1970-04-05 — Page 14

頁二第張四第日九廿月二年戌庚展夏 WAH KIU YAT PO

報日僑

日期星 日五月四年〇七九一曆公年九 五國民華中 眘僑華

170英文中學會考試題預習專欄

一名與路報 中文中學會考試題預習專欄

(a) & AC-a, §] Bc=a, LABC-45° &#££*£

AB2=a+a=203,

AB=√7a=BD.

堅道英文書院主編

數學科 (廿二) 喬仲强

# LD+LDAB=LABC=45° <D=LDAB=1x45-22.5°

=22(4+2/2)

AD2=AC22+DC=a+(√za+a)=a+20 +a+25Q

生物科

(f)

$ AADC¢, tan 22.5”—~^

數學科

(AF=)

***

a Eata

BIOLOGY (22)

(2)JE

(花+1)(5~10

第廿一次預習題解答

証罩

22.5

AC

14+22

4+2√2

觀景

由餘弦定 ®

2(4

2x3

ཚད་མ་ ི་རྣམས་

C=120" (32€).

(co 285 (năm 225

(c) 31

(d) #E==

Answers to the exercise of last week

Make a fully labelled drawing to show the structure of the skin of a mammal and give an account of the

functions of ita various parts. What functions of the mammalian ■kin do you consider are similar to the

functions sarried out by the spidermis of a flowering plant.

AND WAT 1

The stagram below is a vertical section of human-skia

Epidermis

Dermis

Sensory Organ

•Sweat pore

Nerve

Blood wear Vessel: gland

Hair -Sebaceous. gland

(1) AABC & sinA: sino: sinC=3:5:7, *TEC=/20°

(JE)ḍœš*£#‡ a:b:c=sinA: sinB: sinC=3:5:7.

-k, gla-sk, b=5k c=7k.

a+b=c2 (38)+(SR)~(7R)*

Rab

30龙

E cos 60°== THE LOT (180°-60°)=-t. (813x) d £15, a=3k, b=5€, c=7k

·· S= (a+b+c)=2(3R+5k+7R)=12k A—| 5(5−q) (5-b) (S~C) – ££* £ £ × = £ * = k

= 15/158

2- 15158 152 1515h, a 13k.

tan B

~Horny

layer Living

Cells

(B) AABC

2

Malpighian

layer Erector

muscle

Fat tissues

Hair follicle

Hair papilla

Skin is the external covering of the body of

mammal. It consists of two main layers. epidermis and dermis.

(a) Epidermis 1′′

(1) Outer part (stratum corneum) 1 This is dead and serves as a protective layer for the

functional and delicate underlying tissues.

This layer is frequently covered by a tough protein called Keratin,

(ii) Inner part (stratum granulosus): Which is

alive and vivid. Cell division praceads and

continues. The deepest part of this Lavar forms a Halpighian laver..

(b) The dermis: is vascular contataing fatty tissue,

nerves, the sense organ of touch, hair follicles, sweat glands and elastic fibres, which make the whole skin supple.

The hairs, made of Keratin, proiect into the spidermis.

The sebaceous glands open into the hair follicles. secrate sebum preventing the follicles from becoming too dry and from bacterial invasion.

ட

The sweat glands, which are aussrous, tubular in form, soiled round the dormis, help to regulate the mormal body temparature of the mannal. They -can secrete sweat which may carry dirt out of the

mammalian body.

The similarities exist between the functions of the mammalian skin and the epidermis of a flowering plants-

(1) They are both a protective layer for the

underlying funotional and sensitive tissues. (15) They both prevent eroess loss of water from

their internal vital tismmon,

(118) They both forek layouter coverings.

(iv) They both thick layers.

(v) They are both oily (mostly in mammals) and

watery (noatly in flowering plants).

(vi). They both keep their body trunks from being

wet easily.

Questions for this week

I. This is the skeleton of a rabbis as seen from the

laft: Bida.

JOINT

JOINT Y

Brierly answer the following questions im

(a) Name the parts 1

=6070

(34)

£a+b=2c, ★1⁄2 tan tawa (BE) ♬ tan a

..tang taw = (5-a) (5-8)=x (-a) (6-4)

5(5-a)(5-8)(S-C)

S^(s-a)(s—b)

S=(a+b+c) = £ (20+c)=32c.

s-c=c-c-c

琥

tan & tan

(3) 3£ A+B+C=180° #22

C

Q.E.D.

cot 8-cot Ccac A (sin C coc B – sin 8 coc C).

证法)A+B+C=180°,故必可作出一個三角形使 其各角分别為 A, B, C而令其对各骂abc.依正法 2442=2R sin A= sin B

定律

paint

The cot Bars are t £= R(a+c=f").

zac

R(a2+f-c2).

R(a+c2=b")_R(a2+f=_c2)____2R(C2=_f3)

abc

cocĂ (sin C csc B¬sinB coc C)=

ZR

(in C sin B

-RR (C32 - 1 x 2R) 2R (26)

22 x cz f 2R (C2 f3)

(=Eik =) cot B-cot C ===

abc

CosB Cod C sing sinc

sin (C-B)

ain Bain (

cos B-cos Csin B

pinėsin C

toisia) in C-sin B

C

sin A sinB sin C

he sin C = 1⁄2 (1-cos2C), sin2B== (1-Col2B)

sin C—sin B——— (|--C062C) - = (1-c012B)

代え

+(cos2B-cos 2C) —— (-2 sin 26+20 in 20-26)

- sin (B+C) sin (B-C) =) 祐十一 sin Asin (C-8)

hinĄ sim♬ Ain L

·左方一右去

n Asin (C-B)

sin (C–B).

AMBANC

Q.ED.

(主) 第二証法要用複育及和差化積公式,是高级數學】

的範圍

(4) { utv+x+y=180° #FIE

Coil cos y + cos x cos y = sinu sin V+ sinx viny

(EIE) ♬ u+~+x+y=180, tk u+v=180°(x+y) cos (u+v) = cos [180°~(x+4)]= --cos (x+4). 用複角公式展開,

COS UCOS V — sin usin v=-(cosxcosy—sinx_ciay)

• Cosicos + cos x cos y = sinv+ sin xainy (or () (5)設如右图:ABC為等腰直角三角形,延長CB至

DBD=AB,試由此图註明:

(a) tan 22.5°—R-I,

(b) cst 22.5"

(c) sin az-

(d) cos 22.5°

(4) (11) (111)

cot 22.5=20 Nata

• cor22·5 == √2+Jā.

(6) (a) hò ± #3 #149]*, *an 15*, cos 15° tam 15°2{1

(用最簡根式表示)

(解)作一個每边尊之單位長度的正三

角形ABC,则各角為60%

X1F BDFO LABC, E

<ADB=90°; AD=±AC=1 ¥45 2

(等腰三角形頂角平分线,垂直且平分其方地 延長DB至E BE=AB=>單位長, MLE-LEAB <ABD=X36=15°

& ABD, BD=√ AB=AD2 = √2~==√3.

AE — AD+ED—1+ (2+√5) — }+4+3+4/3=8+43

=8+2512—6+2+2√6x2={16+5}

• AE=√6+E.

ain 15"=-AD

ED

AE

Ian 15=-AD

7-2 (16+13) (7-1))

JE

(2+3) (√T-E)_____ JENE (6+5)(6-

sin 15° = √6-12, co: 152 [+E (= E(FH))

tan15-2-3.

(b)7#A** tan 75°

(M) • ± 614 cot 15

ton (90°-15°)+ cot (90°-150)

cot 15+ tan 15

= (2+√3)+(2−√3)= 4 [A]

(7) The tea to B, AD=CD=1, BD=72

4ACB=4, I tano=n tano. (E) AD=DC,

~<ACD=<A=0(41441)

FBCD=-0.

* ABCD &, his s¤ *1 sin 2BCD

去分母,

*[180 ~(++8)]

"nin B

sin (p+8)

2 sin (++8)==== sin (4-8)

naimpicos ô + cos of air 0) = sin foot) – coepsin 9

cos & sino+n cos & sin 9 = sinfcos 0-n sind cos 0.

(I+n) cos&sin@ = (1-n) sint care

(1+n) sinė) (1-n) sint

n tand.

註)本題如2=1時,則△ACD, BCD的写等腰,而中=90°

第廿式次預習題

(1)設abcd成H.P(調和級數,求証

3(a-b)(c-d)=(b−c)(a−d)

(2)設 A笃两不等正數al的等差中項,G蔫等比中項

H4042 * A>G>H.

*££, ŽE (ab+cd) (ac+fd)>4abcd.

2 (btc) (eta) (a+b) > 8abc.

(3) ta, u, v, b x H.P., Z

(a) & ux a, b t u v = 12.

( XV—

yu ab

CybÆ AP

(4) to a, b, c zx H.P. §] a (b+c), f(c+a), c(a+b)

你試證明之,又其逆亦真否?

(5) % HA a, b = 424 Hπ H-ak

H−之調和中填

(6)=2A=2(k2 + k2) x3 + (1) k=2£)x+(k+5K)X

+5/2-1

B=2(k+ k) x2+(11£-2)x+4

A,B两式有公因式,試求之值.

(7) 32 (a+b+c+d) (bc+ca+ab)=abc+abd+acd+bed

*SE (X+C) (c+a) (a+b)=0. (8)設pg.rs成連比例,求証 (8—2)+(\~p)2 + (5~g)2 = (p~5)?

are adaptations of the animal to its environnent (a). A rinh (1)

What type of joint is present at (i) X and (11) X? (1) X

(14) Y

(c) State six functions of the skeleton of

(d) What are the Five types of vertebrae making

up the vertebral column of a mammal?

(1) (111)

II. State Four external features in (a) a fish,

(b) a bird, (c) a rabbit, which you consider

(11)

(av)

(b) A bird (1)

(it) (111)

·(AY).

(e) A rabbit (1)

·(11)

(iii)

(LV)