2007 Promo Ans.doc - TJC/Promos07/H2Maths/Solutions 1...

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TJC/Promos07/H2Maths/Solutions 1 Differentiate the following with respect to x , where , 0 1 x x ¡ , simplifying your answer.
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TJC/Promos07/H2Maths/Solutions 3 (a) Digits are to be chosen from 1, 3, 7 and 9 to form a 4-digit number. Find the number of ways in which this can be done if (i) no digit may be used more than once, [1] (ii) digits may be used more than once. [1] (b) The digits 1, 3, 7 and 9 are to be placed in a 2 2 grid with the condition that a digit in the second row must be greater than the digit directly above it. Find the total number of ways in which this can be done, explaining your answers clearly. [2] Solutions 4
(iii) Given that as n , S n S . Find S . [1]
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TJC/Promos07/H2Maths/Solutions (ii) 1 5 5 1 3 f 1 f 2 ( 2)( 3) 4 r n n n r r r S r r r r f 6 f 7 f 7 f 8 f 1 n M M M f 2 n =f 6 f 2 n 1 729 3 3 2048 2 4 n n (iii) 1 729 3 3 729 lim lim . 2048 2 4 2048 n n n n S S n   5 The graph of f y x is shown below with maximum points at (– 3, 10) and 2 1, 3 . Given that f y x is a cubic function and that it intersects the line 10 y at only one point where , , 0 x ¡ , (a) sketch the graph of x y f indicating clearly the coordinates of all stationary points, [1] (b) express f( x ) in the form of 3 2 ax bx cx d , where a , b , c and d are real numbers. [5] 3 10 , 3 3 2 , 1 0 y x

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