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+$=Q----{1}
(3)解膜立方程式:(a){24+2+24=0
(解)因两式中会有y的项(xy典y)之係數成比例,顿
可用加诚法以消去之,以4乘(2)式
(i) of
·
and Y
2 caprio a ta terma stj
(ii) +8x=1
to and d as urmily aroossible.
#lve the simulianrous equationa
答:
犟
(x+5)(x-
BCH DR D
4 DR D'or de.
(証明). AD並延長之交口因
★E, ROD, § 20DA=&.4 (*1#<88%)
2. AD DE(遇园心引法之法线,分此弦)
3. ✯04, AD·DE=BD•DC ( &»***££¥) 4 AD2= BD·DC (4#)
5. THE AD2=BD'D°C (4134) (注)(1)加∠A為直角,則の実在BC ±‚Ã0A=08=00, #1*041 £64#**§‚%0A11 ADIBC, §1Ì AD** BD-DC, #44*£#£ *#414-##84.
(2)∠A鋭角、制味美在三角形 ABC之内,则视乎P园與BC之 住而其解答え數時、相 對灞碼解,相加則有一解,相離則县解
Q.E.F,
(8) BOTH A BHUSAN'IN TAQ★128&**P,Q
5 - MAR AP AQ # L##$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,
味
·
(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