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Section A(2) (33 Marks)

Answer ALL questions in this section and write your answers in the spaces provided.

10. Let f(x) = (x –a) (x – b) (x + 1) – 3 , where a and b are positive integers with a＜b . It is given

that f(1) = 1.

(a) (i) Prove that (a – 1) (b – 1) = 2

(ii) Write down the values of a and b. (3 marks)

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(b) Let g(x) = x3 – 6x

2 – 2x +7 . Using the results of (a)(ii), find f(x) – g(x). Hence find the

exact values of all the roots of the equation f(x) = g(x) . (4 marks)

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2006-CE_MATH 1-8

11. In Figure 5, ABCDEF is a thin six-sided polygonal metal sheet, where all the measurements are correct

to the nearest cm.

(a) Write down the maximum absolute error of the measurements. (1 mark)

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(b) Find the least possible area of the metal sheet. (3 marks)

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(c) The actual area of the metal sheet is x cm2 . Find the range of values of x. (4 marks)

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2006-CE-MATH 1-9

12. In Figure 6, CM is the perpendicular bisector of AB, where C and M are points lying on the x-axis

and AB respectively. BD and CM intersect at K.

(a) Write down the coordinates of M. (1 mark)

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(b) Find the equation of CM. Hence, or otherwise, find the coordinates of C. (3 marks)

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2006-CE-MATH 1-10

(c) (i) Find the equation of BD.

(ii) Using the result of (c)(i), find the coordinates of K. Hence find the ratio of the area of

△ AMC to the area of △AKC.

(5 marks)

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END OF PAPER

2006-CE-MATH 1-22