QUEEN’S COLLEGE
YEARLY EXAMINATION, 2010-2011
MATHEMATICS
Secondary:
3
PAPER II
Date:
21 ST June, 2011
Time:
8:30 – 9:30
(1 hour)
INSTRUCTIONS
1.
Answer all questions.
You should mark all your answers on the MC Answer
Sheet.
2.
You should mark only ONE answer for each question.
If you mark more
than one answer, you will receive NO MARKS for that question.
3.
Total Score of this paper II is 80 marks.
4.
Calculator is allowed to be used.
DO NOT TURN OVER THIS QUESTION BOOK
UNTIL YOU ARE TOLD TO DO SO
P.1
1. Simplify
A.
2.
1
B.
(ab) x + y
x
Solve the exponential equation 7  7
A.
3.
a2x b2y
.
a 2 y b 2 x

1
3
Evaluate
B.
49  10 9
64  10 9
2x
C.
(ab) –( x + y )
D.
(ab) 2( x + y )
C.
1
3
D.
1
 1.
0
, express your answer in scientific notation and correct to 4
significant figures.
A. 8.750  10 17
B. 0.875  10 9
C. 8.750  10 8
D. 0.875  10 0
4. Convert 1 101 101 2 into a denary number.
A. 77
5.
B.
C.
109
D.
218
D.
AK47 16
Which of the following is not a hexadecimal number?
A. E07 16
6.
93
B.
AB09 16
C.
AC07 16
The length of each side of a cube is increased by 10%. Find the percentage increase in the total
surface area of the cube.
A.
7.
10%
B.
20%
C.
21%
D.
33.1%
If 12 x 2  13 x  3 can be factorized into (3 x  1)( ax  3) , find the value of a.
A.
9
B.
4
C.
3
8. The least positive integer satisfying the inequality 4( x – 2)  18 – 2x is
A.
B.
5.
4.
C.
2
5 .
3
D.
4
1
3
P.2
D.
4
9.
A straight line L is parallel to another straight line with slope 2.
(1 , 2) and
points
A.
3.5
B.
4
C.
8
D.
6
(2, a) ,
then
If L passes through the
a=
10. If a > 1, the inequality x – 2a > ax + 3a is equivalent to
A.
x< 
5a
.
a 1
B.
x> 
5a
.
a 1
C.
x<
5a
.
a 1
D.
x>
5a
.
a 1
11. In the figure, ABCD is a rectangle. P is a point on AD such that BP  PC. If
PD = 3 cm and AB = 4 cm, find the length of AP.
4 cm
B
A.
3 cm
B.
3
C.
5 cm
D.
5
1
cm
5
A
?
P
1
cm
3
3 cm
D
C
12. In the figure, ABCDEFGH is a rectangular block. Find the volume of the pyramid CEGH.
D
A.
8 cm 3
B.
12 cm 3
C.
15 cm 3
D.
18 cm 3
C
B
A
6 cm
E
F
P.3
4 cm
G
3 cm
H
13. If 8 solid metal spheres, each of surface area A cm 2 , are melted and recast to form one large
sphere, what is the surface area of the large sphere?
A.
2A cm 2
B.
4A cm 2
C.
8A cm 2
D.
32A cm 2
14. The volume of a right circular cone of height h is V. What is the base radius of the cone?
A.
3V
h
B.
C.
V
h
D.
V
h
V
h
15. In the figure, ABCD is a trapezium and AB = AD. Find x.
A.
A
36
D
124
B. 44
C. 62
x
C
B
D. 68
16. In the figure, ABCD is a parallelogram. BEF is a straight line. Find x in terms of y and z.
F
A. x  270°  y  2z
A
B. x  270° + y  2z
z
D
2y
x
C. x  90°  y + 2z
E
D. x  90° + 2y  z
C
B
17. Factorize
9x 4  6x 2 y + y 2  z 4 + 4z 2  4.
A. (3x  y + z  2)(3x  y  z  2)
2
2
2
2
2
2
B. (3x  y + z  2)(3x  y  z + 2)
2
2
C. (3x  y  z  2)
2
2
2
2
2
D. (3x  y  z + 2)(3x  y  z  2)
2
2
2
2
18. In the figure, ABE, CDE, AFD and BFC are straight lines. Which of the following must be
correct?
A
A. y  z
x
B
B. y  2x  z
F
C. y  90  z
D.
y  2x 
z
2
C
P.4
y
z
x
D
E
y
19. The figure shows a straight line L. Which of the following is correct?
Slope of L  0
A.
B. Slope of L  Slope of x-axis = 
x
O
C. Slope of L < 0
D. Slope of L is undefined.
L
20. In the figure, BC // DE where C is the mid -point of AE.
If AED = 90, AD = 26 cm and BC = 5 cm,
A
find the length of CE.
26 cm
A.
10 cm
B.
12 cm
C.
16 cm
D.
20 cm
B
5 cm
C
E
D
21. In the figure, three points A, B and C are joined to form an equilateral triangle. If the bearing
of B from A is N40E, what is the bearing of A from C?
B
A.
N40W
B.
N80W
C.
S50W
D.
S75W
N
40
A
C
22. The slope of straight line L in the figure is
A.
C.
 3.
1
.
B.
1

y
.
3
150
3.
D.
3
O
x

L
23. Given two points A(3 , −5) and B(−7 , −1), the coordinates of the mid-point of
AB is
A.
(−5 , −3).
B.
(−5 , −2).
C.
(−2 , −2).
D.
(−2 , −3).
24. A straight line with slope 2 intersects the x-axis and the y-axis at A(a, 0) and B(0, b) respectively. If
O is the origin, find the area of AOB.
A.
1 2
b
2
B.
b2
C.
1 2
a
2
D.
a2
P.5
25. Which of the following is the front view of the given object?
A.
top
B.
C.
front
side
D.
26. If the given net is folded to form a dice, which
E
line segment will be stuck together with EF?
A.
BA
B.
CB
C.
DC
D.
JK
A
B
1
C
D
2
N
F
5
G
4
3
M
L
H
I
6
J
K
27. In the figure, the top and the base of the right frustum are rectangles. Find the volume of the
frustum.
V
112
A.
abh
3
127
B.
abh
3
C. 150abh
h
D
C
A
B
4b
h
4a
H
G
D. It cannot be found.
8b
E
8a
F
28. Find the volume of the frustum in the figure.
A.
632 cm3
B.
635
π cm 3
3
6 cm
632
π cm 3
3
8 cm
C.
D.
A
D M
B
338
π cm 3
3
P.6
N
3 cm
E
7 cm
C
29. According to the following front, top and side views of a solid, choose the
corresponding 3-D object.
front
A.
top
side
C.
top
top
side
front
side
front
B.
D.
top
top
side
front
side
front
30. The figure shows two similar solids.
Find the value of V.
A.
180
B.
237
C.
250
D.
490
14 cm
Volume = 686 cm3
31. The figure shows a right prism. The angle
7 cm
between DF and the plane BCF is
A.
ADC.
B.
DFB.
C.
DFC.
D.
EFD.
10 cm
Volume = V cm3
F
E
B
5 cm
A
C
8 cm
D
P.7
32. The figure shows a solid consisting of two hemispheres and a cylinder. If the
volume of the two hemispheres is the same as that of the cylinder, find the curved surface area of the
cylinder.
A.
54 cm2
B.
81 cm2
C.
108 cm2
D.
216 cm2
9 cm
33. Refer to the given figure. Which of the following expressions represent(s) the
dimension(s) of the quantity/quantities of 3?
I.
a2 + 4ac
A.
I only
B.
II only
C.
III only
D.
I and III only
II.
2a b 2 
a2
4
III.
1 2 2 a2
a b 
3
2
b
c
a
a
34. Which of the following cannot be the probability of an event?
I.
1
II. 0
III. 1
2
37
IV.
V.
1
VI. 3
19
A. III only
B. III and VI only
C. IV, V and VI only
D. I, II, III, IV, V and VI
35. A bag contains 8 coins. x of them are gold coins. A coin is selected at random from the bag.
The probability of getting a gold coin is doubled when 4 additional gold coins are put into the
bag. Find the value of x.
A.
1
B.
2
C.
3
D.
4
36. A coin is tossed 200 times and the experimental probability of getting a head is 0.6. If 55
heads show up in the first 80 tosses, how many heads are expected to show up in the remaining
120 tosses?
A.
55
B.
60
C.
P.8
65
D.
70
37. In the English Club of a school, the ratio of the numbers of boys to girls is 1 : 6. If a student
is chosen at random, find the probability that the student is a girl.
A.
6
7
B.
1
6
C.
1
5
D. It cannot be found.
38. In the figure, find the value of a.
A.
5 3
45
B. 10
20 cm
C. 10 2
D. 10 3 
a cm
39. Jessica is at point A. She finds a dragonfly at point C which
is 5.5 m above the ground. The angle of elevation of C from
A is 25.
A bird at point B is 15 m above the dragonfly.
B
15 m
Find the angle of elevation of B from A, correct to
3 significant figures.
A.
60.1
C.
64.5
5.5 m C
B.
62.2
D.
65.3
D
40. Find x and y
in the figure.
A.
x = 5, y = 6
B.
x = 5, y = 5
C.
x = 6, y = 5
D.
x = 6, y = 6
A
?
A
25
6 cm
L
D
M
B
— End —
P.9
5 cm N
5 cm
y cm
C
QUEEN’S COLLEGE
YEARLY EXAMINATION, 2010-2011
MATHEMATICS
PAPER II
Answers:
1
D
11
D
21
B
31
C
2
B
12
B
22
D
32
D
3
C
13
B
23
D
33
C
4
C
14
A
24
D
34
B
5
D
15
C
25
B
35
B
6
C
16
D
26
B
36
C
7
D
17
B
27
A
37
A
8
A
18
A
28
C
38
C
9
C
19
D
29
A
39
A
10
A
20
B
30
C
40
A
A = 9,
B = 10,
C = 11,
P.10
D = 10