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 32 y ax bx cx d . y -intercept is -4 4 d  34 12 8 4 2 4 59 27 9 3 4 abc a b c      3, 2, 0 a b c     y = 3x - 2x - 4 2 2 2 sec tan sec dy xx dx dy xC dx  y = ln(secx+ tanx)+Cx+ D 3 Let P( n ) be the statement   1 11 5 1 1 5 5 4 5 1 n r n rr     , n When n = 1, LHS = 1 1 1 1 1 6 6 1 5 5 4 5 1 1 6 1 6 r    RHS =   1 61 5 = LHS Hence P(1) is true. Assume P( k ) true,   1 5 1 1 5 5 4 5 1 k r k     for some k Prove P( k +1) true, i.e.     1 1 5 1 1 1 5 5 4 5 1 k r k     LHS of P( k +1) = 1 1 1 5 4 5 1 k r   = 1 5 4 5 1 5 1 5 6 k r r r k k     =   5 1 1 5 5 1 5 6 k kk     =   1 1 5 1 5 6 5 1 1 5 5 1 5 6 5 1 5 6 k k k k k         =     5 1 1 5 1 5 6 55 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
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2007 ACJC Prelims MA H2 P1 Sol - Anglo-Chinese Junior...

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