2007 ACJC Prelims MA H2 P2 QP

2007 ACJC Prelims MA H2 P2 QP - ANGLO-CHINESE JUNIOR...

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Anglo-Chinese Junior College H2 Mathematics 9740: 2007 JC 2 Preliminary Examination Paper 2 Page 2 of 6 ANGLO-CHINESE JUNIOR COLLEGE MATHEMATICS DEPARTMENT JC2 Preliminary Examination 2007 MATHEMATICS 9740 Higher 2 Paper 2 Calculator model : _____________________ Arrange your answers in the same numerical order. Place this cover sheet on top of them and tie them together with the string provided. Question no. Marks 1 2 3 4 5 6 7 8 9 10 11 12 13 / 100 Index No: Form Class: ___________ Name: _________________________
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Anglo-Chinese Junior College H2 Mathematics 9740: 2007 JC 2 Preliminary Examination Paper 2 Page 3 of 6 Section A: Pure Mathematics [40 marks] 1 The diagrams below show the graph of f and its derivative ' f . State clearly, with reasons, which is the graph of f and that of ' f . [2] 2 A cup is obtained by rotating the parabola 2 4 yx about the x -axis. If it holds exactly 32 cm 3 , find the diameter of the rim of the cup, given that the radius of the base is 1 cm. [3] 3 A farmer raises chickens in a farm. Taking into account various conditions, such as sale of poultry, deaths etc. that affect the population of chickens in his farm, the number of chickens at the end of n months is modelled by n u , where 1 0.875 50 nn uu  . Express 1 u , 2 u and 3 u in terms of 0 u . Show that 0 0.875 ( 400) 400 n n and deduce the value of n u when n becomes very large. [5] 4 (i) Given that tan , show that 2 2 2 d y dy y dx dx . Hence find Maclaurin‟s series for y , up to and including the term in x 3 . [5] (ii) Using the standard series expansion for   ln 1 x and Maclaurin‟s series for y , find the series expansion of   ln 1 tan x , in ascending powers of x up to and including the term in x 3 . [2] (iii) Hence show that the first three non-zero terms in the expansion of 2 sec 2 1 tan 2 x x , are 2 1 2 8 xx  . [3] [Turn Over Diagram 2 Diagram 1
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Anglo-Chinese Junior College H2 Mathematics 9740: 2007 JC 2 Preliminary Examination Paper 2 Page 4 of 6 5 (a) Solve the equation 3 4 1 2 zi i    , giving each answer in the form x yi .
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This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

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2007 ACJC Prelims MA H2 P2 QP - ANGLO-CHINESE JUNIOR...

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