1972-03-28 — Page 12

白緻頁四第張三第日四十月二年子壬雇夏 WAH KIU YAT PO

【 1972英文中學會考試題預習專欄-

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數學科

(#)

Mathematics

(Lesson 22)

Solution to exercise 21

(1) Lot - -

(yk)2

(wk)?

(wk)?

1)

eight or the disca

radius of the diso,

thickness of the dis

Constant

WILBIL

報日僑華

二期星:日八十月三年二七九一年一十六國民華中

Let d be the common difference The 3 sumbeza are

1972英文中學會考試題預習專欄 3

5. Who wants to go for a valk

A.

堅道英文書院主編

(a - ¿) + a + (a + d) - 27 Ja 21

英文科

(#)

(LED (1-0)2 + + + (a + 1)* • 293

the three numbens are 4, 9, 14

Prove that the sum of the terms with in the n bracket of the serier 1) + (3 5) + (7 + 9 + 11) +

*

1315 +17 + 19) + ***** 18 2° and that the sum of the terme ini

the first n bracketa i8 2x2( n + 1)2

solutions. The first term

bracket

-32 x 1 → 1

The first term in the bracket.

73 x 2 +

The first term in the 4th bracke

- 4 x 3 + 1

first term in the nth bracket (n-

+1 = n

number of terms in the

bracket

The sum of terma in the nth bracket

- |2(n − n + 1) + (n − 1) x 2]

the common difference in

21 + 2 +

Sum of terme in the first n bracketi

- (a + 1) - (• the first bracket has tera second bracket has 2, etc.)

Sum of terms in the first a brackets

플(n

constant

..w = kr) - where k is a constant】

Lot w1r 2, and hq be the weight, radius

and thickess of the first diac,

Let W and h2 be the weight, radius. and thicmess of the escond discs

Geometrio progression

A number of quantities are said to

when they be in geometric progression increase or decrease by a constant factor.

The constant factor is called a Dommon ratio,

We have the following formulası

株

~~ fiv

The ratio of their radii i8 41

Series

A series is a succession of quant

ities which are arranged in order accor ding to Bom definite law.

Each quantity in the serien is cal➡ led a term of the Bezien./

the e

The term written in a fora de- pending on a fe usually called the gen- eral term. This general term must be such that by substituting particular values of ʼn we may obtain any particular term which is required.

Arithretical progression

An arithmetical progression is series in which successive terms increase or decrease by a common difference.

We have the following formulas:-

where

(= a + (n-1)d

lant term

n no. of terms

(3) Find 3 numbers in G.P.. whose sum ia

19 and whose product is 216. Solutions

Denote the numbers by

When

Thus the nu

or 2/3

are 4, 6, 9

(4) Insert 4 geometric means between

160 and 5

Solutions

We are going to find 6 terms. G.P. of which 160. is the first and

the las

Let x be the common ratio

Then

160%

Taglish Language (22)

Answer to Isthe 21

There are different ways in which an Adverb Clause of ConcERRION CAN be expressed

Examplest

A. By though* or sitnough" i

Though the weather was bad, we ge- cided to go on our journey.

notwithstanding that (in spite of the fact that)'

We decided to go on our journey “ notwithstanding that the weather was bad,

By

'however, followed by adject ive (or adverb)

However bad the weather was, we decided to go on our journey. By as with an adjectiva

(or an verb) going before it?

Bad as it was, we decided to go on our journey.

By all the same " I

The weather was bad, all the same, we decided to go on our journey. Answer to Question 1-8 of the last issue:

a. R

It 18 always possible to change the Degree of Comparison of an Adjective or an Adverb in a sentence, without changing the meaning of the sentence': Examples.

A, Tokyo is the biggest city in Asia

No other city in Asia is as bi as Tokyo..

C. Tokyo.ia bigger than any other

city in asia.

Answer to Questions

10 and

10. S

3. Causative Use of

Interchange of Aotive and Passive

17. R

18. B

Anewer to (20)1 - R

19.

Complete the following sentences with the most suitable answer

you fond

1. Ara:

A. Yes, I do

B. No, I don't

C. Yes, I an

D. No, I ghan

Were you at the cinema last night?

A. Yes, I did

B. No, I wasn't

C. Yea, I were

D. No, I am no

Must I go by train?

A. Yes, you need

E. Yes, you are

No, you needn't

No, you mustn't

Need you leave all your papere

all over the floor?

4. Tea, I'm afraid I must.

E. Yes, I need

C. No, I need not

D. No, I mustn't

The proof of this theorem is avak1- able in any standard textbook Discriminant of quadratic equation

gome want to

B. No, no one wants

C. Yes, someone docą

D. No one does

3. Nat do I

There is a hole in youF COAT,

P. Of course there íá...

Q. Yes, it does

R. Yes, it is

S. So there ju

T. So it is.

Why didn't you weita to me?

I didn't

P. NO

Q. Yes, I did H. So I didn't S. But I did

Of course I did.

I feel sure this dog vill bite ne,

P. Yes, I feel

Q. So I feel

R. But I don'

S. Of course I don't

• You couldn't undexatauk a gorg

No, I could t

No, I couldn

R. Yes, I couldn'

9. So I couldn't

10. It wasn't mê,

P. Yes, it wasn't

Q. No, it was

R. But it was

S. So it was

11. The

The situation couldn't be much A. Hoj

could

B. So it could

C. Yes, it couldn't

D. But it could

12. The train never used to stop her

A. Yes, It did

B. Yes, it didn't.

G. No, it did

D. So it did.

I have never been to Berlin.

A. So does he

B. So hasn't he

C. Nor hasn't he

D. Nor he has

14 Ee-

always makes flatākons

A. But you too

B. So you ão

C. No, you don't

D. But you don't

Bis shoes didn't fit him well.

A. So didn't his shirt

B. So his shirt didn't

C. But his shirt did

D. But his shirt didn't as well He wasn't late last fine.

P. No, he wasn't, wasn't he "Q, Yes, he was, was he

R. No, he wasn't, was, he 8. Yes he wasn

HAB he

didn't come early encuch No, I didn't, did I

Yes, I did, didn't I

R. No, I did, didn't I

T: (P) and

18. The chair wasn't broken yesterday.

P. Now it was, want t

Q. Yes, it wasn't, was 1s

was it R. No, it wasn't.

3. Yes, it wasn t wasn't 1. (P) and (B)

19. You are rather late.

P. Yes, I an, aren'

Q. Yes, I am, an I

B. No, I am not, am I not

S. No, I am, an I

They gave us a

a lovelý teav Yes, they did, did they Yes, they didn't, they did, R. Yea, they did, dim't they

No, they didn't, did they T. (A) and (s)

Let and be the roots of the

common dif:

ference

first term

sum to n term

When 3 quantities are in arithmetical progression the middle one is said to be the arithmetical mean of the othar two.

The arithmetic mean

Examples

The sum of 3 numbers in A,P. 18 27 and the sum of their square is 293. Find then, Solution Let a be the midale ora

160

32

** The means are 80, 40,

Theory of quadratic equatio:

Theorem".

where 8,

constante and a is called a quad- ratic equation' in

à quadratic equation in x cannet have more than two distinct roota. (In general an equation of nth degree cannot have more than ʼn roots)

— 480 is called the disorining ant of the quadratio equation

Coneider, the following

(AV)

4a070, there are two distinct

real roots..

there are two equal real roots

<0, there are two imagina

sry roots and they

are conjagate of each other.

perfect square, there aze two rational roots

Relation between the roots and coeffic~ ients of the equation

Exercise 22.

(1) For what alues of n has the squa➡

tion

equal roote?: (2) Let and be roots of the equation

fana tie value of

(2) ∞ B2

(3) Given

(111)d-f

are roots of (1

0, find the equation whose roots are 13 and K.

(4) Prove that the sum of n terms of in

"series 5 +55 + 555 + 5555

+1

10

11