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GCE JUN 2010 : AS, C1: Core Mathematics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2010 Mathematics assessing Module C1: AS Core Mathematics 1 AMC11 Assessment Unit C1 [AMC11] WEDNESDAY 9 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. 5191 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 and B are the points (4, 7) and ( 2, 3) respectively. (i) Find the midpoint P of AB. (ii) Find the equation of the line through P which is perpendicular to AB. 2 [1] [5] When divided by (x + 1) the expression ax3 3x2 + bx + 6 has a remainder of 12 (i) Write down an equation connecting a and b. [3] The expression ax3 3x2 + bx + 6 has a factor of (x 3). (ii) Write down a second equation connecting a and b. (iii) Hence find the values of a and b. 5191 [2] [2] 2 [Turn over 3 The diagram in Fig. 1 below shows the graph of the curve y = f(x). The point A, (5, 4), lies on the curve. y A 4 x 5 Fig. 1 Sketch, on separate diagrams, the graphs of: (i) y = f(x) 1 [2] (ii) y = f(x) [2] (iii) y = f(2x) [2] clearly indicating the image of the point A on each sketch. 4 (a) Simplify as far as possible 9x2 4 3x 2 2x + 1 6x + 3 [5] (b) Rationalise the denominator of 3- 7 7 -2 [4] 27x 3x + 1 = 9 [5] (c) Solve the equation 5191 3 [Turn over 5 A curve has the equation y = x4 2x3 dy (i) Find dx [2] (ii) Find the x coordinates of the stationary points on the curve and determine their nature. 6 [7] (i) Sketch the graph of the curve 10 y = x [2] (ii) On the same diagram, sketch the line y = 3x + 13 (iii) Find the coordinates of the points of intersection of the curve and the line y = 3x + 13 7 [1] 10 y = x [6] (a) A rectangular field has a width of 2x metres. Its length is (x + 10) metres. The area of the field is 800 m2 (i) Show that x2 + 10x 400 = 0 (ii) Hence find in surd form, the width and length of the field. [2] [4] (b) Find the range of values of p for which the equation px2 3x + (5 p) = 0 has two distinct roots. 5191 [7] 4 [Turn over 8 A sports field is to be built in the shape of a rectangle with a semicircle on each end as shown in Fig. 2 below. > > l > > r Fig. 2 The length of the rectangle is l metres and the radius of the semicircle is r metres. (i) Write down an expression in terms of l and r for the perimeter of the sports field. [1] The perimeter of the sports field must be 400 m long. (ii) Find an expression for l in terms of r. [2] (iii) Using calculus, find the dimensions of the sports field which maximise the area of the rectangle. [8] THIS IS THE END OF THE QUESTION PAPER 5191 5 5191

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Additional Info : Gce Mathematics June 2010 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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