1973-04-02 — Page 27

MEFERENCE LIBRAPY-

#82 =R-d, a Ratd.

£4

(a-d)+ a +(a+d)=15-

2 APR 1973

育數量 頁三第腿七第日九廿月二年丑癸醫夏

LE CITY HALLE

報日橋

罗兰

उस

138)

4.三數成等差級數,其和為15,其平方

*和為83 求此數

1978

中文中萬會考試題預習專欄

數學科 (廿三)張正邦

第廿二次預習題解答

(a-d)2+a2+ (a+d) == 83 — (2)

30=15, a=5.

Atλ (3) (5-d)2 + 52 + (5+d)2=83 25-100+de+25+25+100+d2=83. 2d2= 8, d=2R-2

故數為3.5.7 或7.5.3.

求證 a b = 數之等比中項,亦為等差 5.謢a2 63.C2成革差級數,註明 ++

BBQ A. GB H ka, b = $£ +1,

寻比中項及調和中值得

A= a+b G= Jab

H = ab

ab

AH= tx240

ab

a+b

G為A.H之等比中嗅

btc cta atb #k

35 a2, b2 B. C2 & EMB

知

及に成等級皸

13 b2 a2-c2+b2

得

(b+a)(b-a)=((+6) ((-b)

7572 b-a

C+b

[JP) (C+a)

2.三數成調和級數,未記各數減即

以中項之半,其結果成等比級數

3582=abc billet

b-áčb

(2) (3) Q-2

tu

ट

(2)

* (a-3) ((-)

{{{

16.

3. 有四數,首三数成等差級數未四數

成幸比級數第一與第四之 二與第三之和為8.求回數

2 vt a, atd, a+zd

B (a+2d) but q

a+d

::(a+2d)2

at

a+d

= 8

(2)

8-3d

(3)

(a + d)+(a+2d)

由口牌

8-30

+d

4d2+16d-128 =

d+4d - 32 - (d+8)(d-4) = 0

d+8=0.

Ey d-4

d=41tλ(3) a

atd

a+2d

d=-8 d.

+4=2

-2 + 2x4 =

(A+2d)2_ (-2 + 2×4)2

at d

-2+4

4

18.

故所求えや敷為→2,26度18

((+6) ((+a) (6+a) ((+a)

a

(b+c)(c+a)

(a+b) (c+ a)

a-a-b

· (b+c)(c+as (a+b) ((+ a).

c+a

a+b b+c (b+c)((+a) (b+c)(c+a) (a+b)(cta) (a+b)(c+a)

-eta b+c a+b

C+

亦為等

b+C c+a & Q+b 3 差級數

151 112=32 AB. CD SHIK #K

JL B B BJ EA2 + EB2 + EC2 +ED2 等於此圓之直径之平方.

ZAD AB LCD

DOF為直径 EATEB

TEC+ EDDF

BEBA I ABLCD

NACRECT E+EC = Ac2

its BEDP, EBTED = BD2

EA+EBTEC + ED = AC +BD2

4 <FCD=90° (¥QFjj<@@@bhà

5. CDL CF

6. AB //CF (同平行於一直線之語線

平行)

7. Ac=FB (4

8. AC = FB (B

1. ER+EB+ECTED = FB + BD

nts DBF * BD +FB2 = DF2

11. EA+EB+EL+ED2 = OF2

第三次預習題.

Q.E.D.

1.2A為直角,由直△ABC之各邊上向外 101 EO ABED, CBFG, AC HK, EF EF GH BNBL EF2 + GH2=5BC2 2. JEP A D A B C 2 K BCE ZM BP = n CP | m. AB + n Acm. BP

+ n pc2 + (m + n) AP

3.風の直径AB上點P平行 AB CD PC + PD = PP TE

4. SABC 3 BCY $8605 BAZ

外梅回直怪作垂線,並延長之與因

E. WE AAC = 2AE

校平常事告

EKER

·利各盛化期元

鹪是

日二月四年三七九一曆公年二十六國民華中

S. 5

1973英文中學會考試題預習專欄 年

父怒院主編

歷史科 (廿三)

History (23)

Multiple Choice General Revision: Far East History.

17. Which was the main reason why England and Japan signed the Anglo

-Japanese Alliance in 19027-

A. Both of the countries wanted. to stop the influence of the U.S.A. in the Far East..

B. Both needed an ally in case

of war in the Far East:

C. Both considered France as a

threat to their interests in the Far East.

D. Both wanted to partition

China.

E. Both wanted to improve trade

between the two countries.

18. All of the following were the characteristics of the Tung Meng Hui except

P secret society elements. Q. new student leadership. Roverseas Chinese financial

contribution.

S. revolutionary ideology. T. Pan-Asian ideal.

19. Which one of the following was not included in Dr. Sun's revolutionary plan?

P. Overthrow of the Ching.

dynasty.

Q. Establishment of a republ R. Power to be in the hand of

the Han race.

S. Enging of all foreign contro. T. Redistribution of land.

20. During the period 1927-1936 the Kuomintang faced many problems Which of the following did it pursue most actively?qu

P. Land reform to improve the conditions of the poor. peasants.

Extermination of Chinese Communists.

Industrialization to catch

up with the west.

Stopping Japanese aggression:

in China.

Raising China international position by putting an end

to all unequal treaties.

21. Which of the following did not contribute to Yuan Shih Kai's failure to restore the monarchy in 1916?

P. The disloyalty and hostility

of his generals. Opposition from foreign countries.

R. The loss of public support

and confidence. Opposition from the Chinese Communist Party.

After the 1911 revolution monarchism became unaccept- able to the Chinese people. 22. Which of the following countries took immediate action when Japan imposed the 21 demands on China in 1915?.

P. The United States

2. Breat Britain

R. Germany

S. Russia

T France

23. Arrange in chronological order:

R.

Li-Ito Convention

2. Nanking Puppet Govt.

3. Anglo-Japanese Alliance 4. Triple Intervention 5. Shufled Treaty

24. Arrange in chronological order:

1. Long March

2. collapse of the Kiangsi Govt. 3. capture of Chiang Kai-shek

in Sian

northern experition against the warlords.

establishment of the commun-

ist party.

4, 1

5, 4, 1,

R. 5, 4, 2, 3.

I. 4, 2,

25. Which statement is NOT TRUE?

P. Before the Teungli Yamen was

set up, foreign affairs were handled by the Li-Fan-Yuan.

Treaty of Bogue was an

Thement treaty for the

Treaty of Nanking.? Extra-territorility was. introduced by the Treaty of Nanking.

The Margary murder 1876 led to the return to the gun-boat policy.

Foreigners helped the Self- strenthening Movement by sending Chinese students abroad.

26. Which statement is NOT TRUE?

Yuan Shih-kai rose in military power because of his defeat of the Progress- ives in Korea.

The defeat of the Taipings caused the rise of regional military power under Tseng, Li & Tse.

Yuan Shih-kai accepted the Twenty-one Demands because. of the treat of Japanese support to the Kuo-Min-Tang. Hsuan Tung had been Emperor on 3 different occasions. 1. Marshall's mission was to

help the Nationalists to defeat the Communists.

In each of the following questions state which statement in NOT TRUE

a military revolt is called, Mutiny.

B. a seizure of political

power is called Coup d'etat C. the right to vote is called

Franchize.

D. gifts given by vassals to the overlord is called tribute.

3. the situation prevailing

previously is called Balance of power.

28. A. Chian took no active part

in World War I.

30%

The peace settlement for World War I was the Versall -es Conference 1919.

The Washington Conference was called for by U.S.A. to check Japan's expansion. The Four Power Pact was to check naval armament, China regained Hankow, Tientsin & Wei-Hai-Wei from Germany.

Burlingame first started sending Chinese students abroad in 1867.

The Tsungli Yamen was cancelled in 1858. The Maritime Customs Service was set up in 1858. D. China abolished the old

educational system in the Self-strenthening Movement.

E. The Self-strenthening

Movement did not abandon the traditional Chinese moral beliefs.

B.

Germany leased the whole Shatung Peninsular includ- ing Wei-Hai-Wei.

Taiwan was ceded to Japan by the Treaty of Shimonose- ki.

C. Russia gained Liaotung

Peninsula in 1898.

D. Britain's interest was in

the Yantze.

E. France's interest was in

Indo-China.

31. A. The Hundred Days Reform

caused Kuang Hau to became a puppet king.

The failure of the reform caused Republicanism to grow in strength.

Six reformist leaders were executed.

D. Kang Yu-Wei fled to Hong

Kong

E. Tzu Hsi started to support

foreigners.

Answers

QUAWN:

17. B

22. P

27: 0

18. T

23. Q

28. E

19. R

24. S

29. B

20.1Q

25. R

30. A

21. Q

26. T

31. E

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