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GCE JAN 2011 : AS, C1: Core Mathematics 1

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Assessment Unit C1 assessing Module C1: AS Core Mathematics 1 [AMC11] AMC11 Mathematics *AMC11* ADVANCED SUBSIDIARY (AS) General Certificate of Education January 2011 MONDAY 10 JANUARY, 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 not permitted to use any calculating aid 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. 6055 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 not permitted to use any calculating aid in this paper. 1 (i) If y = 5x + 4x3 find dy dx [2] (ii) Hence find the coordinates of the points on the curve y = 5x + 4x3 at which the gradient is 8 2 [4] (a) (i) Using the Factor Theorem, show that (x + 3) is a factor of 2x3 + x2 13x + 6 [2] (ii) Hence fully factorise the expression 2x3 + x2 13x + 6 [3] (iii) Hence solve the equation 2x3 + x2 13x + 6 = 0 [3] (b) The remainder when the function f(x) = px4 2x3 4x 6 is divided by (x 2) is six times the remainder when it is divided by (x + 1). Find p. 3 Simplify to a single algebraic fraction 3 2 x+1 + x+4 x 1 x 1 6055 [5] 2 [6] 4 Points A, B, C and D form the vertices of a kite as shown in Fig. 1 below. A B C D Fig. 1 Point A has coordinates (2, 1) and point C has coordinates (4, 5). Find the equation of the diagonal BD. 5 [6] (a) The graph of the function y = f(x) is sketched in Fig. 2 below. y A 2 x 3 Fig. 2 Draw a sketch of the graph of y = f(x + 2) clearly labelling the image of point A. (b) A rectangle has an area of 12cm2 Its length is ( 7 + 2) cm. Find the width of the rectangle in the form (a b + c). [2] [5] (c) Solve the equation 1 3 1 3 x = 2 + 15x 6055 3 [6] [Turn over 6 The number of bacteria b in a Petri dish after time t hours can be modelled by the equation 64 b = 4t + t + 7 t>0 (i) Find the number of bacteria after 16 hours. (ii) Find the rate of change of the number of bacteria after t hours. [3] (iii) Hence find the range of values of t for which the number of bacteria is increasing. 7 [1] [3] (i) Find the coordinates of the points where the curve y = x(9 x2) crosses the x-axis. [3] (ii) Find the coordinates of the turning points on the curve y = 9x x3 and determine their nature. [9] (iii) Hence sketch the graph of the curve y = 9x x3 8 [2] A rectangular sheet of cardboard has width x cm and an area of 48 cm2 Small squares of side 2 cm are removed from each corner and the sides are folded up to form an open box. The volume of the box must be more than 16 cm3 (i) Show that x2 14x + 48 < 0 (ii) Hence find the possible range of values of x. THIS IS THE END OF THE QUESTION PAPER 5303 6055 4 [6] [4]

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Additional Info : Gce Mathematics January 2011 Assessment Unit C1 Module C1:Core Mathematics 1
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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