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GCE JUN 2009 : AS, C1: Core Mathematics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2009 Mathematics assessing Module C1: AS Core Mathematics 1 AMC11 Assessment Unit C1 [AMC11] FRIDAY 5 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 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. 4045 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 Points A and B have coordinates ( 1, 3) and (2, 3) (i) Find the equation of the line AB. [4] The line CD has equation 2y x = 3 (ii) Find the coordinates of the point of intersection of the two lines. 2 Solve the simultaneous equations 2x + y + 2z = 6 4x y + 2z = 13 2x 2y z = 3 3 [3] [7] (a) Find the equation of the tangent to the curve y = 2x3 4x + 5 at the point where x = 1 (b) (i) Find [6] dy where dx y = 4x2 + x 1 [2] (ii) Hence find the coordinates of the turning point of the curve y = 4x2 + x 1 and determine its nature. 4045 [6] 2 [Turn over 4 (i) Use the factor theorem to show that (x 1) is a factor of 9x3 9x2 x + 1 [2] 9x3 9x2 x + 1 [3] 9x3 9x 2 x + 1 x 1 3x 1 4 [4] (ii) Hence fully factorise (iii) Hence simplify fully 5 The temperature, C centigrade, of a cup of tea t minutes after it has been made is given by the formula C = 80 10t + 1 t 2 2 which is valid for 0 t 10 (i) Find the initial temperature of the cup of tea. (ii) Find t when C = 50, leaving your answer in surd form. [4] (iii) Find the rate of change of C when t = 3 4045 [1] [4] 3 [Turn over 6 A closed box in the shape of a cuboid has width x cm, length y cm and height 3 cm, as shown in Fig. 1 below. 3 y x Fig. 1 Its volume is 66 cm3 (i) Write down an equation for y in terms of x. [2] The surface area of the box is 101 cm2 (ii) Write down a second equation connecting x and y. (iii) Hence find the dimensions of the box. 4045 [2] [5] 4 [Turn over 7 (a) Simplify as far as possible 5 1 3 +1 1 3 [4] 5x =5 25 x 1 [6] (b) Find x given that (c) Fig. 2 below shows the graph of the function y = f (x) y 1 1 x Fig. 2 Sketch the graph of y = f (2x) clearly identifying the points where the graph crosses or touches the axes. [2] 8 Find the range of values of k for which the equation x2 + (3 k)x + 7 = 0 has no real roots. Leave your answer in surd form. [8] THIS IS THE END OF THE QUESTION PAPER 4045 5 [Turn over Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright holders may have been unsuccessful and CCEA will be happy to rectify any omissions of acknowledgement in future if notified. 936-002-1

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Additional Info : Gce Mathematics June 2009 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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