1972-12-12 — Page 24

1913英文中學會考試題預習專欄

二期星

日二十月二十年二七九一展公年一十六國民華中育教僑

11lustrated below and other pro- cedures are introduced in the

various other-examples and exer- cise.

頁四第張六第2日七初月一十年子壬磨复

WAH KIU YAT PO

報日橋單

1973英文中學會考試題預習專欄

數學科(八)

英文科

(八)

MATHEMATICS (8)

Solution to exercise

English

1 (8)

(1)

For C: U?

2ad.cosd

(132) + (224)

Model Essay (based on the plan in

the last issue)

ine store near my home.

Until a few years ago I used to live in Cheung Chau, It is so primitive that apart from a few stalls there is just one general store on the d

one and only main road near my home. This store was noused in an old brick house. whicł looked as though it might have gone through the Second World War. Two wooden-framed windows with bright cily green storm shuttera: flanked the old creaky doors. When you want to enter the store, you had better bend your head or else you would end up with a lump. (95 words),

On entering, your nostrils. would be assailed by the mingling. odours of salted fish, home brew, vegetables, soap and incense. Your eyes would be attracted by the strings of dried fish dangling from the low ceiling in one comer by the assorted bottles that lined the back wall, by baskets. of vegetables that bordered the door -way, by bundles of joss oticke and inconse scattered here and there, and, one or two cats stretched out leisurely among the:

wwas words)

em told that whenever, as

a small child, I was missing from home

I would be found sitting on the ground outㄖide the store, cuddling one of the cats or help- ing Mrs. Wong, the lady at the store, fold the incense papers. Mrs. Wong was indeed a motherly soul; liked by all the village children who loved to hear her tales. She was never too busy to dry a tearful face or soothe an tangry heart. Her endless patience, both with the odd, fussy customers and her own two brats, made me feel.ashamed of my own hot temper. (100 words)

... As there were but a hand ful of villagers, Mr.Wong was not only the most prominent businessman but the village elder as well. As it was not convenient to go to Hong Kong for everything, the store became everyones convenience Far from taking advantage of this, cas some others might do, Mr.Wong do not sell second-rate goods at high prices. He made every effort. to stock the shop with articles of good quality and, more important great necessity. Not only that. he seemed to have everything one would want. Once, I found myself without a pot of ink for my newly: acquired fountain pen. Not wanting: to be without, T pestered Mr.Wong to sell me a bottle. It so happen- ed that the store was crowded that day. But, with a pleasant smile and a pleasing voice, he calmed me down and began searching for it I don't remember ever having to leave the store without what I went in for ! (162 words) ______

Nowadays, though I live in town. I find myself longing for that quaint old store. I compare the service in department stores.

their impersonal, slov- enly and disinterested assistanta

* with the kindly and patient,Wongs. T often regret not being able to go to that 'store near my homer anymore and hope 'that it will never lose its image and become commercialized and un- friendly! (63 words)

This week, I shall get a narrative type of tope and leave. Y9) A visit to Macau or An Unluoky

to plan it and write it.

Di Weekend.

(2) Escape.

Here are a few pointers:- (1) A good story must have a plot set against a background. (2) I has to have a climax, usual-

ly involving characters: (3) It has to have a suitable and

logical ending1.

(4) There must be justificatzon.

-2(132) (224) cos 28°40′ 15714 125

For A: sinA = a sin

= 300301

C

132 sin28040•

125 132(0.4797) 125 0.5066

For B: sin B = b sin C

120950

C

224 sin 28°40′

125

0.8596

The required parts are A=30°30

B=1200501 01259

(2) In our figure, Bu represents the tower DB represent the cliff and A is the point on the opposite "shore.

In triangle ABC, 10 - 900- 28°40 / B = 90° +18°20

A = 180° - (B + C)

10°20

A:

sin A

610201 1:08 20

25.46

H

C125 sin 61°201 sin 100200

125(0.8774) - 611.

0.1794

In right angled triangle ABD,

c sin 18°20′ = 1923 AD = c cos 18020580

The river is 580 yd wide and the cliff is 192 yd high.

(3) PR2 = (125)2 + (125)2

PR

Mein/ QPF

– 2(125)(125) cos13°20′ 843.7 29.0.

125 sin 139201

29.0 0.9940

/ QPR = 83°40" / RPT = 83°40! 45°201

38020

the pilot must fly a course.

S45°20W for 2 Ves in:

going from R to P.

Trigonometric équations.

Equations involving trigono- metric functions of unknown angles are named:.

(1) Identities if they are satis-

fied for all values of the unknown angles.

(ii) equations if they are satis- fied only by particular. values of the unknown angles. Take for instance, sin x cosec x - 1 is an identity because it is satisfied by every value of x, while sin x = 0 is an equation since it is satisfied. only by

There is no general method for solving trigonometrie equations, Three standard procedures are

(1) The equation may be factoriz=

ed

EXAMPLE 1.

Solve sin 9 -

ine cose

Solutine cose.

sing 2

sinë (1 – 2 cose) =

sine

Or

0.

or 12 cose.

or cose

The solutions are

1/3,5T/3.

☺ = 0, T/3,π,-511/3-

(2) The various funetions appeare

ing in the equation may be

expressed in terms of a single function.

EXAMPLE 2.

Solve.

2tan-0" + sed"

Solution: 2tan 0 +

2tan®

wan2日)

3tan

3tan

When tang

When tang

tane

tang.

and

The solutions "are.

(3)Both members of the equation

ware squared. EXAMPLE 3:

Solve sine + cose Solution: sine

sin

cose)

2cose

ធាន

20080

2cuse

2cos = O (cosa - 1) = 0

or cose

(Check: For 9

For e

Ty2, sine · COSU

For 6 = 3/2, sine + cose

required solutions 20. √/2.

1..

3/2 1s called an extrane- ous solution which was introduced

by squaring the two sides of the equation.

The followings are same further examples of solving trigonometric

equations using the above methods or a combination of them. EXAMPLE 43

Solve 3tan X

6secX

Solution:

Btan secX 16tanx

sin

COS X

16sinx

cosx cos》

COSX

COSX

3sin x

UsinX + 16sinXcosX 6cosx + 3cosx J(sin2x + cos2x) ·8ginx.

cos 16ainycosx =

dsinx)(1 1200BX】 O

海菜小北

到了

完全把做到他們這個間將源步風的健永歯列向,雖給如此,在我們

論來

作

橋

白くく!

組小會委調俸薪

薪適教文 級當師憑

督港呈日昨書告报

技

犨編

訂

三天,捐到十校全

较有缆,

工業教育師資固缺、黃膩,急部使氣,在鈴在曼城距明內, ,那宋東南亞和非洲拉丁实視各練,以可術而藝

「炒蛋不些,香港的經濟,總有一日會此受 ,去年該按所屬五校,博得於邊四萬四千的元,統計,已有凌灣正當工商業投礎之數。如果此風一易數字拔計,但祖堂強人意,全類工商業人士, 賴坐座一般高級結晶,甚至船够醒造斯工業岠是一批待明天再想吧。」人無還想,必有近防,安圈 的工商界在十多年,大家的你手空拳,始

「但總尙有坐眾可做,今後十年,我們不能像「 克勤克儉,任勞任絕,累起來的,也包含率 以單獨作直承慨大圍生活的資格,所以本港的留

否勤過依賴告沙。鍵述情形,花如一九七點濟運動,宫耢晚年當維性善形,而已經缺乏信心和興起,將據每日股市交剀的數字轉機,書生科營美國的來民越,始終没有此項同一用力,致失信心。如果我們有了背船而良 LEGATS)到有八十七成,由於不斷一

第一,是非常害的。過去十多年,跳級到宮些

東诺亚各國由於其本身工樂的鮨步,包不硬

·徐平

,記得工業教育家訴士克博

賴廉價勞力,此語已到站不卻到,由於物價指數 面增強工灤A才,也向工業軍。因此,香港

小組提出了證見,我們也和他們進行了多次會談。范丛人所共知的。我們

在的樹胗。但思我們胡石P瓦纘 來一 好熱詣,發展市沸的工業設有,調

在於工業致育衆的缺乏,實

當您

《特斯 瑞OH卡 利瑪竇書院五校

有劭文影故肼的钻薪被的報書,一併 出海中。就會工作小組主諾良根在昨徒的 昨*十一時稍後,已焱製了一封信,如同

在資批政府手上,所以不说在這通露其

在調校發起茶運動,變

聖誕藝欸濟清貧 张,民主朝明的發起皖糖九五股,讓林月,國產,世日降息多變的股撬权後之險,將有用的天地,那是無賴國家與拼家的關係-力可在國際銀行來,高峰,今发改造高級流高,以至於工装和站:已離不逃的一般出版錄,曾因力有宋述,化學物理 冖枨♪啕痕蝥呲岿设述動,但盆食劳大一提莫徘影,不累可以發出一般隨有安企業,有一天文數字的轵過覺易,一定不會交易的,料,他就將上一般人士影猛烈祧的正定已經地和出循之效。而對化學物爾二門,科學日新月異, 始走下步,穩亞重重,無喜市多的风狂的到大的红限,尤其對海與S。張因盡部射中的瑞:我們絕不能因从手,可對工業教育不,張龍與俄國恊財和潛規疱合滿驊,當可收相因 物品的傾訴,能有東南西各置的工業性日轉調中,紀海曼在工業技幅上,商品質量上,偉雄安茲城:今日政府的高級人員術向外國話渺,那來,打好,額頭上,今日的教科慊裹都已改詹子 「業激育,煮出本港的工菜永落在歐美及日本先有,可通爲統盤。在評估工商業安全門代時一成的,工業教育,因缺細究,不免但我們感到,我們也應及早注癒,以通被計劃。學工程的 洪國家之,旦於日前的君來,近有中共價一,却也說不在國際貿易上聽到一崑大散,而台一年,不過此是棘手,非棘手無策-科技本無國人,在中小學的時代,一定要把斯現化的基茲

,由於這些商的华智人才,也不赢促淮安落成工 范的里港裨。

此尼安警示出我們工業界的潛力,此是方興未艾 好的工業學校,正在微满地拼盤面的工業人才,

外加宋延聽。而書籍一般是佔箫知識按繼顯的 工具。本港的文化代版記林立,雷是經常出版文 工業教育,師資而缺,我們會不難可以向

半已供此风教科書,提出骨質高見,希望教育常

「我們的商化教科書不被增訂,那誠所謂「 体,愛因斯坦的相對除。科技在新知,胸健 1.李政道發現了對等定律後,已經推了牛頓定 推大的。至於物與學,栾所週知的,比如楊政業 我們和證過期後對於學化學的人關係十分 也由於化學原國的琳多,影响了刚案的遇貼 的被狂习和應用,早已於至一百四十九袛之多, 的二門教程打,撥陳陳相因。英知化學與第一

|癞低廉的地方,何况上述各吨,都是有自己的一,相信及可,入於正當的工商業的用降

此博荈 商道而求發展,蕭之墓園,親之千風 和程之主從已低區。計藝漸織業工商設於本傳統阿濟分,荔枝此於正當的臨安金可議,由工業教育之間,相信不久將來一般科技致料 的 ,競爭不過一萬國家的牢品,若統宋書張品展康之局,浣花朝餓,一面寬蘭坐車內後越高,一號後,名鈴山,實業館路,近來營書擁有自無大戰,但是對於我們與受工向發育的學生, 日涨,水漾染态,工程息随密上升,對自營之,上面許又有了英愛的熱,發門市氾般劉维数,帶有見及此,帕学以指導改制。陸此用的人士,那影响可就大了。因即以後离深的黏技1系不以

的缺乏,從不來過個發展本准的工‘國家和政行,不時好壞,几乎無意洒包易生長等,当運士尼照十的活浸台證禮,嫽馬不是一天來,段的工莘以司的影响是中分爾大的,索甫柳因我有志及此,那維爾是一件利人利己的事業。 其珩,喝粥得其蹤,此訊科技上訴,對於我們 科技传栢之關们也宜及早計劃,如果有規模之川

2sin2 9

sine

sing 10 (2sine + 1)(sine - Either 2sin0 + 10

or sine 10

71 117

Ceithen cosx =

or

60° and 300° sinx = 3 i.e

220

and:1570590元

the required values for X are 2291 600 1570591 3000

i.e. sine =

or sine

EXAMPLE: 5:

Solve 2 aine - cosecy = 1 Solution: multiplying the equatior by sing we have

281n20

The required so

Einde

tions are

22, 117

6.

Exercise : 8. (1) Solve: tane + 3cote = 4.

(2)Solve: cosecd + cote = 3 (3) Solves cose - 13 eine -