翼四第滕九第日三初月九年未已腦
1980
ive. f(x)=x^-3x“-13x+15
2
WAH KIU YAT PO
報日僑
二期星
a2-2ab+b2 > 0
=(x-1)(x2-2x-15) =(x-1)(x+3)(x-5)
+2ab+b]
the other factors of
the expression are K+5。 x−5.
中學會考試題預習專欄
數學
(三)
Mathematic
明德出版社女長波提供資料 (3)
13. Given: PR is the diameter
and NRM is the tangent of the circle
Section 8.
Solution to Exercise 1
11. Given: ABCD is a
//gram
LADY/YDC, DY // BX
Tn prove:(a) △ABX = ACDY
(h) BXDY is a //gram (c) AABY
ABCY DC
To prove :
AD
C
Proof: (a) *. ABCD is a
//gram (given)
. ABCD AB//CD
(or); sides //gram)
BAX=/DCY
(alt /s AB//CD) DY//BX (given)
.*. [ABX=[YDC
(8 between 2 pairs
of // lines)
AABX = ACDY (A.S.A.)
·(h) DY=BX (curr sides = As)
BXDY is a //gram
(0)
(opp sides equal & //)
AABY AY △BCY YC
(same altitude )
LADY=/YDC (given) e(/bisector,
AY AD
YC DC
property)
AABY AD ABCY DC
12. Solution:
(a) a−3+2b=}
12
(subst)
5b+3ab-8-13-0 from (1), a-3-2b. Put (3) into (2)
(1)
:83
5b+3b(3-2b)-(3-26)2-13=0
5b2+9b-6b2-9+12b-4b2-13=0
(b)
562-21b+22x0 (5b-11)(b-2)-0
... b-11-0 or 2
bal
When be
0-3-2(2)=-
When b=2
1-3-2(2)=-1
the solution of the equation is
-}
11
fa=-1
or
b=2
X-1 is a factor of
f(x)=x3_3x2+px+15
f(1)w1-3+p+15=U
p=-13
洽近
驗
二版
黃心小車
PQ*PN-PR2
APUS and APMN are similar (c) QSMN is
cyclic
Proof:(a)"." PR is the
diameter
[PQN:=90° ([ in
(PRN=90°
gemicircle)
Tproperties of
tangent)
.*. PQ•PN=Pn2
(b) Similarly, PS-PM-PR2
i.e.
PQ PN PS PM
PQ PS
PM PN
LQPS=/MPN (common) APQS and APMN are
similar (ratio of 2 sides, inc.
(c) [PQS=(PMN (corr /s,
similar As) [PqS+/SQN=180° (adj £s
on st. line)
i.e. [PMN+/SQN=180°
QSMN in cyclic
(opp. 8 supp.)
14. Solution:
(a) Hadius of the
hemisphere
44
44cm
2 cm x 7cm
(a+b) 2 >
248b
log(a+b)">log4ab
210g(a+h)> 21og2+1oga
+logb
log(a+b)>19g2
+查(loge+logb)
log(a+b)-10g2
> (loga+logb)
ive. logan > b(loga+logb)
10. Solution:
Let x he the number of animals that he bought
1200(1+5%)
x-5
1200 6
-
X
1260 1200 6
x-5
+
1260x-1200(x-5)=6x(x-5)
2
60x+6000x6(x2-5x)
10x+1000-x2-5x
2
x-15x-1000=0
(x-40)(x+25)<0
x-40 or -25 (rejected)
the farmer bought
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PHYSICS (3)
|Exercise 2
Mechanica
(Take acceleration due to
gravity g m 10mg~2)
1. Two blocks of masses 10kg and 15kg are connected by
a light inextensible string which passes over a amooth fixed pulley. Initially, the 10kg-block resta on the floor aud the 15kg block is held 2u above. the floor as shown in figure 1. If the system is now released, (a) determine the accelera- tion of the /system, (b) find the tension in
the string,
日三廿月十年九七九一瑟公年八十六國民華中 育教僑
2. A pile-driver of mass 10kg
a height of
is raised to
12 and is allowed to fall on to a pile of mass 12kg. which is to be driven into
the ground.
(a) Find the velocity of
the pile driver as it strikes the pile.
(b) If the pile driver and the pile move together after impact, calculate their common velocity just after the impact. (c) If the pile then cumes to rest after penetra- ting 0.5m into the ground, calculate the average retarding force exerted by the ground on the pile.
5. Three blocks of masses
10kg, 20kg,and 30kg are connected by strings as
shown in figure 2. It is
then pulled to the right.
with a force F-600N.'
(a) If the horizontal floor
is frictionless, find
(i) the acceleration
.
of the system,
(ii) the tension in
each string.
(b) If the coefficient of
friction between the
30 kg 20%
horizontal Floor
figure 2
4. As shown in figure 3, a
load of mass 50kg is raised by means of a pulley
system. The efficiency of the pulley system is 40%.
Effort
figure 3
(a)(i) What is the uptimust
of water
on the cube,
(ai) Find the fraction
of the cube immersed,
(b) If oil of density
1_of -3 720kgm is poured onto the water until it just covered, (as shown in figure 5) how much does the cube rise? plastic
WATER
figure 4
OIL
plastic.
WATER
figure 5
數字推理練習五 英文字母的排列 選出下列各類的正確答案,如在它的下面 畫一橫線。
先看下面按次序排列的英文字母,然後 解答問題。
ABCDEFGHIJKL MNOPORS TUVWX YZ
下列第1至第10題序列最後一项的字母是付 麼,試把它應出來。
2. TSROP ?
AW
3. AZBZC
AX BZ CY DA ED
7, ZYYX W
PV 8.BABCB ?
來口
11. AGH|
12.ACCC
NRM is the tangent
1.ACEGI
40 animals.
AJ
BH CK
DF
EB
(mean proportainal)
1980
BV CM
DN EO
?
2
中學會考試題預習專欄
blucks and the floor
is 0.2, find
4. ADGJ M
?
物理
(三)
(i) the acceleration
of the system,
AP BN CO DL
EK
(ii) the tension in
each string.
5. GHGIG 7
AE 6.ABEFI
PC QD
BF
CK
DJ
EL
?
RJ
SH TG
FC500N
?
QU RT
SW TX
PE POI RH SO
TQ
9. L MNKP ?
PJ Q1 RH
SO
TQ
10. ZAYB X
?
PW QV RC
SD
TE
下列第11至第20題的五組字母中,有四組是 有一定關係的,試指出沒有關係的一組字母
BCEF
CJ KL
DABC
EX Y Z
BEEE
CYYY
DP PP
EUUV
13.AFEF
BMNM
COPO
DS TS
EXY,X
14. AY X W
BTS R
CFGH
DP ON 15. AEGG
ELKJ
BJLL
CQs S
DACC
EMNN
16. PBDF
SJLN
QWY Z
RACE
TMOQ
17. PABB SEFF
QGHH
RCDD
TIIJ
18. PIHI
QYZY
RKL K
SABA
TEFE
QOPQ
RGH1
SFED
TL MN
20.PACC
QCEE
RGHH
SB DD
TDFF
Oc QE 3)B
答
QA
OD
GR OS OP
0Q OR
OB
DE
箫
® A
@C
OT
P
S
車汽
79
欄專賣買
港
補體】
熊小
科
島
大 補
考生
溫補 預
預大 石蒜蚊
七美理國
下午楠小.
圆太一四大四三
(b) The volume of the vessel
-xx(7)+(7)2+(30-7)
-1898.6 cu.cm,"
(c) Slarit eige of the.cane
√232.72
cm = 24.04cm
Surface area of the vessel
•jx4x(7)x+x(7)(24.04)
-836.54 84.CM.
15. Solntion:
- •
(mb} ?>
20
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(e) find the velocity with
which the 15kg-block strikes the floor, (d)'find the time required
for the 15kg-block to reach the floor,
(e) find the maximum height
reached by the 10kg-block.
15kg
炒
figure 1
10 kg
Fiocr
(a) What is the velocity
ratio of the pulley system?
(b) Find the mechanical
advantage of the machine.
(e) Find the minimum effort
required to raise the load.
(d) if the effort applied
to the system is 600N, what sort of motion
will the load perform,
5. A plastic cube of side -3
10cm and density 900kgm” floats in water (density= -3) with the upper 1000kgm
face horizontal, (as shown
in figure 4)
606769 7373 73 73747475767677 78 7878
全新貨車 23
19. PABC
○午學鑒
預
碩
科
預
香港學生輔導中心教
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