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GCE JUN 2008 : AS, C1: Core Mathematics 1

8 pages, 17 questions, 2 questions with responses, 2 total responses,

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2008 Mathematics assessing Module C1: AS Core Mathematics 1 AMC11 Assessment Unit C1 [AMC11] MONDAY 2 JUNE, 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. AMC1S8 3049 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 The points A and B have coordinates (3, 2) and (9, 5) respectively. (i) Find the gradient of AB. (ii) Find the equation of the line through A perpendicular to AB. 2 [2] [3] Simplify ( 2 x + 3) ( 2 x + 1) ( 2 x 5) + 4 ( 2 x 1) ( 2 x + 1) 3 [5] (a) Rationalise the denominator of 3 7 7 2 [4] (b) Solve the equation 27 x AMC1S8 3049 1 2 = 125 x 2 [5] [Turn over 4 Differentiate with respect to x 6x3 3 x + 5 2 + 10 x x [4] Find the range of values of k for which the quadratic equation kx2 + 4x + (k 3) = 0 has no real roots. 6 [6] The stopping distance d ft for a car travelling at speed x mph (x > 10) can be modelled by the equation d = ax2 + bx + c When a car is travelling at 20 mph the stopping distance is 14 ft. When a car is travelling at 30 mph the stopping distance is 26 ft. When a car is travelling at 40 mph the stopping distance is 42 ft. (i) Find the values of a, b and c. [9] (ii) If the stopping distance for a car was 86 ft, find the speed at which it was travelling. [4] AMC1S8 3049 3 [Turn over 7 A theatre is being designed. The floor plan can be modelled by a rectangle and a semicircle as shown in Fig. 1 below. 2x 2y Fig. 1 The breadth of the rectangle is 2x m and its length is 2y m. (i) Write down an expression for the perimeter of the theatre, in terms of x, y and . [2] The perimeter of the theatre must be 200 m. (ii) Express y in terms of x. [2] (iii) Show that the floor area of the theatre can be expressed as A = 200 x 2 x 2 x 2 2 (iv) Find the exact value of x that gives the maximum floor area. AMC1S8 3049 4 [3] [5] [Turn over 8 (i) Show that (x 1) is a factor of x3 + x2 2 [2] x3 + x2 2 = 0 [6] (ii) Hence solve the equation (iii) Find the coordinates of the turning points on the curve y = x3 + x2 2 and determine their nature. [10] (iv) Hence sketch the curve y = x3 + x2 2 [3] THIS IS THE END OF THE QUESTION PAPER AMC1S8 3049 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. S 11/06 529-043-1

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Additional Info : Gce Mathematics June 2008 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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