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GCE MAY 2010 : A2, C4 : Core Mathematics 4

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ADVANCED General Certificate of Education 2010 Mathematics assessing Module C4: Core Mathematics 4 AMC41 Assessment Unit C4 [AMC41] MoNDAy 24 MAy, AftErNooN tIME 1 hour 30 minutes. INStrUCtIoNS to CANDIDAtES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator 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. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z 5189 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Points P, Q and R have position vectors OP = 4i + 4j OQ = i + 2j + 3k OR = 8j + 6k (i) Find QP. [2] (ii) Find QR. (iii) Show that the triangle PQR is right-angled at Q. 2 [1] [3] A vase is formed when the area bounded by the curve y =3 +2 x and the lines x = 0 and x = 4 is rotated through 360 about the x-axis, as shown in fig. 1 below. y x fig. 1 Find the volume of the vase. 5189 [7] 2 [turn over 3 (a) The function f(x) = x2 + 4x with domain {x: x R, x > a} is a one-to-one function. By sketching this function, find the least value of a. [3] (b) The function g ( x ) = 4 x has domain {x: x R, x b}. x 3 (i) Write down the value of b. [1] (ii) Find the inverse function g 1(x) stating its domain. (iii) Hence write down the range of g(x). 4 [5] [1] In the atmosphere, the air pressure P (Pascals) decreases with the height h (km) above sea level at a rate that is proportional to the pressure. (i) Model this by a differential equation. [2] At sea level the air pressure is 100 000 Pa. At 1 km above sea level the air pressure is 88 000 Pa. (ii) By solving the differential equation, find the air pressure at 400 m above sea level. 5 [8] (a) Use the substitution u = x 2 to find y 3x dx x 2 [7] (b) Evaluate p 4 4x cos 2x dx [7] 0 5189 3 [turn over 6 A curve is defined by x = t4 6 (i) Show that and y = 2t 2 8t + 6 dy t - 2 =3 dx t [4] (ii) Hence find the coordinates of the turning point and determine its nature. 7 [9] (a) Sketch the graph of y = sin 1 x State the restricted domain of this function. [3] (b) Solve the equation sin 2 = cos for r G i G r [5] (c) Prove the identity 1 + tan2 x / sec 2x 1 - tan2 x 1847-006-1 [7]

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Additional Info : Gce Mathematics May 2010 Assessment Unit C4 Module C4 : Core Mathematics 4
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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