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2005-2006 F4 Mathematics Term 2 Paper 1

# 2005-2006 F4 Mathematics Term 2 Paper 1 - Form 4ABCDEF...

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Form 4ABCDEF Mathematics 14th June, 2006 Paper I Time allowed: 1 hour 30 minutes Answer ALL questions. This paper carries a total of 94 marks. 1. Rationalize 5 2 3 1 . (3 marks) 2. Solve the simultaneous equations: 0 12 4 4 0 2 2 y x x y x . (6 marks) 3. (a) Solve the equation 18 45 y y . (b) Hence, or otherwise, solve the equation 18 ) 5 3 ( 5 3 45 2 2 x x x x . (8 marks) 4. Consider the quadratic equation 0 ) 2 ( ) 3 ( 2 2 k x k kx , where k is a non-zero number. (a) Find the discriminant of the above equation. Simplify your answer. (b) Prove that the equation always has two distinct real roots. (5 marks) 5. When a x x ax x 7 2 2 3 4 is divided by 3 2 x , the quotient is 1 4 2 x x and the remainder is c x 5 , where a and c are constants. (a) Expand the product   1 4 3 2 2 x x x . (b) Using (a), or otherwise, find a and c .

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