第三第張六第
日六十方四年日乙展变
WAH KIU YAT PO
以磲恹人,的小照堆的
華僑教育
英中會數學科答案,容明建。
MATHEMATICS
Lemons
to the questions in Mathemalos,
Paper II.in the English School Certificate Examination, 1965.. It will appear in the same column every day until the whole.
paper is finished, followed by that of Paper I..
SECTIUN
(Attempt ALI questions in this section)
Calculava" the size of an exterior angle of a regular polygon
with 2n Biden:
In right angles
in degrees
A radians (in terms of
......
The sun or
exterior angles or any polveon - 4rt.
The size of one oxi
2n aided
∙rt. 18.
180.
degrees
degrees
180
*180 rad
radians.
2 A plane figura 18 in the shape of a sector of a olrola, radiva 14 cm, in which the anela at the mantra in ons radian In this figure find.
-sub: perimeter..
b) the area
Find the area or an equilateral triangle of aids 15 o hence state which ana
che sater (the sector or the triangle
Let OAB beta sector; Radius DA 14 om.. ZAOB - 1 radian.
ARC. AB
dr.
The Perimeter
The area
(14)(34)(1)
98 sq cm.
The angies in the eg. trig, are each 60° The area of a trig,
ab sin C.
The area or an ego trag, of side 15 cm
• 4 (IB)(15) sin 600
-21.65.
很我的仍有
論來
個
論教師可爲不易爲
黄勵存:
... 曼期研究,從經政府忠棍通 汁與時間,更不足含外天范。 論,管系以爲假如一種經專家 惟萬轉移,開放日的熱劃帶篓,所用的腦中
·個敎師,實在無意加以論 困難。此外,還要對問題克蛮致導,不進 小學一點一狄師謝 辛苦萬倍,因此,畿高年級的,有發高年 座,是否適宜?朱著作爲一級的辛苦;製低年級的,亦有漪低年級的 話
過的法則,想來必然有其成立的理由:
過去行一點二周時,我們的工作:
實我們杲日要難腦筋的。在人人察 得到的幾小時中,我們可以向天:最 的話,那麼,這只是表面的看法而已1 概有二百本以上),於低限度狹用四個 的問題。
教師的工作如何?社會有識之士早已 完全没有歇患,而在ㄆ乾脚網下急税直落
仍有人以為我們的工作晚间像是五六小時 堆積如山的作痈,馬上從要附上,你自起 的;放墨了(這是人家以爲可以体馬的)
有所圖點,實難用多台。從時間可,如果
以同情與檢諒。 「社會人士,學生家長及學校當局,亦要予
此地的就會有此所。因此,如果眞的要 宮,對政府的决策,自然要都對服從;惟於我們不絕,而是事實上不易? 工作多 有困醮,亦要盡其在我,竭力以赴;將一些或少一些,在既然立志就身教育的人, 實行新制時,那獸,站在献身致育的教師·于我們的使命,恐怕更感困難。這不是由選 許是從大處著想的是粱之計?成許是此院 巴吃不消,對兒童德育的培養,日架感時(二) 間不足:如果再改一一世,則會
·如何教好翦們的功瓤?如何去激好 「致」的問題,同降還有「源」和「做] 的後一代了組知該师的工作,收服 制度,讓你事歉育的,他有一感特大道 因此,認爲最好仍保留一點
智安然過:再根還些,更不懼。 激情不是教师本身,而是整個就宙所失望
·的下一代——從案狹育者,念及此,心 及效果如何。如果到時力不從心,很尖的 ,基换不會計取的,問題只在轉否做得到
以爲很輕鬆,其實他們比較高年腾的,被承使各人的工作勞逸平均。 課外補課,教低年級的,而來,或許 尤盼能對我們固帯諒解,分配工作時,
·俨要不斷的露學生預警中艺,甚致要,須热舞鄀行,竭力以赴,至於學校當, 的功悌了!因此,人體,飛行新:那麼,該者使要不自覺力 小時,其餘飄下來的時間,又要預備明日泰後退一步,假如政府爲裤有此
英中會考數學 钅試題
MATHEMATICS (m)
rime allowed
Attempt SLL questions in Section à and FOUR questions from Section B There are 40 marks for Section & Each question in Section B has 15 marks Tables may be used whenever required. except in question 3(b)
should be taken. U required. as
SECTION A
b
433
DEL
97425K
tAttempt all questions in this section)
Calculate the size of an exterior angle at a regular polygon with Zn aides a). in right angles.
b)
in degrees
c)
in radians (in terms of m
A piano rigure is in the snaps of a sector or à fircle- radius 14 ors
in which the angle at the centre te one radian
In this figure find
the area
al: the perimeter:
Find the area of an equstateral triangle of side 15 cm
otste which ared is the greater (the rector or the trionale)
Construer a triangle ABC such that Bet nenes the angle ABC is 42. and the radius of the inscribed circle is. J Inch (Na latement or proof is required but all construction lines musku be cicáriy shown).
Find, by conéstuclion, ae accurately as you can, the value di tan 31 Using this result and without using tables calculate the value al sec2 1495
三期星
相令現閦如中的的
甜酒表多成有生新 改您示牛健 開學 強的:學趨价 深覦?
香港啭视教育前途
·茧於香港的倩影又怎都呢?
危墨 學以道我
未透險生生千香們
日六廿月五年五六九一带公年四十五國藝中
☆粉猫校學說一用合黨老深部中,問 馬推 其的話 校泪 無幫作大遠有鄉澳平是 來行“他。學件 蟲撥些在调,和的中村之始箱
後一
·意大利的空中教育:
【論電視教育
潘朝彦
拳問相常嚴明,中十一歲至十四歲的克
後薈決。試在眼,一無過入廿 例,溫失不成過敏將法非大五
冠設學過去分全然接陡有學人,
一
·學和學非小索學案和
【英文中學 [F]英數科先修專欄 繼賢開
Example:17:
(五)
NDED PROBL:ENS (四則混合類)
Find the cotal cost of tal-3 pencil-boxes at 33. each,
(b) 6 pencils per dozen and
求(A)筆盒3個匋语3托名; (b)銷辈6校,每村道 4先节ㄡ}
(C)間尺5把,每把值3先令,便上之總值,
(a) The cost of, 3.
*338
9.a.
(b) The cost of b peic118
12 x 4
(c) The cost of 5 rulers
178, 6 d.
Therefore, the total cost
28. 179, 6d
£18s. 6d.
Answer: The total coat is £1 81.ódi
Example18:
(其總值為1鎊8先會6便士。
Same as the above.
What is the change for a £5 nota?
承上題若旅攒德^5鏘紈幣一張問璩找回若干?)
The required. change(應找图)
£5:21 8. 6a.
£3-116,6d
By comparison, the area
UND DECLOT, BLUve
greater
construct a triarcle ABC such that BC 15 4.5 Ingles, the angle ARC is, 42, and tho radius of the instined: Circle is 1 inch (No statement of proof a required, but all construcrion lines must be clearly chowado
onstructions acurately as you can, the value or tan 31 Using this result, and without using tables, da Feriate the valie of sea=1400:
Utven) HC = 4.5 yiches:
MABC - 429元
Radius of the inscribed circle I in
To consti the trim ABO
Const
Solve the equation 0° and 360.
SECTION B (Attempt any FOUR questions in this section)
zhe required, changa 180311
(應松回3鎊11元命6便士
Example 19.
If I pay $36 for 50 catties of rice, how much should I pay for 2
Pleuls 50 catties?
(送50升值36元,今買者2鞴5斤,需付款若干?)
The required.
d amount which I should pay.
+36 +250 + 50
between
$180
Answer The required amount which. I should pay is $180
(雷付款180元)
Draw the graph of the function y 2 in x cos x- in the range for x of 0 to 180. (Suggestions plot: 7 goints and then draw your curve), From your graph find the greatest value of 2 ain x* • cos x* in this range. For what value of x does it occur?
The diagonal PR of a convex quadrilateral FIIRS divides it into two triangles POR and PSR of equal area. Prove that PR bisects Q& 1. in addition, PQ is parallel to SR. prove that OS divides the quadrilateral into two triangles of equal area.
ABCD is a cyclic quadrilateral BD bisects angle ABC.
Prove this
AD DC If angle DAB and angle ABC = 80", find angles BCD, BDA. BDC
In terms of x and find all the values of x which make EITHER triangle ABD OR triangle BDC isosceles..
A man wishes to measure the width of a straight, river with parallel
make without crossing to the other side. He takes the
Bearings of a point C on the far bank from two points. A and 2, on the near
B
• Bearing of Cifrom A
Bearing from N 52 270W
A is 100 yards due, West of B. calculate the perpendicular distance between the two banke
10% two chords XY, ZW of a circle, centre interseci at right angles at a
point k inside the circle, show that the sum of the squares on XK. YK, ZA and WK is equal to the square on a diamanter of the circle. (Suggestion a trigonometrical formula may be usefull
IP any point inside a triangle ABC prove that
BC + CA + AB SPA + PB + PC> HBC+ CA+AB)
12 A 20-10or pole with one and on level ground se inclined it Ju- in the vertical:
towards the East. At noon one day the angle of elevation of the sun was 70% due. South of the pale. What was the length of the shadow of the pole at this- tline:
Then, in 44 XAO and XBO
A
080-1499 - (-880)1°)2.
AXOBXO
proved
proved
LDP measurement;
A KAO
Aman walks 5 miles in the first hour, 4 miles in the second hour,
miles in the third hour and 2 miles in the fourth.⠀⠀⠀ What is
his average speed
(芥火第一小時行5哩,第二時行4哩,第三小册行3哩
原國小行2哩,求其平均速度?
The total distance (猴人之所行路程)
14 miles
Flierefore, înë mạn's average speed
14 miles
4hours
J1⁄2 miles per hour ( 31 m.pcha)
Answer: The man's average spese 18 35 alles per hour. ( or 32 s/pchi
(該人之平均速度為每小時3哩.)
EXERCISE 3
(1) add together 214, 328, 128 and 304
(2) What is the difference between the product and the quotient
of 36 and 47
(3) Find the aum of a cheang o chuan, y chek 7 chuen and 5 thoung
4 chek 3 chuen.
(4) and the quotierit when ↑ snuare värd 5 square feet 12 souare
inches is divided by 13
One pound of bork costs $3.40 How much would 4 pounds 8. Q2
basta::
(6), How many pints are there in 6 gallons and 2 quarts? 77) Find by subtraction how many times 2 pal luns i nint
con be taken from 11 gallons pint?
(8) How many hours and minutes elape between 7.45am, and 3pm.7 fo What is the difference in weight between two parcels if one weighs 1 ton and the other 1340 0. 5. 02:1
(io) I go out at half past three and return at three minutes to Divi
the sane afterhoan. How'Inng 'haus. I been wa
Givent X and Y out at A and B):
XY cuts AB at 0.
To proverXX 13. the perp. bissetor pr as:
Const. foin XA and XBI
48... XAY and XBY
adi.1. of the same sirol#)
AO BOW ZAOX-BOX
ZADX + /BOK
AxLom:)
wides of
XY bisseth AB at rt. A
| by definition):
Solve the equation 2 cos*x + sin x - 1 - 0 for values of lying batween 00 and-3600
2
(281hr 1)(aan
X
(sorri endi09-02 2005
#To÷86-continued toNONTON"
{Radii of the sam
:((2)
90o
EXERCISE &
I left home at 9.30 in the morning and walked to John's house in 45 minutes, There I rested for half an hour
I rode home on a bus; and epens. 55 minutes shopping. arriving at noon. How long did I spend riding on the bus)
bawker bought 300 oranges at 20. each and sold them at 210 each. How much money did he gain?
If the first-class railway fare is 3d. milk and the
class 23d. « mile, what is the difference between the first and the third class fare for a journey of 150 miles?
(4) Row buon money must be given by oach ot. 5 persons to raise
fund of £214ks. 24.7
Three numbe
together, kaka 3640, TVD B£tne
the third number?