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2007 TPJC Prelim Paper 1

2007 TPJC Prelim Paper 1 - TAMPINES JUNIOR COLLEGE...

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1 TAMPINES JUNIOR COLLEGE Preliminary Examination 2007 Mathematics Higher 2 9740/01 12 September 2007 8:00 11:00 hr Answer All questions. 1. Codes can be formed by using any of the six characters from the set S , where , , , , , S . a) Find the number of different five-character codes that can be formed. [3] b) How many of these five-character codes begin and end with ? [2] 2. The function 2 3 2 1 y q r x r x is obtained by transforming the function 2 y px qx r through the following transformations: Step 1: Translation of 1 unit parallel to the x -axis; Step 2: Scaling of factor 2 parallel to the y -axis. i) Show 4 2 3 2 p q r   . [3] ii) Hence, find the exact values of p , q and r by forming three equations involving p , q and r . [3] 3. A sequence is defined by 102 , 3 0 1 u u u n n . i) Find u 1 , u 2 , u 3 and u 4 . [1] ii) Obtain a conjecture for u n in the form [102 f ( n )] for n = 1, 2, 3,4, expressing f ( n ) in terms of n . [2] iii) Prove the result of u n by Mathematical Induction. [4]
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2 4. i) Express the following equations in matrix form and solve the equations 7 x 3 y + z = 19 2 x 5 y + z = b x + ay 2 z = 19 when a = 3 and b = 3. [2] ii) For a = 12 and b = 0, show that the equations have infinitely many solutions. Give
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