進入七十年代，AMaths的部分題目，開始有點似曾相識了。
1970 I 4. Evaluate (Integration 1, 0) (2x + 1)^1/2 dx correct to one dcimal place. (4 marks)
（註：(Integration 1, 0)代表著定積分，range是由1去到0）
很普通的Integration短題目。
可是，由於此科仍是初出道，部分題目仍然很odd的。
1970 I 3. A space-ship travels round the earth in 90 minutes. What is the constant angular speed in radians per hour? (2 marks)
對於修讀AL Physics的人來說，這道題目的確是circular motion入門且必須答對的題目，但是對於現在的會考生來說，其實只要心水清的，難度都不算太高的。
Physics和AMaths融為一體的例子，何只這樣少？
1970 I 9. At any moment the volume v and the pressure p of gas are connected by the relationship pv^1.5 = c, where c
is constant. When the volume is 64 cubic inches, the pressure is 20 pounds per square inch. If at this moment
the pressure is increasing at the rate of 1 pound per square inch per second, find the instantaneous rate of change
of volume. (5 marks)
從前CE Physics不Out Syl，今天AL Physics必須知的題目。
還有一道Prove summation of G.S.的MI題目。
1970 I 10. Prove by induction that the sum of the series a + ar + ar^2 + … to n terms is [(a)(r^n - 1)]/(r - 1) where r is
greater than 1. (6 marks)
長題目，從1970年至73年，分佈大致和69年差不多，三張Papers皆是六選三，Paper 1和I3分groups，Paper 2則是自由選擇。分別在於，從70年開始，Paper 3的兩個groups各自有三題可供選擇，這是有別於69年的四題，變相考生的選擇是少了的。
Group I 的長題目，頭兩題是挺普通的trigo，第三題則是利用binomial計算的compound interest。
Group II，題目則較為有趣了。
1970 I 14. (a) A, B, C, D, E, F are six points.
How many different circles can be drawn, each passing through at least three of these points
(i) if no three points are collinear and no four points are concyclic,
(ii) with the conditions in (i) except that A, B, C, D are collinear.
(iii) with the conditions in (ii) except that A, B, E, F are concyclic.
(b) In a given plane there are m lines parallelt to one antoher in direction and n lines parallel to one another in
a different direction.
(i) How many points of intersection are there between the (m + n) lines in this plane?
(ii) How many different parallelograms are made up by these parallel lines?
頭昏腦脹了嗎？
繼續Physics！
1970 I 15. The period T (in seconds) of swing of a pendulum is given by T = 2pi(l/g)^1/2, where l is the length of the
pendulum and g is the acceleration due to gravity.
(a) Find dT/dl if g is constant.
(b) If g remains constant, show that 2dT/T = dl/l. Is T increased or decreased when l is decreased by 0.1%, and
by what percentage?
(c) Find dT/dg if l is constant.
(d) If l remains constant and g is increased by 0.2%, is T increased or decreased, and by what percentage?
(e) A clock with a simple pendulum keeps correct time in Hong Kong. It is then taken to the South Pole, where,
compared with Hong Kong at this time, l is decreased by 0.1% and g is increased by 0.2%. Is T increased or
decreased and by what percentage?
披著AL Physics的外表，實則是考微分的應用。
老實說，(d)和(e) part，在今天的SHM（Simple Harmonic Motion），並非罕見。
最後一題，則為積分計算面積和容量的題目，最後指出這是一座radio telescope的dish，要命吧！
Paper 2，看見System of equations……
1970 II 2. Solve the simultaneous equations:
3x + 4y - z = 0
4x + 7y + 2z = 0
5x + 3y - 7z = 0
(4 marks)
除了這一題外，其他的短題目沒有太大的驚喜，只是最後兩題出現了現今會考數學課程的Remainder Theorem與及logarithm而己。
長題目，此年Paper 2沒有令人詫異的題目，不是Trigo，就是Calculus／Coordinate Geometry，都是一些今天常見的題目。
Paper 3，雖然之前說過，盡量希望蜻蜓點水，但實在忍不了手，因為部分70年的題目和現今AL Physics的實在相似得太厲害了。
1970 III 3. A garden roller of weight W and radius r is to be pulled up a step of height h (<r) by a force of magnitude P
acting through the centre of gravity of the roller and perpendicular to its axis. The direction of the pulling force is
as shown in Figure 2. Find the least value of P required.
是一道經典的AL Physics「車輪上樓梯」的題目，大部分的教科書在「Moment」一節應會用作例子之用。
還有一道在Group II長題目，是CE Physics和AL Physics的混合體。
1970 III 13. A truck of total mass M1 + M2 is moving on smooth horizontal rails at a uniform velocity V1. The mass M2 is
projected from the truck with a velocity V2 relative to it and in the same direction as V1.
(a) Using the principle of conservation of linear momentum, find the new velocity of the truck.
(b) If the projection of the mass brings the truck to rest, find V2 in terms of M1, M2, and V1.
If the mass M2 is projected from the truck with velocity V2 relative to the truck and in the opposite direction as
V1, find the velocity of the truck after projection.
容易令人混亂的一道momentum題目。
踏入71年，淡淡如水。
Paper 1的短題目非常普通，沒有太多驚異之處。
長題目方面，Group I頭兩題非常「九唔搭八」，第一題是把Probability和Binomial，第二題則是把MI和Trigo毫無關係地，捆在一起。
第三題則是一道簡單的Trigo數。
Group II方面，第一題是比例數，第二題是plot graph的題目。至於第三題，則有點令人卻步了。
1971 I 15. Consider two regions A and B in the first quadrant.
Region A is bounded by the lines
y = k(x^2), y = k(a^2), x = 0,
and region B is bounded by the lines
y = k(x^2), y = 0, x = a,
where k, a are positive constants.
(i) Show that the area of region A is twice the area of region B.
(ii) If both regions A and B are rotated about the y-axis, show that the solid generated by A is equal in volume
to the solid generated by B.
一道挺怪的Integration題目，混雜了一點點的Linear Programming。
Paper 2的短題目，仍然維持著obvious的狀態，偶有一些現在Maths Syllabus的Remainder Theorem及A.S./G.S.的題目。
長題目的第一題，竟與Paper 1的Group II第二題形式差不多，亦是plot graph的題目，也就是給予你x和y的值，然後再plot一個graph出來。在近年（未合併兩份Paper以前），這種情況可謂十分罕見的。
接著下來的，都是一些Trigo、Calculus和Coordinate Geometry的題目，只是有一道潮汐題，和68年Paper 2的第十三題有一點的相類似。（請參考帖子：
會考故事之十八：AMaths風暴（第四集，力學之旅））
1971 II 11. At a certain place the height of tide above the low water mark is 6[1 + cosA] feet, whre A = (pi)(t)/450 radians
and t is the time in minutes after high tide.
(i) What is the time interval between high and low tide?
(ii) At what rate is the tide falling, in feet per minute, 75 minutes after high tide?
(Leave your answer in terms of pi.)
(iii) A bridge is 30 feet above the low water mark. A boat can just sail under the bridge when the ditance
between the bridge and the sea level is 21 feet. How long after high tide will it be before the boat can sail
under the bridge.
Part (iii)，相對於68年而言，是淺易了一點。
總括來說，就Paper 1、2而言，71年的AMaths無疑是比67-70年的淺易了一點。
給數學弄得昏亂了？下次繼續吧！
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本帖最後由 Doraemon 於 2007-6-29 07:26 PM 編輯 ]
