1979-02-12 — Page 23

13 (Ans.)

[號 頁三第張六第日六十月正年未已曆夏

1979

WAH KIU YAT PO

報日僑華

Area of sector AOB

5 0

60622

360

X

(==) x 702

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(+2)

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MODERN MATHEMATICS (19)

Zgested solutions

Seven

TON A

rsinë

(2)

raine

2

(4)

sin 0

(2)

0.6667

33°41' (Ans.)

(3)

3.606

2566.67 cm

rea of quad, DATB

2 x (Area of rt. A OAT)

- 2 x (3 x 70 x AT)

70(AT)

70(70tan30°)

2829,26 cm

Area of the shaded region *(area of

-quad

OATB)

-(area of sector (AB) 2829.26

2566,67

262.59 cm

(Ans.)

5

As shown in the figure,

✅PTA »ZĪBA (≤ in alt. seg.

4TPB is the common angle of

of triangle PTA and triangle

TPB

Therefore

APTE

ATAP

PA

PA PB

2b+3c

4(4+5) 36

(2)

(2b+3c)x

(3)

2b) (2b

3c) x

(Ans).

)+(2)+(3)

+ 3c =2(a+2b+3c)x

(A×9.)

er

A(x +x+2) + (nx+C)(z...] }

Ax+2A +Bx ¬BX÷Cr÷C

AAED is an

later

8. The area of the outer

circle

(10)2

100T

The area of the shaded

region

20T

(4)2

The required probability

20 100%

(Ans.)

SECTION B

(i) The angle between line

VA aud plane ABCD is the

angle VAG

AC

AB

BC

BAC

5cm

tan Z VAG

▲ VAG - 63° 26° (Ans.)

(ii) Let M ̧N be the mid-points

of AB and AÐ

The angle between the

planes VAB and ABCD is

ZVMG.

In rt. AVMG

VG

10 cm

GN- BC 5cm

10

3.3333

VMG - 75 18* (Ana,)

(iii) The angle between the

planes VAD and ABCD is angle ỨNG

-期星

18. not help meaning to be unable to stop oneself from doing a certain thing (may also be used with but and a bare infinitive)

日二十月二年九七九一屦公年八十六國民華中

followed by an if introducing a second or third condition. We use the second condition for present or future requests not because the action is impossible or impro bable but merely out of polite- ness for it would be impolite to say that we are sure someone will help us before we have even asked for his help.

I couldn't help getting angry at what he did.

I couldn't help but get angry. at what he did,

She couldn't help crying when she heard the news." She couldn't help but cry when she heard the news.

She couldn't resist, cating the

ice-cream.

She couldn't resist trying her luck at mahjong.

20. forgive, excuse

We excused his coming late. We forgave his not knowing the answer

"Forgive" and "Excuse' are also. commonly used as follows:

We forgave him for coming late.

We excused him for coming

late

Please forgive my arriving late.

Please forgive me for arriving

regret (may also be used with clause)

I regret coming late.

I regret that I have come late. She regretted missing, that film.

She regretted that she had missed that film.

I regret not studying harder when I was young:

I regret that I did not study harder when I was young

22. postpone, put off

They postponed going to Shatin until the next week They put off going to Shatin until the next week.

Let's postpone holding your birthday party until after the examination.

spend

He spent the whole day studying,

He spent the whole day doing mathematics.

He spent the whole day sleep ing.

He spent the whole day eating:

If a noun is used after spend, we must use the preposition on". However, when a gerund follows 'spend', we may omit the preposi tion altogether or use "in" or even "on", though this is rarer.

}x2+(¬B+C)x +(2A−c)

(1).

ZEDA 60

ZEDC. — 150 DEC 4(180°

15

150)

(2)

Similarly,

(3)

AEB

In rt, A NG

(2)

BEC

2A

(4)

AED - Z CED

BEA

VG

10cm

NG

AB 4cm

VG

bai VNG

NG

30° (Ans.)

10

ubstitute

Since 2431 is the

solution of the quadratic equation

2.5

ZVNG = 68

(Ana.)

24. resent

ita

Substitute the

to (3)

Rü

2(1)

3 (Ans.)

Therefo

(2+31)2 + a(2+31) (44121.91 )+2.43ni+b + 121 -9:42a+3ai (2a+b −5) + (Ja+12)i

2a

Ja + 12

Corrections to

Modern Mathematics (18)

10. Plot the graph of the

function f, where

He spent an hour (in) doing Mathematics..

He spent an hour on Mathe matics.

She spent thirty minutes (in) reviewing her lessons.

She spent thirty minutes on a review of her lessons.

He resents our being here.

He resents our telling him. what to do. :

He resented our coming late,

-appreciate

I appreciate, your helping me.

I appreciate Peter's lending me his car.

I appreciate your explaining this point to me.

When appreciate is used with

Future or present request

Past

I

I would appreciate your helping me

I would appreciate it if you would help me..

Peter would appreciate your lending him your car.

Peter would appreciate it if you would lend him your car.

did not happen

would have appreciated your lending me your car. (but you did not lend it to me)

-I would have appreciated it if you had lent me your cart. (but you didn't)

26. phrasal verbs such as keep on,

keep up, account for, carry on, set to, etc. may also be used with gerunds since a gerund may follow

a preposition.

He is fond of smoking. She is tired of living here. He has made up for cheating.

me.

27. intend (also used with an

finitive)

I intend going to Canada to study

(d) to answer

surprised

I intend to go to Canada to study.

(f) was calling

In direct speech he said, "I am calling from the airport.”

(8) to stay [See the Answers to Unit 6, Part (1) (m) of Effective English Language Answer Book and to (c) above]

(h) secing (a gerund after the preposi

tion to')

(), 'ringing

After conjunctions expressing time such as "after","before", "since, while "when", etc. we usually use a clause (a group of words having a subject and verb.) However, when the subject of the verb in the clause beginning with one of these words is the same as the subject of the main clause of the sen tence, we may substitute a participle for the clause after these words, We use a present participle for an active idea and a past participle for a passive one.

While Tom was eating, he read the newspaper.

(Omit he)

While eating, Tom read the news-

paper:

After she had left here, she went to Japan. (leaving)

After leaving here, she went Japan

Before he was arrested, the man robbed three shops. (being)

Before being arrested, the man robbed three shops.

When he was asked his name, he replied that he had forgotten, (Omit he was')

When asked his name, he replied that he had forgotten.

(1) was staying

(k) to have

y«x=-2x+2

+3}

(1)

(2)

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From (2)

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ENGLISH

shown in the figure above

Substitute the value of

a inte (1)

EF O'Neill

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"would' (would appreciate) as a type of polite request, we may use a gerund after it or the word it?

'Aşk' someone to do something.

He asked me to help him.

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