育敎僑華頁三第張六第日三十月二十年酉辛緜夏
AX-
1982
中學會考試題預習專欄
數
(十四)
Bx+1
"C. x+2
D.x-3
E. x+
7. If siná= and 0 <A< then sin(90°-A) =
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A. 0.2
B 0,4
C. 0.6
MATHEMATICS(Sy11.2) (14)
C.P. Man
MILL & DALE PRESS LTD.
Exercise 6
Multiple choice questions
1. The ratio of the
length of a rectangle
to its width is 5 to 4. Find the length of the perimeter is 36.
D. 0.75
E. 0.8
A wire of length 5 cm is bent to forma complete circle. What is the radius of the circle?
10
cm
cm
C.
cm
27
WAH KIU YAT PO
報日僑
四期星
A. 2 5
B. 52
G. 4. 25
D. 25 4
E. 1. 4
15. If n is a positive
integer, which of the following numbers is/are oddy
(1) g2n+1
|___ (2) 3(27)
(3) (2n+1)2 A. (2) only B. (3) only
C. (1) and (3) only D. (2) and (3) only
A. 112 B. 118
C. 124
D. 146 °
日七月一年二八九一公年一十七國民華中
Let the volume
of
mercury required be
cm2
B
50.135 1.018
49.2485 cm
Apply the formula
d.
(1+rt)
(i) the density at 54 C
ater.
E. cannot be determined
Answer:
1000
1+0.0005x50
1000 1.025
16. In the figure, AB / DC.
1. E
If the area of AABE 35q,em and area
of AADE=48q«cm, area of A ECD is
6. E 11. E 16. C 7. C 12. D 17 D 8. C 13. D 18, E
975.61 kgm
Ang
(ii) Coefficient of
then
5. C 10, A 15. B 20. B
E. All of them.
2. B 3.C
4B 9. B 14 D 19% A
20
Since
m+1
the slope of m against v is From the graph,
slope 12
cm
C
5
D. 6
B. 10.
In the figure, ACDB is
a semi-circle and CD
is a quadrant, then ZAEB is.
D. 5 em
E. 10
9. In the figure, BC=BD,
then
A. 30
B. 45°
C2 60°
D.75
E.none of the above
25 men working 8 hours. a day remake a road in
63 days, the time taken taken for 45 men, working 7 hours a day is
A. 5 days
B. 8 days
C. 40 days
D. 20 days
3. 50 days
Kind the sum of the
marked angles
4. 270
B. 360°
C.
2. 480
£. 540°
5. The sum of the first n
terus of a progression is n(n+). The nth
téro is
An+2
+3
20+1
30+2
.2
Y+z y+2z
2y+7
D. x+y+z=180
·E. x+2y+z=180
10.
If sina.coSA=p then
siná+cosä
A.
B. √1-2p
C. 1-p D. 2p
E. cannot be determine
(3)
A.
2(x2)
12. If f(x)=x
then
I (x+1)-
A. 1-
B. 3
C.
D 2x+2
2
Ex+x+1
13. A group consists of
n boys and n girls. If two of the girls are replaced by two other boys, then 51% of the group members will be boys. What is, n?
A 50
B. 51
C: 52 D. 100
-E. 102.
En-1
If x+x+k is divisible
x-2, then it is
also divisible by
1982
14. If 3x-2y=
then
The polar form of
13
中學會考試題預習專欄
附加數 (+=)
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Additional Mathematics(13) S.P. KO
(Mill & Dále Press Ltd.)
12
=(1)(cos240 +isiu240°)
cis120
cis240
9q-cm
B. 5. sq. cm
5 sq.cm
D. 6 sq.cm
E. 64 sq.cm
17. a, b and c are integers whose average is 9. If abc70 and b=3, what is the greatest value that a can be?
5
B. 12:
C. 13
D. 23
E 24
18. If 8 is an acute
angle and 3tand-2-0, then cos✪=
19. The radius of a
sector is 3 cm and the perimeter is 10 cm. What is the area of the
sector?
the
cm
B. 12 cm
G. 15 cm
D. 18 cm
E 45 c
20. In the figure, AB and
AC are tangents of
the circle. 0=
isine
(1+co80)+isino 1+cuse)—isin☺}{[(1+cose)
+18ine)
(1+cose) +sin e
1+coś0+ïsinė
1+cos0+ising
0+sin
物理 (十四)
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PHYSICS (14)
H.K. Lo
MILL & DALE PRESS LTD.
(a) Assume x kg of ice
are melted.
Assuming no heat. loses to, or gains from the surroundings (0.2)(420)(20-0)
+(0.8)(4200) (20-0)
336000x
X = 0.23 Therefore,
0.3-0.23 - 0,07 kg
of ice is still
unmelted,
(b) Suppose y kg of steam
are blown into tfie mixture and raising to 20°C
Heat evolved by steam
2268000y
+(4200-)(80)y 2604000y
Heat gained by the
calorimeter and its contents
0.07x(336000) .......
+(1,2)(420)(20) +(0,8+0,3)(4200)
126000
cubical expansion of glass-
3x0.000008
= 0.000024 c Volume of water
contained
capacity of the flask at 54 C.. 1000(1+0.000024
1001.2 cm
1.0012x10
x50)
Mass of water in
the flask
(975.61) |-|(1,0012×10 0.97678 kg
is the critical angle
sinc
sina
(20)
2604000y - 126000
y 0.0484
Ans: 0.0484 kg of steam are required.
(a) Let the correct
length be xm
x = 1+(1+0.00002×30)
=1.0006 ·
Ans: The correct length
is 1.0006 m.
(b) The cuefficient of
cubical expansion of glass
5x0.000009
000027°c
Capacity of the flask at 100 C
= 50x(1+0.000027×100)
50.135 cm3
3. Find the locus of z
such that (z+i[~[z-i]
Solution:
Put z=x+iy
The given expression is
|x+1y+1|~ }x+1y-i |--1
• * • (x + (y +1 ) i|-|x+(y-1)i||
√x2+(y+1) 2 - √x2 + (y-1).
*2+2cos@
1+(2cos -1)+2isingcos
20
2+2(cos
Squaring both
Complex Number (1)
Worked examples:
1 Find the modulus and
=cis (120°-24
=cis(-120°) =(1) (cos(-190°) +isin(-120°)]
modulus=1
and argument=-120 An
14c080-isine
in the form a+bi.
Solution;
2cos(congising)
4 cas
conftising
argument
Solution:
The polar
(1)(cos120 sin120°)
cis120
Express
1+cose-ising
*(1+1 tang)
+ tan분
x2+(y+1)2=-1+x2+(y-1)2
sides,
x2+(y+1) = 1 + 2√x2+(y−1)2
+x2+(y-1)2
2
2y+1=1+x2 + y2
+2] x2+(y−1) = ky-1-2√x2+(y-1)2
Squaring both sides again,
(4-1)2 - 4 [x2 + (y-1)"]
180-60 120°
180
21 19
sini-1.Galu21 19!
=1.6x0.3656. =0.5818
Ans.
35°29! Ans
(a) A
20 16.
15
(b)
15 cm
0.25 16.cm 0.3333 18 cm 0.5.
20 cm 0.6667 30 cm 1.5 2:0 36 cm 48 cm 3.0 60 ст
4.0
10y -8y+1=4x
12y-4x -3
the locus of z is a
perbula whose
equation is 12y--4x
Exercise 7
Ans
Express the following. in the form a+bi:
(a) 1-cose-ising
(b) cos☺-isine
5+41
(c) 5-41
2. Find the modulus and
argument of the following expressions:
4+4i
(a)
(b) (i+1) (2+1)
12 cm
(a) Let the appromimate
Trequency be f
the
wavelength of the note emitted be A (approx.)
As shown
gram,
--1.25 m
L=125m
The approximate
wavelength
The approximate frequency
velocity of sound in air approximate wavelength:
330 Hz
Ans.
(c) The actual frequency
of the tuning fork. greater than the approximate value obtained in (a) because ende correction is not taken into account in (a),
(c) The direction
along the axi
the tube,
(d) 0.5m, 7.5m and 1.250
from the open end.
(c) Cose–isine
cuso-isi not
3. Find the locus of z
such that
(a)
iz+1
(b) (2−1|+|z+1}=4° (c) 2{z−2]=fz-61|
(a) Given that z=x+iy
and [2]=1, show that z 2-1, where
z is the conjugate of Z.
(b) ir
8. Kare also
complex numbers. and 92+d f0, using the result of (a), find the value of