真四第張六第日十三月九年午戊歷
WAH KIU YAT PO
報日僑華
二期星
1979
meters farther before drops
down
600 - 10(10) 500N (Ans.)
Since the volume of the cube
· (0.1)3
中學會考試題預習專欄
v122 - 2(g) (h)
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To 30(10) 300N {ADE,).
(b)(i)
10-3
日一卅月十年八七九一年七十六國民華中 青收堡饰
6. Find the values of a and
if 3x-2=a(x−1)+b(x+2)
is satisfied for all
values of x.
2
If 5sin -2co
Find
物理
PHYSICS (4)
8
fraction of the cube in-
mersed
the values of tarß.
8
~ 9 x 10"
Suggested solutions to
exercise two
·30kg
SOON
20kg
་ཚ་
The value of a cachine: depreciates from $2000 to 81280 in 2 years. the yearly decay factor, assuming it to be constant. Section B
Find
1(a)
115 kg
jokg.
As shown in the above,
lét ↑ - tension in the
string
acceleration of the
system.
Apply Newtond: Law
the blocks seperatěly,
15(10) T➡ 15a
(1)
(2)
-
10(10)
-10a
50-25a
· (1) **
शोण
= 0.4 (m)
Ans: The maximum height reached by the 10-kg block is 0,42 - 2.4m above
the floor.
2(a) Let the velocity of the
pile driver as it strikes
the pile be v
ma
By conservation of energy,
mgh - tmv-
where m - mass of the pile-
driver 10kg
height fallen.
As shown in the figure above, fje fg and f. are the frict- ional forces on the 10 kg, 20kg and 30-kg blocks res-
pectively.
20N
f1 = 0,2(10)(10)
0.2(20)(10) 4ON 60N
2
fz = 0,2(30)(10)
Let the acceleration of the
system be a the tensions in the strings be T and Tj. Apply Newton's 2nd law to
Ti - 20 - 10%. (1)
and h
12m
the blocks seperately.
600
2gh
2(10)(12)
TI
T
4020
240
60
30
-15.492
(Ani
(1).
(2) ) + (3)
600
(b) Let the common velocity
required be v ma
(2)
Initial momentum of the
system
-1
(10)(v,) kgma
Final momentum of the
system
120 ·60m2
。(2).
(3)
8 ma (Ann.)
(ii) Substitute a' - 8 ints (1)
500N (Aus)
Substitute a' - 8 inte (3)
T 300N (ang.)
V.R.
2
(b) Substitute a
(Ans into (2)
4.(a)
(Ang.)
(10 + 12)▼ kgos
(b)
MA
· 10(10)
10(2)
By conservation of linear.
x 100%
momentu
x 100 40:
(1012)
M.A. 1.6 (An■.)
(c) Let the minimum effort
required be E
Load
E
1.6
500N
500
1 x 10
9.
10 (An.)
(b) As shown in the figu
below.
Leth
Plastic
Cube
(720 km)
depth of oil
-water-
A cross-sectional
area of the cube
(~ 0.01 m2)
Upthrust due to oil
the cube
(720)(g)(ha)
7200hA
Upthrust due to water-
the cube
=(1900)(g)(0,1-h)A
10000(0.1 h)A.
Total upthrust exerted on
the cube
7200A + 10000(0.1–h)A
1000A -28001A
(1000 2800h)A
Weight of the cube 900(0.1)(A)(g)
900A
Total upthrust.
weight of the cube
· (1000 2800h)A = 900A.
h 0.0357m
the cube rises
0.0357m- 1cm
0.0357m - 0,01m
0.0257m (Ans.)
9. manufacture produces two.
different models A and B of a product. Each model. must be
marlines. and Mo. To
complete one unit of each model, the two machines must work the number of hours inlicated in the following table.
A B
1
Ma 1 3
No machine may operate more
than 12 hours per day," The profit is $3 on each unit of model of A and $6 on each unit of model B. How many of each should be produced daily in order to maximize his profit?
19. If an A‚P, and a G.P. are
added together, the sum of their first term is 6 of their second term is −1. and of their third term "i
"If the first term of the G.P. is twice the fir term of the A.P、 find the common difference and the "common ratio: 11.A right circular cone
divided into 3 portions A, B and C by planes parallel to the base as shown in the figure. heights of the portions- are 10, 2m and 3mm* respectively. –Calculate () The ratio of the
volume of A, B and C. (b) The ratio of the
„curved surface ares
of A, B and C.
B
2.
C
3m
T = 120N (Ann.)
(c) Apply the formula
+2as
Letv be the velocity of the 15-kg block when it strikes the floor.
The initial velocity is Ons
(d) 1
2(a)(2) 2(2)(2)
8
2.8284
(Ana.)
Let the time required for
the 15 kg block to reach the floor het (seconds) Apply the formula
initial velocity
-tat2
Substitute
2
-12
■ 1,4142 • (Ani.)
15kg
15 y 10kg As shown in the figure above let the velocity of the 10-
kg block be when it rea-
ches the level at AĢ
2
2
2(a)(2) 2(2)(2).
8
the string slackens, hence,
assume the block moves h
-39(15.492)
7.012 maTM (Ans.)
(c) Let the average retarding force exerted by the ground
on the pile be F newtona.
Hence,
work done against F loss in kinetic energy
+ less in potential energy
Work done against P.
F(0.5)
Loss in kinetic energy
· 4(10 + 12),2
--1(22)(7.042)2
545.5 J
Loss in potential energy
• (10 + 12)(10)(0,5) ➡ 1103
P(0.5) (545.5+110)
Load: ➡ 50g.
E- 312,5N (ADE.)
(d) Let the tension in the
string connected to the 50-kg block be T newtona
-1.6
effort.
When effort. 600N
Hence,
- 1,6
600
T➡ 960N
the net force acting on
the 50-kg block
P = 1311N (Anm..)
- 960 - 50g
➡ 960 - 500
3(a)(i)
'Q ms
- 460N
30kg
20kg 10kg
smooth horizontal floor
600N
As shown in the figure above
let the tensiona in
strings be T
Tand
the
T2 the
acceleration of the system
bé a.
Apply Newton's 2nd law to the blocks seperately,
600 1 - 10■ ...(1) T1 - T2 - 20
(2)
(1),
T2
30a ...(3)
+ (2) + (3)
600 m
(10 + 20 + 30)a 10 ms (Ans.)
(a substitute
Apply Newton's 2nd law,
460- 50(a)
录 = 9,2 mm
(Ans.)
Ana: The block will move
upwards with acceleration 9.2 s
-2
5.(a)(1) Upthrust of water
on the cube
of the cube
E
900(0.1)3(10)
(ADS.)
9N
(ii) Let the volume of the
cube immersed in water be y
Upthrust on the cube (1000)(g)(V*)
-2
a
= 10 into (1)
บา
and (2), we have
1000(10)vi
- 9 x
9
104
Exercise 2
12. A man borrows $8500 to
repaid with interest at 124 in 2 equal annual instalments, the first payment being due at the ́end of the first year.
Find the annual payment correct to the nearest $10.
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數部 #
Mathematics 4
Attempt All questions in
Section A and any Six questions in Section B.
Section A
13.
12Aix 10% more than B and
Bis 10% more than C. What is the percentage of A more than C?
2. It the roots of the
equation x2+kx+9=0 a.e real. Find the values of k. 3. In the figure, the area of
the parallelogram. ABCD. is equal to 600sq.cm. Find 24.
50cm
40cm
In the figure, AB is the diameter of the circle. BAP, RQP are straight lines. 4Q9R=36", Lapq=20°. Find Z RQB. (Geometry theorem need not he quoted when used.)
5. In the figure, AP÷PB=2;1;
AC/./PQ//BD_\\\\If &C=8em, BD=5¢1), find Pų. (Ge one try theorem need not be quote); when used.) c
In the figure, the squRTES and the circle are of equal area and have the same centre. Calculate ZP9Q.
18. A hill-side is a plane inclined at 10" to the horizontal, Astraight path across it slopes upwards at 4" to the horizontal. Find the. bearing of the path
if the line of greates slope bear dne North. 15. In the figure, ABC in
equilateral triangle and ZPAQ-120, PBCQ is a straight line. Prove that:
2 PB.CQ-BC2 PB: CQ-AP:AQ]
16. IP, TQ`are the tangente:
from a point Ț to a circle; N in the mid- point of the chord PQ+I/ is the mid-point of To If PH cuts the circle at , prove that q, N, R, I are concyclic,
T