1965-03-24 — Page 15

買三第四集

日二廿月二年巴乙岁

KIU YAT PO

# A

日四廿月三年五六九一腚公年四十五國民中

19659文中會時試題預習專利:1965年度

數學科 (十六)

模擬會攷試題(乙級數學試卷二)

喬仲強。

(試題分甲乙两部甲部四題全做,乙部選做四题,合共

八題完拳:作图題要寫出作法不须却明,保留作)

(4)三角形两边不等

1. PM

証大边上高线,小於小过上之高线

由等腰三角形底边上任一奌,至两腰作=讖线之和為一常量即 等於其一腰上之高

210)作一同心國弧分の豆知扇形毒=等積部分

(在三角形春上向形外作正三角形則此無稠正角市立外接

园共奌

3(a)ER DABCT

a=7.64.

C=843, <C= 63°30′

1/2 acco= m + I see + tan ☺ = m

nees- tang 2 1 2 19 ?

5 SABC 20§H, $~ŽO, ODLOC, E

AH— 200

(b) The old man worked Hard for a living

中学入学試

(c) The cobbler has sented my shoes,

英文科

(十六)

姚述要

TEST 16

Zine allowed 25 minutes.

Complete the word on the right. The first and last letters are already

put in.

(a) person who shows the way.

(b) The son of one's brother or sister

(b)

(c)"A place where monay is kept

(0)

(d) A person who makes and sells bread

(a) Strong wind that blows in Hong Kong during summer(e)

2. Write one word instead or the words underlined

(a) The story came to an end.

(b). They answered all at the same time, (0) Mr. Lee is a man whose wife le de

..(b). (c) (4)

(e) I shall do it before long,

(herself, hers, her)

6. 8 11 2 1 47 44 £ - 31 ( ♬ 4 1 2 3 £<): q#4,9}a#

趾必典园等距.

7 mənə + on2 = 2 (KLIK 168113).

+ cse A+ cot A

cac A + cot A-/

•...... (d) He visits her every zeek,

3. Choose the best work from the bracket to fill in the 'Dimia, or

santande

(a) She finished the work

(b) is the

o idea is pr secret details pla sink

(d) You should take care of

I spoke. (who, whon, that){

la very silly. (you, yourself, yours?

4. A word has been miseed out at X. Write the word in the space.

天遇图上一定要求作一

8 =

7 $145

Acre Aoot A

cut A - CAGAT

***

-(e) To kill

(aine, I me) (yourself, you, hey

(4) My teacher punishes the papile every day

(#) Every-one must not stax) things

10. In each line underline the ward which has the same and sound sa

the word on the left. Be careful to choose for somand

(a) 011

(b) Last

(c) Date

(d) Bri

voice / Join / show / John / boil

dust/ fast / basket / best / fizet may / vay / paid / rat/ mats.

fight / write / mice / side / kind › ⇓ win / won / tongue/month / funny

Read the following carefully ›

It was summer.

The sun was shining brightly on the lake a very beautiful lake, and it looked prettiest of all when the shone on it, making all the little wavon shine like silver..

On the bank of the lake there were some tall plants, a. brautiful

among theas planta a mother-duck built her nest,

she had sade the Best, almost ready for her eggs. åfter a few nest quite ready; and she laid her egg). She laid five white aggi

in the nest.

-TOTUFARA

Then she went for a little walk. Sook/she

to her nest to look again at her beautiful shining white eggs. *Such nice eggs!" she said. "After a very short time I shall see. five beautiful ducklings (young ducks) come out of thim.” How read these sentences.

you think is right.

Bach has four parta, Underline the one

The first one is done for you.)

(a) It was

ok al css3 GABC2

(b-c) cot £+ (cwa) cat & + (a_b) cot £

71 41 7 4 ¥ » 23

4.三园的半福分别需4吋,4吋5吋,两两外切,求其中間平圍成之

面積

第十五次試題解答!

1.(2)求準確至小數後第五位:

11200

1189.

11.00

343 1025

7100

3462

(15+1)*

12

Q

334647008|27 2 12 8 0 14

MAX=323 205 (X)

(4) 32 124 — 0.4836 af 1 of =2140/2* i data/j

圧力な若干谷/平古屋東

(解)

-3695 × 0.4636

0191公斤/厘米

LOG

36.98 |1.8L L4

0,4836 7,666)

3.540 0.4048] 0.8096

2(2)甲於主哩競賽中,可勝220碼兩膝的30碼,問在女哩蔬

賽中,乙可媵两若干碼?

解)乙、丙二人速度比=(880-20):(880-30)=86:85

#2 22 440 28 Mazzab(

*ZTIAK 420-43423 —£735 (%)

(H)一直用錐体帳幕,其底面積美160万呎,共容量為400立方尺 求此帳墓之表面積,

MOUSELA¥182]

創百=160

*#*

表面積。

600

NO

160

LOG

KO 404

0.49711-713309536,

3,204/

य

1970 2012 1832 211245 2126 33771

建(低)解方程式; x+b.

(AR) $§¥À (±±2§-a)+(x+2 € - 8} + (x2) + 0) = 0

Latteghetti + zxca-af the,

$25

(HW)

(x+be+carab) ( +c+ ac + ate)

-ab=0,

T-C

ast

(b) ¥R__x=a(d−c), y== $p-a).

(BE) @ Z=t»c, 4.

· *+*+2=(+-c)+(c-a)+ (a−b)—s

(4)+(4)+(4) − 3(2)(4)(4)

• (− + ‡ • ‹ ) (â + † • † - Z-R-2) =

(x)‍+(-4)+(3) == 32

(答)

試任

QE

4描繪y=242图线(X文值由--丸至+4),再拍同图中给出

2x+y8.直线,試证其交真舳適合ax-jx+2=0 求此

(清)洗製成不到的,分别描桌,

(a) · She told us al) X her journey to Europe,

(b) Ee wants to travel X. the world.

(a) (b)

(c) The old man talked foolishly. They 11 laughed

I him.

(*)

(0)

(4), 2 sha11) ba bagk X Five ninten

(e) She wants to borrow some money i ne?

090

5. The word on the right should be so the sentence. Put a mark / _32_show,

where it should be placed

(*) The servant jumped into the river wave his master. (10)

(b) The baby sixed because it was afraid the dark, (of)

(c) She went into room to dress herself, (the)

(8) This is the place the pirates buried the adney, (where), (*) The carpenter made wooden chair), (a)

6, unange all, tai plurejs into singulare adó naka

in the polloving sentences s

(a) The children brought the loaves into the kitchens.

(b) The policemen ran after the thieves,

[(a) The women have pain in their teeth,

(4) There are cinemas

in the towns,

(*) The children thought that their toys were broken, í

Underlins the right word in the brackets in each of the following »

(a) The day (threw, through), a stone into the river),

laty for the wxamination” läst year.

(c) The aan (rode, rowed, road) the boat across the river.

(d) To (limp. limb) means to walk lanely.

(e) They did not (let, may, oan) kia join in thɗir gone,

-BP£13 in much of the FOLLOWING DINNER WAWA UKE OF FAgue words, sy

often, just, ever, early, never, ((a): Have you

been in England? having a good rest.'

(0) The old WOMAD

(d) to bare

(-) John

fall down.3.

LIBRA

been in England. goes down into the we11.

Change the following sentences into questione s

દર માં ન મ ય - ક

-2-1

23

14 23 22 23 24

(1) spring

(11) Bummer

(iv) winter.

(115) Kutumn.

makes all the little wases shine likel

(b) The

(1) gold.

(111) iron,

The mothar duck was building

(1) a big house. (111) a nest.

(a) The mother-duck laid

(1) five ducklings. (111) Five #gge.

(a). After she had laid eggs

(1) she stayed in the nest. (141) she looked at the eggs.

(f) The colour of the eggs wae

(1) yellow,

(111) grey..

(11) silver.

(17) Copper,

„11) a small hut.}

(iv) a road.

(tv) four egg 1

(11), went for a walk?". (tv) she quacked loudlyg.

[[:517- beautifully white,

(iv) brown

112, F11) in the blanks with quitable corda

(a) Knife is to cut as suh ta to

(b) Gone th to go as

fo) is to se as you is to

(d) Six is to sixty as five is to

(*) Tooth la to teeth as

ia, to ride,

18: to

Angrers to Test 15:

(a) cloudy, (b) pesosful, (c) foolish, (4) muddy, (e) useful.

2. (a) festivala, (b) drinks, (0) metals, (d) alothing,(e) building,

3. (a) through, (b) to,(a) on, (d) to, (*),with/ again

belonging to, (2) or, (h) st, (1) with, (3) on, art.

his, it. I, he, you, I; their

Se(a) You must take care of yourselvas,

(b) They like the bábisa.

(c) We were singing songs•

(a) The children drink mäik.

(=) The policemen caught the thievon,

(a) sha12 sall, (b) gel, (0) vent, (d) have written, (*) wil),

BITĪTA.

7. (a) (8), (b) (5), (e) (7), (d) (2), (e) {9), (8) (2).

6. (a) daar, (b) safe, (c) wild", (4) rough; (*) beat.

9. (a) before, (b) until, (c) although, (d) how, (e) whorner,

10. (a) 3. disobedient to her husband, (b) 3. to get some advice to deal

with his wife, (c) 1, to go to a bridge," (d) 3, he beat it very hard, (e) 2, he beat her

(=) y =

設

X 7 +2

2 4

(22)

*^* 6(14-x)=2(4~x) (x+11)

化簡得28-7元

***** 2x2=7x+2=0 z tk, 由固中得交真之橫坐標!x=0.31或3.19()

5.有甲乙两三人,解數學題時甲平均每5題触解4题,乙每10題 黏解了題,两每5題能解4題今有數學題150,甲乙丙三人 分别解之,問三人能同時解答之題目,最少有多少?

(解) 先列右表, 解釋較易明白能解答題數 不能解題數 由右表可知而不能解答題最多 甲150×4=1H20 故着甲乙二人听不能解之题均在乙 150x1=135

70

雨呀不能解答題中則三人能同丙150=140 30 時解答之題數為120.(注意此為最大值)

但希甲乙二人好不能解之题,若均在丙岈能解答之题内,則三 人不能同時解答ż超數增至130+15+10=$5,而触解答之息 高150-6=5, 此葛最小值!

答:三人能同時解答之題 数最少為然

6.有歇一宗,以年利率5%計算,則3年後每半年三结之複利息較

颦利息多北元,間此宗疑額為差千元?

(解)設本金1元,則3年後=複利息為

} /× (1+25%) =|= 1,015=1=0,16

15THL W 6% x 3 = 0.157

NO LOG

44.0.25

0:0107

1.160 0.06421

故本金為35元+(0.16-0.15)3500元(答))

(更正)上次登試題時漏去“3年後,合割明

7. Mõ$ [x+6=C +√x+

(解)移項!

自来

G-a c

2-21+3

a+b

alba) (-a)

a+b

att

9.解方程式

(AB) 74 ×x; #1-A

談

b (a+b)=a(a+b)

ab(b-a)

ab-f

(a+b) (b=a) ab(b-a).

(M£i) x& a, b = 884«4»A.

6(x2+ £) +25 (x − Z )+12=0

y = x + -

2)+25y+12=0 &q by2+z6y+24=

(2y+3) (34+8)=

2x-2=-3x

(@A} (3x-1)(x+2)=0]

y=

3x+8x-3=0

(3x-1) (x+3)=0

(註)本題為負倒數方程式,亦可利用因子定理分解法解之

[10, ¥ ax2+28x+ c = 0 ± m *& ZAK, HIE ·

ax2+2(a+b)x+a+2b+c=0 2 @ * * * Ak. (30) ® ax+abx+c=02@ # $ /K *‡*N*

D= (28)-4ac = • 4 (f−ac) * 31 K & tracko,

#Lax2+2(a+b)x+(a+2b+c)=0 ≥ 1/

D'=[2(a+b)]" ~4a{a+2b+c)=4(a+zab+b2)=4(a*+zabrac)

=4(b-ac) <0 故其根亦為虛數: Q. E. D

x+a-c+c-a-2{(0-0) (x+a−c)=0−6. +4-C-2/1c-8)(x+B-C '17. a, b, c, d, e, f I &* 4*, ** (+=2)===

{{c=a]{x+8=c)=== | (c—b)(x+b+c),

依和比是理各比的等冷!

'(C-a)x~(2~R)":

• = (<=4) x ~ (c-b3

() @ 2-4-1

tk (bad)

a-c

x=2c-a-b

(c-a-c + b) x=(c=a+c=f) (c¬a=c+b)

X=20-R-

此值验算後知為真棍

RARY

(G. E. D]

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