1968-06-06 — Page 22

華僑日報 All

二第張六孵

在一千月五年审虎層室

WAM KTO TH

英中會考數學(=)試題

1968

“ALATHEMATICS, "Syllabus *}

試題習好酒

点六月六年八六九一廠公年七十国现学

PARES

Algebra

1

Time allowed. One, and, & KAIPEDO PR

CHIRIYSITE-AVG,

Attempi All questions to Sesudaa and any COUR-QUARTERIOSUSEDNO ES

SECTION A (40 marka}

Credit will only be given for the correct answer which; 465IFT60-g@VERSONŠTI, KUS BĪSKI” terms. Put each Korver so the soaca oravided on the question paper.

Any WorkIPS required may be done on the lazì têm pages al-tha anawanboOM DULWIELKONADE FOR LAND

1.

( marks)

Mak * the subject of the formule

we gath

(2)

12 10 the product of two abbandulíma idingars. Hild-112 cướgn[h=6]

„such inte garsi

13maFRS1

Find the C. C. t. ar «2 # ¿ãy – 54*. ́6) 42*+%. (omyl”, giving your j answema.factory.,

Simpli

Answeet

اوه

ALW

數學科

(十二)

+

喬仲强,

1

Ly -

第一次預習題解答

(1): <C=st.4, AC=BC, AB=AD.

試由此團求 22.5°角之正弦;餘弦,正切

及餅切.(用最簡根式表示之

(#) #¿C=st.2, AC=BC.

X ABAD,

• ¿BAC=▲ A B C = 45°

#8=1, 91 AC=1,

= 22.5.

•. AB={AC+ BC* ===√2=AD

#ADBC, DB*— BC*+ DC*== }22 + ( 8€ + 1)2=—=—= 4+ 2/2.

.. DB 4+22

ain 225°—

14-2/52

cof*22.5*-= {~,

[4+2/1⁄2 *

2+E

夏僑

$#$%$#$%$#$%Q#3%3#3%3#3%%$%$#*#75#7%4

उस

*#$%$#$%$#$%$##$%848%$#$%$#$%$#$%$#$%$#$%$#S%3 #3%$#$%$#57

8 a, b, c Q.P. .. bat,

x x, y b a, b z best yoshd # x 2 + y + 조

+-20

ab+2c+b+&c

2a(b+c)+xc(a+b) 2a6+2ac+ zea+afe

(a+b) (b+c)

2(ab+zac+bo) [wac##b]

a&+ac+ac+BC

Q.E.D

(5) ABCTLA為鈍角、就在BC上求作田美、使

ADBD DG.

(已知)△ABC中,CA為鈍角

(制作)在BC上作使 AD2= 8D-DC

□ marks

The cost of y

carnes of vegetaties v + teach

4 cents per catty,

If the price is increased by find the number of casives thai can be bought for e ceals.

** Cat 23.5*

tan 22.5=CT+1

2-1

(+)(1)

$-1.

(作法) 1作△ABC的外接

国劓兵必在△ABC之外 2. IX OA.

B

天以QA為直径作P园,典

A H

Fied the value of in the formulk

1 63

and

ing in sumkan

The Ty

49.

And a

There missring in the Corinero

www.k

1ávafiösa 240; 129:43, - tumdyma_k2, Jungmės 5. The cer

ប្តឹង ទ

If the Study ELES ESTARITZAT BESPREKKVERte co-andair 23A FIZ Wedziba finer LEKIRJ

A geometrićxt-pregristiði-käT-SUVER-LETNA__ņš-diat@pm 423 van 120) 6ìbtaxm4a 14%. Fiadau inerterms/

SECTORUL (60anseks)

Deang TOUR questions fromthis Section. Sumercknow question-an e nan pagt

'dilnočensacy working must be clearly akaun. Marks will be deduowd for poor / ́ PERSHDÍSTIDA of isterial, D

est 22.5 DC

*: sin 22.5′′

E+!

at 22.5°➡E+/

(2) AABC", 2, 4. c>$] ¿ «A ̧«8, 7C KHL, ABE a‡. (a) (b+c) cs A+ (c+ a) coq B + (a+b) cop C (証)由餘弦射影走行號

acet C+ C 601 Ä

• a com 8+ & cos A

10@a+b+c={B+c) cos A+ (c+a} cm B+ (a+b){

Q.E.D.

(f) 44(cotA + cat 8+cot C)=a+b+c (DE)

Ecos A

7. sin A

act Am

同理可將 Com

A=+bcainA

bucra

catc

MX, 44(coTA+wt B+ cot C)

=40 (£2+c=a", c2+at+a+f-c")

=(b+c=a2)+(c+a-f*)+(a+b2(3)

O.E.D.

(+3x2=4x+8y+$=Q----{1}

(3)解膜立方程式:(a){24+2+24=0

(解)因两式中会有y的项(xy典y)之係數成比例,顿

可用加诚法以消去之,以4乘(2)式

(i) of

·

and Y

2 caprio a ta terma stj

(ii) +8x=1

to and d as urmily aroossible.

#lve the simulianrous equationa

答:

(x+5)(x-

BCH DR D

4 DR D'or de.

(証明). AD並延長之交口因

★E, ROD, § 20DA=&.4 (*1#<88%)

2. AD DE(遇园心引法之法线,分此弦)

3. ✯04, AD·DE=BD•DC ( &»***££¥) 4 AD2= BD·DC (4#)

5. THE AD2=BD'D°C (4134) (注)(1)加∠A為直角,則の実在BC ±‚Ã0A=08=00, #1*041 £64#**§‚%0A11 ADIBC, §1Ì AD** BD-DC, #44*£#£ *#414-##84.

(2)∠A鋭角、制味美在三角形 ABC之内,则视乎P园與BC之 住而其解答え數時、相 對灞碼解,相加則有一解,相離則县解

Q.E.F,

(8) BOTH A BHUSAN'IN TAQ★128&**P,Q

5 - MAR AP AQ # L##$K-U*I**{

(ckv) o,o'ngi K A, B. S ★ TI#{, VJ Ka.

CARLA DIW*** 0,0 # @XPAQ

BY MIR AP AQ==Q

*(ISK) 1. JE BA É μÃ÷ICA 42-

在0因上配任意美D,联 ADD

CPP'AKTAP'A.

4 TË PAÆPA £*£££*o*@

**QM.

15. TAQALTAQ'MBER.

LIBRA

(HE GA) I. ZE BP, BQ, Dİ

4Qm¿D=48CF

(对刷弧园周為,作法)

2. 8, Q. C, Paita.

CA

(MAS BUÉÂU, TÃ A 20 ¥8 & M48, <1]]¥8),

3. PA·AQ=CA•AB (B*****)

'4 CA·AB=α2 (4% #1)

5. PA∙AQ=a (#‡k)

m. m

Tay

A numbbe has two digits." The offto fight to tone than and tons digit By $ and the square-of-the-unijs giglt in greater than the tens digit by lɔ Find the muniber,

[1" Use the Remainder Theorem to dinë pas fâ¢ibe of ˆ da* + 547 s 12y & Ki

thow facepřiče iße expression completely.

•AL” (? • "Pund the suht of the firar sight teema of the geomviriend @[987001108,

·

(B) 84-9x== IXY

69+

[+6x:

(AE) *074 84-97

xy

·(2)

69+6x

89-92#424+42%.

• 풍성

64+6(-†y)=(-74)4,

*M. 43-1 SM,

#4=-3.

以第一代入(1), -9%=0

* Y= 2.

4(4+3)=

O.E. A

(6) A@Schuß, ? § EM 1W ££ - 24 §. #LEPEAK 一园使园心在线上且與A国相切

(2) AQ110, PÁZ

知直线总上定是

Cen ̄n perrangutan glat el Tanā «n avrebonātāΜS» » 200 V«#giante, ShareGECEPKETS

of the area oftium planie a rectangular plaýyng frate and the remaining amea 14.

s' path fan werde eide reprousdías the playing field. Find the dimensības di She plow

Find: the apend

other varies on the saxare si che äpped, han santh

home 23 dis-Prad's formula expressing * 46 Termin

la sketched in the gives diagram).

It passes through the painiD.

Bingo cha value of #

Find the values of Pant Ca

Find the 40-ordinaresinf lie potuin- where the cranb/cuts.tby. HARRIS,

What additional linase)

secensary, to solve ya, equation

poundr

Euro 3DS

ive you=34xU,

(註)本題如以x47

次联立方程式,將會失去 (many oth. x4U17 用加減法以消比嘎碱手套真

(4)(2)時間、挿入一佃等港中頃~、押入

#18 #+* † g. txtz the q3

041-K a, b, al a n, & $$ lukk

*

nabin

Animat b

x Q a f g b é fuis sk

pras

b = gr = ar

• (as)'+ (a4")" = @°*°V (1+49

as' (1+&) — aa13 (a+£)

• as (a+b)=(24) (al) (q+4)

•13(2n)

成等比級數,

£ c < $ $ +1 44 #1

(8)設

antg

Q.E.D

(44)–28428-

B在总线上,且遇

(14) 1. A WI

PC-PC=AQIE

2. AC, AC' \>#}

19★★1 m, m' BRI

相甫於B茂B

P

38 (6) @S OP (✯ BT) 344

40.90841fanent.

A

(RE) 1.1X DA, § BA=8C (❤##*AUDIL TAJ

C➡ BP¬PC (A1¥*>**

4. BC=

3. BQ

BQ*13 - AM*AR (414, MPR).

KB园,园内切(园心距離等拎半径差,则两截内切

5. 1994 6'A= # @ ¥*£4« ( 0 1 3 3)

Q.E. R

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