青漱備 頁一第張七第 日九十月二十年辰丙麻豆
WAH KIU YAT PO
報日僑
三期星
日六十月二年七七九一届公年六十六國民中
2. Look at the
1977中學會考試題預習專欄
明德社主編
13. Let the statement
P(n)
What date
is it today?
2.()
atar +, ar
n-1
數學(十五)·交長波。
(A directory
B. calendar
ar
c. book D. dictionary
E. picture)
新數學(十五),魯榮家,
-1) 1
3. "Can you come
Henry.
called 3.
when n = 1
Modern Mathematics (15)
L.H.S.
a
Answers to Exercise 6 (cont.)
R.H.S.
=
(-1) (r-
11. (a) An figure shown;
TA and TB are the tangents to
the circle.
TA TH
The center of the circle is
2, 1)
TO
1)2
It is true for n=1
Aasume P(k) is true.
a + ar
P(k + 1)
aar
K-1
1) + **
13 units
The radius of the circle
221
5 units
Apply the Pythagoras' Thai,
*(k+1 = 1)
k+1
1)
.". It is also true for n=1+1
By principle of mathematical
induction the statement is
true for all positive inte-
gers në
+
-(-20)
since
angle TAO =
90°)
TO2 TA
132 - TA2 + 52
=
TA =132 52
parabola :
14.
Mathematics 15
Exercise 7
Multiple choice questions,
2
1. If x+x+k is divisible by
x-2, then it is also divisible by
'A.. x-1 3. x+1 C. x-2 D.x-3 E.
x+3
2. Ir B exceeds A oy 20% and C
exceeds B by 20%, then, the
ratio of A to C ie
A.
25 136 B. 5 7. 0. 1 :. 1 D. 75
E.
25 : 16
BC ia a tangent and AEB,
a diameter. AC cuts the
circle at D. BD DE and
CBD = 209, LADE =
200 B. 30° C.
A.
D. 50°
E.
60°
.40°
13. If is an acute angle and
2cote - 3 = 0, then cose
D.
E:
/13
14. A gold bar with dimensions
2 cm x 3cm x 4cm has all of its faces rectangular ca If it is melted and re-post into three cubes of equal volumes, what is the length. of an edge of each cube in ст?
B. 2
In the figure, x=
·A.
C..
a+btand B. a+baine a+bcose D. a+bcote
a+bsece
A.
D. 4 B. 5
15. If
x2-6x+9=x-3, what are
the values of x?
A. No real number satisfies
the equation
Every real numger
D.
In the figure, what is the sum of the six marked angles?
180 B. 2709 ・360° 5400 B.
B.
C.
3 or -3 only
D.
3 only
E.
·x 3
7209
16.
then
In figure, LKAB ="ZXYZ ≈ 90. XB6 BY 2 and AB = 4. What is the ratio of the area of AKAB to the area of AXYZ?
12 units
Ans
the length of tangent
24
11
11
is 12 units
he
ph shown
(b)
By the definition of
(1).
- 2x + 1 is drawn
=2x
- 2x + 1 = 9
A.
,B,C subscribed $3800, $5700 and $7600 respectively for running a business. profit after one year, 18, $270, according to the ratio of capital. A shall share
350 B. $55
The
C.
$60
i.
7:
310
(-2, 29)
A parabola is the locus
of a point in the plane such
that the distance of the pt.
to a fixed (focus) is always
equal to its distance from a fixed line (directrix)
Let (x,y) be an arbitrary point on the parabola required
The distance of the point (xy) to the focus (3,3)
2
3)2 + (y
3)2
The distance of the point. (x,y)
to the directrix x+y=6=0 is
12
therefore :
√(x-3)2+(y-3)2==+7-6
(x-5)2+(y-3)2 = {———-
(Ana.)
3x + 3y #2xy-12x-12y+36 = 0
12. As figure shown, :(i)/
=
→
g
=
AB + BD
$ +
$
*)
Ans
=
= 1⁄2(p + q)
(ii) Since BC. =
AЕBC = 1⁄2{p + q)•(q − 7)
+
qp
= %{q•q = p•p)
=( 1922 - 182)
·But {q}= [P|~ (Since AB=4C) AD-BC
The scalar product of ÄD and BC is sero, therefore
AD L BC
= 0
added.
An additional linear graph
y = 9 is The intersection are (~2) and. (4,9) 8.8. =
(11).
2x +1
y= x + 7 is added
the intersection are (-2,9) and (3,4) {-2, 3}
B.
(111) 2x2
- 5x
y =
*
(5/2)x
12-0
- 2x + 12
بالماسة
In figure, a circle, centre
O touches the sides of a
quadrilateral: Which of the following is not true? A. PQRS is a cyclic
quadrilateral
6
B..
c.
+ 7 is added.
the intersection are (~3/2,22)
and (4, 9).
Number of Candi- dates falling in this range.
{-1.5,
15.(1)
Range of
marke
0 - 4
6
9
9
10-14
20
15-19
10
20-24
(**) The mean" SCOTO'
≈ (6x2 + 9x7 + 20x12 + 10x7
+5 x 22) 50
= 11.9 (Ans.)
ZPOQ + ROS # 180°
LP + LQ + LR + L$ =
D. OQ bisects LPQR-
E. PQ SQR + PS
5:16
3:5 9:25 D. 4:5 E. 3:25
17. If the sides of a right-
angled triangle have lengths of x-7, x and x+1, find x. 7 3. 4. C.12
AT
D.
4 or 12- E.. 7 or 12
18.
In figure, DE AB, BC LAB, AC = 5, HG 4, BA 12,
360°
DA
8. If loga + logo = log(a+b),
the expression that a in terms of bis
B.
D.
The value of x in sin(2x+30)°
cos(x-30) is (1) 0,(2) 10, (3). 30,(4) 150, which of the following is true? A. (1) only
B. (2) and (3) only C. (3) and (4) only
D. (1) and (3) only B. (2) and (4) only
10. If 3P amounts to $Q in n
years, at г per annum simple intereat, then r =
3, CE
50.2
5/2 B.
13
10/
10/41
13
can
ever be zero?
C:
.20
D.
The chords AB and DC meet outside the circle at P. The chords AC and BD cut at Q. If LA-a and LAGD=q then 4p-
A, (q+a). B. (q-a)° C. 2(9-8)0
D. (9-28)° E. 90°-(q+a)
1. E 6. C 11. C 16. 2. A · 7. A 12. D -17. 3. D
A.
1000 nP
B.
100ng P
(ii) 46% of candidates failed in the test implies 23 cand- idates failed in thé test, From the graph, the“ pasa mark is 11.5 for: it indicates 23 candidates below this sark.
C.
100(Q-F)
D. 100(4-2)
nзwer.
E.
100(Q-P)
11.
23
TO
The graph of y ax+bx+c in
Which the sketched figure.
of the following statements is/are true?
A > 0 (2) a < 0
(4) c = 1
and (3) only
and (4) only and (3) only
0.0 0
A.
D.
(2)
E.
and (4)only
(3) only
B
C
8. A 13. E 18.
E
4.
E 9. C 14. B
19.
5.. D
20.
10. E 15.
འ་
·1977中學入學試試題預習專欄
·智慧社主編
英文科
(十五)
ENGLISH (15)
Choose the best answer. write
the LETTER in the brackets.
to talk during lesson time.
1. We are not
(A. aloud
B. allow C. allowing D. allowed E. loudly)
(A. ? Dick? B. ? Dick
G. Dick? D. Dick I E.. Dick 1)
4. Tony invited Sam and
his party. (A. she
D. we
B. they 0. I E. me)
5. How many friends
bringing ?
(A. has
Tom
5.()
B. have C. is
D. äre E. were)
6. The lady a dog is 6.( walking down the street.
(A. have B. with C. and
D. has E. carries)
7. "Excuse me
"Can you speak English
(AT 1 "
C. 71
E.
said he.
BA
D.
8. He never drinks coffee,
?
B.C
(A. doesn't he B. does he
C. was he D. is he- E. isn't he)
9. He looked forward to
his old friend.
(A. seeing B. see C. sees
D. have seen E. saw)
10. The dootor tried to save
the
10.0)
man.
(A. dead B. died C. death
D. deadly E. dying) Read this passage carefully. Then answer questions 11-15 which are about the passage.
Tom was not wel Не stayed in bed. He did not want anything to eat. He could not even drink his milk This was very unlike him. Mother felt his head. It was very hot so she rang up the doctor and told him about Tom. The doctor cane a few hours later. He gave Tom some brown medicine. He told Tom it was not nice, but it would do him good. Tom made.
a face wher he drank it.
The next day he was much better. So he said, "That nasty medicine must be some good."
11. Tom was
(A. well B. bad C. had a
fever D. unwell
E. very ill)
12. Tom generally
(A ate only a little B. was
not hungry C. wanted his food D.. did not want his food. drank only milk) 13. Tom stayed in bed because
13.
(A. was hungry. B. was
naughty C. was very cold
D. had a fever E. was hurt)
14. Tom's mother
(146)
(A gave him some medicine
B. called the doctor
C. made him drink his milk D. did nothing E made him cry)
15. The doctor came
15.0
(A. at once B. next day c. in an hour D. next morning E. the same day) Choose the answers which best complete the following fassage.
John Erown and his wife, Jeny, lived in London. They, were tired 16.(A.. for B., at C. of D. on E. in) living there. There were too many people, and too 17.(A. much. B. very.
C. many D. lot of E. all) noise, and too many cars. They wanted to live in 16.(A. the street B. the
D. town garden C. the country
that place).
"We'll go down to River's End tomorrow," said John to his wife one day. "It's a nice place. There are some very nice houses 19.(A
B. there C. nowhere where E. anywhere), and the country is beautiful.
we..can B. on C, by
look 20.(A. in D. at E. with) some of the
house."
!
16.) 17.( ) ( ) 19.( ) 20.( ).
ANSWERS
"
1.()
1.D
2.B
3:0 4.E 5.07
6.B
7.E
8.3
9.A 10.8
11.D
12.0 13.D
14.3 15.E
19.8 20.D
16.0 17.A 18.0
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