頁二第張七第 日八初月二年午戊屬夏
WAH KIU YAT PO
報日僑
11 4 16 *
1978
|中場會考試題領習專欄
The circle is
2
(x h)2 + (y - k)2
-
Also, (h, k) is on 3x-4y=0
Since the circle passés through. (0,0)
+
= 25
h)2+(0 - k)2 = 52
(1)
3h 4k
新數學 廿四 番榮家
From (2)
MODERN MATHEMATICS (24)
Answers to Test Nine Section A
Substitute into (1)
k =
= + 碌
The circle is
25
(2)
(x-4)2+(y 3)2= 25
or
+ 3)2
= 25 (ans.)
As shown in the figure
AC AL BQ
AB a + b
BC b
= √AB2 - BC2
(*
?
rt.
ABC
+ b)2-
-Maj2·
Hab
ab (Ans,)
But PG AC
•PQ=
2/ab (Ans.)
2. Let the length of each side of the square be a and that of the equilater.. al triangle be b
48 - 3b
Area of the square Area of the triangle
+(b)(b)sin60°
-2/2
(Ans.)
3.
2kx + (4k
X
19-20 13
n+1
12 2012-1
11
1
210 (Ans.)
8. Scos20
-3sin@cose 3sin@cose
= 4(sin e + cos28) Cos20
38inecose-4sine
(cose-4sine)(cosê+sine)=0
(COB✪ - 48ine = 0 tane - 1
@ -14°2′ or 194°2!
(Ans.)
cose + Bánе = 0
tane =-1
3)=0
-135° or 315°
(Ans.)
Since the equation has
no real roots,
(2k)2 - 4(1)(4k-3) 0
-
16k+ 120
- 4k+:30
(k-1)(k−3)<0
1 < k < 3 (Ana.)
(2x −1)2 + 4(3-y)2 = 16
2(x-
1) 24(y-3)2- 16 2)2+ 4 (y-3)2 (x - ¿)2 + (y-3)2
4(x
= 16
22
It is a circle with centre at (1, 3) and radus 2 units..
pč
(3)
5. ā =
21 +31
no
(31 +53)
+ n(41
+ 73) (3m. + 4n)Ï
+ (5m + 7n)J
3m +40= 2
(1)
50+ 7n3
.(2)
7x(1)
4x(2)
** 2 (Ans.)
Substitute into (1)
| 3(2) + 4n = 2
n-1 (Ans.)
6. Let the centre of the
required circle be (h,k)
Section B.
9(a) Since k = 2n
the statement is found to true only when
2,4, .... 2000
A is the correct ens.
(b) When n = 1
=
12 is divisible
by 12
it is true when
n = 1 Assume5 7 is divisi- ble by n when n = k,
12 N
where N is an integer
When n k+ 2
sk
+2
52.5+ 72 7 52(12N-
128 (72 52k 52.12N + 24.7k 2.pky
= 12(25N + 2.
is divisible by 12 Since the statement is. true when n1, and if it is true for n = k, then
it is also true for n=k+2, therefore, the statement
is true for all odd inte-
gera n.
經濟與公共事務(廿四)
·孔繁盛、
Economic and Public Affairs
(34) Education in Hong Kong
(continued)
5. Technical Institutes
【四期星
The government has given considerable priority in recent years to the provis... ion and building of techni- oal institutes, most of ki whose courses are designed for Form 3 leavers..
At present, there are four technical institutes in Hong Kong. They are the. Morrison Hill Technical Institute, the Kwai Chung. Technical Institute, and the Haking Wong Technical: İnati- tute.
The institutes offer a wide variety of courses, including mechanical, elec- trical, electronic, building and civil engineering; plas- tica shipbuilding and ship repairs textiles and cloth- ing; commerce; and service. industries, including hotel keeping and tourism,
All these courses are.
provided on a full-time,
blook release, part-time day
or part-time evening basis. The institutes maintain close contact with industry. and commerce.
6. Post-Secondary Education
There are two post-second- ary collages registered with the Education Department under the Post-Secondary Ordinance. They are The Hong Kong Baptist College and The Hong Kong Shue Yan College.
The Hong Kong Baptist Col- lege was registered in 1970. It has four faculties arts business, social sciences, and natural sciences and en- gineering.
The Hong Kong Shue Yan. College was registered in 1976. It consists of three. faculties arts, social sciences and commerce.
7. The Hong Kong Polytechnic
The Hong Kong Polytechnic was formally established in 1972, when it took over the work of the former Hong Kong Technical College.
The polytechnic has 15 te- aching departments grouped under three divisions. They are Applied Science Division, Commerce and Design Division, and Engineering Division.
The polytechnic offers two year full-time courses lead- ing to a diploma, three year full-time courses leading to a higher diploma, and one- year full-time post-higher. diploma courses leading to an Associateship of the Hong Kong Polytechnic.
The University of Hong Kong
The University of Hong Kong was established in 1911 with a land grant from the government. Substantial government, grants are made towards the university's annual recurrent and non- recurrent expenditure.
The university offers und- ergraduate places in the following faculties: arts, science, medicine, engineer- ing and architecture, and social sciences and law/
It also offers a number of degrees of Masters and Doot- ors of Philosophy in certain fields for apsoially-qualif- ied and selected candidates, Its Department of Extra- Mural Studies also provides evening and day courses for adult students.
9. The Chinese University of
Hong Kong
The Chinese University of Hong Kong was inaugurated in 1963 as a federal university It is a self-governing cor- poration that draws ita income mainly from government grants, The university com- prises three constituent colleges Chung Chi, New Asia and United.
Following the enactment of a new Univeristy Ordiance in December, 1976, teaching methods at the university were ohanged to provide a balance between *subject-oriented' teaching and student-oriented teaching.
The university consists of four faculties arts, business, administration, science and social science. It also has the Gradiste School which offers instruction at post- graduate level through 17 divisions.
10. Teacher Education.
Except for technical teach- er training, teacher educat- ion is provided at the Educa- tion Department's three coll- eges of education – Grantham, Northcote and Sir Robert Black.
They offer two-year full-time courses for produ- oing non-graduate teachers
in primary schools and junior › forms of secondary schools. The college also have third- .
日六十月三年八七九一屦公年七十六國民華中育教華
year courses aimed at raising
the standards of teachers and
preparing them to teach the
new curriculum in junior secondary forms.
The
Technical teachers receivė training at the Hong Kong. Technical Teachers college, which is administered by the Education Department. college trains technical teachers for secondary schools prevocational schools and te- chnical institutes. The pollege also provides in-ser service courses of teacher training. A centre de being developed for technical
tenohers to gather and exch-
ange ideas.
數學 二十四女長波
Mathematics 24
Solution to exercise 10 Section B.
11.Solution:
Ans. (a)The cars meet at 9.50a.m.
(b)The distance from
I when the cars. meet is 25km. (c)The speed of the car returns to X is 75km/hr. and the speed of the car return to Yis 45km/hr.
12.Solution;
His sale for of the estate at a gain of 20% -$240000x4x(1+20%)
#$72000
His sale for of the estate at a loss of 15%. »$240000x x(1–15%)
$81600
His sale on the whole at gain of 10% 520 -$240000x (1+10%) -8264000
His sale for the remainder -$264000-$72000–681600.
-$210400
The gain % for the remainder part of the estate
110400-240000x(1–1–3)
-31
13.
240000x ( 1 −1-
Solution:
x100%
Let AB be the length of the shadow of the longer pole
AR 10
44
AB-7.5m. AG-(7.5-4.5)m
In AAGC
tane
8-30 58
LNCA-90°
-59
The bearing of the
shadow cast by the rope is N59°2:W or E.
Solution ZBAD-180
-84 *4-20
*-35o·
4x84-28°
In 4 ABC
BC
AC sin56' sinɓl"
sin61"
i.e. Bc ACsiu56′′
In AACD
CD
AC
ain28"- ain35°
i.c. cp ACsin28“
AOsin56
BC
sinól
CD
ACain28
sin55
ain56 sin
sin61 sin28 -1.16
Given: ABPC is a cyclic
quad. PXLAB
PYLBC; PZLAC
To prove:(a)ZPYX=ZPCA
Prove:
(b), Y, Z are
collinear.
(a)Since PXLAB; PY1BC; PZLAC
• £PXB=¿P¥B=90°.
ZPXB+LPYB=180*
(Given)
X, B, Y are coucyclic
opp. La supp.)
Similarly, P, Y, Z, C are concyclic..
¿PBX=/PCA (Ext. 4 cyclic
quad.)
¿PBX-ĹPYX (4s in the same
segment)
< PYX-LPCA
(5) ≤PCA÷4ZYP=180° (opp. 28
16,
cyclic quad
‚ĹPYX+ZZYP×180° (subst.)
Z are collinear (Adj. Za supp.).
Given: RC is the diameter.
of the circle
CE is the tangent of the circle at C. BC//AD
To prove BC AEBD
Proof:
Join DC AC and AB.
ZBDC-90 (4 in semi-circle) Since BC is the diameter and CE is the tangent at
C of the circle.
LBCE=90°
AD//BC (Given)
LAEC-90° (Int.
AD//BC)
i.e. ZBDC-ZAFC-90′′*
ZDBC-ZDCE (Z in alt.
segment)
/ ZACH=ZCDE (3rd 2 of 4)
BDC CED
are similar (Equiangular ás)
BD CE
(corr. sides,
BC CD
similar As)
Similarly, AACE are
CE AE
CD AC
BD AE AC
DE similar
(subst.
BC AE BD-AC
LCDE-LABC (Ext. 4 cyclic
quad,}
LCDE-4BCD (proved)
.*:/ABC=4BCD
.. AC-BD (Equal¿, equal
chords)
i.e. BC AE-BD2