PRAR
育教僑華 頁第滨四第 檢梨十月正年戌庚磨夏 WAH KIU YAT PO
報日僑華
5#%#E# #%3#3%5##%#$#3#%$#$%$ #%$#$%$#$%#S
19 a+b=20
art, & ix cos C
zab
四期星日九十月二年〇七九一曆公年九十五國民華中
(接第四張第二頁)
僑榮
itx, (a+b)2==a 2abx 去括号,及去分母
(a+b2)2+2ab (a+b2)=4(a+b)=1ba2f;
#he M3(a+b)-zab(a2+k”)-16a2ba—
*** [3(a+b2)-8ab] [(a+b)+2ab]=0
(a+b)+2ab=0, Alatrik #760.
// 3(a+b)-8ab=0, qj a+f=fab. fox cosc att sab
zaf
2x 좋아
(証章)
(5)設△ABC中,為外接园半,九為内切园半径,
S為半周,△為面積,試證
(a) cot A+ cot B + cot C
#$%$#$%$#$%!
中文中學會考試題預習專欄
數學科
(十六)
喬仲強。
第十五次預習題解答
(1)一人沿直路行,在第一表哩石(milestone)處,見一屋 字典此路成61°之角,至第二表哩處則此角茑17問此 屋宇興路 距離為若干码?
(解)設C為眉宇,A.B為相隔一哩之两
hea
cos
及
R
表哩石,CD為屋典路之距離,
11⁄2AABCY, LACB=61-17-44′′
依正弦定律
ACE
AB
AC
REAACD Cl=rimbl
CD-ALAIN,
1760 sin17
-688
D
NO. LOG
1760 3.2455
Aims 774659
sins!" T9418 G
2.6532
sin 44 78418 -
477
2.8114
答:屋界路相距648码
(*)) # A ACD + y = xcot 8! =0.5543%,
#ABCD
・本日
4+1760=x cot: 17":
=3.2709%
1760=2,7166x
1760
=648
CHA
J
(DEX= sina sin B
2R(COA+
a+b+0
Cod C sinc
C01B
A L xb+c=a
C+a-f
zabc
abc, Ax
44:
abc (fic2
44 ·zakc
afc, at
Rabc
(f) sinA+ sin B + sin
(2) Ek‡‡ stunt
sint
sinA† sinB+sin
(2)在相距一哩之两地,同時觀測在其間之一開機 其仰角絡為768及46"若两测桌典該飛機同在一鉛 岳平面上,問飛梭之高,葛关于吸?
(解)設如图,A,日為两地,則
LACB=180° (76+46")=5}*
在△ABC中,依正弦定律
AC
(C) Cod A+ cos B + cos C
(註)由餘珐定律
AB=5280
AL
40
b+ca a
cor ==== a+b=0",
zabc
LJ. Q.E.D.
代入
cor A+ 2018 —
atc
^3=ab+ac-a2+al+&c=f3
-(abrab)+(ac+bc)–(a2+f3)
-(a+b) [ ab+c2(a2-ab+b")}
(証)
abc
inth T.98694
3.5664
T.9284
ab(a+b)+c2(a+b)-(a+b)(a-art.
=(a+b) | c2 (a-b}]
=(a+b) (c+a-b)(c¬a+b)
== (a + b) 12 (s - b) x2(s-a}
- 4ra+b)(s-a) (s—b) A+ cos B.
2(a+b)(5-a)(S-}).
(a_b)2=_c2 (a-f+c)(a-f~c)___2(s-f)-2(s-a]
a2+f=c2-1
zab
+b2 0 208
204.
丸AACD
AACD
= sin 76"
CD = AC Air 78*
5280 | 3.7226 7.8569
5280 sin 41 skin?”
34 3.6380
af
cos A+ Cor 8+ cos C-1
2(8-4)(5-8) [(a+b)-c]
__2(a+b)(5-2)(5-f)−20(8-0){
abc 4(5-a)(s—b)(5-OL.
4A
abc
(3) AB ACCB
=4350
答:冰機高4550呎
幹路今有汽車一輛,在小路
上行駛,時速為20哩,在幹路时為
30哩間由A至B应如何取道較為有時,又可苍时差 千分鐘?
(解)依正弦律,
2sin 200 2X 0.3420
-0.1368.
查表得 B= 7*5元
BC
1=180*~(160+7°58′)=12′′8.
NO. 204.
0.6990
(Aus 12′8′′ T32260
[0:0R15
由小路需時 0×60=15分鐘 由幹路需時2+3
simas
753416
3672 0.487.4.
72x60=10.145 相差15-10.14=4.86分鐘
答: 由幹路行駛,可有486分钟
(証法)由正弦走律
(4) A ABC
17 furt
a+b=2c, A=B=
cant cond 45=
sin(90°
Esin
•£=0 x cos 45° To sin
in
cosus = √x/==/
}@ C&C=1-2sin2 & = 1-2× &
(SLW=)18 A IF DALAC & BCTED.
§14 DAB= A-90°***&B.
· AD-DB-X 32 CD=y
q x+y=a
又在△ACD中,依畢氏定理,
(2)
(2)+(1)
(1)+(3), 2y=a+k-
zaf atf
又在△ABC中,依餘法定律
zabon C
4(5-a)(s~b)(S~C)
abc
cos A+ cos B +cos C-1-
14-3 Bp 13
(a) (f=c2)cot A+(c=a) cotB+
(正)由正弦定律,
指定
abc
(b_c)ootA=(f=c2) CMA -(8=c2)x·
=(f=c2)»
(甘辛)
2R(D2 (3) COMA
R[(f"_c")—a (f=c) abc
ZR CORA
• ZR(32 C2) x.
fice 2000
(c=α) at 8=.
R[(c¢a*)—f3(c_a)] abc
(a^-8") out ( == R] ( tt"-b") = c "(a =_b"]}, #Rox 18
(c) cst A+ (C **B+(a−1)est (=
第十六次複習題
(I)開配足方法或用其他方法,分解下列為因式:
(a)x+40x+391. (b) p+10p-551,
(2)(a)† A, B ∞) EX TEEN.C.F. πYŽ CEMA+MB)
式文因式.
(f) 30 A=3×3-13x2+23K-2/,
6x+x-44x+2/.
##ILŻ✨Z, KA, BZH.C.F
(3)有等差級數,活其第八項尊第十三項之两倍試 任其第二項為第十項之两倍
(4)有成等差級數之五數,其和為10,芥平方和高
50. 求此五數
(5) 在下列各式之平方根:
(a) |+√2/+1213 (8) 3x+1+2√2x2
(6)詖a, & c 满不尽相等之塞數試證
(b−c)(c-a)+(c-a)(ab)+(a−b) (b−c) x ́ ́ ́k (7) ££ x+y=a, x-y=b, £#£
x2-18xy2+y4—3ab ̃_(a^+f")
(8)解方式
24(4+
1770英文中學會考試題預習專欄
堅道英文書院主編
生物科
(FX)
ourriers of malaria, JOLLOW TOYSr, elephanti-
asis, and dengue fever, all of which affect uan and in many cases can be fatal. Kethods of control
(1) Spraying standing water and swamps with
insecticides to kill the larvae.
(ii) Spraying buildings, caves eto, to kill the
hibernating females.
(iii) Introducing fish, which rese on the larvae.
te the water where the larvae breed,
(iv) Drainage projects in the breeding grounde (v) Clearing water of weeds to induce a flow
of water and thu check the life cycle. (vi) Spraying water with paraffia to suffocate
the larvae.
(vii) Treatment of the diseases carried,
malaria in treated by the used of quinin or more recently by maqaózine and paludrine.
(b) Insecta may be dither useful or harmful. The
butterflies' are important in pollination of the flowering planta, but a great damage can be caused to crops by the larvae of the cabbage White Butterflies and often complète defoliation will result, from a revere attack. Hany. £uss ots act as scavengers, destroying and burying dead animals and plants. Gall- riies modify plant tissues into substances which can be used for industries, such as tanning, dyeing and ink manufacture. Silk- Moras provide silk,
Many animals which are used as human food feed themselves on insects. Insects therafera occupy a place in human food-chains,
Isjurious insects are mainly of thi aa types s. the housefly, mosquito ato. which cause the diseases of mans the crane-flies and green-fly etc. which damage orops; and those which damage or destroy useful commodities such as clothes and furnitures. Examples are the clothes-moth larva, feraitės and death-watch beetles.
(a) Give brief reasons for classifying a Cabbage
Whitë Butterfly as
(i) an invertebrate, (ii) an arthropod, and (iii) an insect.
(b) With the help of diagrams, give an account of the life-history of a Cabbage White Butterfly.
A Cabbage White Butterfly is classified se an invertebrate because it resembles all invertebrates that possess no bɛok bones,
(ii) The Cabbage White Butterfly, also au
the group of the arthropods, for it dointed appendages and possesses a chitinoun exo-skeleton which encloses segmented body,
(111) The Cabbage, White Butterfly is again
classified as an inseot, for it possesses all the characteristic features which are commonly found in insecte.
The female butterfly lays clusters or crean- coloured eggs on the undersides of the leaves of cabbage plants, å green caterpillar emerges from the egg. The caterpillar is the larva of the insect. It is long and slender, with a segmented body. The head has biting
an jame,
and the first three segments behind it carry three pairs of segmented lega. Four segments of the abdomen have projections. unich are called pro-legs. On the front of the bead in a silk producing gland called a pinneret,
The larva eata its egg-case at first, ana then turns its attention to the leaves of the cabbage. It feada greedily for some time "and then finds a sheltered spot and spins a
silken pad with silk which it squirts through its spinneret. Attaching the pad to a firm support, it gripe it with claspers and spins round itself a silken sling, banding bead- downwardsTE
After a couple of days the larval skin splits, zolls up and falls off, leaving the pupa exposed. This has at first a transparent skin, through which all the features of the future butterfly can be recognized; but the nkin is quickly covered with a fluid which hardens and darkens in oolour. In this "condition the pupa rests while internal
changes occur. At the end of the resting përied the pupal case splits down the middle. and a perfect adult butterfly, the imago, energan,
Questions for this week
1. (a) The nature of an insect's dist is often
reflected in the structure of its mouth-parta. Show how far this is true of the cockroach and the honey bee.
(b) By describing the essential parts of their
life-histories, explain what is meant when the cockroach is said to have direct development whilst the housefly is said to have indirect development.
Keive a BROTT GBBRY on the habita mosquitoes.
(b) How are the mouth-eaves oz A FENOLON
#ême mosquito aúnyvez blood susking?
·Bleroing and
Page 15Page 16
真四第張四第10日四十月正年戌庚歷夏
WAH KIU YAT PO
請今院 勿晚期 錯最關 過後係
「臺舞大港香
華特場兩晚今
元十二十六七七四 七四 八二。元。
周街菜華中
序爲畫藥以名排。員藝流一中集
·您在莳谈宛非郭制背三者身 王爽愉糕,突說
任
·碑皆口有衆觀。但虛不名然果
座講
黎明光大
聯合
映天
̇萬華
矚鮮異 目花彩