1977-01-26 — Page 19

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頂滅

郭日僑

三期星

日六廿月一年七七九一公年六十六國民中

育敦聞港 算三第張五第日八月二十年辰丙襃 WAH KIU YAT PO

琴 后有 时

專在辦

良好。

其粉蕊

TIDAK AR BIO

各十呼救

《云物 在大

作:○公玫酒、往生 火 拒及 壓器 防效庙澳大人時 29. 11M PHOT

凍飲

人社 銀助 乘九

攜手

**

心人

洗

菜麵 救辦法:

助

糖後·英料 已

廣代明

來信今

(一九六二年一月廿六日.

: 為半米音樂社、編商會、英語菜

與會四商酒機酒店工會,嫁大爲有

近明霸中题 杜本負能型链

:1977中學會考試題預習專欄

明德社主編

0.70712

+2(0.866)

0.4142

= 5,56051.

But BDCos45° - AB

AB

BD =

新數學(十二)·魯榮家·

cos45°

20 COS45°

▲ XDM

Modern Mathematics(12) -

Answers to Exercise 5(cont.) 11. When n =

87

= 8 + 7

-1

1

14 is divisible by

therefore it is true

when n = 1

Assuming that the state- ment is true when n k i.e. 8+7^-1 is divisible

by 7

k

8 +7-1 = 7N

where N is an integer

or

= 7N-

yk + 1

when n= k + 1

8*+1+7k+1-1

=

8.8 +7.7* .k

1

8 (7N-7 + 1 ) + 7.75-1.

= 56N-8.7*+8+7.71

56N

qk + 7

= 7(8N-7k-1+1) is divi-

sible by 7.

Since the statement is true when n=1, and if it is true for n=k, it is also true for n=k+1;

= 28.284

*. 28.284 = 5.5605

r = 5.0866 (Ans)

14. r+gi is a solution of

ax2+bx+c

a(P+qi)2+b(p+qi)+c = 0 a(p2+2Pgi−q2)+bP+bqi+C

= 0

(ap2¬ag2+b+c)+(2aDq+bq}í

= 0.

0.

(ap2-aq2+bp+c)+q(2ap+b)i

0-

ap2-aq2+b+c=0- q(2a0+b) a(P-qi)2+b(D-qi)+c

(1)

(2)

= a(p2-2pqi−q2)+b¤¬bgi+c

(ap2-aq2+b+c)-q(2a+b)i

=00 = 0

satisfies Since D-qi also,s the equation ax2+bx+c=0, therefore it is also a solution of the equation.

15. (i)

Range of

marks

Number of Can- didates fall- ing in this range.

therefore the statement is true for all natural numbers.

10-20

20-30

12

30-40

25

12.

aji) the sum is odd if one

40-50

30

50-60

40

card is an odd number and the other is answer

60-70

35

70-80

30

number.

80-90

20

Probabiliti ty

90-1.00

0

The mean

52-5125 - 3

102

ii) If two cards are drawn

one after one, then the Probability

5

1001 901

=

the numeration is multi- Ply by 2. because the first card may be an odd number or an even numbers, the denominator is 101. 9C, because when a card is taken away, there will

nine card remain's. be iii) if two cards are drawn

one after one with- replacement the probabi-

2.5 1.5 1

la ty

101 101

*1

P(E)

(F)

C

=

52 1

==

b) i) Let the Probability be

•*. (E) = 1201 - 1

521

(Ans.)

ii) Let the Probability be

(F).

iii) the required, Probability

P(EAF)

iv) the required Probability

52

P(BUF)

= P(E) + P(F) P(EGF)

MD=

=

1

1

+

13

52

In rt.4 XDM

r

tan22.5

(1)+(2)+(3)

BY + YM + MD

(Ans.)

8X15+12X25+25X35+30X45 +40X55+35X65+30x75+20x85]

- 200 55.35 (Ans.)

2 5

iii) From the histogram, the

number of candidates

with marks more than 54 is

20 + 30 + 35+ 40 x 945

= 20 +30 + 35 + 24

= 109

Pass%

132)

109 200

X 100%

= 54.5%

Q B

1

(Ans)

2

As figure shown, and XY are Produced and meet at P.

AB

AXYZisan equilateral

*riangle

.*. £XYZ = 60°

...LXYD

-

4

(Ans.)

1.

(3)

1/2 x 60° = 30°

30°

45°

4 ABY = LBY

+ 4BPY

-45°

= 15° (Ans.)

+2rcos30°.

Sin45°

tan2225

But BD BY + YM + MD

T

BD=

Sin45

2rcos3

tan22.5

1

sin45+2cos30+tan22.5°

.*.ĹBYR

LABY

=

..

30° + (BPY

ii) Let the radius of each

circle be r

In rt.A BQY

八街 德加·低的

休假上

問號 蕸請大 水午近阿合八 ▶畢度中先寫,後瞰孵,時

BY =

sin45° In rt. A YXM

YM = XYCOs30°

長風野外之友

、之友』一月三十

東北丘崗賞遊日(星期日)

「長威野外

-(1):

2rcos30o -----(2)

ROM = 45° X

22.59

數學(十二),女長波

Mathematics 12

Solution to exercise 4.

Section B )Each question carries 10 marks)

11. Solution: p =

which k

k+k29 in and *2. are

constants.

.900 k2+10000k 2

-(1) 1000 = k2+12000k -(2) (2)-(1) 100=2000k2

=

1.

2

Subst. k2 into (1)

900

20

·k1 + 500

1

= 400

400 +

C

If his sales im a month is $30000, his income

X

= $(400 + 20 x 30000)

= $1900

If he gets an income of $2000, his sales

.......

~$(2000 400) X 20

= $32000.

12. Solution: volume of the

cuboid 10X6X4, cu.cm.

240 cu.cm.

volume of one pellet

4(5)3cu.m.

= 523.6 cu.mum.

Number of pellet that

can be made-

240 X 1000

523.6

= 458(correct to 3 figures)

Weight of each pellet

=

11.4 X 523.6gm

1.000

= 5.97gm(correct to 3

figures)

13. Given: PQRS is a square.

4ca

PV VS. PQ =

To Prove:

a) XPR is an isos.4. b) rx is a tangent of

the circle at P.

c) Calculate the area of

trapezium PORX

- roof • Since FQRS is a

square (Given)

.*. ES // OR

OR (properties

of square)

4 XVS = ZXQR; 4XRQ=XRQ

(corr.Ls VS//QR) (common)

(Equiangular)

(Equiangular

A's).

LVXS = LQXR

XVS

As

are similar

XQR

VS

XS

=

OR

PV

=

. 'VS =

1PV = 1QR

XS

=

米粒

vs (Given)

i.e. XS SR

rss (Common)

<SX + ASR = 90°

(Properties of square)

APKS APRS (S.A.S.)

PX = PR (corr.sides of 4s)

APXR is an isos. A.

LERS 45° (Proper- ties of

square)

FRS = LEXS = 45° (base 4s isos A)

¿ XR = 90° (2 sum of a )

A)

X is the tangent of the circle at (to radius)

Area of the trapezium PQRX =

1 x (4+8) x 4sqm

-24 sq. M .

14. Given: AQLOB. M = MQ.

To Prove:

a) MC = MO

b) PC2+0C2

AB

Froof: Join 50 AO = OB (radii) ZOAB = ZOBA ..

(base Ls isos a )

院禮業舉行,參加者 時假基尼地道經鐵被— 之學生股務團,非常收

·嗎·舞吧·朗誦比賽,那飈此次比賽,可加過 「傷強之音」音楽・歌 千傷人士之發揮 一锄院社會服務團主辦之」洪比赛,乃提供一個給 於昨日由下午二時毡五他們的自信心,而主辦

敬安赞助-香祗挪需破主任在致詞中略謂: <> RIKENNE-

【灣仔 民政署鄧鏡波書院合辦

【本港新聞

傷殘之音歌唱比賽

|五十多名傷殘勇女 年

| SALOKOHEK

( 一買決分奪证,季軍,養好,溫秀英,關潔英 陳英躪以一曲「未了費優異號:朱萬安 阻 j冠軍,携鵩英;秒, 沐歌唱組-郭第 ,禇果由一位失明少女應關英,李 寶珠, 「比賽結果如下: WEAKS EX?

Į KRESKRESKE (KZ) (1#BRE)

「媽踐之音」歌唱比賽,爲:灣仔民政主任梁

:

#

Q//AB,

▲ AOB = 90o (Given)

LOAB = LOBA = 45° (4 sum of A): FQ // AB (Given) LOCM = LOAB = 45°

(corr. £'s FQ//AB) M = MO (Given)

OM LEQ

(centre to the mid-

Point of the chord) i.e. OMC = 90°

ZCOM = 45°

(4 sum of A).

MO = MC

Pc2 + Qc2

**

sides opp

equal L ́s)

··{*M−MC)2+(QM+MC)2

FM2-25M.MC+MC2+QM2+

20M.MC+ MC2

25m2 + 2MC2

2(+M2 + OM)2 (subst.) 2-02(Pythagora's

=

Theorem)

A02 + OB2

(rythagoras

Theorem)

www

2A02

Since AO PO (radii)

A

AB2.

B

15. solution: Let they meet

after travelling for n days.

[2x30+ (n−1)(-2)]

n'

+

[2

=330

x 20+ (n−1)(4)]

(62-2n)+(36+4n) = 330

31 - n2+18n+2n

-M

2

n +49n 330 = 0

(n+55) (n−6) = 0

330

n=6 or -55 (impossible)

They will meet

after 6 days..

16. solution: Let 35+1

$5 and $5, be the cost

2

3

of the manufacturer, middleman, shopkeeper and the customer res- pectively.

then S = 5 X (1+30%)

1

S = $,X(1+10%)

2

$.3

i.e. $3

=

S2X(1+40%)

S1X(1+10%)(1+

40%) = S(1+30%){1+

10%) (1+40%)

= 2.002 S

Example: Many

huts

by

the

fire last week. (E) (A burnt B. are burnt C. being burnt

D. had burnt

E. were burnt)

1. The bank

by three thieves yesterday. 10)

(A. had robbed .B. was robbed

A would rob D. is robbed

S3 exceeds S by 100.2%.

. S = $1002 X

= $1000

100 100.2

Profit of the manufacturer

$1000 X 30% $300.

1977中學入學試試題預習專欄

智慧社主編

ENGLISH (12)

Write

Choose the beat answer..

the LETTER in the brackets.

E. robbed)

2. The great man

everyone.

by

(A remembers B. will

reuenber C. will be

remembered D. haa

remembered E.

3. A lot of pigs

2.0)

(A. keep B. are keeping

C. kept D. are kept

E. have kept)

4. The old house

them.

(A. has been pulled:

bered}

by Mr. Ho,

3.()

down by

4.0)

B. pulling C. is pulling D. has pulled E. pulled)

the lost child'

5. Where

found? (A. had D.did

6. This film *cinemas. (A. shows

В. ате C E. WAR)

#5.0)

were

at many

6.( )

B. is shown"

C. showed D. is showing

E. will show

7. The newa

very quickly.

C. is

CA. knew B. knows

known D. has known E. are known)

8. A lot of fumiture

Hong Kong.

(A make B. has made

7.0)

in

8.0)

C. is making D. will make

E. is made)

9. We

carefully.

to cross the road

(A. tell B. are telling

C. told D. are told. E. shall tell). 10. A new tunnel"

9.0

between

in

Happy Valley and Aberdeen. (A. will build B. building C. is building D. builds E. is being built) 10.( ) 11. This exercise should fifteen minutes. (A. finish B. is finished C. be finished D. have finished E. finished)

12. Several ships

the typhoon

11.6)

during

12.()

(A sinking B. were sunk

C. has sunk D were

sinking E. sunk)

13. They

not to do it again.

(A warning B. have warned

C. had warned

D. have been

warned E. warned) 13.00)

14. The bad man

angry crowd a

up by the

14-()

(A. beat B. has beat en

C: was beaten D. beating E. should best).

15. Many workmen

daily.

(A. are paying B. pay

G. are paid D. paying E. is paid)...

16. Gambling should

every country.

15.00

in

16.()

(A. be stopped B. stops:

C. stopping D. being @topped E. has stopped) 17. By whom will the floor

(A. cleans B. be cleaning

C. be cleaned D. have cleaned E. clean) 17.( ) 16. Has the hole in your tooth

?:

18.()

(A. mended B. been mended

C. mending D. mend

B. being mended)

19. Fupils

to sleep during lesson time.

(A. don't allow

allowed

19.0)

B haven't.

C. aren't allowed

D. shouldn't allow E. aren't allowing) 20. Who

to be our captain?

(A. has chosen B. will

choose C. choose D. has been choosing E. is chooen)

ANSWERS

20%()

1.8 2.0 3.D 4.A 5.E

6.B 7.0 B.E 9.D 10.E 11.0 12.B 16 A 17.0

14.0 13.D

15.0

18.8

19.0

20.E