1981-01-25 — Page 15

人工育教貝三弟張四第日十二月二十年申庚播夏

WAH KIU YAT PO 日僑手

1981

歷史

1981

Argand viagram of cube roots of -81.

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(c) The fourth routs of

-2-2√31

中學會考試題預習專欄

Let z

-2-2√31

16cis(360n+240°)

(+*)

(+)

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[2acis(360n°+240o)]

Add.Maths (16)

where n

0

when n

14402,

2cis600.

when n

1

附加數

C. Y.

Shum

MILL & DALE PRESS LTD.

Solutions to Exercise

,(a) iz2+52-1 - 0

Using the formula for solving quadratic

equations:

-b±√b-4ac

2a

-5±√52-4(1)(−1)"

ஆருர் -ஆறு

-51/21

21 (5±√21)1

(35±√21

24(2)(4)

2(2)

(~3±41) i

Ans.

(a) The fifth roots of unity:

1

1401

cis(360n

360n

cis

cis72n

when

when n

2eis(90n+60°)

when n

where 207

2cis 1500

2,

2cis240°

2(-1)

-1-51 3. 2ci8330°

24-0

and

23.

1222 are the required roots.

Argand Disgram showing the fourth roots.

3. Given z còs9+isinə,

cose-isine

(a)

(2 + 2) 3

+3222+z3 z3+z3+3zē (z+7) On substitution, we have (2ce80)3¬(cos0+isine) 3.

ciso

cis72

0.309+0.9511

when n

2,

cis1440

8cos

-0.80940.5881

when

3:

cia216

-0.809-0.5881

when n

Cox30

cis2889

0.309-0.9511.

and

(b) (z-z)3-

Argund Di

the roots of z5,

roots PATTERfifth

(b) The cube roots of -81

ALSO!

-8i

8(-1)

8cis(360n° 270°)

ci s ( 360n° +

2cis(120n® +90°)

ere when n

when

0, 1, 2.

is90o 042

2cis2100

2(-0.866-0.51) -1-732-1

when n 2,

2eis530o.

» 2(0.866-0.51 );

- 1,732–1

211 22 are the

where

required ro

(cose-isine), 3(1)(2cose)

(as 22-1)

cos30+1sin30+ cos30-isin30+ bcose by De Moivre's Theorem 2cos30+6cosü

4cos 0-3cos8.

Ans.

-387(z-z)

..(2ísine)3 = (cose+isine)}

- (cose-isinə)? −3(1)(2isinə

-8isin Özcos30+isin30-

cos30+isin30–

6sine

=2isin30-6isine

sin30-3sin0-4sin 0 Ans.

5z2Z+10231⁄22.

(z+2)5

10 z2 235 z 2 +z5

5zZ

1022z2 (2+2)

~(cose+isine)5.

(cose-isine)5,

5(1)[(cose. isine)2+(cose+ isine)3]+10(1) 2 (2c0a0)

32coa Oscos50+isin50+

cos50-isin50. 5(cos0+isin3p+ cos30-isin30)+ 20cose. -2cos50+10cos304

20cose

cog50=16cos 0-10cos8-

5co830

-16cos 8-10c080- 5(4cos30-3cose) -16cos30-20cos Dr

5cose.

僱主,亦歌迎爽核棗任何一繃事處聯絡,其地址

)及甩括如下:

一睹·五——二七〇二七六。

CT 香港金箜九十九樂◎大厦地下,一

Ans.

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HISTORY (16).

Philip Y. L. Woo

MILL & DALE PRESS LTD.

In the following, we are going to look at the background of the Second World War (1939-1945). Pernaps many of the topics between the two world wars (1919-1939) you have learnt. But it is one thing to know about these topics (like the rise if Nazism in Germany) and

another thing to be able to relate them to the outbreak of the war itself.

BACKGROUND OF THE SECOND WORLD WAR

1. Defects of the First World

War settlement - Many of the problems facing Europe were still unsolved after the First. World War, such as:

a. Germany felt that she was

unjustly treated by the Versailles peace conference of 1919. When Hitler: claimed to revive German power, many Germans listened to him, expecting that he could undo the

humiliation of 1919,

b. The traditional balance of power between the great powers was destroyed, but a new international order that guaranteed peace was absent. The fall of the Austrian Empire in East Europe was followed by the rise of small, independent but weak states. They could be easily conquered by

agressors, especially when Soviet Russia (which

replaced the fallen Tsarist government of pre-1917)

did not cooperate with the Western powers like France in foreign policy.

c. Before the First World War,

Europeans were often

optimistic about their

culture. After 1919,

because of the harmful

effects of the First World War, they began to become pessimistic about International peace and, above all, to fear the coming of another equally destructive war. Many people of the allies (such as France and Britain) wanted to prevent war at all cost. Dictators like Hitler and Mussolini knew this well, and made good use of the fear to commit aggressions, d. Economies were disrupted by the First World War. This led up to, in part at least, the Great Depression of 1929-30. The Great. Depression had two important effects:

I. It led to the rise of Hitler

in Germany.

ii. Its harmful effects

preoccupied Western powers like France and Britain and made them more and more unable to take positive steps to check agg essions.......

13.

作鵝

心欣仙於生

日期星

日五廿月一年一八九一圈公年十七國民唯中

2. From 1919 to 1929, Europe

slowly recovered from the First World War. But the peace was actually unreal, as later events were to show.

3. From 1930 to 1939, Europe gradually stepped into war. a. After the Great Depression, the allied powers became concerned about their only interests only, rather than cooperating with each other to safeguard peace.

b. Fascist Italy and Nazist

Germany made use of the opportunity to expand their territories.

1. The Italian war against

Abyssinia in 1935.

ii. The German annexation

of Austria in 1938. i. The German threat to Czechoslovakia in 1938-39.

The German threat to Poland in 1939.

At first, the allied powers. (Britain and France) tolerated the aggressions. One of the reasons was tha people felt the Versailles treaty with Germany to be really unjust. The powers hoped to satisfy Germany with gains so that peace could be maintained. Historians call this "appeasement", which means trying to peace. dictators.

d. In the end, in 1939, it

became clear that further appeasement was useless. Thus war broken out

between Germeny and powers like Britain and

France. This marked the

outbreak of the Second World War.

1981

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經濟

(十六)

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「陳勵德

Economics (16)

K. K. Wong & L. T. Chan "MILL & DALE PRESS LTD,

Population:

III: Effects of rapid growth of

population on the society of Hong Kong:

Hong Kong's rapid growth of population since the Second World War has resulted in the following social problems:-

Land and Housing:

Dense population in urban areas has made rent creeping and the supply of houses insufficient. Therefore, overcrowdedness, unhealthy squatters and tenancy.. disputes arise.

b. Health and Environment:

Due to overconcentration of population in urban areas, space for public amenities and medical facilities have long been felt insufficient. Moreover, industrial growth has made many residential and industrial buildings mixed

together. All these result in

五麻加公游

pollution and traffic

congestion,

Social Welfare:

As a result of increasing population, the need for social welfare services arises. Social problems such as crime, drug addiction, family problems, and juvenile delinquency are thus created. IV. Reasons for the population

control in Hong Kong

Population control is Significantly important in Hong Kong for the following

а.

reasons:

On the negative side of population growth, it can be an impediment to economic progress. It poses a heavy burden on the community in the sense that the provision of adequate employment for a growing labour force can be difficult, and that resources for economic development may be diverted to meet the immediate demands of an increasing number of people for basic goods and services, such as foodstuffs, housing, education, medical

care, transportation, etc..

b. As population grows rapidly, per capital income may be reduced. This means that the income earned by each individual falls since the Gross National Product will be shared by a greater population size.

c. Unlike most Asain countries, Hong Kong is characterized by an extreme shortage of natural resources. Population control is necessary to

reduce the growth rate of

demand for foodstuffs and

other necessities,

d. In the past few years, Hong

Kong has experienced a rapid

process of industrilization and becomes an

export-oriented place. But

Inevitably Hong Kong has lost

her comparative advantage in labour-intensive products because of rising wages at

home. The only beneficial way

to maintain her export's

competitiveness in overseas markets is to improve the labour skills and industrial technology. To achieve this, a good human capital must be improved. Thus it is necessary to have adequate. training programmes for the

young generation, while at the same time population control is essential.

e.. In recent years, Hong Kong

has experienced serious Inflation which adds difficulty to her export sector. To curb inflation, one of the effective way is to control the rate of increase of demand for foodstuffs and necessities by keeping down the growth rate of population. f. Population control in Hong

Kong can ease the burden on the government in providing economic, social, and administrative services to the community, thus releasing public funds for the improvement of the economy and assistance to industry.

THREE LO

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