養安群碟
有二第張四第
日三十月正年午丙麽x
WAHKIU YAT PO
九六六年度
中中考試題預習專欄
華僑教育
3)-(1)7
數學科
(五) ̇鰲仲强®
一九六六年度
第四次預習試題解答
英中會考試題預習專欄
(三)由国外一奌作一割线,令全割线為闯外线段之三倍、
化學科 (五)
(巴知)A為口国外已知点
王錦釗
(求作)過ALO因割线ABC而使AC=348
自二月二年六六九一震公羊五十五殖民華中
Hence by substitution in (1), we obta
(解析)設如右: ABc 為求得之割线
A03AD Y DE OC.
則 AD:ADAC:AB=3:1
AAPB & ADC,
£ OCDB3 T
故日奌在以為心吉°C為半径之园周上。
(作法)上联A口交园於E.
品在AD上取工奌使
AD
AD
联AG, AB' 并各延長之
5. AC AC均為昭求:
(証明)與DB.遇口你之平行线使典
AB延线交拎K(遇线外真,可作其丑行线)
2. AADE O A AOR(4底边平行线,截两腮研成之三用形,與原形相似, 3.OK:DB=A&:AD=3:1(相似形對主边) 即OK=308= 08 4K真在0园周上(一点奖园心距離等於半種,則此奌在上》
5.K英重合於c吳(一线典园相交,至多只有两交类)
6. AC: AB= AD AD = 3:1 (184)*}***)
• AC=3AB.
比等於言本題亦可利用切线割线定理,作如下之
【解析)設,如右图過A藥作口园切线AT.
•AB=Xx
*=*=it
Q.E.F
CHEMISTRY (5)
4.1 (a) (1) Ethylene burns in air with the fertation of carbon dioxide
C2 H2 ▼ *ä 102 £• 2 CO2 • 2 Ba O
If there is insufficient air, some carbon will also be -formed which causes the flans to become smoky and luminous,
Ethylene can also be oxidised by atmosobaric oxygen ta form formaldehyde...
Ethylene combines rapidly with chlorine and bromine at room temperatures to form pily Tiquids called ethylene lichloride, Cy H, Cly, "and ethylene dibromideas Cy Hu Bra
C2 H
Br2-C2 H Brz
It will also react with fodine in alcoholic solution forming ethylene di-iodide, C
(111) Ethylens reacts with cold copentrated sulphuric acid, to
form ethyl hydrogen sulphate, C2 its.. HSQLD
C2 H2+ M2 302 H5 HSOL
(iv) Ethylene: combines directly with hydrosen, in the presence
of nickel, at temperatures from 75° to 120°C and also in the presence of platinum black at ordinary temperatures. t for ethane C H
C2H6+ H2O
Q.1 (b). (1) Acetic acid can be converted into sthyl acetate:
esterification with ethanol.
Volume of CH in mixture" Volume of CO in mixtLLTE
Volume of C2 H2 in mixture Volume of N2 is mixture,
2139*35+5+16 x 3).
245 888.
-22.4.x litres at M.T..
Vol. of Oz liberated from 4-9 g
2H80 2(201+16) gms
1. KGIC03
at V.T.P.
-1.344 litres
-litrs at M.T.F.
of kgo required to obtain 1,344 31tres of 02 at N.T.P.
=-434 x
22.4 434 x 0.06
- 26.04-2
Vol of On ldberated from 3.9 ms KC10y at 180°C and 75.cm.kg,
litree
by
CH3COOH + C2 H OH
4.2 (0)
CH3 000 C2 H5 H2
ethyl acetate
463.5+16 -29.5
Acetic acid ethanol
(11) Acetic acid in ethereal solution can be converted into
ethanol by reduction with lithium aluminium hydride, L1H1 H
(from hydride)
(111) Acetic seld can be converted into ethane in three stages.
The scid is first reduced with lithium aluminium hydride to form ethanol as in, (fi) above The ethanol obtained
is treated with excess concentrated sulphuric acid to torm ethylenew
The ethylene may thens hyurage to form etha
2.02
273
1.451
litres
weight of 02 in black copper oxide in mixture
We or D2 in 79.5 of Cù o
wt. di Cu U in the mixture
:45 - 4.2) 89
0.8.
16 p.
79.5.x 0.8
3.975 8.
Thus weight of tu powder originally in mixtrue
(5 - 3.975)
1.025 .
#C2 H5
Hence % of Cu powder originally in mixture.
to combine directly th
C2 Hor
1.025 20.5
x 100
00%
2H2
。
unest lens for next week
【作法】 1.遇A作圆切线 AT..
品以AT為直径作半园:
3在AT上取R要
ARAT
车遇R作:AT之垂线典
丰国交村
S. 以A爲心,AS為半徑作
孤交0园於日及6
6联 AB AB 美廷長之各交口国
7. AC, AC均為那求
(証明)).联 AS TS, AS=AR-AT=AT*
(沈一腰為特运及腰在斜边上射影(比例中項)
2. AB'={AT* (1012) By AT"=3AB*
3. AB AC = AT* = 3AB (切為割线及其团外线段之比例中項)
* AC=3AB
(2)求作一直线垂直於三角形元一边,而平分其周界,
(已知)△ABC (求作)-直线 PQ, 使 PQL BC 而半分三角形 ABC之周界」
(解析)設如團:PQ 经已作出,
作△ABCC角之豪切
并今X,Y,Z弟各论上切类
因由周外一奌至园两
切线等五
CX=CA+AX=CA+AZ
cy=CB+BY=0B+Bz
• CX+CY= CA+C8+AB
#CY={{CA+CB+AB) TM 5
R PC+QC=3(GA+C&+AB)=S.___XL YO F** ** CAFES ME 於T美,则PQITY,故TC:PS=YC:ac.
今梭 TC=t,PC=x,到 acw s»Pc=S4可以元代入得
戴汉可以作出即P类可以求得
B
(作法) 1.作对C角之孕切园,至令CB延线上之切奌為Y 2.联YD (為旁)并延長之交CA·延线於下奌(并设 CT=t 早在CY延线上取K莫使丫K=CT(即YK=t)
5. 通P 作PQLBC,則PQ 美丽求
(ÈFog) 1. YP 1 KT (49k)
2.PC:TC= YCKC 但角形底边平行线,分两腰成比例)
∴PC==号(CY=ㄜAB+AC+BCI=9,已在解析中定!?
ke
3. DYLYC(切线奖切美串红,王相垂直)
本:TYHPQ(同金直拎一直线之两直线互相平行,POL BC 是作法)
5.YQ:YC=TPTC(三角花边平行线)
C. YQ=1C + TP=÷(TC- PC) =+ (2 - 2+5)=
∴PC=YQ(等校同量)
* · PC+Qc=YQ+QC=YC=$==(AB+BCTAC) ($#ND
1 molecule 2 molecules. 1 molecule 2 molecules
n
n
By applying Avogadro's Hypothesis, we are able to convert. -molecules. to volumes,
1 volume
we have
200
2. volumes:
2x.0.0.
2 volumes (whian con-
denses to water of negligible volume,,
2002
200g + 2Hy
Anal volume
Then
Similarly for the reactions between CD and O2, and Czih * 02.
State the name and formula in each case of a carbonate which! con heating the
(a) leaves a black powder, as a residue
leaves a fusible, yellow residue
Leaves no residue.
(d) is not decomposed,
Describe briefly two chemical changes which are influenced bi
3. State four uses of sulphur.
fa) Wame three gases which are epairingly soluble in water ani
aneutral to litnus.
(b) Name three gases which are soluble in water, and are acad
to Litmus.
5. Describe briefly how you could obtain a sample or copper from (a) black copper oxide. (a) comper sulphate. Give muations) where, possible.
(a) What volume of chlorine, measured at N.T.P., could be
obtained by compitely oxidising one litre of decisorma 1- hydrochloric acid?
What volume of carbon dioxide measured at N.T.P. could be obtained by dissolving 10 gram. of pure marble in excess dilute hydrochloric acid?
(a) A white crystalline solid, x, on pezzino wvolves a zas 9.
which relights a glowing splint.
On adding dilute hydrochloric acid to the residue a brown gas is produced.
(c) x give a lilac colour to the bungen Tlame;
Daduce the nature of x giving your reasons,
Equating the contraction in volumes, ve obtain
(16+30) 2x + y + 20
((2)
Aquating the volume of wy formed, we have..
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QED.
注意間於三角形周界等類問題,旁切园牢為補助图形:
1共CA文延线主義下美時 本题究应如何解答?
(3) 束作-园典一已知圈相切且弊两直线相切
部
{解)此題之两直线,可能為平行线,亦可触為相交线,现在先 純討論平行线之解法,
(巴)两平行线 AB, CD, 及O园,
(求作-园奖。因相切且奖 AB, CD相切
(解析)因典 两平行线等距離奐之軌跡為其公垂线之中症
且府求园之直径为公委线,故為定長,
又因有定長半径而典定园相切之因心之軌跡 為同心园,西半径 則為两半径之和或差,由是本题可用軌跡玄截法 (Inter section of Loc)以解之..
(作法)).遇A作ACLCD
2, 你 AC的中盘线MN..
日返港
媒教授,超像,换 馥名計像本
《感斯博士·戴蒙教
,以為心,口园半程典古AC (即AM)的和及差為半猎作弧
分别以PR,P及P美国心,AM萬半纽作园,均属诉求 (证明) 1.因 P园半冠一AM,即P园心至AB,CD的距離等
半狸故园切于ABCD (PP PR 等国体闻理相切》
得興:
班業畢院學會浸
TE訊
台抵團光觀國囘
待接薯妥方各獲
一直线典园心距離等于半径,則為該國之切线)
OP=两园半径和;OP两外切(及国依同理)
(联心线等於两园半径和,则两园外切)
心
OP=两园半经差,故O,P。两园内切(园依同理)
(联心线等於两园半挂差,则两国内切)
(討論)),0周半種大柊 AM,且口园典AB,CD的相交,则本
有四個解答(如上园所示)
20国半徑小於 AM 且O园在AB, CD之間,本題亦有四解,
3. 0园奖 AB, CD两线之一相切時,本题有三解
40国典船相交而與CD相離時本題完有着于解?讀者
試自行解答之
0园奖AB,CD.均相切時,本题又有發汗解?
Q.E.F
至於AB, CD 两线相交時,因篇幅所限,留待下次討論
第五次預習問題(軌跡典作图) (1)求作一园典一已知园相切,且费两相交直线相切。 (2)以三已知点美国心,求作三王切园、
(3)一動奌典两已知相交线之距離之和等搽乙和長求此動莫之九
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