報日橋茶 五期星日十二月一十年〇七九一瑟公年九十五國民華中 育教偊華
真二第五第日二十月十年戌庚曆夏 WAH KIU YAT PO
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1971 中學入學試試題預習專欄
1971 英文中學會考試題預習專欄
智睦出板牯主編
新光出版社主編 SUNLIGHT
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數學科(四)
歷史科 (四)
最大公約數及最小公倍数
(一)茶歡间時兩個或兩個以上於數的彩數,某數就是這些歡的公約數(秦因數)。所有公 豹數中,其數侦好大者,畔形大公共數(HCF)。求多大小然數的方法有三:
甲、分解因數法:先把谷歌分成質因數連城式,然後憲出备數中相同的因數,環在們溫兩起來 廚得心微优虽有大公約數。
36-54278H.C.F.
(RE) 36-2x2x3x3
42-2×3×7:
78-23 x 13,
相同的因數2
所3642278的表大公約數:
12x3-6
Z BMAKER:ÆRGENCY KEYAK › HESKYE · ÉRZNY 直至去中兴有公歙存在為止。居後把所有丛於數霋起來,就得液大公約數。
電
(B)
1834 54H.C F.
2) 18 › 35 51...
9 18
6.
F1183654NGAMEL:
2x3x3-18
不是它們的公然數
它們辦公
1是它們的公約數
沒有公煎數
A TUTAE,SHENKIJAKÄNT RE-OK › FRAKENNEAGR 二個職,燕用第二個家數去焱第一個數,如形者極轉相除,餘歌為禁止。及後那個榮(就是 多大公約數。如果求三個數的5大公約數,要先求得其中任何兩個的激大公約數。用這個大公 的歌端第三個長轉相除,求出另一個長大公約數,這個新的要大公約數,使是三個數的派大公約
"(RA)
R$23391MH.C.F.
3.2.3 391
2721-323-
501) -68
5.1. 51
17
#71:1323 · 29165EXANDE :17
(二)撤禸特里兩個或兩個以上的數的倍數,其數就是這些數的倍數。换言之,一個數可 我國時被幾個整數除時,則該被除數就是各除數的公倍數。所有公倍數中最小的一個,就四販形水 公倍數(L.C+M.)。公倍數是沒有浸大的,因爲任何一級數的公信數有無期個,春小公倍數 的方法有三:
甲、分解因數法:先把各數分解或贊因謝跳式,再找出各趣乘式中揭一個質因數,把它們說
樣本,就心浱小公倍數。
$ 18 20 + 30# L
(8) 18-2×3×3
20-2×2×5
302×3×S
断(18,20,30的米小公倍數量
2x3x3x5x2-180
乙,推出的數:先用各數的質因數去除各數,得各商數,其用它們的質均數除之 無數出有公約數為止。差欲把至部質因數視海數我乘起來,使為怎小公倍數。
(HB)
90 15:21 33 -1.C.M.
390 15 21 33
5 30 5 711
7 11
所以90,15,21,33的忎小公倍數: 3x5x6x7x11-6930
先用轉泪系⺾出阴的EC.F.然後將H.CF
911903 » 224905 L ·
(R) 51903;2249)
1750:1903
173346-2
346
7.1903224984CC.ME
1903 +173 x 2249 - 24739
3是各數的公的世
5-12.30 15 1ÍZDE
(三)類類動的應用類要先了解想寫,所求是R...還是LC.M. 甜新六豆除飯: 難屬於H.C.F類,如所求是被除數,則變於RL.C.M滅。RH CF時,需要先 不足要先加,然後將所得的歡求H-C.F.,但示L.C.M.時,將求得的數後,有能要加,不足要
藏。現舉例說明之。
除142不足2,除254鈐2,問業數表大惠多少!
(**) *AME 142+ (Y) - TE
(RE):
FRATERN
254+ () -2
-142420144 (沒有不足)
254-2-252 CRAWFO!!
#144 252 RH-CF DREK 36
答:表數笺大是36
144232, RS27
144909 FM:43
WER 42+ 2-44
辣智題四
還出正確的答案,用船在右方海當的小格內滿卻
A5的倍數B5的因數
A1. 10-15 20254
D5的最大公約數
B:5的激小公款
TE
carrying through the army reforms
collecting the increased taxes with parliament's consent
R dissolving the Prussian parliament
S the combination of Q and R.
I the combination of Q and P-
Bismarck's first achievement in foreign policy was the con solidation of
at the expense of Poland Bismarck supported the idea of brutal suppression of the Polish revolt in 1863.
Q. Franco-Prussian friendship R. Russo-Prussian friendship
of
S. Italian-Prussian friendship.
T Turkish-Prussian friendship
10. Bismarck believed that Germany could be united only by means
and the experience of the great French Revolution (1789) showed that he was righ
P. Austro-Prussian friendship
HISTORY
1-1970.
LESSON FOUK
Suggested answers to Exercise 3
6.P
11B
16. R.
2. E
7 R
12. A
3. A
8. S
13. D.
18. P
4. E
9 R
14 C. 15 E
197 20. T
EUROPE
Topic Two Nationalist movements in Germany Italy and the
Balkans in the second half of the neteenth century
The obstacles to any form of Germany national unification.
were
A the difficult choice between an "Austrian Germany
a Prussian Germany***
B than other powers would interfere because a powerful në Germany u the centre of Europe was a potential enemy
the questions whether Austria was willing and whether
Austria could be detached from the Habsbury monarchy
to join the new Germany at all
D the combination of A änd C
E the combination of A, Band.
In 1850, war between Austra and Prussia was narrowly avoided over the issue of Hesse (à member-state of the German Con federation) Prussia yielded to Austria by signing the Such a diplomatic defeat and loss of "face" for Prussia herefore precipitated a war of revenge against Austria
A. Peace of Prague-
3. Olmutz Agreement
C. Congress of Berlin
D Convention of Gastein, E Alvensleben Convention
Meanwhile, reaction was triumphant Austria maintained her supremacy in 1851, the old German Confederation was revived Liberal constitutions gained in 1848-1850 were revised or abolished by reactionary rulers un
A Prussia, and Hanover
B. Mecklenbery and Saxony
C. Bavaria
D the combination of B and. C
E the combination of A and B
The nations which were most opposed to the idea of German unity were
A Spain and England.
B France and Russia.
C England and Belgium.
D Denmark and Italy
·E Italy and England
What event was responsible for stimulating the Germans" d'estre
of national unity in 1860-18619..
A. industrial boom in Germany B. the accession of William I to-
the Prussian throne
C. Italian success at unification.
D French assistance iz states
whihc sought national unification
E Prussian military reforms
The German Liberals' efforts at leading the liberal and national
cause failed chiefly because
Pthey feared republicanism.
Q they were chiefly lawyers.
R: they were afraid of the masses.
S. they suffered from religious differences.
T. they put too much faith and confidence in principles
without real power
Which statement does NOT hold true for King William (becoming king in 1861)?:
P. His interest was in the Prussian army
Q. He had Roon as his Minister of War
R. He witnessed the Prussian unification of Germany
3. He was a true Liberal
THe appointed Bismarck Minister President.
The cuase of the Liberals was soon discredited by Bismarck He successfully steered through the Prussian political crisis (1862) in which the parliament had refused to accept Roon' expanding military expenditure Bismarck gave a death-blow to the Liberals by
E39
360
E 17C 18
13,用7,16或35去系茶數,其数诗儒4,然被除数展小是多少?
561 B: 278
1124 C328
14,164,172的帶小公倍數和最大公約數的和是多少! 7052 4028 C 7056 D 8642
P. civil war
Austrian co-operation R. foreign war
5. terrorism
principles of liberty, equality and fraternity
The so-called Schleswig-Holstein question proved to be the Second success of Bismarck's foreign policy It is doubtful however, whether Bismarck had really foreseen this question (like a prophet) as a future cause of war with Austria. Nevertheless, Bismarck did secure initial co-operation with Austria by commonly fighting
Belgium.
Denmark.
Piedmont
D. France E England,
By intervening in the Schleswig-Holstein issue, Bismarck also
"A" hoped to challenge Cavour's. success.
Brevealed Austria's weakness.
Cumpressed Russia of Prussia's military strength.
D tried to scare England away from Europe.
E. created the impression totthe smaller German states that
Prussia was eager to serve the national cause.
13, The Schleswig-Holstein question soon provided Prussia with.
a casus belli to fight Austria. Before going to war, Bismarck made sure that Prussia got French neutrality the military alliance of Italy, Russian consent. British indifference. and Austrian isolation. The battle of story of Prussia's victory,
A. Jena
B. Metz
C Solferino,
**** Completed the
D. Sadowa E. Magenta
14 Bismarck was careful not to make Austrai too angry on her
defeat However Austria was forced to transfer her rights
in Schleswig-Holstein to Prussia, to agree to the dissolution of the German Confederation and the formation of a new or- ganization of Germany without the participation of Austria", The result was that the new organization formed was the
D.North German Confederation. E; Zollverein:"
A. Bundestag.
B. Bundesrat
C. Reichstag.
15 On Prussia's victory, the French Emperor Napoleon III demanded
the territory on the left bank of the Rhine as "compensation" for previous French neutrality in the 1866 war Such a demand greatly alarmed T and threw into military alliance with Prussia
A. Luxemburg
B. the south German states C. Austria
D. Austria
E the North German Con-
federation
Bismarck calculated that German unification would not be completed until after a full-scale German war against France France, however, soon fell into such a trap" through her folly in the in the
se
P Mexican Adventure
Q. Fete Napoleon
R. Spanish Succession issue
S. Dreyfus Affair
Panama scandal
17 The conventional interpretation of the Franco-Prussian War
is that the unmediate cause leading to its outbreak was
P the French ambassador's attempt to secure King William I's
guarantee over the Spanish Succession issue.
Q the Ems Telegram-
R. Napoleon [fl's attempt to annex Belgium and Luxemburg
binge frustrated.
Napoleon's list for national glory. --
T Bismarck's contempt for French military weakness.
The political union of Germany by Prussian military strength was finally achieved when King William I was proclaimed. Kaiser William 1 in 1871 at the French city-of
P Marseilles
Q Rouen
R. Rheims
S Paris.
Versaille
24; HEM=23; 1502 • ##200724) BIKEFALE
68或9除苿數都剛好除暴,間某數爆小是少皇
BABODE
23. 某贩去除蜘
A B C D E
ABCDE
2. 168 2529EKANKE
A 12 B 21
ABCDE
E 5782
ABCDE
□□□□□
3,下列三個數中,哪一個是105及175的海
B105
ABCDE
15,有甲乙丙三號,甲5分鐘呢一次
錄呢一次,今三藏濟嗯,問膠
乙每8分鐘鳴
一個數5去除
4. Tänake » - £30 › 24E60§§H C-F.
A 10.
- A:20分鐘:B30分鐘
D452
ABCDE P□□□□
E25分鐘
ABCDE
15. MOOIE
B
1厅4面和2斤的教大公約數是: A 2
ABCDE
P 900 Q958
26、2860的小公倍數共多少!
P 5460 Q 5040 R
下列三個數中,有數是70,15
P861 Q-420
5064
傘,在1000以內,5135及60的湿大公借异
16.
::
下列佳話結果,並在指定的零位上作鉴
24 120 » 723AKES
5406
5046
FQRST
A17 -
12NE
R 860
340
PQRST
A18. RUSSIER12014
R 420
1000
3斤6*24面的界小公告形多
19. 3:1205567MH.C.F
12的公告中,那一個是7的海小倍數!
用一個最大的除數決跳30號2,去除12期不足2.未然
29.以英數去除100欠5,去除40期第5,承載數(長大儒若干。
A30,来阴數的老大小約是5,最小公倍是30,若該復數不
QHEMEHE
注:凡謂次之前有「心」號者,均為近年來中學入學冥之日。
E.327JEAN J
108Q 180/7
斤12間
5 GTBEN
TOTA
PQRST
辣蟹
三答案
A10. XSAR
一次。兩人今天首次在公園
20. 36, 510LNL.C.M..
(2) BE
(3) E
(4):0
(5) B
( 6 ) P
(7):8.
C8) P
(10) R
相遇、門營難天,他們方廠第三次在公司
(12) B
(13) E
(14) E
(15) A
·天
24*
PQRST
2:有一個畋,同時態整除36,66,問這個數要大气参数列
(17) 2×3×5x7x9
(18) 294.
(19):25.
都不足4,問某數愛大是多少
(25) 36
203145 (26) 20FL
(22) 27
(23) 15
(24) 48
·6277128,
(28)97
-(-29.) 3
ASB10 C15D
E25
ABCDE
22.汐茶數141181,均不足3,問某歡表大是金
(30)
12.茶数除211不足10,除491余10,其數量大
《本糖逢星期一、三、五刊出街)