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2007 ACJC Prelims MA H2 P1 Sol

2007 ACJC Prelims MA H2 P1 Sol - Anglo-Chinese Junior...

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Page 1 of 8 Anglo-Chinese Junior College H2 Mathematics 9740 2007 JC 2 PRELIMS PAPER 1 Solutions 1 Let the equation of the cubic curve be 3 2 y ax bx cx d . y -intercept is -4 4 d   3 4 12 8 4 2 4 59 27 9 3 4 a b c a b c a b c 3, 2, 0 a b c   3 2 y = 3x - 2x - 4 2 2 2 sec tan sec d y x x dx dy x C dx y = ln(secx+ tanx)+Cx+ D 3 Let P( n ) be the statement 1 1 1 5 1 1 5 5 4 5 1 n r n r r , n When n = 1, LHS = 1 1 1 1 1 6 6 1 5 5 4 5 1 1 6 1 6 r r r RHS = 1 6 1 5 = LHS Hence P(1) is true. Assume P( k ) true, 1 1 1 5 1 1 5 5 4 5 1 k r k r r for some k Prove P( k +1) true, i.e. 1 1 1 1 5 1 1 1 5 5 4 5 1 k r k r r LHS of P( k +1) = 1 1 1 5 4 5 1 k r r r = 1 1 1 5 4 5 1 5 1 5 6 k r r r k k = 1 1 5 1 1 5 5 1 5 6 k k k = 1 1 5 1 5 6 5 1 1 5 5 1 5 6 5 1 5 6 k k k k k k k = 1 1 5 1 1 5 1 5 6 5 5 k k k = 1 5 6 1 5 k Therefore P( k +1) is true Since P(1) is true and P( k ) true P( k +1) true, P( n ) is true for all n .
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Page 2 of 8 4 I : A scaling parallel to y axis with scale factor 1 4 units II : A scaling parallel to the x axis with scale factor 1 2 units III: A translation of 1 unit in direction of the negative x axis OR I : A scaling parallel to y axis with scale factor 1 4 units II : A translation of 2 unit in direction of the negative x axis III: A scaling parallel to the x axis with scale factor 1 2 units OR I : A translation of 2 unit in direction of the negative x axis II : A scaling parallel to the x axis with scale factor 1 2 units III: A scaling parallel to y axis with scale factor 1 4 units OR I : A translation of 2 unit in direction of the negative x axis II : A scaling parallel to y axis with scale factor 1 4 units III: A scaling parallel to the x axis with scale factor 1 2 units OR I : A scaling parallel to the x axis with scale factor 1 2 units II : A translation of 1 unit in direction of the negative x axis III: A scaling parallel to y axis with scale factor 1 4 units OR
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