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GCE MAY 2008 : A2, C4 : Core Mathematics 4

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ADVANCED General Certificate of Education 2008 Mathematics assessing Module C4: Core Mathematics 4 AMC41 Assessment Unit C4 [AMC41] FRIDAY 16 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 AMC4S8 3172 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 The functions f and g are defined f: x 4x 2 g: x x 1 x x1 Find the composite function fg and state its domain. 2 [3] A curve has the equation 4y x = xy dy y + 1 (i) Show that = dx 4 x (ii) Find the equation of the tangent to the curve at the point (3, 3). 3 [5] [3] (a) Points A and B have position vectors OA = 4i 7k and OB = 2j + 5k Find a vector equation for the line through A and B. [4] (b) The vectors p and q are p = 2i j + 2k and q = 3i + 6j + 2k (i) Find p.q (ii) Hence find the angle between p and q AMC4S8 [2] [6] 3172 2 [Turn over 4 The acute angle A is such that sin A = 3 5 Using the double angle formulae, find (i) sin 2A (ii) cos 2A 5 [3] [2] (a) Using the substitution u = 2 + x find x(2 + x) 10 [7] 8x cos 2x dx (b) Find the exact value of dx [6] 4 0 6 (i) Express cos x + 2 sin x in the form r cos(x ), where r 0 and 0 90 [4] (ii) Hence, or otherwise, find the maximum value of cos x + 2 sin x and the smallest positive value of x, in degrees, for which it occurs. AMC4S8 3172 3 [3] [Turn over 7 While on a skiing holiday in the Alps, Ben pours a cup of hot coffee from his flask. The initial temperature of the coffee is 85 C and the temperature of Ben s surroundings is a constant 10 C. The rate of change of the temperature x C of the coffee after time t minutes (t 0) is proportional to the difference in temperature between the coffee and the surroundings. dx (i) Show that = k(x 10) dt where k is a positive constant. [3] After two minutes, Ben s coffee has cooled to 65 C. (ii) Find the temperature of Ben s coffee after one further minute. (iii) Find t when x = 35 8 [9] [3] (a) Find sin3 x dx [5] (b) Find the exact value of the volume generated when the area bounded by the curve y = 2ex, the x-axis and the lines x = 1 and x = 4 is rotated through 2 radians about the x-axis. [7] THIS IS THE END OF THE QUESTION PAPER S 6/07 530-055-1 4 [Turn over

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Additional Info : Gce Mathematics May 2008 Assessment Unit C4 Module C4 : Core Mathematics 4
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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