RE
育教僑華頁一第張七第日五初月二年戌庚態夏
WAHCITY YEALE
鄲日橋
6575%%85%$#$#5;
四期星日二十月三年〇七九一曆公年九十五國民華中
CIB sinė
cos o sina
-
Zamorato (4) Q E‚D,
170英文中學會考試題預習專欄
(b) cm28 co*4,
= 0 (1—sin 4) -(1-cor20) sing
美文書院王編
24+ cor*0 sinó
生物科
(十九)
1- rin0-sin 4 (*)
Q.E.D.
BIOLOGY (19)
Answer to the questions of last week
1. (a) Describe, giving labelled diagrams, the life-
history of a named mosquito.
Stato the similarities and differences betwaan"," the life-history of this mosquito and that of / a frog.
僑樂
11243
24
-
(E)
中文中學會考試題預習專欄 數學科(十九)
喬仲強
第十八次預習題解答
(1)(a) 已知△ABC中的B角及a,两边,問在何種情况下,
此題為两解題?並作團說明之。
(A) Z BAZA £ a>f>asin B
時,則此題為两解。
(b) *k a=7.81, &=6.24,
B=51°15; 解此三角形。
(解)由正弦定律
624
2411 A=77°27′ (4*€ 77′2
故本题有两解,
=51°18′′
9) C=180-(A+B)=26°12′
79°30′= }} E 1062° 33′
NO.
7.81 ·0.8927
*M51"15" | "F8 9 20 6
28 10.7847
6.24 0.7952€
-77227 7.9895 0.7952
6.24
(1) A=77°27
91 C=1802
B
(ú) 1⁄2 А=102°33,
bunc¦ balain: 26"
sin B
3.53
A=77°27′
9=102*33*
(a)
ALSINS T8920
0.5431
2=3.55.
(2) £££ • B=61°, D=35, +
求醫之比值,
(18) @ 0+4=180°~(35+619.
=84
K4=20, 4λ 8+20=84",
BC
simi 51°18′ 78923· AM51° 15′ 7.8920. 6:244 07955
0179520 7.6449
在△ABC中,依正珐定律,
NO.
AC
LOG. |·79418
Aim:28" T67168
76134
AC.
79126
又在△ACD中,
7.75868
|1/772
76134
0.0638
HAM, BC AC sin 56"
sim 61°
1.16
(3)由餘玹第二定律 c=2dB+feoA及正弦定律
of (a) sin(A+B) == sin A cosB±cos A sinB, 1✯
*®}] (b) sin2A=ZANA CORA.
(*) •£!£**15 a=2RninA, b=2RsinB,
CzRainC, if t^^13*=***
2RunC=2Rain Acos BT2R sinB cos A.,
_sinC=sinĄ coc B + cos A sin B.
除以
10 năm C sản [180 (A+B)] = CATE
sin(A+B) === sin A coi B+cos A sin E
*X(B) 4 B, RJ & co<(B) = cos B, sin(~8);
sin(A-E
sin Å cos B-pos Amin B,
Hp sind AB)=sin A cos Biticos Ąsinḥ. e) ŽEŽ
XAKB, 5 sin(A+A)=sin Acos A+ cos A sin
n2A=2 sin Acos A.
*LACB=60°, <B=75,不許用表,利用上題
(4)設如右图:BCD為一直线,<D=45
#RA DC=DB
ABC
<BAC=180 – (60+75")=45°
依正弦定律
Be
B&
AC
XEAACDE ¿CAD-
BC
(1)÷(2).
器
(b) *
依正弦定律
BC2CD,
CD BD
3CD = BD
BD
(5)証恒等式:?
(a) sin20 tan 84 cor 0 cat 0+ 2.sino cos §) — Tan 8+cot0,
+0086. C+2 sind cos 0
(前回)
(sin 0+cos^0)=
001 OʻSIM O
Bos & sinl
5.0+cos"0
ÇOL O SİNƏ
(6)解方程式:(答案小於3600元正角) (a) 16 tan2=0=15 sinf)
(KB) ♬ tand = sing, it'x Thain o
*&G, BU F sin2 0 It cos20,
16 sin 8-15 sino (1–sin30)
**5, 44>I 1428 15aučô+16sin 0-15sin
分解
sinė (3sin)+5) (5 sinf-3)-
Za sino-0, $4.0=0° 180° (+77th co0-0)
Baino+5=0, §] sins === : (不合理)
5amo-3=0,@sino-==0.6000
0=36°52′ 3143 8
=0° 36°52′ 143°3′ 3, 180o.
(b) 5 aimx+10cax=11.
(34) 424, 13, (5unx)=(11-10006K)
25 sin x = 121-220cosx+100 cosxx.
25(1-00530): ====121-22000SX + 100 cos2x 化箱 125 cos2x-220 cOSX + 960
分解
(5-4) (25 0124 0
36
323*8*
(A4) X=36°52′ of sinx=06, *^RJI£XLAR.
X=323°8′
-0-6.不能满足原方程式,秦之。
·(u) #: 25 00805-
343 44 (驗宴)x=16°16,則sinx=0-2801.触满足原方程式,
~X=-0.2801,不能满足原方程式,故為根
7=16°16′ 3, 36.52
£ 5unx=11-16cosx ☆ 5 sinx=-(11-10cotx) Z‡k,m1) * 开得,即骂增根(根),故此法必需驗等,但可用下法解之。
#413 5×2una cosa + 10 (cos2 - sin x)- 化油 21 sin3 2-10 sinx col 2 + costz 除以12隻, 21 tam &-10 tan + 1-0. DAB (Stan−1) (7 tanx−1) =
23tan-1=0, #1 tanz=0.3333
而登=18°26' (第三象限角可令x23600)
7tan=-1=0,9 tenz=0.1429 m ==8°8!
如此解法,不致引入根,故不需驗(但要用複
(7)7848%, of (a) |† acro°- cot 30°cot 40°
(BE) !+ sec 20° = |+ cm 20°
Ca$ 40°001 30°.
Zain 20
2.ain 20° coCRO"
sin 40°.
CM70
[2ain 30]
Raen 50°cos 30° Zicor 40°cof 30°
Ainho".
cot 30°cot 40° (SE $)
(f) cot 52°cot 68° + car 68°cos 172°+Cos172°c
(SE) cotxeOS Y - [Cos(x+4)+ces (x−y)},"
cos 52°cor 68°—cor 68°cos 52° {(cos120°+co/2°), cos 68*cot 1 72° —— (con 240°1 698 104"), 304 172 car 52 == (co1224°+cot)20°),
XB 008 120=com (180° 60°)
201240°=001 (180° +60°) ===co+60°:
/>== (=+CH 16°/+col 104°+ cos 224"
油
=== ( - / + cos / 6° + cos 104°+ cos 224°)
cos A+ cor B=2 cod 1⁄2 (A+B) cosŹ(4-8) _*
Cat 224 + CD8 10/2
= cos(180~16");
豹入,左方
16 - cot 16")-
第十九次預習題.
(1) 35, 6, 3, 4, 16 @U = ★A-P. (FILM),
=*G.P. (YUM). Exy.
(2)設三數成AP.其和高9;若依次加1,3,13,则
*或G.P. 求此三數
(3) A ta z I-C MAP. XILELORES 1*14* a, b, c & G.P.
(4) 32 arbre, sic-a, clav att cm G.P. ✯ 証其公比袋,且将什
(5)一遞減無窮等比級數,第二項為2,若餐窮
項之和高金求此狠數.
(6)某人購樓宇一層,即付30,000元,以後每年付 8,000元,十年付请(再付10次)如照年利率8厘,每年 一期複利計算,問此層樓宇,現價爲关于? 7)在半径2寸的园内,作一内接正方形,又在鼓正方 形内,作内切园,再在談园内作正方形,如此循環不 巳,試求(a)有各园面積之和
(B)时有各正方形面積之和。
(8)寫出下列各级数的第几项,並求其首項之和:
(a) }+3×2+5x2 + 7×2 +-
(B)1+++++
Adult (femiate
Siratory.. trumpet Compound
Tail-plate
Dupa
Thorax.
Larva
Respiratory
Siphon Anal gills
"Mouth brush
•Life-cycle of a culex mosquito
The life-history of a Culer mosquito is described as the followi
Egy stage: The eggs are spindle-shaped and are laid in masnak of 200-300 floating on the surface of stagnant water,
Larval stage: A larva soon emerges, consisting
of a head, 'thorax and a nine segmented (Par abdomen. It grows through four ecdyees, itu
aquatio habit necessitates frequent visite to the surface for respiratory purposes. It
attaches itself beneath the surface film with spiracles of the eighth abdominal segment projecting for the intake of air. The
spiracles, are situated at the end of a tube
the opphon. When the larva is moving through
the water, the spiracles are plosed.
The head of the larva bears a pair of 3
'syen, a pair of abort antennae and two
maadibules. There are also two small mouth-` brushes. By the movement of the mouth-brushes small organisms and other food materials are draw into the mouth,
Pupal stage : After a few wasks, the larva is about half an inch long and changes into a papa. The pupa consists of an enlarged head and a thorax together with a slender abdomen, The whole body of the pupa still hange beneath the surface of the water by means of a pair of respiratory trumpets. In the head of the therax parte, developing eyes, wings, legs and antennas of the future adult can be found. A★ the end of the abdomen is a pair of tail- plates which act as a tail-fin for swimming merenent.
After a few days time the pupa case splits and the imago emerges.
Adult stage : A newly formed adult which remaing for a short while on the papal skin above the surface of the water, where the wings' moon dry and the cuticle hardens, after which the ässeet forsakes the water för its life on landi )
(b) A comparison of the life histories of a Culex
Mosquito and a frogt
The various
atages in the life- history
Egg stage
Larva and
pupa stager
Adult stage
Mosquito
Its ogg is a Cigar--
shaped, and is laid
in water. Usually -
Frog
Its egg is round or oval-shaped,
and is laid in
the eggs are produced water. A jellyw iá:"rafts" of 200-300 11ke subetanos"
floating an the
surface of stagnant water.
Its larva lives in water, and breathes by the help of a siphon. After 4 times of moultings, it pupates, and breathes by a pair of respiratory trumpets.
An imago emergen from the pupal case, and lives in air and on land. The male dies: off in Autumn while the female Hibernates,
zurrounds the
egg to help the
egg floating on
the surface of water.
Its tadpole also lives in water. It first breather the dissolved oxygen in water. by means of 3 pairs of external gills, latter internal gillm are used for breathing.
An adult is mmphibious animal. The young fully developed frog. still takes thros years to grow before it can
reproduce
sexually.
(未完轉入第七張第四頁)
Page 25Page 26
頁二第張七第2日五初月二年戌庚歷
WAH KIU YAT PO