日期星 日六月一年七七九一肠公年六十六國民中
1.e.
ing b sible by a+b
自授育教 旟三第張六第日七十月一十年辰丙
-13 and 2
1977中學會考試題預習專欄
明德社主編
WAH KIUYAT PO
or -1 and -1.
報日僑
MODERN MATHEMATICS (9).
Assume P(n) da true for
n=k":
14.
is divi-
數學(九)
女長波
Mathematics 9
Solution to exercise 3
k
a
The centre of the circle
= 0
Solution: The new posi-
tion of the man to the chimney and to the old position makes an of 909 at C.
LAOC = 180°
In A BCO,
BC
65°
Pogle
=100tan650m
= 214.5m
In A ABC,
AB
"20
The height of the chimney is 23.8m.
Solution:
a) Sirice AB i9 the dia-
meter of the,circle
月
the Lin
= 90°
semicircle)
CX LAS (Given ).
✪ + X = 900
B (Subst.)
CX
tan $ =
and
AX
XB
tan B= 颈
CX XB
AX CX,
1.e.AX-KB = CX4
Ap = 9cm::AX =
XB = (9-a)cm
acm
450
Area of square of side
CX=
cx2
:
= a(9ma)sq.cm.
Area of square of
side CX
日(9日)
81
4
81
+ ga
-- 81 - (a-2)2
The maximum area of
the square is 1.
or
20/sq.cm.
4
Bg.cm.
Solution: Let a and d be
be the first term and the common difference of the A.P. and r be the common ratio of the G.P. then 2a is the first term of the G.P.
{e+d)+2ar
+ 2a
6
= -1
= 1
(3)
(8+2d)+20m2
from(1) a = 2
from(2) 2+8+4r = -1
- i.e. d = -4r-3 ...(4)
Subst,(4)into(3),
·2+2(-4x-3)+4r'
4r2-8r-5
(2r-5)(2r+1)
1
218=-4(21)-3 -13
=
when 1-2 a=-4(24)-3=-13
Xem
Solution: The height of
the box is 40-38xen.or
(10-2x)cm
12
The volume of the box
x2(10-2x)cu.cm 2x2 (5-x)cu.c
3 14 15
|B|24|36|3210
The maximum volume of the.
'box is 37cu.cm wwhenrxis 3.3.
3.3.
15. Let 100x be the number
of artioles By be the cost price of each: article.
Number of articles sold
at marked price
- 100x- 5x - 20x = 75x
Total receipt on articles
sold at marked price
$(yx160)(75x)
= $105x3
Total receipt on articles sold at half cost price
- $20 x
=
$10xy
Total receipt on selling all articles
= $105xy + $10xy
m: $115xy
The profit=
115xy - 100xy 100xy
15%
16.
Solution:
Sun
a) A3 = 2cm
AC = (3-2x1)cm
= fon
BC/22-12cm
-
4.04
= 1.732cm
9-2 Since
1.732 Their are (4+1)) or 5 spheres can be filled into the box.
b) volume of the empty
space of the box
9cm
= 9x3x2cuem 5x (1)3cc
(54 - 20.94 Jeu.cm
= 33.06cu.co.
when r=-1 d=-4(-)-3
J-3 = -1
·The common difference
and the common ra
ratio are
新數學(九)·魯榮家
待關1年 金日巿證天 #民,賽表面 時所守香一。 編號現車
銀上行氣、玉卅馬十 間防砖 分鐘股在交三一廠
代今晚
,名
=
=
x2+y&_10x−14y+54
is (5,7).
Let be the mid-point of A3. Hence the perpen− dicular distance of the centre from AB is the length of OM.
Length of OM
=
70 (units)
Length of OA
radius of the circle
√2+72-54
$20 (units)
AM =
=
20-10
10 (units)
AM = OM.
LAOM
45°
also,
= 45% LBOM LAOM ZAOBLAÖN÷Z BOM
=
90°
AB subtends a rt. at the centre,
12(1)
idi) When x=0, y=4.00
4= asino + bcoso 4 = b. (Ans.) when y=3.00, x=90
3= asing0+bcos90°
= 3 (Ans.).
13. At the end of the 1st
year, he has $5000(1+8) At the end of the 2nd.
·year, he has $5000(1+8%)+ 5000(1+8). Similarly,
at the end of the tenth. year, he has:
5000(1+8%)+5000(1+8%)2+
5000(1+88)3+
5000(1+8%) 10
= 5000(1.08)+5000(1.08)2+
5000(1.08)3,
=
5000(1.08)
10
5000(1.08) 1+(1.08)+
(1.08)2+... (1.08)9)
= 5000(1.08) (1.08)10_1
(1«08-1
= 78169 (dollars).
Ans: The total amount
return ds $78160,
14. Let P(n) be the state-
+
or
a2+b2 = (a+b)f(a,b)
where (a,b) represents a
function of a,b.
=(a+b)f(a,b)-bt
When n = +2
P(x+2)
10+2.
2
=a+b
2
a2 [(a+b)f(a,b)-
2
a2(a+b)f(a+b) a2b2 + b2 bk. a2(a+b)f(a,b)
a2(a+b)f(a,b) + b*(b+a)(b-a)
is divisible by (a+b).
3ince P(n) is true for n=1, and if it is true for n=kj then it is also true for n = k+2. Therefore the statement. P(n) is true for n=1, 3, 5, 7 ........; iie. it is true for all odd natural numbers n.
15. 1丿 The probability. that.
the first ball is a white ball
271
=
51
=
Since it is replaced before the second draw. therefore the probabi- ilty. that only white
bails are drawn
(Ans.)
11) In three successive draws,
the probability of having
a white, a black and a white ball respectively is
2.
12
2 x 23 x 3 = 125
Similarly, the probability
of having a black, a white and a black ball repec-
X
18
tively is 125 Therefore, the probability. of different colours alter- nately 12
=
+
125
30
18. 125
125
6
(Ans.)
25
iii) The probability of no
white ball is drawn
(1-2)3
27
The probability of at least one white ball is
27 drawn = 1
125
(Ans.)
98 125
1977中學入學試試題預習專欄
智慧社主編
1. Tim wants to be an engineer
he leaves school. 1.(^)
and B. or C. but D. after
E. since)
my uncle is old, he is very strong.
(A. But B. Why O. Because
D. Although 5. Unless)
3. The beggar didn't leave
he was given some money. (Athan B. that C. where
D. or 前、until) 4. I can't buy t
no money
3.()
I have
4-( )
(A. while B. since C. than
D. because E. till)
5. Can you tell me You
Palled in the test ? 5.00 (A. why B. unless C. that
D. hut E. and)
6. Keep quiet.
punished ..
you'll be
(A. and B. or C. unless
D. since E. if);
7. She came in
she hed
khocked at the door. (A. for B. after C. before
D. but E. why)
8. They haven't come again.
last Sunday.
8. C (A. Since B. unless C. for,
D. when E. nor)
9. Neither Tony
B. nor
good swimmer. (A. if
E. and)
10. He ran away
policeman
(A since
Dick is a
9.0
D. but
he saw the
10%(0)
B. as soon as C. before D. why E. either)
11. She won't pass the test
she works harder. (A. unless B. or c. but
E. and) D. that
12. Her bark is worse
13.
bite.
114()
her
(A. thet B. if C. though
D. than E. unt11)
eat
12.( )
we may live. (A but B. if C, where---
D. after E. so that) 13.( )
14. Is that ruler yours
hers?
(Aands. past C.
D. but E. for)
15. No one
hurt.
()
the driver was
15.0)
(Ay if B. and C. except
D. for E. until)
Taipo.
16. Mr. Au used to live in
he was young. (A. unless B. or C. that
D. when E. until)
17. They have been here
over an hour... (A. since B. for C. if
D, whether E. but)
18. Both Tom
16.()
17.0)
his brother
are in my class. 18.() (A bit B. for C. where
D. though E. and)
19. The night was not only/cold.
also very windy. 19.().
(A but B. or C. if D. as well
E. and)
20. He was so excited
couldn't Bay a word. CA. till B. but C. that
D. unless E. and)
he.
20.( )
(A. but B. though
C. if D. and E. for)
(C)
ANSWERS
2.D 3.E 4.D 5-A 6.3. 7.B 8.A 9.8 10.B
11.A 12.D 13.E 14.0 15.0.
16.D 17.3 18.E19.A.20.C.
英文科
(九)
ENGLISH (9)
ment
Choose the best answer.
Write
sible by a+b
When n =
the LEFTER in. the brackets.
1
Example: We asked Tom
he
bn
= al + b' is
1.D
could play with us.
divisible by a+b
Therefore, P(n) is true
when n=1"
天心
十萬
第十世九:五天八
·北時界時 轉氣時
二 天氣煜告 -- 四重彩-四
午
分開
祝報一八分十一代十
掾民稱、閞 分氣 测分氣
天告時
秦國新婚費新,
旋關童血聞。天新一分新 號路的 周丽 甜
島的新告新雅天 消旋 閔趣艇
册。
房行息報中聞 的新
情交官分聞、
午報嘛報上所午癥餘雜,無價最上報侑交日報退館 紐
交交日
突快報 ,今天科報
人新, 午今股施: 有漁禪位多午告 ,易上,報堂小日氣,
一報的。
分最 三齡,分 人卅分之眯。
一站天。 五
Q
麗馨
九時十分,教育信
分州
「目驚心」片集。.
佳藝電視
二時,敦藥電視。
十二時廿分・「新
映名片;特務雙子座。
十一時五分,最後
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八時五份,無戲
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#
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明 珠 台
新珠糖
術報源
- 四時•『艺床
一化外奇女子」。
麗的中文台 NDERS OF THE WI
一卅分,新聞簡報,天氣 八時四十五分,
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曲。
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: 1時,個才對遷
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咸七虎將一片集。
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第十九要
小戰」
民的相 漁分
天食:
天
觀氣片
:
映與
片传九天八縣七
十分進十
一度五分
樂府
商業一台「還年青人際間),天小獲清卡通片鐵、鮑明
崇禎卡通片集、奇妙小
完 分鐘拼天報苑報語關 指民 時數 市達所氣 時間特民
時新告時繼
,花,踝九橋淳天八小蘭族人天妾,雜五彎,親國告年
年分齡 年分
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綠榔電台
時間: 花新報 毪新報選 分中報·簡銀下行您報
_七時三片
片。
社,八時,新出及天氣
张午情交
心糖
分罐
您
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鷹建永時十分:「柔道