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,  (ii) digits may be used more than once.  (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.  Solutions 4
(iii) Given that as n , S n S . Find S . 
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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,  (b) express f( x ) in the form of 3 2 ax bx cx d , where a , b , c and d are real numbers.  3 10 , 3 3 2 , 1 0 y x
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