Download Mathematics II - Queen`s College

QUEEN’S COLLEGE
Half-yearly Examination, 2007-2008
Mathematics II
Secondary 3
Date:
Time:
16th January, 2008
8:30 am – 9:30 am
1.
Write down the information required in the spaces provided in the Answer Sheet.
2.
When told to open this question paper, check that all the questions are there. Look for the
words ‘END OF PAPER’ after the last question.
3.
ANSWER ALL QUESTIONS. All the answers should be marked on the Answer Sheet.
4.
Note that you may marks only ONE answer to each question. Two or more answers will
score NO MARK.
5.
All questions carry equal marks. No mark will be deducted for wrong answers.
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1. Factorize 9x 2 – 16
A. (3x + 16)(3x – 1)
B. (3x – 16)(3x – 1)
C. (3x – 8)(3x + 4)
D. (3x + 4)(3x – 4)
2. Factorize a 3 + 27b 3 .
A. (a + 3b)(a 2 – 3b + 9b 2 )
B. (a + 3b)(a 2 + 3b + 9b 2 )
C. (a + 3b)(a 2 – 3b – 3b 2 )
D. (a + 3b)(a 2 – 3b + 3b 2 )
3. Simplify (
2a 3 2a 5 0
) (
) .
3b
3b  2
A.
27
2a 3b
B.
27
8a 3 b 6
C.
8
27 a 3 b 6
8b 6
D.
27 a 3
4. Evaluate 21600000000000  0.000000000000009
A. 2.4  10 -3
B. 2.4  10 27
C. 1.944  10 -3
D. 1.944  10 27
5. The difference between the value of the digits 3 and 1 in 2367510 10 is
A. 2.
B.
29999.
C.
D.
299990.
299999.
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6. Convert F4 16 into binary number.
A.
244 10
B. 1110100 2
C. 11110100 2
D. 11111100 2
7. Find the smallest integer that satisfies the inequality 
5 x 3x 1


3
2 3
A. 0
B. 1
C. 2
D. 3
8. A card is selected at random from a pack of playing cards. What is the probability of
obtaining a Queen?
9.
A.
1
13
B.
1
10
C.
1
7
D.
1
4
Two dice are thrown. Find the probability of getting a sum of 9.
A.
1
8
B.
1
9
C.
1
18
D.
1
36
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10. In a competition, the winner can have an award of $4000, whereas the 1 st runner-up and
the 2 nd runner-up can have an award of $2000 and $1000 respectively. If Man Ching takes
part in the competition, and he expects that the probabilities of being the winner, the 1 st
runner-up and the 2 nd runner-up are 0.11, 0.16 and 0.22 respectively, find the expected
award.
A. $1000
B. $980
C. $880
D. $800
11. The following shows the monthly salaries of the parents of 10 students:
$23000, $30000, $12000, $20000, $32000
$20000, $42000, $22000, $22000, $25000
What is the median salary?
A. $22000
B.
$22500
C.
$23000
D.
$25000
12. Four numbers a, b, c and d are in the ratio 2:5:2:3. Find the value of a if the mean of the
four numbers is 18.
A. 6
B. 9
C. 12
D. 18
13. If x<3, then which of the following must be true?
(1) x 1< 2
(2) x1< 3
(3) x1< 4
A. (3) only
B. (1) and (2) only
C. (2) and (3) only
D. (1), (2) and (3)
14. When a cube is cut along the lines into small cubes as shown in the
figure, find the percentage increase in the total surface area.
A. 100%
B.
150%
C.
D.
200%
250%
-4-


15. 0.35 9 0.19 =
A.
13
50
B.
17
100
C.
4
25
D.
17
50
m7  m m =
16.
A.
m4
B.
m5
C.
m6
D.
m7
17. Rationalize
A.
5 3
8
B.
5 3
2
C.
5 3
2
D.
1
5 3
1
2
18. ( 3  2 )( 8  27 )
A.
 6  13
B. 5 6  5
C. 5 6  5
D.
5 6  13
19. If
2 =a and
A. a 2 +b
B.
a2b
C.
a 4 +b
D.
a4b
5 =b, then
20 =
-5-
20. In a game, the top of a table is divided into many squares with side 3 cm. A coin with
diameter 2 cm is thrown onto the table by a player. The player will win if the coin does
not touch any line on the table. Find the probability that a player can win the game
lose
win
1
A.
9
B.

9
C.
4
9
D. Cannot be determined.
21 . In the figure, the target for archery consists of two circles with diameters a and 3a. If an
arrow is randomly shot onto the target, what is the probability that the unshaded region is
hit?
A.
1
9
B.
1
3
C.
2
3
8
9
22. Factorize (a+b)(p+q) – (b+a)(p–q )
D.
A. 0
B. 2q(a+b)
C. 2(a+b)(p+q)
D. 2p(a+b)
23. Factorize xy – 4x – 28y +7y2
A. (y+4) (x+7y)
B. (y+4) (x–7y)
C. (y–4) (x+7y)
D. (y–4) (x–7y)
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24. Which of the following contains the factor (1–y).
A. m – y2 – y – my
B. y2 – m – y + my
C. m – y2 – y + my
D. y2 – m + y – my
25. Factorize m 2 (n – m) + n 2 (m – n)
A.
(m + n) 2 (m – n)
B. (m + n) 2 (n – m)
C. (m – n) 2 (m + n)
D. –(m – n) 2 (m + n)
26 . There are 1500 students in an international school in which 65% are Chinese. If 40% of
the Chinese are girls, how many Chinese boys are there?
A. 210
B.
315
C.
D.
390
585
27. The mean of 15, 19, 22, 22 and 2n is 20. Find the value of n.
A. 11
B. 13
C. 15
D. 22
28. The table below shows the marks distribution in a S.3 Physics test. Find the mean mark.
Mark
Frequency
1  10
24
11  20
42
21  30
75
31  40
51
41  50
8
A. 24.35
B. 19.85
C. 28.85
D. 27.85
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29. The cumulative polygon shows the ages of
the employees of a company. What is the
median age of the employees of the
company?
A. 30
B. 35
C. 37.5
D. 45
30. A bag contains 10 red balls and 12 green balls. If a red ball is drawn without replacement
and then a green ball is drawn without replacement, what is the probability of getting a
red ball at random in the third draw?
A.
9
20
B.
7
20
C.
9
10
D.
3
10
31. A thief has stolen a safe from a company in a night. However, he needed to input a
three-digit password in order to open the safe. If he chose each digit randomly, what is
the probability that he could open the safe in only one trial?
A.
1
10
B.
1
100
C.
1
1000
1
999
32. Two years ago, John’s monthly salary was $10000. Because of his good performance, his
salary was increased by 20% and 30% in following two years. What is his present salary?
D.
A. $14400
B. $15000
C. $15600
D. $60000
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33. Two dice were tossed many times. The sums of the two numbers obtained are recorded as
follows:
Sum
2
3
4
5
6
7
8
9
10
11
12
Frequency
28
34
45
14
20
18
10
19
17
20
25
What is the experimental probability that the sum was 7?
A.
17
250
B.
19
250
C.
9
125
D.
9
231
34. The area of a rectangle is 100. If its length is increased by x% while its breadth is
decreased by x%, then its area becomes
A.
100 – x 2
B. 100 
x2
100
C. 100
D.
100 
x2
100
35. The number of bacteria in a culture decreases by 20% per hour. If there are 38000 bacteria in the
culture, how many bacteria were there 4 hours ago? Give your answer correct to 3 significant
figures.
A. 15600
B. 68400
C. 78800
D. 92800
36. x 2  2bx  a 2  b 2
A. ( x  a  b)( x  a  b)
B. ( x  a  b)( x  a  b)
C. ( x  a  b)( x  a  b)
D. ( x  a  b)( x  a  b)
-9-
37. If 4 x 1 (256 2 x )  64 x 1 , then x=

2
3
B. 
1
3
A.
C. 0
1
D.
4
38. The passing mark of an examination is 60.The mean mark of 260 pupils in the examination is 64.
The mean mark of passed pupils is 67 and that of failed pupils is 57. The number of pupils passed is
A. 78
B.
100
C.
D.
130
182
39. The mean of a – 2, b + 3, c + 5 is 6. The mean of a +4, b +6, c – 1 is
A. 5
B.
6
C. 7
D. 8
40. A manufacturer has to produce 400 articles in 10 days. If the average number of articles made in the
first 9 days is 38, how many articles should he make in the last day in order to meet the schedule?
A.
40
B.
48
C.
50
D. 58
END OF PAPER
- 10 -

ANSWERS
1
D
11.
B
21
D
31
C
2
A
12
C
22
B
32
C
3
B
13
D
23
C
33
C
4
B
14
C
24
B
34
B
5
C
15
C
25
D
35
D
6
C
16
B
26
D
36
A
7
D
17
B
27
A
37
B
8
A
18
D
28
A
38
D
9
B
19
B
29
C
39
C
10
B
20
A
30
A
40
D
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