1990 Mathematics Paper2
1990 Mathematics Paper2
1990 Mathematics Paper2
HKCEE 1990
Mathematics II
90 (a2n)3 =
1. A. f(1)
B. f(n)
A. a6n C. n
B. a8n 2
C. a 2n
3
D. 1
D. a 6n
3
E. n
E. a 8n
3
90 1
If 2 = 10p, 3 = 10q, express log in
5. 6
90 x y
1 terms of p and q.
2. x y
x y p q
1 A.
x y B. 1
pq
A. yx C. 1
x y pq
B. x y D. pq
x y E. p+q
C. x
y 90 Let a > b > 0. If a and b are
6. respectively the 1st and 2nd terms of a
D. x+y
geometric progression, the sum to
E. xy
infinity of the progression is
90 ab 1
If x = , then b = A. 1
3. a b
ab
B. a
A. ax 1
1 b
ax
C. ab
B. ax 1
ba
ax
D. a2
C. 1 ax
ax ab
D. 1 ax E. a2
ax ab
E. ax 1
ax
90 a3 + 8a3 =
7.
90 1
If f(n) = n(n 1), then A. 2 2 4
4. 2 (a )(a + 2 + 2 )
a a
f(n + 1) f(n) =
90-CE-MATHS II 1
B. 1 1 90
(a )(a2 + 1 + )
2a 4a 2 11.
C. 1 1 1
(a + )(a2 + )
2a 2 4a 2
D. 2 4
(a + )(a2 4 + 2 )
a a
E. 2 4
(a + )(a2 2 + 2 ) In the figure, the circular cylinder and
a a
the circular cone have the same height.
90 If p and q are the roots of the equation The radius of the base of the cylinder is
twice that of the cone. If the volume of
8. x2 x + 3 = 0, then (2p 2)(2q 2) =
the cone is 20 cm3, what is the volume
of the cylinder?
A. 1
32 A. 40 cm3
B. 1 B. 80 cm3
8 C. 120 cm3
C. 1 D. 240 cm3
2 E. 300 cm3
D. 8
E. 32 90 The length, width and height of a
12. cuboid are in the ratios 3 : 2 : 1. If the
90 If a : b = 3 : 4 and b : c = 2 : 5, then total surface area of the cuboid is 88
9. a2 : c2 = cm2, find its volume.
A. 3 : 10 A. 6 cm3
B. 9 : 25 B. 48 cm3
C. 9 : 100 C. 48 2 cm3
D. 36 : 25 D. 96 2 cm3
E. 36 : 100 E. 384 cm3
90 If 1 U.S. dollar is equivalent to 7.8 90
10. H.K. dollars and 1000 Japanese yen are 13.
equivalent to 53.3 H.K. dollars, how
many Japanese yen are equivalent to 50
U.S. dollars?
A. 1463
B. 3417
C. 7317
D. 8315
E. 20 787
A. 9 9
B. 36 9
90-CE-MATHS II 2
C. 40 9 90 4
If tan = and lies in the second
D. 10 10 18. 3
E. 40 10 quadrant, then sin 2 cos =
A. sin x = 0
B. 1
sin x =
2
C. sin x = 2
D. cos x = 0
E. cos x = 1
90-CE-MATHS II 3
90 P 90 A
20. 22.
D
A 48o
T Q
F G
B
B C
E
90
B E
21.
R
F
O 44o
M
Q C D
I. Mean = Median
II. Mode = Range
III. Median = Mode
A. I and II only
90-CE-MATHS II 4
B. I and III only
C. II and III only A. a
D. None of them b
E. All of them B. b
a
90 Ten years ago, the mean age of a band C. ab
25. of 11 musicians was 30. One of them D. a
is now leaving the band at the age of
40. What is the present mean age of b
E. b
the remaining 10 musician?
a
A. 40
B. 39 90 y
C. 37 29.
l3 l2
D. 30
E. 29 l4 l1
90 x y
If the line y = mx + b and = 1 are
28. a b
perpendicular, find m.
90-CE-MATHS II 5
In the figure, a circle cuts the x-axis at D. 1.245, correct to 3 decimal places
tow points 6 units apart. If the circle E. 1.2475, correct to 4 decimal
has centre (4, 5), then its equation is places
A. (x 4)2 + (y 5)2 = 25 90 1 1 1
+ + +
B. (x 4)2 + (y 5)2 = 34 33. 1 2 2 3 3 4
C. (x 4)2 + (y 5)2 = 52 1
D. (x + 4)2 + (y + 5)2 = 34 =
4 5
E. (x + 4)2 + (y + 5)2 = 25
A. 1
90 y
31. 1 5
B. 1
x 5 1
O C. 1+ 5
D. 1 5
E. 1 + 5
90 x Sign of f(x) A. 1
32. B. 2
1.22 + C. 3
1.23 + D. 4
1.24 + E. 5
1.25
1.245 + 90 If a < b < 0, which of the following
36. must be true?
From the table, a root of the equation
f(x) = 0 must be A. a < b
B. a
<1
A. 1.20, correct to 2 decimal places b
B. 1.24, correct to 2 decimal places C. a2 < b2
C. 1.25, correct to 2 decimal places D. 10a < 10b
90-CE-MATHS II 6
E. a1 < b1 90
40.
90 The H.C.F. and L.C.M. of three
37. expressions are xyz2 and x3y5z4
respectively. If two of the expressions
are x2y3z3 and x3yz2, find the third
expression.
6 A.
5 1
2
5 5 B.
A B 3
M 2
C.
2 3
2
In the figure, AM = MB = MC = 5 and D.
3
BC = 6. The area of triangle ABC = 6
E.
A. 12 2 3
6
B. 16
C. 24 90 If A is 30% greater than B and B is 30%
D. 30 42. less than C, then
E. 48
A. A is 9% less than C
90-CE-MATHS II 7
B. C is 9% less than A E. y
C. A=C
D. A is 9% greater than C
E. C is 9% greater than A
A. 1
B. 1
2
x C. 1
O
4
B. y D. 1
4
E. 1
2
90 y
45.
x
O
C. y
x
O
90-CE-MATHS II 8
90 C
90 A D 48.
46.
3
A 30o B
60o
B 4 C
90 E D
A 49. o
120
C
B C A
A. I only A. 1
B. II only 2
C. I and II only B. 1
D. I and III only
3
E. I, II and III
C. 2
D. 3
E. 2
90-CE-MATHS II 9
90 A In the figure, if CD = CF, CE = BE and
50. DA = DB, then C =
P 48o A. 30o
B B. 36o
C. 40o
C D. 45o
E. 60o
In the figure, PA and PC are tangents to
the circle ABC. If P = 48o, then 90 A
ABC = 53.
A. 84o
B. 96o
C. 106o D
D. 114o
E
E. 132o
90 B F C
51.
C B
In the figure AB, AC and BC are three
tangents touching the circle at D, E and
E F respectively. If AC = 24, BC = 18
D and ACB = 90o, find the radius of the
circle.
A
A. 3
B. 4
C. 5
In the figure, TA and TB are tangents to D. 6
the circle ABC. If TA TB and E. 7
BD AC, find CBD.
90 R
A. 30o 54.
B. 40o S
C. 45o
D. 50o Q
E. 60o
90 A
52.
U T
E
F P
90-CE-MATHS II 10
I. UPT RQT
II. PU = QS
III. PQSU is a parallelogram
A. All of them
B. None of them
C. I and II only
D. I and III only
E. II and III only
90-CE-MATHS II 11