1970-01-13 — Page 21

買二第張六第日六初月二十年已聯言 WAH KIU YAT PO

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日三十月一年〇七九一座公年九十五國民静中 育教僑

1979英文中學會考試題預習專欄 10英文中學會考試題預習專欄

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XATHEMATICS. (11)

Elementary Algebraic Operations & Tranformation of Formulae

1

:

Example 1: Two men are walking along a straight road in the game direction, The faster man is walking at 'x'm.p.h., the other at 'y' m.p.h. At the start, the faster man is a' miles behind, but after 'z' min. he is only 'b' miles behind. Find an expression for 'b' in terms of a, x, y and z. Find also an expression for the time (in min,) at which the faster man will be 'c' miles behind the other, (where a<a)

The spead of the faster man is x m.p.h The speed of the other an 18 y m.p.h..

.. in 1 hr., the faster man'catches up (x y)mb.

-

(a

-

y) ml, in 1 hr.

a-b b). #1. in

x-y

hr..

(i) The faster man catches (x

Which is equal to 'e' min.

z (x − y)

60

60

(ii) At the beginning, the ranter man ir '■' al.

behind, ▲ for 1 hr., the faster man will catch up (x - y) ml.

•*. Time for ostching up (a – o) ml. 60(a=0)

min

I-Y Example 2: In an examination, 'a' candidates wara, boys

and 'b were girls; 'x' per cent of the boys and 'y' per cent of the girls passed. What percentage of the whole number of candidates failed?

Total no. of candidates ☐ + b

Total no. of failures

(1 x%) of 'a' + {2°

-

y%)

of 'b'

(100 - x) + (100 -- 7)b

του

per cent of candidates failed -

*

Total no. of failurek Total no. of candidater

x 100

a(100 - x) + b(100 - x)

100(a + b)

(100 x) # b(100 -1)

( a + b

Szample 3 The volume of metal in a tube is given by

the formula - TL {2 ~ (R - t)2]

where - the

length, R the radius of the outside surface and t the thickness of the material. Find in terms of the other letters, and hence find E, correct to 2 places of decimals, when V - 200, £ 7. π- 22, 2

v = π 2{R2 - (B

+)2}

.

▼ • ↑ L [2 - (R − t)] [ R + (1 - 4)].

T R

V = T L (+) (28

... (28 *)

-

V

R-

है [ata

+ t

+]

R-

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ENGLISH LANGUAGE (11)

Enswers to Exercise 10

Precia

The religions teachers are benefactors of mankind. They were founders of great religions and hosts of all saintly life, By their noble teachings, they raised the level of human norality and pointed ben to God and spiritual truth. The social reformers who work to abolish public abuses, bad laws and customs, help to release the poor and the miserable. The good kings and rulers are also benefactors of humanity because they establish and maintain a sound organization of society. Doctors and scientists bensfat people by releasing pain of the sufferers. Phe inventors. bring material benefits to people and great poets introduce to people their lofty thoughts which help to develop the higher nature of mankind..

Comprehension

1. (D) may be good at heart

2. (D) the socisty to which he has accustomed

3. (C) is always humblè

4. (C) rude and uncivil

5. (C) not limited to the upper olass only

Exercise 11

Choose the best answer to each of the following sentences ?

1. This medicine will soon

newsy (3) newly. (0) news (D) newt

денде

10. These numerous defeats robbed the army of ite

(A) moral (3) morale (C) mortal (1) mortar

11. She gave the young men a book.

(A) languishing (B) Languid (0) languor (D) language

12. It is

that he did such things.

(A) god-fearing (B) godfather (C) god-forsaken (D) god-like (E) godliness

13. We gave him mone help and he gave us

(A) effusive (B) effusion- (0) effectual (D) offerees CA

-14. The government decided to

thans.

brood supplies when' the workers held their strike. (a) diminish (B) dime (C) diminutive (D), dimpli

15. We put the cocks into the

begins.

~ and the fight

(A) cockpit (B) cockney (C) cockle (D) cockerel 16. In the square, a statue was set up in

great hero.

(A) memorize (B) memorial (C) memory

memorandum

of the

17. After the revolt, the government had lost ite

B

prestige B) pressure (C) pressmAIK presume

18. Had it not been for the accident, be

hurt.

(1) would be (B) would not be (C) would not have been (D) did not

it to us.

19. He said that if he found it, ha

(A) will return (B) would return. (C) would have returned (D) would be returned 20. It is time we all

.

our work done.

(A) have (B) did (C) had (D) make

Take it at ones.

21. I wish I

(A) put you right (B) make you right (C) help you right (D) right you up

place.

2. I like everything to be

(A) on (B) in (C) at (D) by

3. He used to pick

him.

(A) out (B) off

4. We must piok thi¤

whenever he had his gun with

(C) at (D) in

before we 08% use it.

(A) out (B) off (C) at (D) over..

5. We like to pick

them since they are friendly.

(A) up with (B) over with (C) at with (D) by with

b. He picked the whole matter

thought for a moment.

her better before we got married. (A) know (B) knew (C) had known (D) should know

22. We did not know him,

the girls.

(4) either did (B) nor did (C) and either did (D) and #o неге

23. "Have you seen him * "Yes, I have",

gone (D) going

24.

(A) BO (B) went

we went out for a walk.

(A) Being fine (B) Having been fine (C) It being fine (0) we baing fine

25. We found a dog with its legs

(A) wound (B) wounded (C) being wounded (D) having wounded

after he had

26. Wa

(A) up (B) off (C) to piecas (D) away

a bargain..

7. He tried hard to pick

(A) up (B) down (C) out (D) at

B. He picked another person's

own book.

French when we were young.

(A) had studied (B) studied (C) were studying (D) would study

the work by the end of this week. shall finish (B) shall have finished (c) shall be finishing (D) finish

27. We

when he wrote his

A

28.

the prisoner escaped. (A) Breaking the door

(A) mind (B) thought (C) braina. (D) work

9. I have just received a letter from him. It is

2{a - 2b)(a + b)

a(a + b) (a

-

2b)

Example 5 Change the subject of La

to

1.

(B) Having broken the door (c) Being broken the door (D) Broken the door

Squaring both sides (p − q)2 = b2 (x = 0)

2(b - d)x

2

11

X

[P

L =

Squaring both sides

(1)2 - 1 - 24.

912(5

-B).

-

-28 (4m2)

2

ལ

--45L2

(82

·

912) --451.2

2]

45L

8m2

200

+ 2

+ 2

1 2

(x + a)

+ a(p − q)2 . b2x - ab2

2

-

*(p − q)?

[(p − «)2 - b2 ]

L

· [b2 + (p − q)2] -10(104)2 [1.3

(104) 2 [9

q +

· 0.9 − 3] [1.3 - 0.9 +

+ (1.3 - 0.9)2]

3]

1⁄2 z 6.546 3.27

Example 4 Simplify (1) (2a + 1 − 2) + (3−4x~4a2)

2a

3b (11) (a+b) (-26)-(4-20)-2(x+5)

(1) 202 and

I

3 - 4a

• (26+3) (0-1)

3+28) (1−2′′)

(11)

3b {8+b) (n =

2b)

Jab-

2b

2 + b

+

a(a +

Example 6 Simplify

9.65

2

Example 8 Simplify

1+ y

I

1

1

ww

y(x + y)

]

301

12(1-x)(1 +.x).

.

Example 7 If » » q+ b/==

3(x+

√, find x in terms of

P, q, a and b. Also find the value of a to two

decimal places when » - 1.3 x 104, q = 0.9 x 104.

x(x − y)

x(x+7)(x-7) +72(x+y) + y2(x+7)

(x + y) (x

y)

[ 2* (x + 1) − x^(x-7) − X(X-2)(x+x)]

2

x2y (x − y) (x + y)

2

2

■ [1⁄23 - x2 + x2 - ̧3 - x2 +Z] ÷

#

+

(x + y) (x − y)

3

2

+ ** - Iy

− x) (x + y)

27

33(x - y)(x + 1)

I

zb

+ 2a

2b(a + b) + (2a + b)(a ~ 2b).

m(a + b) (a 2b)

- 2ab -

a(a + b} {a

2

x w

10, b = 0.3 x 105

+ ab - 4ab

2b2

2b)

NI+

2

4b

- 2 b

2b)

z3y(x2