RARY
27 DEC1968
育教保额
CITY HALL 買三第張四第日七初月一十年申戊屡夏 WAH KID
YAT PC
報日僑華
四期星
資優蹤
Given Ke{a,b,c,d, indicate which of the "ollowing are trus
K £2
文中學會考試題預習
false
15:
現代數學科
(八)
Solutions
MODERN MATHEMATICS (8)
Given A= {1,24, is {b,craj and C={book
find AxBxC...
This is accomplished by a branching. sketch.
›rder trip!
(1:8,0) (1.6.口)
(1,C,A)
(1,60)
(1.0.0)
ww
(1.d.A)
(lid. o)
(1.da)
(264)
(Lo)
(2,2.0)
(X,C,A)
(2,0,0)
(2.00)
(a,a,a
(2,α.0)
(0,1,0)
Therefore, AxBKC= {0,b,A),(1,b,0), (1,0,@)
.(2,8,9)}.
anat is the number of elements in XXY 1f X has 4 elements and Y has 3 elemente: Why?
... There are 4x3 or 12 elements in XxY. This da because every element in Xhan
to pair with each of the three elements in ?. But there is 4 elements in X. Therefore the number of ways of pairing. 18 4x3 Or 12.
Application of set notion to arithmetic.
Some verbal problems are difficult to
solve if you apply ordinary arithmetic lawa but they can be solved quickly by the use of Venn. diagrams .
Examples:
(a) Of 45 girls readers of three different
magazines, 23 read Voman, 21 Beauty, anc 19 Romance. Three girls read all three magazines . It was found that equal numbers road Woman and Beauty, woman and Romance, and Beauty and Romance... How many read Woman only?
Solution,
BQD
日六廿月二十年八六九一醫公年七十五國民 華中
不先形優
他發是渾館◎三、至變動的帕袛定不法使需姿的。 ....
:,直接我們還发有關政府獎助的申請辦油 一人歡保持空等,然而人的共和狹赛方向往年,便是免息短期保歉了·在學期初,開何渴已 是在大學一、二年無時才發現的,這漁文於石棄,助學金的,由於全感的憲發,同華們很容易面對 性不登斯高模轉紅的辦法,因故可使各立誌動|生的資助方法,對於短期性及邀雄的夯助, 滑如 張對生活水準提萬隉,襲便和所有發生鳴際工作的劇性,黃華生將來有很大的悚然,我 以有ㄛ千不合理之风,我們熱爲當成是應加以改善,兼袖生態。然而在獎助學金未能全面撲布時, 第一、獎助學金額,一張底定妆,不能中牌」。工滙給他得助學生的經情況外,還耪千學生, 分配情形乃按类助奉命者所當守的垫等。足畫的獎助學金,使人人有-
份時間研究問, ;出,八年所開發用約達二千五百至三千元之。故此,我們希望當局袒活建實際的需求牌形 首先,關于接受獎助學金者當守的熱方面,享受真正的大學生活,參與生活動,培業區的 「四片多人肇花五百至一千餘元,而携統計數字 減少湖學數目,英助的目的郜未能有效地對 們以爲校方各部門的演職職位,及各的若能 完善的工讀姚正好在某祺惠義上豬布這間紙
分配有關,這點是浪得,暢的,但能就大名載布 文衰签指出“良好的高等教育,應包括有
1位來
基業局位,應盡可觸煤年工讀生助學金、工馥都是長:
金助種有生
1
提出批評... 產生有過撥動,政府獎助學全的政立於此例不一置况有确切的了解。 [家庭經濟香其群的年,而使一般家境淸备的一題應別得群馬、大學,才可對申請人的經濟 完成高等教育,並對現時政府英助手,來方面經濟狀況的紙,但幸紙上所間的蹲超 「促已府重包括有足,的獎助學金,以協助有無著 得足够的了解。我們知道案核的根據只是一紙有
· 中文大學在的船票也目前逛枝態法對學生實際經濟與境不能述, 故文首先稱:香港的高等教實近年已開放生在家W中的树養俄况等。直難抵上所排出的問 部份到很含糊,尤其是實際的收支問经方面的學
應在
指去不的稀
分
洪府早日本張),本年度感助學金的減少,相信與名額的擴大,
數團助
積
(接第四張第二頁)
五九六九章玄
(八)
數學科
(4)
分解
venn diagraz)
of the problem
代入(6)
y+2)=(y+a)y:
· (ry-4) (2y+1)=
或
Let W,5, and R be the sets of girle who read Woman, Beauty and Romance resp- ectively. Let I be the set of girls who read any two of the three magazine. Then,
(WVBUB) - n(W)+ n(B)+ n(R)- ¤(W/B) 7
̇wn(BaR) a(WAR)+n(WABARY **23+21+19-3n{X}+3
45
•30(X)= 66-45/
n(x)=7
21
Let A be the set of girls who'rend] Woman only. Then
An(A) = 23-2x7+3
12
Therefore there are 12 of thez) who read Woman only.
T question a certain number of people
all drink tea or coffee. Half of them :
drink tea only, 2 drink both, and 7 drink
coffee only. How many people do T questiont Solution:
八次預習題
【聯合書院學生會批評
政
府
合
書
·認爲有三點應予改善
政府獎助學金不合理
| 陈的開鈾,其實上不少獲助金的问 有 不通,因爲他所得的裙助不足以應付其攻渡大學 五,而璵濟條件縠差的同學不棄酸,實在有點 一個每年只甓很補助不足千五元,能点月之數百
•波點在航運金額足郳時仍屬合理;但是科茶
博學助學金,個人對率核方面起了傷疑,同時亦 -酸又狂露--很多時不少家境富裕的同學亦
喬仲强
ón
(1) M 3 AB 31⁄2 + §, MC MDII &* ABILFERF
試证-CD FE共团
2)D EFXAABC 老边的中奌.
∵AX-BC X為番足 (2)試証 XDEF关园
若HX△ABC的要心,而P為AH中
3) ABCD為任意四边形
AB PC 的延线交拾桌;
AD, BC的延线交於F奌
**E ASF, ADE DCF
8CE 四园共奌
PFDE共国。 試証
(3) Given AxØ, and B=[(2ım,ad find AxB.
AxBaß, because there is no element in A to be paired with the elements in B. (4) Given S={0,24}, find 2a..
This can be done by a branching sketch as follows,
§ Let "1" denotes the element is taken and "0" denotes the element is not taken
Sets
10.1,2} 90.1:47.
10.18
10.0.41
{0,2}
{0:4}
{0}
{1,3,4
[1.43
[4
Venn diagram of problem
Let T be the set of people who drink tea iam only, and C be the set of people who drink coffee only. Then,
2n(T) = n(T)+n(C)+n(Tic)
2n(T) = 2(T) +7 +2 Zn(T)-n(T) = 9 10. n(T) =>
2n(T) = 18
Answer: The number of people I question
18 18.
Each of 100 boys plays at least one of the three kinde of music, piano, violin, flute, 46 play piano, 54 play violin,and 40 play flute. Those who play both plane and violin is double those who play plano and flute, and three times those who play violin and flute. If 4 play all three, how many of them play bath. violin and flute ? Solutions::
Therefore (5) liven A={0}.
1,2,4}, {0,1,2}.___.0}
venn diagran of the problen
Let F, V, and be the sets of people wno piano, violin and flute respectively.
n(PMV) = 2n(FAP). n(PAV)=-3n(EV)
(4) ABC為任童三角形ABP
BC Q; CAR各為正三角形试压 {a}AQ=BR= cp
(b) ABP BCQ CAR = {*} {(C) AQ. BR.CP 三线共矣,
\.c. n{F/P) = m(PAV} =3/2 _n(F/V) ~___ n(PUVUF) = n(P)+n(V)+n(F)-n(F∩V)-3(FAV,
-3/2 n(FMV) + N(POV(F) #46+54+40-5)m(FAV)
100:
21 (FAY)= 140+4-100
n(FAV) = 8
Answer: There are 8 of them who play both
Tiolin and flute
16. Work for the week
1)0
watoned
158 TV. viewers questioned, BBC-1 and 85 watched BBC 2. How many watched both 7
(2) In a form of 36 boys every boy carried
pan, 20 had blue pens. 28 had black
pens, and 5 had red pens. 7 of them:
carried any two of the 3 kinds of pens How many of them carried pens of all, three colora ?
Statistice show that more than 70% of
men drink andan 60% of many BROKU
What can you say about the percentage who do both f
Reference: Basio Cóncepts of Newa Nathenation by Y. Lee – Essential Prese, 6-0 Nelson Street
wloon
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