QUEEN’S COLLEGE
HALF-YEARLY EXAMINATION, 2010-2011
MATHEMATICS
Secondary:
2
PAPER II
Date:
7 TH JAN, 2011
Time:
10:30 – 11:30
(1 hour)
INSTRUCTIONS
1.
When told to open this book, you should check that all questions are there.
Look for the words ‘ END OF PAPER’ after the last question.
2.
All questions carry equal marks.
3.
Answer all questions. You should use an HB pencil to mark all your answers
on the Answer Sheet.
4.
You should mark only ONE answer for each question. If you mark more than
one answer, you will receive NO MARKS for that question.
5.
Total Score of this paper II is 80 marks.
DO NOT TURN OVER THIS QUESTION BOOK
UNTIL YOU ARE TOLD TO DO SO
P.1
1.
Correct 0.003 748 m2 to the nearest cm 2 .
A. 4 cm
2
B. 37 cm
2
C. 38 cm
2
D. 375 cm
2.
2
A motor cycle can travel 33 km in an hour. Find the speed of the motor cycle in m/s. (Correct
your answer to 2 significant figures.)
A. 0.55 m/s
B. 0.92 m/s
C. 9.2 m/s
D. 550 m/s
3.
The weight of a steak should be 400 g (correct to the nearest g) in order to fulfill the quality
control requirement. Which of the following weights is not acceptable?
A. 399.5 g
B. 399.7 g
C. 400.0 g
D. 400.5 g
4.
Peter spends 32.4 minutes (correct to the nearest 0.1 minute) on the internet everyday. Find
the percentage error. (Correct your answer to 2 decimal places.)
A. 0.15%
B. 0.31%
C. 1.5%
D. 3.1%
5.
The weight of a bean is 0.35 g with a relative error of
measurement.
A. 0.329 g
B. 0.344 g
C. 0.356 g
D. 0.371 g
P.2
3
. Find the lower limit of this
50
6.
The length of a side of a square tile is 10.0 cm, correct to the nearest 0.1cm. Find the
accumulated error of the area of the square tile.
A. 0.997 5 cm2
B. 9.75 cm 2
C. 1.002 5 cm2
D. 10.25 cm 2
7.
The degree of the polynomial 5a 3  6ab 4  8a 3b 3  1 is
A. 5.
B. 6.
C. 7.
D. 12.
8.
Simplify (7m 2 n  8mn 2 + 6mn)  2n (mn m).
A. 5m 2 n  8mn 2 + 4mn
B. 5m 2 n  8mn 2 + 8mn
C. 7m 2 n  10mn 2 + 4mn
D. 7m 2 n  10mn 2 + 8mn
9.
After expanding (3 y  1)(2  y)(5 y  2) , what is the constant term?
A. 2
B. 4
C. 2
D. 4
10. After expanding (3x 2)(4x  1), what is the coefficient of x?
A. 5
B. 8
C. 5
D. 
11. Expand (1  2d ) 2 (1  2d ) .
A. 1 + 2d  2d 2  4d 3
B. 1 + 2d  4d 2  8d 3
C. 1  2d  4d 2 + 8d 3
D. 1  2d + 4d 2 + 8d 3
P.3
12. Simplify (4 x  3) 2  3 x( x  2) .
A. 19x 2  30x  9
B. 19x 2  18x  9
C. 13x 2  30x  9
D. 13x 2  18x  9
13. Which of the following is an identity?
A. (x  2) 2  x 2  4
B. (x + 2) 2  x 2 +2x + 4
C. (x + 2)(x  2) 4  x 2
D. (x + 2)(2  x)  4  x 2
14. If 6(x  2) 2  Ax 2  Bx + C, find the values of A, B and C.
A. A  1, B  4, C  4
B. A  1, B  4, C  4
C. A  6, B  24, C  24
D. A  6, B  24, C  24
15. Which of the following is identical to (2x  5) 2  (2x +5) 2 ?
A. 
0x
B. 20x
C. 20x
D. 40x
16. Factorize 20x 5 y + 8x 2 y 4  36x 2 y.
A. 4xy(5x 4 + 2xy 3  9x)
B. 4x 2 y(5x 3 + 2y 3  9)
C. 4xy(5x 4  2xy 3 + 9x)
D. 4x 2 y(5x 3  2y 3 + 9)
17. Factorize y 3  3y 2  9 + 3y.
A. (y 2 + 3)(y + 3)
B. (y 2  3)(y + 3)
C. (y 2 + 3)(y  3)
D. (y 2  3)(y  3)
P.4
18. Which of the following can be factorized?
A. a 2 + b 2
B. 2ab  a 2  b 2
C. a 2 + 2ab  b 2
D. a 2  2ab  b 2
19. Simplify
A.
12 q 5
p
B.
12q 5
p3
C.
12 q 4
p
(6 pq 2 ) 3
.
18 p 4 q
12q 4
D.
p3
20. Simplify
A.
B.
C.
D.
b2  a2 a  b

.
3b
2b 2
2b(a  b)
3
2b(b  a)
3
2b(a  b)
3
 2b(a  b)
3
21. Simplify
3p
q
3p
q



.
q  3p 3p  q q 3p 3p  q
A. 1
B. 0
C. 1
D. 2
1
2
P.5
22. Given x 2 + y 2  z 2 , find the value of x when z  15 and y  5 .
A. 200 or 200
B. 220 or 220
C.
200 or  200
D.
220 or  220
23. Make a the subject of the formula
x  4a
 1.
5b
x  5b
4
5b  x
B. a 
4
A.
a
C.
a
D.
4b  x
5
x  4b
a
5
2
y
24. Make y the subject of the formula x 
.
2
3

3(1  x )
y
A. y 
3
2( x  1)
B.
y
3(1  x )
2(1  x )
C.
y
2(1  x)
3( x  1)
D.
y
2(1  x)
3(1  x)
25. If 3y  x and 4x  3y  9, find the value of x  y.
A. 1
B. 2
C. 3
D. 4
P.6
26. According to the graph, find the solution of the simultaneous equations whi ch are represented
by L 1 and L 3 .
y
L3
10
8
6
4
L2
2
6 4 2 O
2
L1
x
2
4
6
A. x  2, y  8
B. x  3, y  10
C. x  4, y  7
D. x  7, y  0
27. If the ordered pairs (4, 0) and (2, 1) satisfy the equation mx  ny  4, find the values of m
and n.
A. m  1, n  2
B. m  1, n  2
C. m  1, n  2
D. m  1, n  2
28. If y is 2 times of x and the sum of x and 5 times of y is 80, which of the following
simultaneous equations is correct?
A.
5 x  y  80

2 x  y
B.
5 x  y  80

x  2 y
C.
 x  5 y  80

2 x  y
D.
 x  5 y  80

x  2 y
P.7
29. In the figure, ABCD is a parallelogram. Find the length of DC.
x3
A
B
y1
2x  1
D
2y  1
C
A. 5
B. 6
C. 8
D. 9
30. The sum of all interior angles of a pentagon is 540°. If the ratio of the 5 interior angles of the
pentagon is 2 : 3 : 4 : 3 : 3, find the largest angle.
A. 36°
B. 72°
C. 108°
D. 144°
31.
1 1 1
: : 
6 2 3
A.
1:2:3
B.
1:3:2
C.
D.
6:2:2
6:3:2
32. The scale of a map is 1 : 20 000. If two buildings are 48 cm apart on the map, then the actual
distance between the two buildings is
A.
0.096 km
B.
0. 96 km
C.
D.
9.6 km
96 km
33. 8.4 km/h : 14 m / s =
3
A. 1:2
B. 1:5
C. 2:1
D. 5:1
P.8
34. In a box of eggs, the ratio of the number of rotten eggs to that of broken eggs are 1 : 4, and
the ratio of the number of broken eggs to that of good eggs are 2 : 5. If there are totally 30
good eggs, find the total number of eggs in the box.
A. 20
B.
40
C.
45
D.
90
35. Let x and y be non-zero number. If 5x + 7y = 7x + 3y, then x : y =
A. 1 : 2
B. 2 : 1
C. 2 : 3
D. 3 : 2
36. The following frequency distribution table shows the weights of a group of students. Find the
class mark of the third class.
Weights (kg) Frequency
35 - 39
4
40 - 44
7
45 - 49
9
50 - 54
13
A. 37 kg
B. 42 kg
C. 44.5 kg
D. 47 kg
37. The following incomplete frequency distribution table shows the Mathematics examination
marks of 50 students. What percentage of students got 59.5 or higher?
Marks
Frequency
0 - 19
2
20 - 39
7
40 - 59
11
60 - 79
14
80 - 99
16
Total
50
A. 82%
B. 60%
C. 42%
D. 32%
P.9
38. The following incomplete frequency distribution table shows the daily exercise time of a
class of students. Find the lower class boundary and upper class boundary of the 4th class.
Time (min)
Frequency
46 - 60
4
61 - 75
2
76 - 90
9
91 - 105
2
106 - 120
10
A. Lower class boundary  105.5 min; upper class boundary  120.5 min
B. Lower class boundary  106 min; upper class boundary  120 min
C. Lower class boundary  91 min; upper class boundary  105 min
D. Lower class boundary  90.5 min; upper class boundary  105.5 min
39. The histogram shows the high jump records of F.2A students. How many students are not
shorter than 122.5 cm?
High jump records of F.2A students
A. 12
15
B. 15
C. 23
Frequency
12
D. 41
9
6
3
0
110
115
150
120 130
125 140
130 135
Height
Height(cm)
(cm)
40. The following frequency polygon shows the heights of a cl ass of 50 students. What
percentage of students is shorter than 166.5 cm?
Heights of a class of students
20
Frequency
15
10
5
0
153.5 155.5 157.5 159.5 161.5 163.5 165.5 167.5 169.5 171.5 173.5 175.5
Height (cm)
A. 8%
B.
16%
C.
84%
~~~ END OF PAPER
P.10
D.
~~~
92%
QUEEN’S COLLEGE
HALF-YEARLY EXAMINATION, 2010-2011
MATHEMATICS
Secondary:
2
PAPER II
Date:
7 TH JAN, 2011
Time:
10:30 – 11:30
(1 hour)
ANSWERS
1.
B
6.
C
11.
C
16.
B
21.
B
26.
A
31.
B
36.
D
2.
C
7.
B
12.
D
17.
C
22.
D
27.
D
32.
C
37.
B
3.
D
8.
D
13.
D
18.
B
23.
A
28.
C
33.
A
38.
D
4.
A
9.
B
14.
C
19.
A
24.
C
29.
A
34.
C
39.
C
5.
A
10.
A
15.
A
20.
D
25.
B
30.
D
35.
B
40.
C
OPTIONS
A
B
C
D
No. of
questions
9
10
11
10
P.11