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GCE MAY 2007 : AS, C1: Core Mathematics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2007 Mathematics assessing Module C1: AS Core Mathematics 1 AMC11 Assessment Unit C1 [AMC11] MONDAY 21 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 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. AMC1S7 1937 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 (a) Rationalise the denominator of 4 7 2 + 7 [3] 2(x2 1) x+1 [3] (b) Simplify as far as possible 2 (a) The diagram in Fig. 1 below shows the graph of the function y = f(x) Fig. 1 Sketch, on separate diagrams, the graphs of: (i) y = f(x); [2] (ii) y = f(x 2), [2] clearly identifying the points where the graphs cross the axes. AMC1S7 1937 2 [Turn over (b) (i) Using the factor theorem, show that (x 2) is a factor of 2x3 + 3x2 11x 6 [2] (ii) Hence factorise fully the expression 2x3 + 3x2 11x 6 (iii) Hence solve the equation 2x3 + 3x2 11x 6 = 0 3 [3] [3] (i) Sketch the curve y = 6 x x2 identifying the points where the curve crosses the axes. [3] (ii) Find the equation of the tangent to the curve y = 6 x x2 at the point where x = 2 AMC1S7 1937 [6] 3 [Turn over 4 A solution to this question by scale drawing will not be accepted. A kite ABCD is shown in Fig. 2 below. y C B M D A x Fig. 2 Point B has coordinates (1, 6) Point D has coordinates (7, 4) (i) Find the coordinates of M the midpoint of BD. [2] (ii) Find the gradient of the line BD. [2] (iii) Hence find the equation of the line AC. [3] Point A has coordinates (3, a) and point C has coordinates (c, 11) (iv) Find a and c AMC1S7 1937 [2] 4 [Turn over 5 The floor of a rectangular shed has length x metres and breadth y metres, as shown in Fig. 3 below. y x Fig. 3 The perimeter of the floor of the shed is 16 m. (i) Write down an equation connecting x and y [1] The length of the diagonal of the floor of the shed is 38 m. (ii) Write down a second equation connecting x and y [1] (iii) Hence show that x2 8x + 13 = 0 (iv) Find the length and breadth of the floor of the shed. 6 [3] [4] (i) By using the substitution y = 3x rewrite the expression 3(32x) 28(3x) + 9 in terms of y [2] (ii) Hence solve the equation 3(32x) 28(3x) + 9 = 0 AMC1S7 1937 5 [5] [Turn over 7 A container for tennis balls is to be made. It consists of an open cylinder with a circular base and a lid in the shape of a hemisphere, as shown in Fig. 4 below. Fig. 4 Sphere Cylinder 4 Volume = r3 3 Volume = r2h Area = 4 r2 C.S. Area = 2 rh The cylinder has radius r cm and height h cm. The hemisphere has radius r cm. 320 The volume of the container must be cm3 3 (i) Express h in terms of r [4] (ii) Hence show that the total surface area of the container is 5 2 640 1 r + r 3 3 [4] (iii) Find the value of r that makes the total surface area of the container minimum. AMC1S7 1937 6 [7] [Turn over 8 A curve has equation y = 2x2 + 5 A straight line has equation y = mx 3 The line intersects the curve at two points. Find the range of possible values of m AMC1S7 1937 [8] 7 S 1/06 0000 7-005-1 [Turn over

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Additional Info : Gce Mathematics May 2007 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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