1973-04-06 — Page 19

someone or

something).

distressed (slang) over

Something

hurry away

育敎儒華真三第張五第日四初月三年丑癸歷夏

WAH KIU YAT PO

報日僑華

五期星

日六月四年三七九一膳公年二十六國民華中

蕎

1973英文中學會考試題預習專欄

堅遊英文断院杰編

E

/ PXB = / PYC

900

(given)

▲ PBX = ▲ PCY

(RHS)

1973英文中學會考試題預習專機

cut up

BX

CY

dash off

Now AX

AB

BX

AB

CY

英文科

(十四)

AB

(AY

AC)

AB

AY + AC

AB ܚܪ

AX + AC

AY

AX

=AB + AC

數學科(廿四)

AX

MATHEMATICS (24)

Fundamental concepts

Exterior and interior angles of a polygon:

The sum of interior angles. of a triangle is 180°. Exterior angle of a triangle. equals the sum of interior opposite angles,

Sum of interior angles of a n-sided polygon is (2n ·4): right angles.

Sum of exterior angle of a n-side polygon is 4 right angles.

(B) Parallel lines

There are two fundamental

1. Two coplanar st. lines are

either intersecting or parall Mel

Two intersecting coplanar st. lines cannot be both parallel to a third st. line.

We have the following propert -ies of parallel lines.

If either (a) alt. s equal or (b) corr.s equal or (c) int.s supp. then the two st. lines are parallel.

If a st. line cuts two or more parallel lines then (a) alts are equal (b) corr. s are equal (c) int. /s supp.

Two or more et. lines which are parallel to the same st. lines are parallel to one anotehr.

st. lines which are perpendi cular to the same coplanar st. lines are parallel to one another.

(C) Congruence of triangles

S.AS.

AS. A

A.A.S.

5.5.S.

“R.H.S.

Isosceles triangles

Base / s, isos ▲ (are equal) 2. Sides opp. equal / s (are

equal)

Example

In the figure as shown, the bisector of / BAC meets at P the line which bisects BC at right

angles. PX, PY are the na

culars from P to AB and

in the figure 3 pairs of congruent triangles and prove the congruence Also prove that AX = ✯ (AB + AC) Solution: With notations in the

figure. La Zb (given)

_ AXP = / AYP

900 (given)

is common

A APY

A AFY (AAS)

- 2(AB + AC)

(E) Properties of parallelogram

Opposite sides of a parallel ogram are equal. Opposite angles of a paralle:

ogram are equal. Diagronals bisect each other, 4. Diagronals bisect the area

of a parallelogram.

The following are the sufficient conditions for a quadrilateral: be a parallelogram.

1. Opposite sides are equal. 2. Opposite angles are equal. 3. Diagronals bisect each other. 4. a pair of opposite sides are

equal and parallel;

Example (2)

ABEF, ACGH are squares outside ▲ ABC, AM is a median and produced to meet FH at 0. Prove that

(1) MQ L FH

(11)

1

AM FH.

Solution: Produce AM to P such

that MP - AM

Thus ACPB is a parallelogram (diagronals bisect each other)

BP AC=AH

/ ABP + / BAC 2 rt.s

(int. / s, AC // BP)

But / FAH + / BAC = 2 rt. / s

/ ABP = /FAH

And AB AF

"BP- ·AH·

A ABP

APFH

(sides of a square) (proved)

FAH (SAS)

AM = 1⁄2 AP = 1⁄2 FH.

Also a

But

ZBAF

AQT AQITH

BAF

Mid-point theorem

The st. line joining the mid points of two sides of a triangle is (i) parallel to the third side (ii) equal to half the third

side.

Intercept theorem

The st. line drawn through the mid point of one side of a triangle and is parallel to an- other side bisects the third side Exemple (3)

D is the mid point of the sides BC of triangle ABC, CA is produced to E. If /BR is the perpendicular from B to the bisector of BAE, prove that

DR-

(AB+ AC)

English (24)

In-

Some words which can be used as prepositions but in the context do not show the relationship be- tween the noun that follows them and any other word in the sentence They belong much more closely to the verb. Thus they cannot be really called prepositions. stead they are known as phrasal verbs. In most cases, they can be replaced by a single verb of practically similar meaning. eg.

1 will put out the light. I will put the light out.

will extinguish the light.

This has taken up a lot of my time.

This has taken a lot of my time

up.

This has occupied a lot of my time.

Phrasal verbs or verb + preposit- ion or adverb vary greatly in meaning according to context, Sometimes, its meaning may be gathered from the individual words that compose it. e.g.

Put the book up there.

Place the book somewhere there).

But frequently, the meaning is figurative and can only be learn- ed by treating the combination as one unit. eg.

Can you put me up for the night? (Can you accomodate me for the

night?)

There are so many combinat- ions in forming phrasal verbs that it is not possible to list them all here. However, here are a few common ones. Try each in

a sentence to show that you know how to use it. Remember, they may have more than one meaning.

Ex- P3

Add in include

Answer back = retort

Ask in invite

Back out of withdraw" Bail out

barge in.

escape from plane by parachute. intrude

bear out = confirm

bed down

black out

blaze up

blow in

board in

prepare a bed to sleep. (slang ise.)

become unconscious burst suddenly into flames.

arrive (slang)

take one's meal where one lives (a boarder) boil down (to) = be reduced (to) break in = interrupt bring round - persuade one to

your point of view

or proposal or ides

burst in - interrupt buzz off - go away (slang) call in = visit carry off = succeed or win over carry on (with) - flirt (colloqui-

al expression)

cast down throw down catch up (on) - bring up to date

(something) catch up (with) = become level

(with someone)

clean out empty come about - ha come round - - recover consciousness

revive.

dine in/out

to eat at home or away from home

do in kill (slang) drag out =

draw out

protract, make it long- er (of conversation,

or music or speech) become longer

dress down scold. (colloquial:

out_expression)

drive out = expel

egg on encourage

end of reach a final conclusion. face it out

see it to the end. withstand

face up to fall out (of) = fall out of some-

thing.

fall out (with) = quarrel with

figure out

flare up

get across

someone.

= calculate, work

understand.

(of temper) become

suddenly angry.

make something under stood (colloquial)

get bypass, manage get on (with someone) be friend→

ly (with)

understood hatch out turn out (colloquial) have it out (with someone)

get on (to something) = manage to

Ex.

argue over something until it is settled.: Complete the following with a suitable word.

The publishers have at last. brought

book on "How

to be slim.

20

If you like bring

the

the

children to the picnic

3. As the car drew

city, the tyres blew.

4. At the sight of the

drew

in terror.

5. You cannot keep

ing that you are rick.

6. That's right, keep

good work."

he

pretend-

the

You may be arrested for letting

fire crackers.

There's someone at the door, do let him

9. The fire was easily put

by fire extinguishers.

10. The actor put/

an

appearance of a King and spoke like one.

Toolate, he realized he had been taken

by thieves.

12. A sort of madness, came

him and he spoke utter nonsen

se:

Never walk

lonely hills.

14. I eagerly jumped

yourself in

the offer of such a good job.

The water is

15. Jump

just fine!

16. What you can do to-day, never

till to-morrow. that man, and

put

17. Take

put him in jail.

18. On hearing the good news,

children jumped

19. The house was let

for joy

man who called himself the General.

20. Jump not

conclusions;

second thoughts are always best.

Answers: Ex.

1. out

13. by

16. off

11. in

2. along

12.

over

3. near/into

4. back

14. at

5. on

15. in

6. up

7. off

17

B. in

bitterly (against

9. out 10. on

19. to:

20. to

.common

cough up blurt out (slang) cry out (against) complain.

away

18. up

XPY.

BN

CN

BNP

PN is

(given)

/ CNP = 90° (given)

ommon

A PEN A PCN

PB PU

PB FC PX PY

} (proved)

(SAS)

B

D

a

Proof: Produce BR to cut CA produced at F.

In ▲ ARB, ARF

(given)

AR AR

ZARB

ARF 900

A ARB ZARE

RB RE

BD DO (given) DR = CF (mid

Bu CF

DR

Exercise

CA+AF CA + AB

(CA + AB)

(ASA)

theorem)

AF AB)

(1) The diagonals AC, BD of the square ABCD intersect at K. The bisector of BAC cuts BK at X and outs BC at Y. Prove that CY 2KX.

(2) In the figure ABCD is a

square. APB = 900;

CXQ // AP DQ //BPX

Prove that

(1) PX = AP

(ii) / APO

PB

459