ABCLVI/Maths/2008 Page 1 of 11
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Mathematics Writing Time : 2 Hours
Total Marks : 100
READ THE FOLLOWING DIRECTIONS CAREFULLY:
1. Do not write for the first fifteen minutes. This time is to be spent reading the
questions. After having read the questions you will be given two hours to answer all
questions.
2. In this question paper, you will find 25 questions in Section A and 5 questions in
Section B. You must answer all the questions. Each question in Section A is worth 2
marks.
3. All answers for Section ‘A’ and ‘B’ must be written in the answer sheets provided by
the school.
4. Once the examination begins, you will not be allowed to ask questions, speak with
others or move around.
5. If you finish before the time is over, close the Answer Booklet, and sit quietly.
DO NOT forget to write your name, class/section and the name
of your school on the answer sheet(s).
IF YOU HAVE ANY QUESTIONS, ASK THEM NOW!
TURN PAGE
(15 Minutes is to be allowed for reading as well as for teachers on duty to
explain the instructions)
This booklet contains 11 pages.
pages
ABCLVI/Maths/2008 Page 2 of 11
© Copyright Reserved
ABCLVI/Maths/2008 Page 3 of 11
© Copyright Reserved
SECTION A
25 Questions [50 marks]
Answer ALL questions
Direction: Each question in this section is followed by four possible choices of
answers. Choose the correct answer and write it down in the answer sheet provided by
the school.
1. Which one of the following symbols represents an empty set and a proper subset
respectively?
A φ and ∩
B ∈ and ⊂
C ∪ and ⊂
D φ and ⊂
2. Which one of the following sets does not have a cardinal number?
A {y : y > 0}
B {w:1 ≤ w ≤ 10}
C {x : 0 < x < 100}
D {a : a is whole number between 10 and 20}
3. From the diagram given on the right, the elements of (A∪ B) are
A {5}.
B {3, 4}.
C {3, 4, 5}.
D {1, 2, 3, 4, 5}.
4. Which of the following fractions has the largest value?
A 1
2
B 1
4
C 1
10
D 1
100
2
1
3
4
5
A B
ξ
ABCLVI/Maths/2008 Page 4 of 11
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5. 11 2 3 3 1
3 3 3
− × ÷ − is equal to
A 11
3
.
B 12
3
.
C 1
3
.
D 3 .
6. What is the missing numeral in the open
sentence15(247 − 47) = 15× 247 − 47× _______ ?
A 247
B 200
C 47
D 15
7. The short form of the 9×106 + 5×104 + 7×103 + 3×102 can be written as
A 9573.
B 95730.
C 9005300.
D 9057300.
8. The fractional forms of three certain numbers are given by 3×52 , 5× 32 and
7× 33 ×5 . Their L.C.M is
A 1567.
B 3154.
C 4725.
D 9452.
9. What is one quarter expressed as a percentage?
A 25%
B 40%
C 50%
D 75%
10. A sum of Nu.963.40 when divided in the ratio 2:3:4 gives
A Nu.321.30, Nu. 214.20 and Nu. 428.40.
B Nu.107.10, Nu.321.30 and Nu. 428.50.
C Nu.214.20, Nu.321.30 and Nu.428.40.
D Nu.428.40, Nu.214.20 and Nu.321.30.
ABCLVI/Maths/2008 Page 5 of 11
© Copyright Reserved
11. Which of the following is not true?
A 3 1 9
3
− ÷ = −
B + 5 − −5 = +10
C −6 × −6 = −36
D 8..2 + ( −0.2) = +8
12. All the following are examples of a single term EXCEPT
A 2(x − 2) + 5
B
( 2 1) 3
5
x − +
C 250 xyz
D
3 2
2
a x
13. The expression ( 2x + 3y − 5) when subtracted from the sum of (3-2x) and 94 gives
A 12y − 2 .
B 4x − 6y − 8 .
C −4x + 6y + 8 .
D −4x + 6y − 2 .
14. Simplification of (2x − 3y)(x + 3y) is
A 2x2 + 3xy − 9y2 .
B 3xy + 3x2 − 9y2 .
C 2xy + 3x 2−9y 2 .
D 2x2 y + 3x2 − 9y2 .
15. 2(3x) − 2 = 10 is
A 10.
B 8.
C 4.
D 2.
16. Given x=4, the value of y from the given equation 4x − 3 = 2y +1 is
A 4.
B 6.
C 10.
D 14.
ABCLVI/Maths/2008 Page 6 of 11
© Copyright Reserved
17. Five times a number increased by 5 is 60. What is the number?
A 4
B 10
C 11
D 15
18. What is the product of 0.00297 ×100000 ?
A 297
B 97
C 0.0297
D 0.00297
19. If one of the base angles of an isosceles triangle is 420 , then the measure of its
vertical angle is
A 420 .
B 840 .
C 960 .
D 1380 .
20. The diagram on the right shows two paints of parallel lines. M
is parallel to N
and B
is parallel to P
. The sum of angles x, y and z is equal to
A 260 0 .
B 300 0 .
C 3200 .
D 4000 .
21. An area of 2.5 m2 equals
A 250 cm2 .
B 2500 cm2 .
C 25000 cm2 .
D 250000 cm2 .
22. How many sugar cube each having a volume of 8 cm3 can be packed in a cartoon
box of size 40 cm, by 30 cm by 20 cm?
A 24000
B 3000
C 1200
D 800
ABCLVI/Maths/2008 Page 7 of 11
© Copyright Reserved
23. The column graph shows boys and girls in classes III to VI in a primary school.
The total number of boys in classes III, V and VI is
A 230 boys.
B 180 boys.
C 170 boys
D 150 boys
24. In a village different types of crops are grown as shown by the pie-diagram. The
central angle occupied by maize is
A 360 .
B 540 .
C 900 .
D 3600 .
25. In the diagram on the right, an angle x0 represents
A a supplementary angle.
B an obtuse angle.
C an acute angle.
D a right angle.
0
10
20
30
40
50
60
70
80
III IV V VI
Class
No. of Students
Girls
Boys
Maize, 15%
Wheat, 25%
Millet, 10%
Paddy, 50%
450
x0
ABCLVI/Maths/2008 Page 8 of 11
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SECTION B
5 questions [50 marks]
Answer ALL questions
Directions: Answer the questions given below as directed. All answers should be
written in the answer booklet provided by the school. The intended marks for each
question is given in the brackets [ ].
Question 1
a. Dorji attends a drawing club every 20 days, Tenzin in every 15 days and Kinley
every 10 days. If all three attended the drawing club on 1st June, when will they
meet again in the same drawing club? [3]
b. Simplify 2 1 11 11
4 3 5
× ÷ . [1]
c. Given 2 , 0, 1
3 5
a b c −
= = = , find the value of
2
9 4 2
2
a + b c − c . [2]
d. Sets M and N are two intersecting sets. If n(M)=10, n(N)=8 and n(M ∩ N) = 3 .
Find n(M ∪ N) using the cardinal notation. [2]
e. The pie-diagram on the right shows three types of fruit trees in an orchard. Find
the number of apple threes if there were a total of 1080 trees in the orchard. [2]
Plum
Apple
Pears
Question 2
a. r ∈W , then r × r × x =_______________________. What is the missing
numeral? [1]
b. 2
3
of a boy’s pocket money is spent for buying a gho, 1
3
for a pair of shoes and
Nu. 120 was left. What was the total of his pocket money? [3]
1000
1900
700
ABCLVI/Maths/2008 Page 9 of 11
© Copyright Reserved
c. Write the sum of 4 3 1
1000 10
+ × in decimal notation. [1]
d. Tashi bought a radio for Nu. 800 and sold it at a loss of 15 1%
2
. What was his
selling price? [2]
e. Construct a ΔPQR given PQ = 6.5 cm, QR = 4 cm and PR = 6.5 cm. Measure
all the angles and name the kinds of triangle constructed. [3]
Question 3
a. Which angle is complement to800 ? [1]
b. Express 12
25
as an exact decimal. [2]
c. A certain sum of money was shared by Dechen, Wangmo and Deki receiving Nu.
210, Nu.525 and Nu. 630 respectively. What was the ratio of their shares? [2]
d. The line graph on the right shows the monthly rainfall in a year. What was the
average monthly rainfall? [2]
0
10
20
30
40
50
January
February
March
April
May
June
July
August
September
October
November
December
Months
Rainfall in mm
ABCLVI/Maths/2008 Page 10 of 11
© Copyright Reserved
e.
(i) Given AB is a straight line. Calculate ∠ADC and ∠CDB in numerical
measures. [2]
(ii) Solve −42 ÷ −7 − −15 ÷ 5. [1]
Question 4
a. A man puts Nu.5000 in a bank as a fixed deposit for 4 years at 11% per annum
simple interest. Find the amount he will get back after 4 years. [2]
b. Multiply (2x2 − 3y2 )(x2 + y2 ) . [2]
c. Dorji has a rectangular block of cheese measuring10 cm×8 cm× 6 cm . Find the
total surface area of a block. [2]
d. The sum of two certain numbers is 87. Find the numbers if one of them is double
the other. [2]
e. In a class of certain number of students 22 students passed in Dzongkha, 35 passed
in English while 7 students passed in both.
Find
(i) How many students passed in English only.
(ii) What was the total students in the class? [2]
Question 5
a. At midnight, the temperature was + 30C . During the next hour it fell by 60C and
during the following hour rose by 40C . What was the final temperature? [2]
b. An equilateral triangle of sides 4y has a height x. Write down the formula for its
area and perimeter in simplest form. [2]
A C
D
B
2x+5
3x
ABCLVI/Maths/2008 Page 11 of 11
© Copyright Reserved
c. Solve the equation 3 2 5 1
4 2
− x = x − . [2]
d. Compare the areas a rectangular field of sides 20 m by 8 m and a square field with a
side 8 m? Write the area of the polygon with greater area. [2]
e. The frequency distribution table given below shows the weight of students in class
VI in a primary school.
Weight (kg) Tally Marks Frequency
45 IIII IIII I
46 III
47 IIII I
48 IIII IIII IIII
49 IIII II
50 IIII
51 II
52 IIII IIII
53 IIII
54 IIII III
55 IIII IIII
Calculate the percentage of students whose weights are less than 48 kg. [2]
© Copyright Reserved
Mathematics Writing Time : 2 Hours
Total Marks : 100
READ THE FOLLOWING DIRECTIONS CAREFULLY:
1. Do not write for the first fifteen minutes. This time is to be spent reading the
questions. After having read the questions you will be given two hours to answer all
questions.
2. In this question paper, you will find 25 questions in Section A and 5 questions in
Section B. You must answer all the questions. Each question in Section A is worth 2
marks.
3. All answers for Section ‘A’ and ‘B’ must be written in the answer sheets provided by
the school.
4. Once the examination begins, you will not be allowed to ask questions, speak with
others or move around.
5. If you finish before the time is over, close the Answer Booklet, and sit quietly.
DO NOT forget to write your name, class/section and the name
of your school on the answer sheet(s).
IF YOU HAVE ANY QUESTIONS, ASK THEM NOW!
TURN PAGE
(15 Minutes is to be allowed for reading as well as for teachers on duty to
explain the instructions)
This booklet contains 11 pages.
pages
ABCLVI/Maths/2008 Page 2 of 11
© Copyright Reserved
ABCLVI/Maths/2008 Page 3 of 11
© Copyright Reserved
SECTION A
25 Questions [50 marks]
Answer ALL questions
Direction: Each question in this section is followed by four possible choices of
answers. Choose the correct answer and write it down in the answer sheet provided by
the school.
1. Which one of the following symbols represents an empty set and a proper subset
respectively?
A φ and ∩
B ∈ and ⊂
C ∪ and ⊂
D φ and ⊂
2. Which one of the following sets does not have a cardinal number?
A {y : y > 0}
B {w:1 ≤ w ≤ 10}
C {x : 0 < x < 100}
D {a : a is whole number between 10 and 20}
3. From the diagram given on the right, the elements of (A∪ B) are
A {5}.
B {3, 4}.
C {3, 4, 5}.
D {1, 2, 3, 4, 5}.
4. Which of the following fractions has the largest value?
A 1
2
B 1
4
C 1
10
D 1
100
2
1
3
4
5
A B
ξ
ABCLVI/Maths/2008 Page 4 of 11
© Copyright Reserved
5. 11 2 3 3 1
3 3 3
− × ÷ − is equal to
A 11
3
.
B 12
3
.
C 1
3
.
D 3 .
6. What is the missing numeral in the open
sentence15(247 − 47) = 15× 247 − 47× _______ ?
A 247
B 200
C 47
D 15
7. The short form of the 9×106 + 5×104 + 7×103 + 3×102 can be written as
A 9573.
B 95730.
C 9005300.
D 9057300.
8. The fractional forms of three certain numbers are given by 3×52 , 5× 32 and
7× 33 ×5 . Their L.C.M is
A 1567.
B 3154.
C 4725.
D 9452.
9. What is one quarter expressed as a percentage?
A 25%
B 40%
C 50%
D 75%
10. A sum of Nu.963.40 when divided in the ratio 2:3:4 gives
A Nu.321.30, Nu. 214.20 and Nu. 428.40.
B Nu.107.10, Nu.321.30 and Nu. 428.50.
C Nu.214.20, Nu.321.30 and Nu.428.40.
D Nu.428.40, Nu.214.20 and Nu.321.30.
ABCLVI/Maths/2008 Page 5 of 11
© Copyright Reserved
11. Which of the following is not true?
A 3 1 9
3
− ÷ = −
B + 5 − −5 = +10
C −6 × −6 = −36
D 8..2 + ( −0.2) = +8
12. All the following are examples of a single term EXCEPT
A 2(x − 2) + 5
B
( 2 1) 3
5
x − +
C 250 xyz
D
3 2
2
a x
13. The expression ( 2x + 3y − 5) when subtracted from the sum of (3-2x) and 94 gives
A 12y − 2 .
B 4x − 6y − 8 .
C −4x + 6y + 8 .
D −4x + 6y − 2 .
14. Simplification of (2x − 3y)(x + 3y) is
A 2x2 + 3xy − 9y2 .
B 3xy + 3x2 − 9y2 .
C 2xy + 3x 2−9y 2 .
D 2x2 y + 3x2 − 9y2 .
15. 2(3x) − 2 = 10 is
A 10.
B 8.
C 4.
D 2.
16. Given x=4, the value of y from the given equation 4x − 3 = 2y +1 is
A 4.
B 6.
C 10.
D 14.
ABCLVI/Maths/2008 Page 6 of 11
© Copyright Reserved
17. Five times a number increased by 5 is 60. What is the number?
A 4
B 10
C 11
D 15
18. What is the product of 0.00297 ×100000 ?
A 297
B 97
C 0.0297
D 0.00297
19. If one of the base angles of an isosceles triangle is 420 , then the measure of its
vertical angle is
A 420 .
B 840 .
C 960 .
D 1380 .
20. The diagram on the right shows two paints of parallel lines. M
is parallel to N
and B
is parallel to P
. The sum of angles x, y and z is equal to
A 260 0 .
B 300 0 .
C 3200 .
D 4000 .
21. An area of 2.5 m2 equals
A 250 cm2 .
B 2500 cm2 .
C 25000 cm2 .
D 250000 cm2 .
22. How many sugar cube each having a volume of 8 cm3 can be packed in a cartoon
box of size 40 cm, by 30 cm by 20 cm?
A 24000
B 3000
C 1200
D 800
ABCLVI/Maths/2008 Page 7 of 11
© Copyright Reserved
23. The column graph shows boys and girls in classes III to VI in a primary school.
The total number of boys in classes III, V and VI is
A 230 boys.
B 180 boys.
C 170 boys
D 150 boys
24. In a village different types of crops are grown as shown by the pie-diagram. The
central angle occupied by maize is
A 360 .
B 540 .
C 900 .
D 3600 .
25. In the diagram on the right, an angle x0 represents
A a supplementary angle.
B an obtuse angle.
C an acute angle.
D a right angle.
0
10
20
30
40
50
60
70
80
III IV V VI
Class
No. of Students
Girls
Boys
Maize, 15%
Wheat, 25%
Millet, 10%
Paddy, 50%
450
x0
ABCLVI/Maths/2008 Page 8 of 11
© Copyright Reserved
SECTION B
5 questions [50 marks]
Answer ALL questions
Directions: Answer the questions given below as directed. All answers should be
written in the answer booklet provided by the school. The intended marks for each
question is given in the brackets [ ].
Question 1
a. Dorji attends a drawing club every 20 days, Tenzin in every 15 days and Kinley
every 10 days. If all three attended the drawing club on 1st June, when will they
meet again in the same drawing club? [3]
b. Simplify 2 1 11 11
4 3 5
× ÷ . [1]
c. Given 2 , 0, 1
3 5
a b c −
= = = , find the value of
2
9 4 2
2
a + b c − c . [2]
d. Sets M and N are two intersecting sets. If n(M)=10, n(N)=8 and n(M ∩ N) = 3 .
Find n(M ∪ N) using the cardinal notation. [2]
e. The pie-diagram on the right shows three types of fruit trees in an orchard. Find
the number of apple threes if there were a total of 1080 trees in the orchard. [2]
Plum
Apple
Pears
Question 2
a. r ∈W , then r × r × x =_______________________. What is the missing
numeral? [1]
b. 2
3
of a boy’s pocket money is spent for buying a gho, 1
3
for a pair of shoes and
Nu. 120 was left. What was the total of his pocket money? [3]
1000
1900
700
ABCLVI/Maths/2008 Page 9 of 11
© Copyright Reserved
c. Write the sum of 4 3 1
1000 10
+ × in decimal notation. [1]
d. Tashi bought a radio for Nu. 800 and sold it at a loss of 15 1%
2
. What was his
selling price? [2]
e. Construct a ΔPQR given PQ = 6.5 cm, QR = 4 cm and PR = 6.5 cm. Measure
all the angles and name the kinds of triangle constructed. [3]
Question 3
a. Which angle is complement to800 ? [1]
b. Express 12
25
as an exact decimal. [2]
c. A certain sum of money was shared by Dechen, Wangmo and Deki receiving Nu.
210, Nu.525 and Nu. 630 respectively. What was the ratio of their shares? [2]
d. The line graph on the right shows the monthly rainfall in a year. What was the
average monthly rainfall? [2]
0
10
20
30
40
50
January
February
March
April
May
June
July
August
September
October
November
December
Months
Rainfall in mm
ABCLVI/Maths/2008 Page 10 of 11
© Copyright Reserved
e.
(i) Given AB is a straight line. Calculate ∠ADC and ∠CDB in numerical
measures. [2]
(ii) Solve −42 ÷ −7 − −15 ÷ 5. [1]
Question 4
a. A man puts Nu.5000 in a bank as a fixed deposit for 4 years at 11% per annum
simple interest. Find the amount he will get back after 4 years. [2]
b. Multiply (2x2 − 3y2 )(x2 + y2 ) . [2]
c. Dorji has a rectangular block of cheese measuring10 cm×8 cm× 6 cm . Find the
total surface area of a block. [2]
d. The sum of two certain numbers is 87. Find the numbers if one of them is double
the other. [2]
e. In a class of certain number of students 22 students passed in Dzongkha, 35 passed
in English while 7 students passed in both.
Find
(i) How many students passed in English only.
(ii) What was the total students in the class? [2]
Question 5
a. At midnight, the temperature was + 30C . During the next hour it fell by 60C and
during the following hour rose by 40C . What was the final temperature? [2]
b. An equilateral triangle of sides 4y has a height x. Write down the formula for its
area and perimeter in simplest form. [2]
A C
D
B
2x+5
3x
ABCLVI/Maths/2008 Page 11 of 11
© Copyright Reserved
c. Solve the equation 3 2 5 1
4 2
− x = x − . [2]
d. Compare the areas a rectangular field of sides 20 m by 8 m and a square field with a
side 8 m? Write the area of the polygon with greater area. [2]
e. The frequency distribution table given below shows the weight of students in class
VI in a primary school.
Weight (kg) Tally Marks Frequency
45 IIII IIII I
46 III
47 IIII I
48 IIII IIII IIII
49 IIII II
50 IIII
51 II
52 IIII IIII
53 IIII
54 IIII III
55 IIII IIII
Calculate the percentage of students whose weights are less than 48 kg. [2]
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