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GCE MAY 2006 : AS, C1: Core Mathematics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2006 Mathematics assessing Module C1: AS Core Mathematics 1 AMC11 Assessment Unit C1 [AMC11] MONDAY 22 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 1 27.6.05BP 2 23.10.05HF 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. AAMC1S6 1565 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 dy Find when dx y = 2x3 3x2 + 4x 6 2 + 3 3 1 2 [4] [4] (a) Rationalise the denominator of (b) Simplify as far as possible (x2 16) (x2 + 6x + 9) x+3 x 4 (i) Find the equation of the straight line L joining the points (1, 3) and (2, 1). [4] (ii) Find the equation of the line P, perpendicular to L, which passes through the point (6, 2). [3] (iii) Find the coordinates of the point of intersection of the lines L and P. [3] 1 27.6.05BP 2 23.10.05HF 3 [4] AAMC1S6 1565 2 [Turn over [3] [3] (iii) Hence write down the minimum value of x2 4x + 5 and the value of x at which it occurs. [2] (iv) Hence sketch the graph of y = x2 4x + 5 5 (i) Find how many real roots the equation x2 + 5 = 4x has. (ii) Express x2 4x + 5 in the form (x a)2 + b 4 [2] At a speed of x miles per hour a car covers a distance of y miles on 1 gallon of diesel, where x y = (100 x) 60 Using calculus, find the speed at which the car should travel to cover the maximum distance possible on 1 gallon of diesel, and hence find this maximum distance. 6 [7] A builder has been asked to construct a rectangular based house extension. The length of the extension must be 10 m greater than the width. Let the width of the extension be x. (i) Write down an expression for the area of the extension in terms of x. [2] The area of the extension must be less than 375 m2 [7] 1 27.6.05BP 2 23.10.05HF (ii) Form an inequality in x and solve it to find the range of possible values for the width of the extension. AAMC1S6 1565 3 [Turn over 7 1 If f(x) = 8x 2 x 1 (i) find f(9) (ii) solve f(x) = 0 [4] (iii) find f (x), where f (x) is the derivative of f(x) with respect to x [2] (iv) find f (4) 8 [2] [2] The expression 2x3 + ax2 + bx + c has a factor (x 1) It has a remainder 1 when divided by (x 2) It has a remainder 14 when divided by (x 3) (i) Find a, b and c. [11] 1 27.6.05BP 2 23.10.05HF (ii) Hence solve the equation 2x3 6x2 + 5x 1 = 0, leaving your answers in surd form. S 6/05 4000 302507(64) [Turn over [6]

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Additional Info : Gce Mathematics May 2006 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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