Section B: Long Questions

Section A: Short Questions.

Answer ALL questions in this section. (80 marks)

(a) Simplify and express your answer in positive indices.

(7 marks)

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(b) If x = – 4, and y = – 0.5, find the value of the expression in 1(a).

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The annual yield of rice grown in a country was increased by 30% from 1998 to 1999, and decreased by 10% from 1999 to 2000. What was the percentage change in the yield from 1998 to 2000?

(7 marks)

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(a) Factorize a2 – 11a + 18. (6 marks)

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(b) Hence, factorize (x + 1)2 – 11(x + 1) + 18.

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A manager of a company interviewed three applicants A, B and C. The following table shows the results of the interviews. (6 marks)

Aspect / Weight / Score
A / B / C
Working experience / 3 / 5 / 2 / 3
Education background / 2 / 2 / 4 / 5
Language ability / 3 / 4 / 4 / 3

Find the weighted mean of the three applicants; hence determine which applicant is most suitable for the job.

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In the figure, ABC ≡ DCE. BCE is a straight line. BC = CE = AD. Let BAC = a, ABC = b and ACB = c. (11 marks)

(a) Prove that ABC ≡ CDA.(5 marks)

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(b) Hence, prove that DAB + ABC = 180o. (6 marks)

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The diagram below is an incomplete net, where CDH has not been drawn yet. EABG and FBC are straight lines. On completion, it can be folded into the object on the right. ABCD is a rectangle of dimensions 6 cm x 2.4 cm. ABF and BCG are right-angled triangles. (13 marks)

(a) Find EAD.(1 mark)

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(b) Find the lengths of the following sides:

(i) BG and GC,(3 marks)

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(ii) AF, AE and ED,(5 marks)

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A bag contains 2 red cards and 2 white cards. 2 cards are taken out of the bag one by one without replacement. (10 marks)

(a)Denoting the red cards as R1 and R2 and the white cards as W1 and W2, show all the possible outcomes. (4 marks)

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(b)Find the probability that

(i)both cards are of the same colour.(3 marks)

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(ii) the two cards are of different colours.(3 marks)

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The figure shows the route of a cross-country race, where A, B, C and D are four check points.

(8 marks)

(a)Find the compass bearing of B from A, (3 marks)

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(b)Find the true bearing of C from B. (5 marks)

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In the figure, ADC is a straight line, AB = BC = AD. (12 marks)

(a)Prove that y = 3x – 180o.(8 marks)

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(b)If x = 2y, find ABC.(4 marks)

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Section B: Long Questions. (40 marks)

Answer ALL questions in this section. Each question carries 20 marks.

In the figure, D and E are the mid-points of AB and AC respectively. F and G are on BC such that BF = FG = GC. DF and EG are produced to meet at H. (20 marks)

(a)Prove that 2DE = 3FG. (5 marks)

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(b)Prove thatHFG and HDE are similar.(5 marks)

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(c)FindHG：GE,(5 marks)

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(d)Prove that EGC and HGB. are similar.(5 marks)

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The figure shows a rectangle ABCD. The coordinates of A and B are (–1 , 3 ) and (– 2 , 4 ) respectively. The diagonals AC and BD intersect at a point on the x-axis. (20 marks)

(a)Find the coordinates of P.(6 marks)

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(b)Find the coordinates of C.(8 marks)

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(c)Find the area of rectangle ABCD.(6 marks)

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