1977-11-29 — Page 28

華僑日報 All

A

JOSEFERIX[R] -WESHEK·DENSHION IS 6 MINNE

师 香港學校朗誦節特

賓四第張七第 22

日九十月十年巳丁服复

WAH

YAT PO

郭日僑

二期星

日九廿月一十年七七九一腊公年六十六國民篩中育教儒攀

元朗信满小學。

29

B**• OFFERERUSA

軍何福堂上午校。合季軍元信小

日小學四至六年男女合誦「落日」;莊東新界元朗上午校。

2. (2x

1)2

The

教僑華

T

20 T

- 4(0) + 17

學能推理練習專欄

17 (Ans)

智慧社主編

文字推理練習二十

∵綜合練習(九)回

選出下列棒選最適當的答案,並在它的下面 糖糖。

試把下列各翻內的字和號,重新柤成通順而 合理的句子,然後選出排在句中第三位的或

SA IBÉ AIRP B

辯論:可將綠論階段

C鲜花:D被

est

ET

不久

HE

EARL

A CIL

BARR

E & IC

HEIDEL

FRILIE

Ex

大自然的

B**

CEM

D知做

E*

5.把者-災民

事發

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B

C

A

DEA

他我那跨大的聽到反感非常富城

E經過

B邵路大的C譏到

T**

高唱中清晨的陶醉

A #M

B✡

SNAG

T

18

area of the shaded

region

The required probability

20T.

100T

A tens

Binëcosë;

in@con@

The equation is

*

(북)=

18x

+ 7 = 0 (Ans.)

(九) 文長波

Mathematica 9

Solution to exercise 3 Section B

4 GME=ZEMK=90°

EM-EM (common) A GEMFAKEM (A,S,A.)

GM-MK (Corr, sides) Similarly HMM..

GHKI, is a rhombua, (Diaga, bisect each

other and cut at rt.L.) Given: BX and EY are

altitudes of BCD and EDC'

respectively

To prove: (a) ABC: DAC 4ABC:6DAC-BE÷DE.

quad' ABCD: ^DAC=BX÷EY

3. AB, BC and CA are the

tangents of the circle,

therefore,

AX AZ, HX - BY and CY = CZ

Let BXx en

BY

[CY=[CZ] BO

AX-

AB

The perimeter of the triangle

11 +13+

32 (em)

2x + 2(13-1) + 2(11-x)

(Ans.)

SECTION B..

9. Let P(n) be the statement

(2n + 1) > 0

for all positive integers n>2.

When n-3

p(3) ► 23 - (2)(§) + 1

-20

It is true for n = 3.

Assume P(n) is true for nuk, therefore

(2k + 1)

2k - 17.0

Consider when n k+1

P(k + 1)

BX - Bem (Ans.

下列各题有五個項目,其中一個和其餘四個 敢不同題,然選出這個不同類的项目

Since AB is the diameter,

therefore

8. P

Q凍

PL

R

RA

S*

TR

10. P#

11, A冬天B警探:C祭長 DA

"Z ADB = 90°

T***

ESI

12. AB47 C44 D**

E斑红

ABCD 180

13. A將来日精阚CAD日前

EAS

DEA

180

14. AL

Bu

CE

D**. E越南

ABCD +

2 DEA

15. A

B

16. P

Q

R

360°-(a 360 270° (Ane.)

90

D* E**

吕汗衫

T#

17,P清秀欢好 R苗锋 S娟好 T秀美

以下各题是一則謎語,試選出每則謎語兼遇

:當的答案。

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謝户外開花

P雨傘 Q纖粉

R.7

S玫瑰

T冬菇

OS OR TODA 2D (BA

CA DE OB @C 6C ®Q OR

45E. (8Q OR GOT 403 20P

新數學(九)

HODERN MATHEMATICS (9)

Answers to Test Four

BECTION A

.<

Multiply both sides by (x-2)2

(2x-3)(x-2) (x-2)2 - (2x-3)(x−2) – (x-2)2 (x-2)(2x-3)-(x-2)] >

(x − 2)(x − 1 )?

xler x 2 (Ana (2x + 1)2 + 4y2

4)2+4y2

2

The centre of the circle 18 (1, 0)

The required circle is :

(x

or

1)2 +

1)2+

52

- 100

榮家

k+1

· 2 (k+1)

2k

since 2k

2(k+1)

2k

1)+ (2 = 3)

- 2k1 0.

Also, k is a positive

integer greater than 2,

عار

- 3 must greater than 0;

therefore

P(k + 1) > 0

Hence, it is true for n=k+1.

ince, P(n) is true fom

and if p(k) is true,

then it is also true for

p{k+1},

true for all positive inte-

gera

greater than 2,

therefore, it is

2 > 2n + 1

for all positive integers n

greater than 2.

10. Since sino and con0ré

the roots of the equation

3x

Therefore,

2

the product of roots =(sine)(cose)

Kindc ose -

the sum of roots

-nine cose

(1)

sino + co80 ■

(2)

From (2)

2

11. Solution:

Sundries Total

Material

Labour

Rent

Original

after changed

20 units

50 units

25 units

5 units.100 units.

20

()units 50()units 25()units 5 units 106,6 units

-17,bunite

=54 units

30 units.

The percentage change in the running cost

106.6-100

x100%

100

=0,6%

12. Solution:

volume of the rectangular block

4x6x8cu.cm,

-192cu.cm.

volume of one solid sphere

*r ?

r(1) eu.cm.

4.19cu.co.

Number of solid spheres that can be made

192

4.19.

45.8

Number of complete solid spheres that can be made is 45. 13. Given: ABCD is a cyclic quad,

GF bisects LAFD.

To prove: (a) x=y.

(b) If EL bisecte

ZAEB, GHEL

is a rhombus.

Proof:

(a) Draw BP, DOLAC.

Since SABC, DAC have the same base AC.

4ABC; ADAC=BP: DQ. Z DEQ= [PEB (vert.

opp. 4)

ZDQE ZEPB➡irt4.

BP, DOLAC)

ZODETM 4EBP(3rd 4 ofA)

aare similar

DEQ

BEP

(Equiangular

As)

(b).

BP: DQ-BE; ED (Corr.

sides, similar 45):

AABC ADAC-BE: ED ABC+ DAC); DAC -(BE+ED):ED

i.e, quad ABCD: ADAC

-BD: ED 4EDY-BDX (Common) ¿DYE=4DXB=1rt4.

(*.*BX, EY-DG).

DEY-4DBX (3rdofs)

DEY ME

*DBX

fare similar

(Equiangularis)

BD:ED-BX:EY.

corr. sides, similar

4s)

quad ABCD; 3DAC=BX÷EY,

Solution:

Tet hm he the height of the hill

AF-hcosec28 m AX-hcosec12 m. AE=hcosech”m.

AF

COS/FAX AX

hcosec28 hcosec

LFAX~63°43′ COLFAE AF

AE

hoosec28" hoosec5o

FAE-79 18 4XAE-79 18-63°43

-15°35

- X

+8

10

(x2-x-9)+1__ (x2-x69)~1

2

3x2

3x2

x-9

(x+5)+3 (x+5)-3

-

-3x-27-x+

4x

+

32 - 0

- 0

(3x+8) (x-4) *--23

on 1 - 4 (Ang. ).

(2x-

(Ana.)

7. Since 2 + 31 is the solut-

ion of the quadratic

equation

Therefore,

(2+31)2.

+8x + b = 0

+ a(2+31) + b

4101 +912)+28+

(4 +121

0

+ b = 0

0

4+ 121 9+ 2a +Jai+b

(2a + b −5)+(Jn +,12)i

2a + b 5 = 0

3a + 12

- 0

(Ans.)

b. 13

8. The area of the outer

cimele

T(10)2

= 100 T

-

= 0

sin" +cos ̃0 + 2ain8c os ✪

16

+2sin8co88 = 16/9

#inecose -7/18

From (1)

k * 3sin@conÒ

k-

7/6 (Ans.)

(b) Let the required equation

be

2

X + px + ( ́ = · 0

qproduct of roats

(tane) (tane)

I..

p-sum of roots

1

- tano +

sine

tano

Wing

Proof:

(a) x=¿GFD+ZBCF,

y=LGFA+LGAF

(Ext.4. ofA)

ZBCF=ZGAF (Ext. 4 cyclic

quad.)

*GFD=4GFA (*.* GF

bisects (AED)

.x-y (Subst.)

(b) ZAEL-BEL (*.* EL

bisects LAEB)

.*. LGMF-LEMK (3rd 2 of 4)

Since ZGME+ZEMK+180°.

(Adj zy on at. line)

Solution: AB-DO-CA-24cm, Area of 4ABC

(2x)(2r)sin60s

22

4q.co

-1.732r sq.cm. Area of sector AFE

2 T

2

◓qcem

sq.CD,

Area enclosed' between the circles

-(1.732x2-3x2)sq.cm

2

-0.161r sq.cm,

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