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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 x x y dx x dx x x x 2 4 4 4 17 2 17 or 2 17 y y Hence diameter of rim of cup = 4 4 17 =8.12 cm 3 1 0 0.875 50 u u 2 1 0 2 0 0.875 50 0.875 0.875 50 50 0.875 50 1 0.875 u u u u 3 2 3 0 0.875 50 1 0.875 0.875 u u 2 1 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 n n n n n n n n u u u u u As n  , 0.875 0 n and hence 400 n u 4i) 4ii)       2 2 2 2 3 2 3 2 2 3 2 3 2 3 3 tan sec 1 2 (shown) 2 When 0, 0, 1, 0, 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 x y dx dx dx x x y x x x x
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Page 2 of 6 4iii) 2 3 3 3 3 2 3 1 1 ln 1 tan ... 3 2 3 3 3 1 2 ... 2 3 x x x x x x x x x x 2 2 2 2 sec Differentiating w.r.t. , 1 2 ...
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