日九廿月三年〇八九一曆公年九十六國民曦中
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|主席啟邦、林王兆h-氆尔舆、何、
昨日出席之保良局患理有主席難走、
1980
The mass of B is 1 it is pulled aside so that
kg
and
中學會考試題預習專欄
it is 1.25 m above its lowest position.
物理
(廿五)
明德出版社番榮家提供資料
PTYSICS (25)
W. K. LO
(MILL* ? DALE PRESS LTD.)
Revision Test
Time allowed: One hour and
30 minutes
Answer SIX questions choosing TWO from each section. Each question carries equal marks. All answers to problens should be given in S. I. units.
SECTION A: MECANICS AND PROPERTIES OF MATTER. (When necessary, take the acceleration due to gravity=10ns 2)
1.
0.45m
1-2-
2-
Figure 1
1.250
The spheres are then
released at the same time,
the spheres collide with
each other and the maximum height reached by B after collision is 0.8m (see figure 2)
(a) Explain briefly why
the spheres will collide at their lowest posit- ions. (2 marks)
(b)
(1) What are the velocit-
ies of the spheres just before collision? (ii) What are the velocit-
ies of the spheres just after collision? (iii) Find the maxinum
height reached by A after collision. (iv) If when A collides
head-on with B, the two spheres remain in contact for 0.2 seconds, find the average force on A during the collision. Find the energy lost during the collision.
(v)
In what form will the lost energy dissipated ? (8 marks)
2. A uniform planck AB of length 12m and mass 50kg rests on two supports P and Q at positions 3m and 9m from one end A. A man of mass 75kg stands on the planck 1 meter from Q and 4m from B as shown in figure 3.
B.
10.82
A
P
Figure 2
3m
5m
im
3!
In figure 1, two metal spheres A and B are sus- pended from X and Y res- pectively by two strings
Figure 3
of equal length. The strings are long, inex- tensible and of negligible mass. A and B have the sane radius r and the seperation of X and Y is 2r. The points X, Y and the centres of the spheres are in the same vertical plane. The mass of A is 2 kg and it is pulled aside so that it is 0,45m above its lowest position.
(a) Find the reactions at
P and Q.
(b) If the man walks to-
wards B, find, how
far near from B can
be reached. before thè planck tilts.
3(a) What factors will
affect the efficiency of a single string pulley system? State briefly how the effic- iency is affected by each of these factors.
(b) A block and tackle
consisting of three
fixed and two mov- able pulleys is used to raise an aluminium cube which is completely ign- ersed in water
(density 1000kgm ̃3)
as shown in figure 4.
If the volume of the cube is 10m3,
the
effort applied to machine is 5x10"N and the efficiency of the machine is
80%. (relative density of
aluminium.
Fiqure 4
Aluminium Cate
[ tom3)
2.5)
of
x in the
2. Find the
furt 3+2x 5
values
a < x < b such that.
3x-4 >
ኃ
3. Find the value of H
where 0% e < 360°, ir
2
-
4 Ssin cos
•
30°
1
In the figure, AR is the diameter, ACE =20° and LEAD = 50°, find the value of x.
Geometry thearem need not be quoted when used)
5. If x is 20% smaller than
y and z is 20% greater than x. Find the ratio of x:yız.
6. If p and q are the roots of
o
- 4x + c = 0) and P:q=3:1, find the value
of c.
7.
•Effort
watter density (1000 kqm3)
(i) What is the velocity
ratio of the system? (ii) What is the upthrust
of water on the
aluminium cube.
(111) Neglecting the
resistance of water,
find the acceleration
of the cube while it
is moving in water. (iv) Find, approximately, the position at which the cube will finally
stay.
(v) What additional effort
is required to apply
to the system in order to push the whole cube out of water?
1980
中學會考試題預習專欄
數學
(廿五)
明德出版社交長波提供資料
Mathematics (25)
C. P. Man
Mill & Dale Press Ltd
Exercise 11
Auswer all questions in Section A and any six questions in Sectiou !!. Section A
1. If sin A + cos A = +
find the value of (a) SIDACOSA
(b) (sina-enga
22
A
E
>
In the figure, AB = 2CD, AB/ CD // EF, if the area of ACDG is 3 sq.ca., find the area of AGFC.
(Geometry theorem need not be quoted when, used)
8. A but went up a hill at a speed of 10km/hr and down the same distance at a speed 20km/hr. Find the average speed of the bus for the whole journey,
Section B
9.
The figure shows a regular hexagon ABCDEF inscribed in a circle of radius 10cm another regular hexagon PQRSTU circunscribes the same circle.
of
(a) Find (1) the area
AICEF, (ii) the area of
PORSTU.
(b) If the average of the
ereas of these two Lexagon is taken to he
the area of the circle, what is the error percentage?
10. Let S denotes the sum of
the first n terms of a
10,3)
<2,-5)
415.-2)
The curve of the equation
y
ax
x + C (where a, b and c
are real numbers) is sketched in the figure. It passes through the points (0,3), (9,-5) and (5,-9). Find (a) the value of c (b) the values of a and b (c) the coordinates of the points where the graph cuts the x-axis.
(d) what aditional linear
graph would be necessary to solve graphically the equation
2
X
12.
E
13.
14.
B
In the figure, ABCDEF is a wedge, ABCD, CDEF and EFBA are rectangles, ABC and AADE are congruent right angled triangles. If FBC= 30 and LACE 53'8', find (a) ¿FAC
(b) AFB
(c) volume of the solid,
if AC = 100m.
In the figure, circle ABPC passes through the centre C of the circle ABQ. If APQ
is a straight line. Prove that
(a) PB = PQ
(b) CP produced bisects
Bq ar right angle.
C
In the figure,
DAC 900
ㄓ
and AE = AB. Prove that
BE-BC =
2A62.
15. An agent purchases 250
bicycles for $18,750 und fixes the selling price at 30% above cost. He sells 180 at this price and a further 50 when this price is reduced by one-fifth. The rest are sold at a loss of $10 each. Find his gain per cent on the whole transaction.
progression and Ta denotes
10.
the oth term of the
progression. In a geometric progression, if
T3
5
T2
+
+ T
T - 91 and
273,
b
(a) the first term and the
common ratin of the G.P.
(b) find the least value
of n if Sp> 100.
X
A
In the figure, ACB is a semicircle, centre 0, its area is hisected by a line XY parallel to the diameter AB,,IT LAOX </,
prove that -20 - siu28°. I -20 - f, prove that
nosfe
F
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