2007 ACJC Prelims MA H2 P2 Sol

2007 ACJC Prelims MA H2 P2 Sol - Anglo-Chinese Junior...

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Page 1 of 6 Anglo-Chinese Junior College H2 Mathematics 9740 2007 JC 2 PRELIMS PAPER 2 Solutions 1 Diagram 2 : Graph of f Diagram 1 : Graph of ' f The minimum point at x = 0 in diagram 2 (graph of f ) corresponds to the x – intercept in diagram 1 (graph of ' f ) . 2   2 2 2 1 1 1 4 2 2 1 32 17 or 17 (rejected) x xx y dx x dx x x x        2 44 4 17 2 17 or 2 17 yy Hence diameter of rim of cup =   4 4 17 =8.12 cm 3 10 0.875 50 uu      21 0 2 0 0.875 50 0.875 0.875 50 50 0.875 50 1 0.875 u u   32 30 0.875 50 1 0.875 0.875       0 0 0 0 0.875 50 1 0.875 0.875 ... 0.875 1 0.875 0.875 50 1 0.875 0.875 400 1 0.875 0.875 400 400 nn n n n n u u u    As n  , 0.875 0 n and hence 400 n u 4i) 4ii)       22 2 2 23 3 tan sec 1 2 (shown) 2 When 0, 1, 2 1 tan 0 1 0 2 ... ... 2! 3! 3 dy y x x y dx d y dy y dx dx d y d y dy dy y dx dx dx dx dy d y d y xy dx dx dx y x x x x   
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Page 2 of 6 4iii)   23 3 3 3 11 ln 1 tan ... 3 2 3 3 3 12 ... x x x x x x x x x x 2 2 2 2 sec Differentiating w.r.t. , 1 2 ... 1 tan sec 2 1 2 8 ... (shown) 1 tan 2 x x x x x x xx x      5a) b) i) ii) 3 2 4 1 2 ki zi e i     , k = 0, 1, 2.
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2007 ACJC Prelims MA H2 P2 Sol - Anglo-Chinese Junior...

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