1 Find u2, u3 and u4 [3] (ii) State whether this sequence is convergent or divergent. [1] A geometric series is formed by adding the terms of the sequence to give 1 + 2 + 4 + + .... 8 3 9 27 (iii) Find the common ratio of this geometric series. (iv) Find the sum to infinity of this geometric series. 3 4189 [1] [2] In the binomial expansion of (1 + nx)10, the coefficient of x2 is 3 times the coefficient of x. Find the value of n, where n 0 [6] 2 [Turn over 4 (i) On the same diagram, sketch the curves y = 2x and y = 1 + 2x. Label any relevant points on the axes. [4] The y coordinate of a point P on the curve y = 1 + 2x is 6 (ii) By solving the equation 1 + 2x = 6 find the x coordinate of P. [A solution by trial and improvement is not acceptable] 5 [4] (a) Prove the identity tan + 1 1 tan sin cos [5] (b) Solve the equation sin2 x = 1 4 for 90 , x < 90 [4] (c) Solve the equation cos 2x = 0.4 for 0 , x < 4189 [4] 3 [Turn over 6 Shown in Fig. 1 below is the curve y = 4 + x2 y y = 4 + x2 4 x Fig. 1 (i) Find the area of the region bounded by the curve y = 4 + x2, the x-axis, y-axis and the line x = 1 [5] (ii) Hence, find the area of the region bounded by the curve y = 4 + x2 and the line y = 5 [4] 4189 4 [Turn over 7 The network coverage of a mobile phone mast M may be modelled as a circle as shown in Fig. 2 below. B M A C Fig. 2 Points A (2, 1), B(k, k + 5) and C ( 1, 1) lie on the circumference of the circle, centre M. AB is a diameter of the circle. (i) Find the gradient of AC. [2] (ii) Hence, write down the gradient of BC and prove that k = 3 [4] (iii) Find the equation of the circle in the form (x a)2 + (y b)2 = r 2 4189 5 [5] [Turn over 8 A silver medal is divided into two parts by a line AB. The medal is in the shape of a circle, centre O, as shown in Fig. 3 below. O x r A B Fig. 3 The radius of the circle is r and the angle AOB is x radians. (i) Write down the area of the minor sector OAB. [1] (ii) Write down the area of the triangle AOB. [1] The areas of the two parts of the medal divided by the line AB are in the ratio 5: 1 (iii) Show that sin x = x 3 [8] THIS IS THE END OF THE QUESTION PAPER 4189 6 [Turn over AMC4W8 AMC4W8 3173 7 S 1/08 937-012-1 [Turn over

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Additional Info : Gce Mathematics May 2009 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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