A cylic quadilateral PQRS is such that PQ p QR q RS r and SP s i Show that Cos

# A cylic quadilateral pqrs is such that pq p qr q rs r

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A cylic quadilateral PQRS is such that PQ = p, QR = q, RS = r and SP = s i. Show that Cos QPS = (p 2 + s 2 ) - (q 2 + r 2 ) (3 marks) 2(ps + qr) ii. If p = r and q = s , show that PQRS is a rectangle. (2 marks) 5

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9. F, P and Q lie in a horizontal plane. F is the foot of a vertical tower FT. P is south –east of the tower and the angle of elevation of T from P is 30 0 Q is 100m from p in the direction 250 0 and is south-west of the tower. Calculate the height, in metres, of the tower. (3 marks) 10. A rectangle has an area of 23.0cm 2 . the width of the rectangle is 4.3cm. if all measurements are correct to one decimal place, calculate the maximum and minimum values of the length of the rectangle. (4 marks) 6
11. Simply (2 mark) 5 - √5 5√5 - √5 12. If 5p + 2q = 5 , find the ratio. 5p +6q = 9 (3 marks) P 2 : q 2 7

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13. If the clock now indicates that it is 5 minutes to 11 o’clock, what time will it be when the minute hand has turned through 435 0 ? (3 marks) 14. Find the number of sides of a regular polygon whose interior angle is 157.5 0 (2 marks) 15. Factorize completely: p 2 x + q 2 y – q 2 x – p 2 y. (2 marks) 8
SECTION B Answer all five questions from this section 16. Water flows through a pipe of internal radius 3.5cm at the rate of 9m/s into a storage tank of

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