1977-01-06 — Page 23

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

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册。

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交交日

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一報的。

分最 三齡,分 人卅分之眯。

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九時十分,教育信

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