育教僑華 頁一第張七第 日二十月十年巳丁麻夏
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WAH KIU YAT PO
日二廿月一十年七七九一届公年六十六國民華中
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望各界人士,成本港各
「錢,自然要補-
·故希」惹者不可錯過!次機會
「帶初期由有關人士捐贈,系會主辦廿億次風
「具展的玩具,都是由蹄之管風琴亦全港最大
*但多玩了,不免有拉纤音樂會,愛好風屖洲 行大厦五
KELSTRERE.
九髄旺角圍創興銀
樓
· 香港灣仔軒尼詩道
四三九號善岛大厦、
̇但初鮮
二期星
心中童兒各會益羣童小
·動活智益康健童兒辦舉
出指華淑余人責負心中山雲慈
倡的有月
耀
BELL!
茶樂音大中
1奏演琴風晚後
辦語
班適週院言科
用
育教僑華
學能推理練習專欄
智慧社主編
文字推理練習十九
綜合練習七
選出下列每願最適當的答案,並在它的下面 - 1 BR 2-
下列各赌是一個句子,就選出最適當的答案! 以完成該句
1.老對舊正成幼谢!
A#B
C
DA
小
2。中必對繁鄭正如英文
在翻輝:B大楷C外文D拼音 -
字母
湖水到清澈正如天生野小學)、
**** B*** CAR DEN ENE
4.抑鬱都消瘦正如都暢對?
AMM BWA CALAP D輕鬆E清減
碗碟對瓷土正如刀劍謝!!)
A
B C#7 DMME BA
把下列各题內的字和詞,重新組成通顒而 合理的句子,然後選出排在句中第三位的宇或詞
6. by Sik
̇他的抑揚頓挫
A怎不令人B抑揚頓挫 C蛆械
D豐富
E學苑讚背
預防注射 最有效的接受 我是
B**
D.最有效的E方法 密码 ***R E
野劃建設點了哭孤
De
設備:具有
B當地
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方法是防捉
CM防注射
快锐務及乾工廠出品,
B. Jo
C
Emi
科學化的
ASER:
·D #$49.
吹走了 枫枫的
綠油油的
A⭑T
D. X
细閱下面一段文字,然後解答所附的問題
以下是一個戲團襄動新表演的情形
狗咬着踽的尾巴,
#7 DEC
****ARNING ·
吹着老虎的是池上
猴子心着的尾巴。
添徠動物还排咇普尾巴闐成一個圓圈
2. Solution:
Let k(x+y)2
2 2
kx2+2kxy+ky +x2+y
{k+1} x2+2kxy+(k+1}y2=0
If the L.H.S. of the equation
is a perfect square, then
the discriminant blac=0.
(2k)2=4(k+1)(k+1)=0_
-4k-8k-4)
-8-4-0
Solution:
kat
Let 8p be the sum of mone
2p=p(1+10%)" ·
2-(1-1)"
nlog1:1-10g2
log2
log1 1
0.3010
0.0414
-7.27.
The time required
7 years.
Solution:
The cost of 1gm of the mixture
100 1.5x81.2.
125
The ratio
of tea at $1 per
gu to tea at $1,6 per go =(1,6-1,2):(1.2-1)
=0.4.0.2
2:1
They must be mixed
the ratio 2:1,
5. Solution::
2sin xa con là
2
2(1-cos x)+Jcosx+1=U
2
2009 x- Bcosx-3=0
(2cosx)(enex (3)
cosx=- or √3 (inadm
Bor (inadmissible)
-150° or 210":
Solution:
By cosine formula.
2 2 2
8-b+c-2bccosA
• Bc2 = (5+1)2+22 -2 (5+1)(2) cos30
+25+1+4–4 (B+1)·31⁄2
=8+2√3-6-2√3
-2
BC=√2
***** [ML?
A B
CAL D猴于E大家
其中一烫動物把口中的尾巴放閃,以便排版
MPAA RANG
12.腓一隻動物的尾巴被软鶴等?
C蚴子:DD老试 EM寺
A
By
VIB
2 E
13 A
54)C
(5)D (608
7 A
C
9.0
14 A ut E (I2C
Given: BCDE is a rectangle
BC-3cm, AB=10cm, AC-12cm.
To find: ADV
Solution:
Let AD=xcm, DC-yem
212122
x+y=12)
BE-DC-уcm AE=(x-3)cm (x-3)2+y2-10
Solution:
Since FAG touches the circle
LCBA-ZCAF-72°
A
DE//FG.
LEDALCAF
i.e. LEDA=72"
(1)
(2)
Section B
9. Solution:
(a) x+2
xy=4k
from (1) x=5k-2y---(3) Subst. (3) into (2).
2
+(5k-2y)y=4k2
2 悲 45ky-2y=4k-
(y-4k)(y-k)=0
y=4k or h
when y4k; x=5k-8k--3k when y=k; x=5k-2k=3k+ "(b) *•*x~y=4
if y4k when x2 ~3k-4k-4
ka-(rejected).
If y=k when x=3k
3k-k=4
k=2
Solution:
Since ad(b+c) and he(c+a)
a=k,(b+c) (where X is
constant)---(1) b=k2(c+a) (where ką is constant)---(2)
from (1) ask b+k, e
a-k, b
from (2) b=kqc+ kn
+kk,
172
Since
and
are constants.
also constants
新數學(八) 魯榮家
MODERN MATHEMATICS (8)
Test Four;
Answer ALL questions in Seet- ion A and any SIX in Seation B. All necessary working must be shown
SECTION A (40%)
1. Solve the equation
2
X
8
2
-(1)
-x-10
2
2
If x
4 = 0, the value of (21
1978
中學會考試題預習專欄
AF Affai
數學(八)
文長波
2
x2-6x+9+y=100
2
2
2
(1)-(2)
-6x+y=91-
6x=53.
-(2)
AB
The length of AD is 8zon.
CA
Mathematics A
Solution to exercise 3.
1+49
Section A
1. Solution:
Since p
q-4
`pq-4p×1+4q
pq-4q=1+4p
q(7-4)=1+4p
P-4
p+q=pe
144p
P-4
_p_−4p+1+4p p-4
2
8. Given: FAG touches the
circle at A. DE//FG ZCBA-72"
To find: ZEDA
find
1)2.
3. In figure 1 AB, BC and
CA touch the circle at X..
Y and Z respectively. If
11 cm, BC 13 cm and
8 cm, find the length of BX.
8
Figure 1.
4. In figure 2, ABCDE is a
pentagon inscribed in a circle. If AB is the din-
meter of the circle, find
4BCD + ¿DEA.,
(ii) the area of the shaded
region.
Figure 2.
5. Selve the inequality
2x3
6. Find the equation of the
circle with radius 5 units
and concentric with the
circle
(2x − 1)2 + 4p2
If 2 + 31 is the solution
of the quadratic equation
+ ax + b = 0, find the
real numbers a and b where
8. In figure 3, 3 concentric
circles of radif are of radii 4, 6 and 10 respect- ively. A paint is marked at
at random inside the outer circle. Find the probabi-
lity that the point is in
the shaded region
[SECTION B.
Figure
9. Prove, hy mathematical
induction that
2 > 2+1
for all positive integers n>2.
10. If sine and cost are the
roots of the equation
2
(a) find the value of k
(b) find the quadratic.
egnation with roots tanë
and
1 tanë.
B
11. In figure 4, the circles with centres A and touch
each other externally at
E. CD is a common tangent
to the circles
Pigure 4.
(a) If AE = 5 units and
BE 3 units, express DE and CE in
terms of EA and AD.
(b) Hence, or otherwise, show
that DE 1 CE
12. In figure 5, circle DEF
is inscribed in the sector AUD. 4A0B = 60°, 0A - OB -12cm, find
(i) the radius of the cir-
ele inscribed in the
sector.
Figure 5.
13. The graph of y=b-(x+a)_
passes
through the points (0,-3), (1,0) and (c,0) as shown in figure 6. (i) Find 8, band c (ii) What is the greatest
value of y
21:0).
Figure
14. In figure 7, frustum
of a cone (formed by cutting a cone through a plane parallel to the base,) has radii 2cm and 4cm and the distance between the two end faces are 3em apart; find (i) the height of the
cone from which the
frustum is eat,
(i) the total surface
area of the frustum (iii) the volume of the
frustum.
ટ
Figure 7.
15. In a certain college, 40%
of the students have brown hair, 25% have blue blue
eyes and 15% have both brown hair and blue eyes. A stud- ent is picked at random from the college
(1) If he has brown hair, what is the probability that he also has blue eyes? (ii) If he has blue eyes, what is the probability
that he does not have brown
hair?
(iii) What is the probabili-
ty that he has neither brown hair nor blue eyes?
16. If a+bi is a solution of
the quadratic equation
2
px
qxr- O where P, 4
and r are real numbers. Shaw that a-hi is also a solution of the equation.
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