1978-04-18 — Page 30

頁二第張八第日二十月三年午戊磨惠 WAH KIU YAT PO

報日僑華

二期星

日八十月四年八七九一曆公年七十六國民華中 育教儒备

k

(1)

育教僑華

12x+20

- (2).

10.(a) Let the first three

terms of the progression

be

4. Solution:

y-5-

-(1)

(x-1)(x-3) 3-x-x-1

y

30000 30000 506----(2)

from (1) y=x+5=-

has only one solution. Substitute (1) into (2)

-(3),

(x-1)(x-3)

-4x+k=2x-12x+20

1978

- 8x + (20-k):

()

【中學會考試題預習專欄

This quadratic equation

9 ar

+a+ar = 39%

(1)

2

729

4x-x(x-1)=2(x

subst. (3) into (2)

30000 30000

HVOR MAI AM

140) % Dale, Presi

must have only one root

4(2) (20

From (2)

:3

3 729

2

4-x+x-2x+6

x+x-2-0

(x+2)(x-1)-8

‚'‚x=-2 or 1 (rejected)

Ans, x--2.

30000(x+5)-30000x-500x(x+5) 60(x+5)-60x=x(x+5)

2

300 : 52

(x+20)(x−15)-0

‚!.x=15 or -20 (rejected) y-15+5-20

.The scholarship-holders

in school A and B are 15 and 20 respectively.

(b)Each scholarship-holder

in school A

30000

15 -$2000

Each scholarship- school B

-500.

12 (ARS)

新數學 廿九

魯榮家

Since

a = mb

Modern Mathematics (29)

Answers to Revision exercise

Paper I

Section A

1. (a)

Length of are AB

60

360

x (2π-r)

x 2 x 5.14 x 8

8.373 cm

Leugth of AB.

xBD

➡ 2(8sin30°)

8cm

perimeter

8.373 +8

16.373. cm (Ans.)

A(x - 1) + B(x 1) FC

12

Ar2+(B-2A)x+(A+B+C)

+B+C 2

A 5, B 7

Substitute into (1)

9r. 39

9r + 9r* 39r

30r + 9 = 0)

2.)

3(3r

1){r

-3)- 0

or r3

(2)

When r

the first

three terms are

• m(í - 23) • n(I +

-(□ + n)ī +(12n

2.

1223

2x(1) + (2)

1en - 7

Substitute into (1)

Since

3k

6K

275 9 and 3 respect-

first

ively

When 3 (the)

hree terms are.

1. (Abs.)

where kia a constant:

greater than zero.

2

376

22) ► 2 (64) 376-

94k

(rejected)

- 3k 6 (Ans.)

k-2

(Ana.)

3,9 and 27 respectively

herefore, the first term

is 27 and the common ratio

19 1/3, or,

the first term is 3 and the

common ratio is 3;

2

(b) If the sum is greater. than 1100, then the progres

sion must be the one with

first term 3 and common ratio - 3. (ice. the progr ession is increasing)

Assume 21 terms are taken

233",

2200

1100

Solution:

Let rom be the radius of the required circle

OD=0Ccoa36°52'

~(3+r). cm DB-5-(3+r)

CD=0C-sin36°52.

(3+r) cm (°

LCDB 90°

•*. x2 - (1 } } r)2 + (}{ (3+r)]2 25r2-(13-4r)2+(9+3p) 25r2=169-104r+1Gx2+81+5%r

60r=250

The radius of the

required circle is

4cm.

30000

20

-$1500

10.Solution:

The equation

2

X-3kx+3k+8=0 has

equal roots

(−3k)2-4(3k+8)=0

2

9kTM-12k-32-0

(3k-8) (3k+4)=0

or

The equation

x=3kx+3k+8=0 has no real roots.:

(-3k)2-4(Jk+8)<0

2

9k"-12k-3240.

(3k-8) (3k+4)<0

<<

+ B(x =

6k - 12 (448)

Section B,

9. (a)

and C - 10 (Aus.)"

3. Total amount returned

from bank A

--810000 (1+ (6)* (1+200)

=$11932,56

Total amount returned

from bank" B

10000+ 10000x

-812250

Therefore, Bank B will pay

more.

$12250 - 81.1932, 56

$317.44

ize. Bank B will pay

$317,44 more than Bank A.

51)+ D{x 451)

41)(x -51) *5(1—A)1:

+25

B.S. - (141)2 - 1

the statement is

'true when n^- 1

Assume the statement is

true when we have

When uk + 1

13. 23+...+(k+1)3

2203

nlog3

log2203log3 log2203. Tog3.

log

➤ 6.0069

Ans: At least 7 terms

must be taken.

1978

「中學會考試題預習專欄

明德社主構

1)2+ {k+!)3

■(k+1)2()2 + (k + 1)]

數學

~(k+1)2{k2 • ** • 1)

(k+1)2 (k + 2)2

(k+1){(k+1) + 1]2

Hence, it is also true

for n kl

Since the statement is true

when oel,' and if it is true

a

for nk, then it is also true for n-kel; therefore, the statement is true for all

patural numbers n,

(+1)

2025

2025

[2 (n+1)]}'> 2025

(廿九)女長波

Mathmatic's 29

Solution to exercise

Section A.

1. Solution:

Since p and q are the roots

of x2+2x+6=0.

.", p+q»-2 und pqw6,

2 2

qppq

==34°

Multiply both sides by

which must

he a positive number

3)2 <h(y-3) 2(x-3)2 - 4(x-3) 40 2(x-3)((x-3) - 9}<0·

5)<0

3 y 5

6. Since the straight line.

Louches the curve, there- fore, the system

Since both sides are positive quantities, therefore it

Is reasonable to take square

root at both sides

(n+1)>45

+ - 90 >0

or 0 <-9 (rejected

__(p+q)=-2pq

pq

(-2)2 -2(6) 3

2. Solution:

Cost price of shoes =$270÷(1–10%)

-$300

Selling price of shoes if a gain of 10% is intended-$300x(1+10%) =$330

Solution:

2(y

-

3)(F

√1+siní 1+sio+ √1-sinx

1+sin30

9) > 0

because a is a natural

BA -71

number)

n = 9

B(13-1)

31.

-(3-3)

Solution:

Amount for $1000 at 3%.

pla, for 2years compounded yearly

-$10000x (1+3%)

810609

Amount for 810000 at 3%p.a.

for 2years simple interest

-£10000x(1+2x3%)

-$10600

The difference between compound and simple

interest A

-8(10609~10600)

Solution:

Since H is the orthocentre

ABFC-LEEC-90°

B, F, B, C are concyclic BM-MC and LBFC-90"

Mia the centre of circle BFEC.. ZACF-180°-90°.

-50°-40°

¿FME=24ACF-80°

Solution:

BC//DE.

LABC-LADE;

LACB-LAED.

BAC-LDAE

ABC

As

ADEare similar.

AB BC AD DE

2DD BC

3BD 6

DC=4

1.e. The length of BC in

4cm.

Section B.

9. Solution:

(a)Let x and y be the number

of scholarship-holders in

school A and B respectively.

學能推理棟習專

文字推理練習(十六)

文字推理辣┛

文肉的理解

選出每勿括弧內最適當的答案,使成為意思 完整的句子:盖在线答案下面第一橫線。

1.他是個足(A至B念C智 D欬Et)

多謀的小伙子。

2.老年人喜歡装遇去,為的是他再熊(A風

BAC背 D達 E光)景点

留得(A滉(B殘 C棧 DE衊]荷 ###..

A B C D E

掩蓋了一切醜惡的東西,大地更可愛了。 5.犬明誤交匪人,終於(A慊B登 C跌

D# E#) 7-

6.楚香春滿後,原野活躍得像有了(P生活

Q生長、R生命S生機 T壽命。

3.這套衣服款式递於新穎,不適宜今晚的(P爆

所:Q所地:R地位S位置:百場合).

·你還是一套吧!

8,那個青年不對自己的前途滿懷(P期望Q希

REZ SAL` THZ) »

9.哥哥做事负责,根得上司(P器重Q注重

R栽培 S提拔T快鞭 )。

一抹斜暉椒傳天際(P繼傳 Q慑異R龌

* SAL T## } #}L •

11. 原為增進人類福利而發明的炸雒老人哭 化B宠動(C-燮作、S燮更T變遷,弑 人兇器,使諾貝爾始料不及。

12.香港地狹人稠,要有足夠他方種植樹木並不 (A困期日容易 C希奇D常见它缺 送

13.自古以來,中國的詩般常以橫柳病(A寫生 B** C** D** ESS) AÆG ̇題材

14.他终日發(A風騷B驅動、C牢固D= 王孝牒),覺得自己空有才幹,卻得不 到别人的賞識。

- 15. SEM ( AM✯ ·BA# CAE, DRA

E燕才)的傢伙,只懂得奉承。

、16.他驾舟海上,不幸遇上(P分水界Q水平 線R毛毛雨 S微微風下暴威南)~以

鬏身腹口

17.工作是曼然最好的(P座右銘

Q##Z

R麻醉劑 S副作用 丁導火線 yo

18.消窮是友誼的(P試金石 Q轉換點R里

程碑·S分永翰T不解缳)。

19.同情是人類(P一時觸發 Q不可抗拒R生 死與共S與生俱來 T不由自主)的天性。

20.他餓就是(P沃沃之交 Q萍水相逢 R就 逆之交 S酒肉朋友 T一面之緣)。當然 關懷備至。

答案:OC

2D

OB

OC.

*A

OR

OT

00

OP

s.

ФС

1B

D DE BC

T TOR

OPOS

DR

Page 30Page 31