賞四第張九第日六廿月十年未已廢里
1980
WAH KIU YAT PO
3.(a)
中學會考試題預習專欄
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3tanx
E
3sinx
4+2Becx
2
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4+
COBX
COBX
= -2
附加數
Additional Mathematics (10)
C.Y. Shum
(Mill & Dale Press Ltd)
-Solutions-to-Exercise~ 5
1,(8) L.I.S.
世
=
+
Binx siny+sinz
sin(x+y+z)
(sinx+siny)+ {sinz-sin(x+y+z}]
2sin.cos -
2cos++**.sin+y
28in
[enskz - osx+y+2z
2sin
[-2sin2x+2z sin-2y-2z3
4sinsinsiniz
45
- A.H.S.
2
cos2x+cos2y+cos2z+1
(b) L.H.S.
20082x+2cosx-2y+
*
cos2[180°-(x+y)] +1
(since x+y+z =180°) 2cos(x+y)cos(x−y) + cos2(x+y) +1
2cos(x+y)cos(x=y) +
2
2cos(x+y)=1+1 2cos(x+y) •
[cos(x-y)+cos(x+y)]
2cos(x+y)[2cosxcosy]
4coa(180°-z)cosxcosy
= -4C08XCOsycosz
- R.N.S.
(c) L.H.S.
***
=
2
2y+coa2z
COB X+C0By+cos z
*(1+cos2x)+4(1+cos2y)+
*(1+co82%)
2+(ca82x+co82y+co52%)
+4[-4COSICOBYCOSZ]
(from (b) part)
- 1-2cosxcnaycosz - R.H.S.
2.(a) 2sinxcos"x-sin ̋x-1
2
2
2
2ginx(1-gin x)+sin2x−1 = 0
12 2sinx-2 in x-sin-x-1 - 0
2sin x-in x-2sinx+1 - 0
232
-2x+1 = 0, where where y Binx: (y-1)(y+1)(2y-1) - 0
y = 1, -1 or
i.e. sinx - 1 - x
(b) 2xin"x
sinx = −1 - x
90°
270°
ginx -
- 30
150
30°, 90°, 15°.
铀
270°.
22in2x-cosx-1
2
✡) *
(Ans.)
2(1-cos^x)-c08x-1 - 0 {cosx-1){cosx+1)
COAX
or COAX
-1
ད་
0
60a,
300°
180°,
X 60°, 180°, 300°
(c) tan x-ta
(Ans.)
nn2x-tanx+/3 - /3tańx tan"x-tanx+/3-/3taox
tanz(tanx-1) – {tanx−1)(tabx-5)
tanx
or tan I
X
=
•
+
0
- ป
1 x - 45° or
225*
R
√3 x
60°
or 240°
45°, 60°, 2250
and 240°
(ADP.)
3sinx =4008x+2 4coax-3sinx
報日僑
六期星
(sin2x+sin4x) 0
2eos2xcosx-2вin3xcosx = 0 E68X(C03LX sin3x) = { .". cosx ≈ 0 ⇒ x. = 90°
or 270" or cos2x sin3x i.e. sin(90°-2x) = gin3x .*. 90°-2x 3x + x = 18"
18°, 90°, 270°.
(Ans.)
1980
中學會考試題預-習專欄-
cashcosx-gindsinx = -
.". cos(+x)
i.e. cos(36°52′+x) = -0.4
where tan() = 36°52′
= -0.4
.*. 36°52′+x = 113°35' or
246°25'
x =
76°43' or 209°33′
(b)
(c)
18
/2
烹
ایم کی
/3coax = 12-Binx
/6cosx 1-/2sinx
/6cosx+/2sinx 1
1
(Ans.)
cosdeosr+sin@sinx = 0.3535 0.3535
Cos(x-9)
-
'. cos(x−30°) = 0.3535 where 8 - tan*1(2)
*
300
76
.*. x-30° = 69°18′ or
290°42'
*
I 99°18′ or 320°42'.
(Ann.)
1
COSX 2sinx-1-
-1 cosx-2sinh m
inx w
Acosx-sin
-75
CosÜcosx-Rinėsini
-0.4472
cos(x+63°26′)=-0.4472
where extan()
-63°26'
.*. x+63°26!
116*34** 243°26'
or
53°8′ or 180°
(Ans.).
4.(a) sin3x-ainkz+sin5x = 0 nin3x+sin5x-sinhx » 0
2sin(3x+5x)cos(x-5)
ein4x= 0
2sinixcos(-x)-
OF
sin4x = 0
sin4x(2cosx-1)
sin4x = 0
360°, 720°, 1080°, 1440°.
x = un, 900, 1800,
270°, 360°;
COBX
$
→ *
I
*
60°,, 300°.
0°, 60°, 90°, 180°, 270°, 500", 360°
(Ans.)
(a) cow cosx+cosJ
0 - 0 (conx+con3x)+cos2x 2cos2xconx+cos2x = 0 coa2x(2cosx+1) 0.
cos2x 0
→ 2x-
OF COSX
-
#
**
20
90°.
270° 45°. 135*
120°
or 240°
450, 1200.
240"
135°, (Ans.)
(c) coax-sin¤x+coaïx-sink x =0
(cosx+cos5x)-
歷史
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History (10)
Philip Y, L. Woo
(Mill & Dale Press Ltd)
Some thoughts on the causes of the First World War
When you are told to explain why a war broke out, either there were factors that made nations declare war on one another (even though the nations did not want war), or there were war-like nations which deliberately made war. Most nations, however, said that when making war, they were forced to do so, either to defend themselves against what they believed was the aggression of other nations, or to prevent other nations from making war first (so it was necessary to take offen- sives before other nations did). One way or another, all nations fought wars because they felt they had to for the sake of defending their self-interests. There were no "good" nations or "bad" countries. There were,
and are, in Cantonese movies but not in history. If viewed from the standpoint of a
country, every war that the
country fought was a just,
necessary and holy war, just
as every war that your enemy
country fought was an
aggressive, unjust war..
The First World War
(1914-18) was one example. There were long-term factors that made war increasingly likely before 1914. These factors, such as militarism, nationalism, imperialism or the Alliance System, could not alone bring about the war. Nor did they collectively. Otherwise why was there not a First World War in 1913, or 1912, or 1911, when these long-term factors or causes were also present? It was man who made war, and no emperor ör statesman could say, after making war, "Well, I did so because I was forced to do, so by the factors of nationalism and militarism and so on.
"
It was during the summer of 1914, when the European great powers reacted to one another's moves in diplomacy, that the First World War broke out. Because it was the total of all the great powers' reactions and diplomatic actions that explained the outbreak of the war, they were the immediate causes. They were like the trigger of a gun that makes the gun fire. There are bullets, just as there were the long-term, underlying factors, "but without the trigger, just as without the immédiate causes, the gun cannot be fired, just as the war which could not have broken out.
日五十月二十年九七九一滕公年八十六國民中 有教僑量
As each of the great
powers contributed to the out- break of the First World War
by the diplomatic steps that it took, they had each their share of responsibility for the war. This is why you are so often asked to discuss the responsibilities of the great powers for the war in examination, which is in fact concerned with the immediate causes of the war.
To make things simple, the causes (or origins) of the First World War can be
11
analysed in two ways. Some people ask "What caused it? and concentrate on searching for the long-term factors before 1914. Other people ask "Who brought about it?" and concentrate on finding out the responsibilities of the great, powers for bringing about the war in the summer of
1914. Without the pre-1914 long-term causes, the great powers would not have been in conflict with one another as they were in 1914. There- fore they would not have reacted to one another's actions so aggressively and would not have led all Europe to war. However, the same can be said conversely: without the 1914 diplomatic actions made by the great powers who each had their responsibility for the war, the First World War would not have broken out in 1914 and peace might have continued even though the long-term, underlying causes were still there in European history. It all depends on
how you look at the problem.
1980
中學會考試題預習專欄
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Economics (10)
K.K. Wong & L. T. Chan (Mill & Dale Press Ltd)
LOCATION OF INDUSTRY Questions
1. What are the main
determinants of the location of light industries in Hong Kong ?
The main determinants
of the location of light industries in Hong Kong are as follows:
:
(1) Avalability of labour is critical to light industries which are mostly labour- intensive. Thus, light industries tend to be located near population centres, e. g. light industries in. Kwun Tong, Cheung Sha Wan.
(2) Water supply, the second determinant, is important
to those light industries which require a large amount of water, e.g. dyeing, laundry, brèwing and chemical industries. (9) The third factor is power which is essential to practically all industries. (4) The fourth determinant is external economies. The dyeing and garment manufacturing firms as well as new textile firms tend to be set in Tsuen Wan for the sake of external economies. (5) The firth factor is land value. The rising land
prices actually force certain industrialists to locate their
industrial sites in less developed areas,
(6) The sixth determinant is transport, and developed transport enables firms to set up their factories away from population centrés.
(7) Another factor is government measures such the setting up of Industrial Estates Provisional Authority, the planned development zones for
industry, e.g. Shatin, Castle Peak etc., the prohibition of certain industries in certain areas to prevent pollution, e. g. the removal of tannery to Kwai Chung, and the assigning of land for special projects.
2. What are the main
determinants of the location of heavy industries in Hong Kong ?
The main heavy industrie in Hong Kong are as follows machinery and machine tools industry, shipbuilding and repair industry, and * aircraft engineering industry These industries are usually localized in certain areas in Hong Kong. The following are the main determinants of their locations: (1) Availability of land:
This is an important factor in determining the location of shipbuilding and repair industry, which requires a large area of lar site for carrying out the production of shipbuilding
and repair. The same.
reason holds true for the
aircraft engineering industry
although this is not the mani factor.
(2) Price of land site:
In connection with the
supply of land, the price of land is also of equal
importance. Heavy industry tends to locate at places wi
rent is relatively cheap or: price of land is lower. This is mainly because land-intensive heavy industr usually seeks a site of low land cost so as to minimizė, its production costs. (3) Nearness to market: The products of the machinery and machine tools industry provides useful support to other local industries as well as
contributing to Hong Kong' export trade. Thus some manufacturing firms of the machinery and machine tool industry are located near the centre of local light industri such as Kwun Tong, Tsuen Wan, etc. The same holds. for the aircraft engineering. industry which is located just nearby the Kai Tak Airport where the inflow and outflow of international flights take place.
(4) Government policy: In Hong Kong, the Government determines the location of shipbuilding and repair industry by granting land release to the firms of the industry at a lower pric and in restricted areas. One can find that most shipbuild ing and repair firms are located in Tsing Yi Island because the Government has, the intention to put all those firms together, so that the regulation of them can be made easier, such as dealit with the pollution problems,