B.
(4) only
C. (2) and (4) only
D.
(3) and (4) only
E.
(2) and (3) only
13. The rational number repre-
sented by the recurring
decimal 0.259 18.
4. He's strong and cheerful.
His health is as bell.
23 A
4.( )
(A good B. loud C. brave
D. sound E. healthy)
5. He bought a duck for paid ten dollars..
(A... it B. what C. which
D. whom E. its)
6. Good cakes
shop.
at that
he
6.0)
2.7832
翼 四第張五第 日二十月二十年根丙雕
WAH KIU YAT PO
郭日僑華
三期星
日九月二年七七九一曆公年六十六國民中
★教僑
1977中學會考試題預習專欄
明德社主編
6. 2.7832 = 7.745
=
[2+ (n-1) (2)]-[4+ (n-1) (2)]
In figure, two unequal
(A. will send B. should be.
sen't
2.
circles touch at P, 27 is
2.217
4.915
n
_n(n+1);
a tangent meeting the
C. dan send. D. must Send E. may send).
- 2.2172 = 2.83
(Ans.)
tangent as to the circles
2. As best is to worst
most to
so is
*
2.0)
(1)
1.
X 2.0334
3
數學(十四)·女長波
2
ZAPB = 900
0.6778
at T, then
AP = #P
TATB TP.
2T is the perpendi-
cular Disector of AB
which of the following
must be true? (1) only
(A. kindest B. largest
3.
least D. first E. well As son is to daughter, so is
to niece.
(A. uncle B. brother
C. friend D. cousin E. nephew)
112
3.( )
Modern Mathematics(14)
Answer to exercise 6.
Section Az
Since ABEC is an equila- teral triangle and ABCD
is a square.
AB-BC-CD-DA-BE-CE.
EBC 60°
LABE=90°-60°=30°
2 BAEL BEA 180°300
2
.
75°
Similarly & DEC = 75° Z BEC = 60° also
•LAED≈360° — (LAEB+ ¿DEC+ZBEC)
36.0° (-75°+75°+60°): =150° (Ans.).
log 108 = 100108
108 = 4.762
2.7832-2-2172
108
4.762 0.594
(Ans.)
7. Let the Profit of the
1st year be $x, the second year be an Sy and the third year be$z.
X+y+z 525-
from (1 x+y+2=1575-
(4)-(5). Z-31.8 (Ans
from (2) x+y=1257-
Sub.into(3)
y=630
Mathematics 14
Exercise 6
Multiple Choice questions.
1. If the first 3 digits of
are 988,
N
(8.42)2(95.1)
which of the following is the beat approximation?
988
B.
3
-(1).
98,8
0.. 9.88
D. 9680
x + y = 628
E. 98600
7
B..
་
(2)
27
27
2
2. If x =
2
= 474 ---
•(3)
-(4)from
and y tana, COSA the relation between
y is
DA
25
25
14. If the 3 ter
6
term of a G. P. are 1
(Ans.)
C.
E.
B.
D.
1
-
+1=0
-27
·9 (3)-1
3. if T
2 T
equal to
21
then g is
C.
(271)2
E.
9- ) - -9(-)-1
9(~3)-1
12
D.
15. In AABC, if
sinė SinB
6 sinc
then
A
B.
D
E.
= 480 sinaz4, sind=5, ainC=6 sinAsinB;sinC 4:5:6
CA: LB: 40 = 4:5:6: Pimeter of
ABC
15
16.
2. The numbers between
and 2001 divisible by 7 form an A.F. The first number is 7.
the last number is 1995 Let 1995bethe nth term
1995 = 7+ (n−1)(7)
n = 285
the sum
282(2(7)+(285-1)(7)]
285285 (Ans.)
3. Let
= ma + nb where
n are scalars.
91-161
(-31-21).
n(~51+43).
(−3m-5n)1+(−2m+4n)]
-3m-5n=9
-2m+4n =-16-
From(1), (2)
m=2
n=-3
2a - 35 (Ans.)
4. As figure shown.
B.
8
Let the Path travelled
be AE
..LAER = 45°
EBC 30°
in rt. a BEC
EC
BE
sin30°
In rt.AABE
BE
= cos45°
EC
BE
BE
AE
A sin30°.cos45°
EC
AE
= sin30°.cos45°
but
EC
= sine
AE
sino = sin30°cos45°
(0.5)(0.7071)
0.3536
=20° 42'
6tan2x
6 sin x
cos2x*
(Ans.)
-4sin x 1 = 0
4sin2x
6sinx-4sin xcos2x-cos2x,
6sin2x-4sin2x(1—sin2x)- (1-sin2x) = 0 6sin2x-4sin2x+4sin x- 1+sin2x = 0
4sin x+3sin2x 1 0
.0
(4sin2x-1X3in2x+1} = \0 (2sinx+1)(2sinx−1 ) · .(sin2x+1)
=0
2sinx + 1 = 0
sinx
*****
= -0.5
x = 210° or 330°
2sinx - 1 = 0
sinx
2 0.5
X = 38° or 150°
(Note: sin x+1 = 0 is im-
Possible.)
x=30°, 150°,210°or330°
(Ans.)
sub.into (5) x=627 (Ans. 8. Let the diameter, re-
quired be d..
The aolume of the ori- volume
ginal sphere- 456293
The sum of the volumes of the three spheres
-3 ( 2 ) 3 + ( 1 ) 3 + 2 + (2) 3
4
- (2) 3 = ( 24 ) 3 + 1 3 + ( 2 ) 3
(물)
(2)3
그릇도 = (동) 3
2
d = (cm)
= 2(cm) (Ans.)
Section B.
9.1) Since
are the roots
of 2x2+7x-3=0 d+p = = 2
df
+
{{K+1} - + B(B+1)
2
(B+1 ) {X+1°)
2+B2 + (α+B)
dß+(a+f) + ̈↑
(d+f)2
dß+ 1
AB+ (a+pol+ (d+B)
(− 3)2 - 2(− 2) + (- Z)
47
(클)
(Ans.)
ii). Let the roots of the..
required quadratic equa- tion be xx
41(1)
In the figure, findt in terms of a,b,c.
tcta-b
t = c-a+
B.
C
t = c+a+b
D.
tc-a-b
E.
t =a+b-ë
5. On a map drawn to a scale žem to 200km, what is the distance between two cities which are 33cm apart
A. 300-km
B. 350 km. C. 700 km... D. 1200 km E. 1400 km
If the sum of the roots of
the equation x2+x+p = 0
is 2p-6, then the product of the roots is A. -4 ·B. 2 C. D. 9 E. 36
Triangle ABC is right-
angled at B.
40=0
BD LAC, DEL BC.
AB
5 = x, then DE =
4. Esin'e
B.
If
xsinecose D. xtane
Excot
出
and
res prectively, the
general term is
B = 60° C = 729
In figure, a circle is inscribed in an equilate- ral triangle of side 2 units as shown. The area of the shaded part in. square units is
A:
2/3
3π
283-
3π
13
E:
13 - 1
17.
D
C
PQRS is a rectangle inacri- bed in AABC with altitude AB=h, BC = b. If PS : SA 1: 2, then PS=
1
A.
B.
2
bh
C.
bh
D.
b+h
b+2h
bh
2.
2b+h
2x
18. If
then
y
X
Y
A.
B.
C.
C.
230°
x
D.
X2 y
E
In the figure, if LCAD=50°, then x+y=
22 +82
24ß
·A...
51
the equation required
is:
+
* + 1 = 0
i.e. 6x2 + 61x + 6 = 0
(Ans.)
10.
a) Let the first term be à
the common difference
be d.
a + 3d. 10
a + 7d 16
d =
2
a =
11
2
180° 1300 B.
D. 290° 5.. 360°
9. The value of 10
10108103 is
A.
B. 2 C. 3
D. 108103 .E.
1081030
10. An article which costs
$100 for X to make, sells to Y at a profit of 10% and Y re-sells it back to
19. sin(-8)sin(2m+e)
cos(+0)cos(2-0) 18 équivalent to
sine B. COSO
D. 1
A.
C.
0
E.
sin -cos
20. With the usual notation of
a triangle BC, if a>basin, then LA is capable of nav- ing
X at a loss of 10%; then A. X gains $10 on the
transaction
no solution
.B.
one solutions
B.
8
I gains. $20 on the transaction
C.
two solutions
D.
C.
Y loses $10 on the transaction
The sum of first 20
terms
・를 [2(글)+(20-7) (글)]
= 10 [11 + 27]
395
(Ans.)
b) 1-2+3-4+5-6+...to 2n term
terms
= 1-2+3-4+5−5+...
..(2n-1) -(2n)
= (1+3+5...(2n−1)] + [2+4+
6+...20]
D. X makes no profit on
the transaction
E.
none of the above is
true
11. A value of x such that
0
einx - cos5x* ia
A, 45 B. 30 c. 20
D.
15
10
12.
either one or two solu- tions
an angle of 90°
D 16. C E 17. D 18. A 19. D
Answer:
1.
B
6
C 11.
2.
C
7.
B 12.
3.
D
8.
4.
D 9.
C
C 14.
5.
E
10. E 15.
C
20. C
13. A
1977中學入學試試題預習專欄
咖智慧社主編
英文科
ENGLISH (14)
(十四)
Choose the best answer. Write the LEITER in the brackets.
1. The injured boy
to
hospital at once.
1.( )
A. are selling B. are sold C. sell D. sold E. have sold)
7. What is : name of your
classmaster?
(д. воле B. an
D. any E. the)
8. Tony's brother works in
Capitol Theatre.
(A. the B. any C. some
·D. a B. an)
9. Here is the lady
you found.
(A. whom
B. whose
D. which E. her)
7-()
purae
9.( )
C. she
10.()
10. Go away. It's none of
business.
(A. mine B. us C. him
D. your E. theirs) Read this passage carefully. Then answer Questions 11-15 which are about the passage.
•
Fees make honey. Len like honey. Se men keep bees. They keer bees in bee-houses made of straw, called "hives! There are three kinds of bees The queen-bee is the mother of the whole swarm. She does nothing all her life but lays enge". Then there are the -male-bees called drones!.
They do nothing but eat honey. But when one. has married the queen-bee, all the rest are killed. Most of the bees are workers. They are always working. So we say, 'As busy as a bee'. In a new hive they first make the wax honey-combs for storing honey. Then some fly out to gather sweet from the flowers to make into honey. Some feed the queen+ bee, and look after her eggs.
Some are always sweeping and cleaning. Some guard the door
of the hive.
11. Len keep bees because
bees
(A. make hives B. make
honey C. are good insects D. are busy E. feed the queen-bee)
12. Another name for male-bees
is
12.()
(A large bees B. ins ecta
C. drones
E. workers)
D. father bees
13. All the male-bees are
killed when:
13.(.)
(A. one is killed B. one is.
lazy
G. they are lazy D. they are old E. one has married the queen-bee 14. The queen-bee is fed by
(A. one drone B. meni
14.()
C. another swarm D. the workers E. Some male-bees 15. We say as busy as a bee"
D. a few
because
are very busy. (A. the male-bees B. queen-
bees C. workers D. men E. drones)
15.() Choose the answers which best
complete the following passage.
Children always like to play in the park. They can 16.(A. swim B. fly C. ride D. pull E. draw) on the roundabout, the see-saw or the swings. They have 17.(A little B. many C. a lot of E. several) fun there. Usually mothers are nearby to watch their little sons and daughters. Older boys like 18.(A. play
B. played C. to play D. to playing E. will play) basket- ball or football. Girls can also play basket-ball 19.(A. also B. as well C. but D. or E. how) they do not play foot- ball. Other small children can play on the grass. They run happily there. Grown-up can. rest in the park. It is a place for 20.(A. only one B. none C. someone. D. the big
E. everyone). 17.1
ones
16.1
19:27:8
i
ANSWERS
18.()
1.B 2.C 3.E 4.D 5.0 6.B 7.B 8.A 9.B 10.D
11. 12. 13. 14. 15.0 16.0 17.0
18.0 19.0 20.3
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