以下是 2009 CE Additional Mathematics Q.18，同學，看看你可否在 16 分鐘內正確地完成它：
The following figure shows a park AED on a horizontal ground. The park is in the form of a right-angled triangle surrounded by a walking path with negligible width. Henry walks along the path at a constant speed. He starts from point A at 7:00 am. He reaches points B, C and D at 7:10 am, 7:15 am and 7:30 am respectively and returns to A via point E. The angles of elevation of H, the top of a tower outside the park, from A and D are 45 and 30 respectively. At point B, Henry is closest to the point K which is the projection of H on the ground. Let HK = h m.
(a) Express DK in terms of h. (1 mark)
(b) Show that AB = h m. (3 marks)
(c) Find the angle of elevation of H from C correct to the nearest degree. (3 marks)
(d) Henry returns to A at 8:10 am. It is known that the area of the park is 9450 m.
(i) Find h.
(ii) A vertical pole of length 3 cm is located such that it is equidistant from A, D and E. Find the angle of elevation of H from the top of the pole correct to the nearest degree. (5 marks)
略談：(b) 可能會因一時疏忽而計不到，(d)(i) computational，(d)(ii) 考幾何…
Let . Suppose is the orthocentre of , || = 1 and || = 2. Find in terms of and , hence determine .
Q.15 Differentiation and Integration：有些新意
The sphere is being pulled at a constant speed of . At the instant when h = 3, find the rate of change of (1) the depth of water (2) the distance between the top of the sphere and the water surface.
只要留意 便 KO 可。
Given ABCD, PQRS are rectangles. Show that the area of PQRS is . Show that and and hence find the greatest area of PQRS.
Q.17 Coordinate geometry：題型舊（相信補習社及非補習社的授課員都捉不到路…），只要小心代數運算便可！
Prove that . Suppose touches at , find possible slopes of and the corresponding lengths of . Suppose is a tangent to from , write down the slopes of .
SECTION A：要盡量淺（取 30 分便可及格）
SECTION B：要盡量深（用來分出取 A 同學，但取 B,C,D 呢？）
不過，相信同學分數分佈是 POSITIVE SKEW…