上回提及的，大多是怪異的短題目，亦有人問及長題目的選擇，以及對Mechanics的深切興趣，今集將會為大家一一解開謎團。
在長題目的選擇方面，Paper 1是自由的六選三；Paper 2的長題目則分為2 Groups，各自有三道題目，考生須在每個Group選1道作答；Paper 3的長題目更厲害，分成3 Groups，Group I和III有3道題目，Group II有兩道。考生須回答四道長題目，每個Group必須選答一題。真是難為當時的考生，在選題的抉擇上，真是煩得頭昏腦脹了。
Paper 2。
Group I的第一道題目，可謂挺驚嚇的。
1968 II 11. The variables x and y are connected by a relationship of the form y = a(x^n), where a and n are unknown constants.
In an experiment the following sets of readings are obtained:
x 5.75 10.5 20.4 39.3 75.0
y 2.01 3.16 5.37 8.91 14.76
By drawing a suitable graph determine the values of constants a and n. Indicate on your graph how these values
are obtained.
數學都有實驗做？要記住，這裡所提及的實驗，有機會是一些物理實驗喔。
資深的老師說得好，越是簡潔的題目（特別是長題目），越是深奧。
上回提到一些很「科幻」的短題目，在Group I 13題亦有出現。
1968 II 13. The height of the tide at any point between high and low water can be represented approximately by
a ‘sine’ and ‘cosine’ curve through half a cycle (i.e. through 180^o).
At a certain place, on a certain day, the high tide is at noon. If t is the time in minutes, that has elapsed since
noon, the depth of water is given by [4.6 + 1.75 cos (0.6t)^o] feet until low tide.
After low tide the depth is given by [5.1 + 2.25 sin [1/7(3t-1530^o)]] feet until the next high tide.
(a) What are the times of the first low tide and the next high tide?
(b) If your boat ,which needs 5 feet of water to float in, is moored at this place, between what times will it be
aground (i.e. not floating)? Give your answers to the near five minutes.
請留意第二段（At a certain place, on a certain day...），想不到AMaths的卷可以這樣押韻的。
當然，這道題目本身，亦有一定的難度，至少在英文的理解上，已經難到不少的考生了。
Group II第一道長題目，簡單得出奇，只有兩行。
1968 II 14. Find the maximum and minimum values of y on the curve y^2 = x(1 - x)^2. Sketch the curve and find the
area enclosed by it.
是一道結合了Curve Sketching和積分的題目。這條curve，現在大多會在Pure才出現了。（雖然坊間的一些AMaths參考書，仍有y^2的例子，但當中的細微地方，仍須用到「可微性」和「連續性」的概念）。
第15題的(b)(i) part，有驚人的發現。
1968 II 15. (b) (i) If (12,9) is the orthocentre of the triangle ABC, of which (1) and (2) are the two sides AB and AC
respectively, find the equation of the altitude of the triangle from A to BC.
ORTHOCENTRE？！不錯，在Mechanics並行的課程以下，那四種不同的centre，顯得尤其重要了。
是故，在古舊的AMaths卷發現這些用語，不足為奇。
進入Mechanics的園地去。
來一個有趣的instruction：
「Do not evalue g or ‘pi’ in any answer, and leave in surd form any answer containing a surd.」
這項instruction，是為了避免有部分考生用一些鮮為人知
的「屈機方法」，去弄出一些numerical answer。與此同時，那些不跟規則的考生自然會被懲罰。
先來一道作熱身吧。
1968 III 1. A small weight of 100 gram is suspended by a light string from a fixed point, and is drawn aside by a horizontal
force so that the string is inclined to the vertical at an angle of 40^o.
Draw the triangle representing the forces acting on the weight and measure it to find the magnitude of the
tension in the string. (Use 5 cm to represent 100 gram weight) (4 marks)
是一道用Graphical Method去找答案的題目，數學性不太強。
再來一道幾CE Physics feel的題目。
1968 III 6. A particle of mass 10 gram is accelerated from rest under the action of a signle force of 20 gram weight.
Find the distance travelled by the particle during the first two seconds of its motion. (4 marks)
雖然是數學卷，但由於牽涉到物理概念，所以亦有一些文字題的。
1968 III 2. Explain clearly but briefly (in two or three sentences) the fault in the following argument:
“P is a force acting in the direction North, and it therefore has a component Pcos45^o in the direction N.W.
Call this component Q. The force Q has a component Qcos45^o in the direction West.
Therefore, P has a component Qcos45^o, or Pcos^2(45^o) in the direction West.” (3 marks)
1968 III 7. Explain clearly (in three or four sentences and using a diagram) the action of the differential pulley
(also called the Weston differential pulley).
You are not expected to mention the velocity ratio or the efficiency of the machine.
可以見到，文字題不是新事物，只是形式上的不同而己。
長題目，三個groups之中，Group II的題目是全部都是沒有圖的，逼著考生必須答一道「閱讀理解」式的題目。更厲害的是，Group II是二選一，Group I 和 III卻是三選一的，真是同題目不同命。
Group I一來，就是之後都會經常見到的lamina
（由於自己沒有修Applied，所以不知道是否在Applied的課程裡邊，煩請各位修讀此科／熟悉此科的人留下一些意見）
。
1968 III 11. A uniform square lamina of side 8 cm and mass 128 g has a square piece of side 2 cm cut from it, and is
suspended from one corner by two light strings as shown in Figure 5.
(a) Use Lami’s Theorem to find in gm.wt. the tensions T1 and T2 in the strings.
(b) Calculate the tangent of the angle between the diagonal AB and the vertical.
甚麼是Lami’s Theorem？
Wikipedia的解釋或許會有幫助：
http://en.wikipedia.org/wiki/Lami%27s_theorem
但看的人必須有一定的物理和數學底子才能明白。
Group II的15題，又有令會考生抓狂的字眼。
1968 III 15. An imperfectly elastic ball is projected from a point P on level ground with speed V and at an angle of
elevation A.The ball stikes a vertical wall normally and rebounds to a point Q on the ground, hal-way
between P and the base of the wall.
Find (a) the distance from P to the wall;
(b) the coefficient of restitution, e, between the ball and the wall.
Coefficeint of restitution？
此乃是一個計算collision中的velocity較pro的方法，運用比例，我們就能夠準確地計算物件撞擊前後的velocity了。（參考網址：
http://en.wikipedia.org/wiki/Coefficient_of_restitution）
不經不覺，去到Group III，為「單位」而癲狂，何只在物理呢？
1968 III 17. A train weighing 200 tonnes travels along a straight line and level track developing 160 H.P. at a
speed of 30 m.p.h.
Calculate the resistance to motion in lb.wt. per tonne.
The train begins to pick up water (from a long water tank beneath the track) at the rate of 1200 gallons per minute.
(a) If the engine develops the same power, what is the new speed of the train in m.p.h.?
(b) What horse-power does the engine need to develop in order to maintain the speed of 30 m.p.h.?
(Take the weight of one gallon of water to be 10 lb.
Assume that the resistance to motion does not vary with the speed of the train.)
附加數，再不是大家想像中這樣簡單！
下一集，會繼續為大家走過69和70年的Past Paper。
