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D. y cose + 1
A
1977中學會考試題預習專櫟
明德社主編
數
墨(廿五)·交長波
Mathematics 25
Exercise 11
Multiple choice problems.
1. If F(x) =
then
£(x+1) =
A.
B.
C. x2+3
x2+2x+1
E.
2. Which of the following
sketches is the graph
of y =
A.
x(2-x)?
A varies directly as b
If b is increased by
20%, then a will be
increased by
A. 20%
C. 44% E. 400%
4. 109,0 100
$10.100
A. -2
c. O
E. 2
B. 40% D. 144%
B.-1.
B
D. 1
62.
5. Which of the following
is (are) arithmatic
progression(s)?
(1) 22, 44, 66,
(2) 111
글
(3):1
2
88
15
+
22
42.
(1) only
(2) only
C. (1 and (3) only
6. cot20
A. 1
and (2) only
1), (2) and (3)
C. sin2e
E.
cot28
1
sin20
B-1
D.
E. y = cos(+1)
事後,考前備上不們供各作,故題張做
的才益的她,是舉圜者答便在長,完
8. In the figure, ABCD is a
rectangle. Which of the
the following expression
is the distance of A from the line XY?
A. asine + bcose
B. a sine+bsine
C.
a+b sine
D. a sine + b
E. acose + bsine.
9. In the figure ABCDEFGH is
is a rectanglar block. tan FAG=
B.
10. Which of the following
Siy
(are) true?
(1) co945° =sin1 35° (2) cos83°-COS2639 (3) tan 69 = -tan344°
(1) only
16 Ar
B. (2) only
C. (1) and (2) only D. all of them
E. None.
11. 0 is the centre of
circle ABC. LA = 40° LC=70°, ZAOC=
A. $1500 B. 140° C. 120° D. 1100 E. 100°
AG
12. In the figure, AXBYI|CZ.
ABC and XYZ are straight lines. AX÷4; BY=6; CZ=11. AB÷BC=
A. 27 B. 4:11 C. 6.11 D. 2:5
E. 2:3
Z
13. A master painter can
paint a house in m days,
and his two vorkers
require x and y days to paint a house. If the master works as fast as the two workers together, find m in terms of x and y..
A. 1
B.
x+y xy
cos2e
xy
C.
D.
x+y
Y
E.
20
14. What is the ratio of
the circumference of a smaller circle to that of a larger circle? (1) the radius of one
circle is one-half the other
(2) the radius of the
larger circle is 6.
卻有圖地我刊象
A. this problem can be:
solved using only the given information. marked (1)
B. This problem can be
solved using only the given information marked (2)
C. This problem can be s
solved only by using the given information marked (1) and (2). D. This problem can be
solved using either the given information marked (1) or (2)
E. This problem connect
be solved with the given information.
A man owned of an
interest in a house. He
•
of his interest,
cost, for 1000. What is the total value of
the house?
A. $3000
C. $6000
E. $9000
B. $5000
D. $8000
16. Form straight lines in- tersect as shown in the figure. What is the sum of the 6 marked angle? A. 2 rt. 4SE
B. 4rt is
C. 5 rt Ls
D. 8 rt 25.
E. 10 rt2's
17. If x-7=0 and y2-25
then xy = A. 135
C. 135
E. $175
B -35
D. 35.7
18. Area of circle 0 = 9T
What is the area of the square ABCD?
A. 24. C. 35
E. 48
B. 30
D. 36
19. What is the maximum
total weight of ten eggs, if four of them weigh 15 to 25gm. each, and the others weigh from 20 to 25 gm.. each? A. 180gm. B. 210gm C. 220gm D. 225gm
E. 250gm
20. The sum of the first 3
terms of an A.P. is 72. The 4th term is 0. What
is the first term?
A. .36
B. 24
C.
18
D. 12
E. 6
新數品(廿五)·魯榮家、
MODERN MATHEMATICS (25)
Revision Exercise
Auswor ALL the questions in
section A and any Six in secin
tion B. All necessary working
must be shown clearly.
Section A
1. The area of a circle in
scribed in an equilateral tri-
angle is 48%. Find the pari-
meter of the triangle.
日七廿月四年七七九一座公年六十六國民都中育教篋章
訴投函來生學考投位三
題問有卷試試學入大中
表圖欠理地確明不示提文英指
向考生作出隔音之揭
水員在考試進行中,
·BECHK - BEEK
始舉行考試- 透天的
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•全部生原已抱有息
但在十九日 考英文.
- *HTERRENO
考者又不作及宜的補-
畫,可憐我們一中
·】考生上
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函來者卖
2. Solve tue equation
3. If {x: 2x2
of
2
- 4x + 3-
o} [{m,n}; \find the value
n + 2
4. As figure shown, ABCD ́ is a rectangle,angle PDA = 30° and angle PUB 45° find the
gratio CD:
PB
5. In the figure, angle XAY * 50°
find the value of
6. Find the equation of the zircle passing through the
origin with radius 5 units and centre lying on the line
3x Ay
7. By using the fact that
n{n+1}
(141)
find the value of
10x11 · TIRETM + 12x13
20. 1-21
8. Solve une equation for
5con20
360°
Jain@cos
Section B
9.(a) Find the equation of
locus of a point ) such that'
Paistue mid-point QA
where is on
(2,0)
2
parabola
by and A is the point
=
mx 4 k is the tangent
2
2 of the circle x ✦ y
* 2 if
the tangent is perpendicular
toxy- 2
(i) fud m
(ii) find k.
10. A cylindrical water tank 70cm in diameter,/300 coi height. It is fed by a ey- lindrical pipé 1.75cm in dia- meter through, which water flows at 30meters per minute.
(i) How many minutes will take to fill the tank?
(ii) If the pipe is turned on 10 minutes find the total surface area of the water Tank which is watted.
11, (a) A
E, F are the mid-points of
AC and BD respectively. Sim- plify
AB + AD + CB + GD
***•
十八日開
#E] *.
*技業技
本生等中
(b) If B) • DE ■ EF = FG
Simplify JBA
2CA
12. AB figure shown, ABCDEFGH is a rectangular prism, if "AB 16em, BC 12cm and
AB 10cm,
Find
(1) length of AG, AC and All (ii) angles between planes
HAB and ABCD
(iii) the angle between CE and the plane BCGF
"
GC
13. John has 105 catties of
tea A, 100 cauties of tea B
and 90 catties of tea C. O
mixtures X and Y are made by
mixing tea A, tea B and tea ̈£
in the ratio 7 : 5 : 3 and
35 5 respectively, The
profit of mixture X is $20 per catty and that of mix- ture Y is $12 per catty. (i) How many catty of each
mixture should be made to
give max) sum, profit ? (1) What is the profit ?
14. (a) Find the range of k if f(x) = 12
is
always positive.
(b) Find the range of c if f(x) 2c+ 3x
is always
negative.
(c) Find the domain of the real valued function f(x) where f{1} 11 10x
·
15. Liquid fuel is pumped into a storage tank The following table shows the number of
gallons of fuel in the tank
at various times after the
flow started.
Time in
minutes
5 15
25:35
45
Quantity qin gallone | 60 160 |260|360 |460|
He present graphically the above data, and use your graph to answer the following ques~".
tions
(1). Do we have reasons to he-
lieve that the rate of the
flow is constant ? why ? (ii) Assuming that the rate of
the flow is constant, find
this constant rate and find
the quantity of liquid fuel that was already in the tank before the flow started, (ii) Assuming that the tank holds 750 gallons,
how long
would it take to fill the
tank from the start of the
flow, if the flow continues at
the same rate ?.
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