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GCE JAN 2011 : AS, C2 : Core Mathematics 2

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ADVANCED SUBSIDIARY (AS) General Certificate of Education January 2011 Mathematics assessing Module C2: AS Core Mathematics 2 AMC21 Assessment Unit C2 [AMC21] MONDAY 24 JANUARY, 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 figure unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES 111535 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. Throughout the paper the logarithmic notation used is 1n z where it is noted that 1n z loge z 6080 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three signficant figures unless otherwise stated. 1 The arc of the sector of a circle subtends an angle of 1.5 radians at its centre as shown in Fig. 1 below. 1.5 Fig. 1 The area of this sector is 36 cm2 (i) Find the radius of the circle. (ii) Find the perimeter of the sector. 6080 [2] [3] 2 [Turn over 2 Fig. 2 below shows a plan of a field ABCD. B 150 m 35 120 C 200 m A 300 m D Fig. 2 (i) Find the length of AC. (ii) Find the area of the triangle ABC. [3] (iii) Find the angle ADC. [3] (iv) Find the area of the field. 6080 [2] [2] 3 [Turn over 3 A circle is given by the equation x2 2x + y2 + 4y = 4 (i) Find the centre and radius of the circle. [4] A tangent is drawn to the circle from the point A (5, 6). The tangent touches the circle at the point B as shown in Fig. 3 below. A B Fig. 3 (ii) Find the length AB. 4 [4] (a) (i) Sketch the graph of y = tan 2x for 180 < x < 180 [2] (ii) State the period of this graph. [1] (iii) Solve the equation tan 2x = 3 for 180 < x < 180 [4] (b) Prove the identity 1 cos2 q tan q = sin q cos q 6080 4 [3] [Turn over 5 (a) Find 6 x 2 dx x3 [3] (b) The graphs of y = x2 8x + 16 and y = 4 + 6x x2 are shown in Fig. 4 below. y 9 4 1 6 x Fig. 4 The coordinates of the points of intersection of the curves are (1, 9) and (6, 4). Find the area between the 2 curves. 6080 [7] 5 [Turn over 6 (a) A sequence is defined recursively by un+1 = 3 u +4 10 n where u1 5 (i) Find the values of u2 and u3 [2] (ii) The sequence converges to a limit l. By forming and solving an equation, find the exact value of l. [2] (b) A solution by trial and improvement is not acceptable. Bill has borrowed a sum of money. His repayments will form an Arithmetic Progression. He agrees to repay 200 at the end of the first month, 195 at the end of the second month, 190 at the end of the third month and so on until the loan is repaid. (i) Find how much he will repay at the end of the 12th month. (ii) Find after how many months he will make his final repayment. [2] (iii) Calculate the total amount of money that he will repay. 7 [2] [3] (a) (i) Rewrite as a single logarithm log3 8 3 log3 x [3] log3 8 3 log3 x = 3 [4] (ii) Hence solve the equation (b) A solution by trial and improvement is not acceptable. A patch of mould increases its area by 12% each day. Initially the patch of mould has an area of A0 Find after how many days the area of the patch of mould is 17 times A0 6080 6 [4] [Turn over 8 If (1 + ax)n = 1 4x + 7x2 + ... find the values of a and n. [10] THIS IS THE END OF THE QUESTION PAPER 6080 7 [Turn over 6080 111535 8 [Turn over

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Additional Info : Gce Mathematics January 2011 Assessment Unit C2 Module C2 : Core Mathematics 2
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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