Vedanta Excel in Mathematics Book 5 Final (2078) NEW

Geometry - Plane Shapes

d) x° e) 55° b° f) 84°

50° y° a° x° y°

(Hint: y° = 50° and i) x° 3x°
x° + y° + 50° = 180°
2x°
g) h)
c)
y° 2a°
z°
9. a) x° a°
45°
b)

60°

y° x° 105° b° a° 100° y° x° 120°

(Hint: x° + 105° = 180° and 80° f)
x° + y° + 45° = 180° x°
y° z° q°
d) e)
a° p°
c° b° 55° 40°
130° a° b° c°
c) x°
10. a) z° b) x°
50° 30° 70°
y° z°
x° y° y° 110° (Hint: x° = 70° and y° = z°
then x° + y° +z° = 180°)
(Hint: x° = 50° and x° = y°, 50° 60°
then x° + y° + z° = 180° c° f) 65°

d) e) c°

a° a° b°

60° (Hint: a° = 65° and a° = b°
b° c° then a° + b° +c° = 180°)

g) 70° h) i)

z° 105° 45°
z°

a° x° a° b° x° y°
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Geometry - Plane Shapes

It's your time - Project work !
11. a) Let's draw two triangles ∆ ABC and ∆PQR of different sizes just by using

a ruler. Measure the angles of each triangle and ind the sum of angles of
∆ ABC and ∆PQR.

‘A ‘B ‘C ‘A + ‘B + ‘C ‘P ‘Q ‘R ‘P + ‘Q + ‘R

b) Let's draw two isosceles triangles ∆ ABC and ∆PQR of different sizes just
by using a ruler. Measure the base angles of each triangle and writer your
remarks.

‘‘ Remarks ‘‘ Remarks

c) Let's take a few number of toothpicks (or straw, or paper strips) of the
same length.

(i) Use 6 toothpicks and make an equilateral triangle.

(ii) Use 5 toothpicks and make an isosceles triangle.

(iii) Use 9 toothpicks and make a scalene triangle.

(iv) Use 12 toothpicks and make a right-angled triangle.

You can stick toothpicks using glue on a chart paper and make these
triangles.

(v) Can you make a triangle by using 4 toothpicks?

16.6 Quadrilaterals C

D

The given igure is a quadrilateral ABCD. It is a plane shape

bounded by 4 straight line segments, which are called the

sides of quadrilateral. AB, BC, CD, and DA are 4 sides of A B

the quadrilateral ABCD. Similarly, ‘A, ‘B, ‘C, and ‘D are

4 angles of the quadrilateral ABCD. Rectangle, square and parallelogram are

special types of quadrilaterals.

Rectangle D C
The length and breadth of a rectangle are equal.

AB = CD and BC = DA. Each angle of rectangle is 90°.

‘A = ‘B = ‘C = ‘D = 90° 90° B
A
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Square Geometry - Plane Shapes
SR

All sides of a square are equal and each angle is 90°.

PQ = QR = RS = SP and ‘P = ‘Q = ‘R =‘S = 90°. P Q
H G
Parallelogram E F
In the given igure, EFGH is a parallelogram.
Its opposite sides are equal and parallel.
EF = GH, FG = HE, EF // GH and FG // HE.
Its opposite angles are equal.
‘E = ‘G and ‘F = ‘H.

16.7 Sum of the angles of a quadrilateral

Let's measure the size of each angle of these quadrilaterals. Then, study the
given table and investigate the fact about the sum of angles of quadrilaterals.

C

D CD C
D

A BA B AB
Fig (i) Fig (iii)
Fig (ii)

Fig Angles Sum of 4 angles
‘A ‘B ‘C ‘D ‘A + ‘B + ‘C + ‘D
90° 90° + 90° + 90° +90° = 360°
(i) 90° 90° 90° 120° 60° + 120° + 60° +120° = 360°
(ii) 60° 120° 60° 105° 100° + 110° + 45° +105° = 360°
(iii) 100° 110° 45°

Thus, sum of the angles of a triangle = 180° 180°
Sum of the angles of a quadrilateral = 360°

= 2 × 180° 180°

= 2 × Sum of the angles of a triangle

16.8 Circle A Circumference

The given igure is a circle. It is a rounded plane Diameter
shape. O is the centre, AB is a diameter, and OC
is a radius of the given circle. OA and OB are also O Centre
Radius

B C

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Geometry - Plane Shapes

the radii (plural of radius) of the circle. The rounded boundary line is the
circumference of the circle.

(i) Radii of the same circle are always equal. So, OC = OA = OB.

(ii) Length of a diameter of a circle is always two times the length of it's
radius.

Therefore, AB = 2 × OC or 2 × OA or 2 × OB
Similarly, OC = OA = OB = 21AB

EXERCISE 16.2
Section A - Classwork

Let's say and write the unknown length of sides and unknown angles of
the given rectangle, square, and parallelogram.

1. a) D C b) S R c) Z Y

A 5.5 cm 3 cm 3.4 cm W 3.2 cm
3.4 cm Q 2.8 cm X
CD = , DA = BP YZ=
, SP = , ZW=
RS =

d) D C e) H G f) P O
120° 60°
140° 110°

40° B 70° N
A E FM

³C = , ³B = ³H = ,³E = ³M= , ³N=

2. a) If a°, b°, c°, and d° are the angles of a quadrilateral,
a° + b° + c° + d° =

b) If the sum of three angles of a quadrilateral is 300°, the size of remaining
angle is

c) If x° is an angle of a rectangle, the size of x° =

d) If y° is an angle of a square, the size of y° =

e) If an angle of a parallelogram is 45°, the size of its opposite

angle is

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Geometry - Plane Shapes

3. In the given circle, Q

a) is the centre of the circle.

P

b) is the diameter of the circle. S

c) , and are the radii of the circle. R

d) If PS = 2 cm, the length of QR =

Section B
4. Let's answer the following questions.

a) Write any two properties of a rectangle.
b) Write any two properties of a parallelogram.
c) How many centre can a circle have?
d) How many diameters can a circle have?
e) Write the relation between a diameter and a radius of a circle.
Let's ind the unknown angles marked with letters.

5. a) x° b) c) y°

40°

30° x° e) y° f) x° 55°
y° a° y° z°
d) b°
x°
z° 110° c°

60°

6. a) x° b) 80° c) y°

100° a° 150°

110° 90° 90° 80° y° 110°

(Hint: x°+90°+110°+100°=360°) 3a° f)

d) e) a° 3x°
4x°
x° 50° 2a°
2x°
2x° x°

100°

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Geometry - Plane Shapes

7. a) w°, x°, y°, and z° are the sizes of four angles of a quadrilateral. If w° = 110°,
x° = 120°, and y° = 80°, ind the size of z°.

b) If x°, 2x°, 2x°, and 4x° are the angles of a quadrilateral, ind the value of x
and calculate the actual sizes of the angles.

It's your time - Project work!
8. a) Let's write any four angles of each of a quadrilateral and a parallelogram

of your own.

b) Let's draw two quadrilaterals ABCD and PQRS of different sizes just by
using a ruler. Measure the angles of each quadrilateral and show that the
sum of angles of each quadrilateral is 360°.

‘A ‘B ‘C ‘D ‘A + ‘B + ‘C + ‘D

‘P ‘Q ‘R ‘S ‘P + ‘Q + ‘R + ‘S

c) Let's draw two circles of different sizes using a pencil A
compass. Mark the centre of each circle by O and P. Draw
2 diameters in each circle and measure the lengths of the C D
diameters and any two radii. O

Now, discover the relationship between : B
S
(i) Diameters of each circle Q
P
(ii) Radii of each circle T R
(iii) Diameter and radius of each circle.

Length of Length of Length of Length of
diameter radius diameter radius

AB CD OB OC QR ST PQ PS

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Unit Statistics

17

17.1 Charts - Introduction

Let's discuss about the answer of the following questions.

a) What types of information do you get from your monthly progress
report?

b) What types of information do we get from a restaurant menu?

c) What types of information do you get from your school's annual calendar?

d) What types of information do you get from the bar diagrams of the
number of students of your school?

A monthly progress report, a restaurant menu, a school's annual calendar, a
bar diagram (or bar graph), etc. are the examples of charts.

A chart is a sheet of information in the form of a table, graph or diagram.
It shows the information of different events (or things) numerically in the
form of table, graph, or picture. We can get various information at a glance
when they are presented in a chart.

EXERCISE 17.1
Section A - Classwork

1. The given chart shows the rate of cost of vegetables in a shop. Let's say

and write the answers of the questions. Vegetables Rate of cost
a) The cheapest vegetable is (per kg)
Green beans
and its cost is Potatoes Rs 60

Rs 35

b) The most expensive vegetable is Broccoli Rs 75

and its cost is Tomatoes Rs 40

c) By how much is the rate of cost of broccoli more expensive than green
beans?

d) How much money do you need to pay to buy 3 kg of tomatoes?

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Statistics

2. Let's study the given symbols of weather forecast of Kathmandu Valley
from the 1st Shrawan to the 7th shrawan, 2078 B.S. Then, say and write
the answer of these questions.

1st 2nd 3rd 4th 5th 6th 7th

a) For how many days would there be heavy rainfall?

b) How many days would be cloudy?

c) Which would be the partly cloudy day?

d) On which day may your school arrange the Inter-House Cricket Tournament
comfortably?

Section B
3. The chart given below shows the departure time schedule of a bus service

from Kathmandu to different places. Answer the following questions.

Destination Types of service Departure time
Dharan Day 5 : 30 a.m.
Rajbiraj Day 6 : 45 a.m.
Surkhet Night 4 : 15 p.m.
Dhangadhi Night 3 : 10 p.m.

a) How many buses are there for day and night services?

b) What is the departure time of a bus for Rajbiraj?

c) If the departure time of the bus for Surkhet is postponed by 45 minutes,
at what time does it leave Kathmandu?

d) Usually it takes 15 h 45 min to a bus to arrive at Dhangadhi. At what time
does the bus arrive at Dhangadhi the next day?

e) If the bus for Dharan arrived at its destination at 6 : 15 p.m., how long
was its journey?

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Statistics

4. a) Let's make a chart of a progress report of a terminal examination using
the information given below.

Full marks of each subject is 100, pass mark is 40, and marks obtained in
different subjects are :

English – 80, Nepali – 75, Maths – 95, Science – 85, Social Studies – 70

b) On the annual school Day of a school, the number of boys and girls
participating in different events are given below.

Sports – 75 boys, 40 girls Music – 20 boys, 35 girls

Quiz contest – 12 boys, 16 girls Debate – 10 boys, 6 girls

Let's show the information by making a chart.

17.2 Bar graph – Review 13 Career choices
12
The graph given alongside is a bar graph 11
(or a bar diagram). We can also show the
information numerically in a bar graphs. We 10
9

usually draw the bar diagrams in a squared Number of students 8
graph paper. 7
6
A bar graph has four main parts : a title, 5
labels, a scale, and bars. 4
3
(i) In the given bar graph, 'Career Choices' 2
is the title. 1
0
(ii) Below the graph is the label, 'Types of
careers'. Just below the bars, the types Doctor Teacher Pilot

Types of Careers

of careers are written as 'Doctor', 'Teacher' and 'Pilot'.

(iii) The Scale is the set of numbers along the left side of the graph. It
shows the information in numbers.

(iv) Bars are the rectangular vertical or horizontal boxes drawn to represent
the given information. The bars should be of the same width and each
bar should have the equal gap between them.

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Statistics

EXERCISE 17.2
Section A - Classwork

1. Let's study this vertical bar graph and answer the questions.

a) What is the title of the given bar graph? 12 Favourite Fruits
11

b) What is the label of the bar graph? Number of students10
9

8

c) How many students like orange? 7
6
5

d) How many more students like mango 4
than apple? 3
2
e) Which is the most popular fruit? 1
0

Apple Mango Orange
Types of Fruits

f) How many students took part in the survey?

2. Let's study this horizontal bar graph and answer the questions.

a) What is the title of the bar graph? Annual result of class 5

'A'
Grade

b) What is the label of the bar graph?

'B'

Result Grade

c) Let's write the number of students

in the table who got different grades. 'C'

Grades Grade

'A' 'B' 'C' 'D'

No of students 'D'
Grade

0 1 2 3 4 5 6 7 8 9 10

d) In which grade did the highest number of students pass?

e) How many students appeared the annual exam of class 5?

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Statistics

3. Let's draw bar graphs using the information given in the tables.

a) Favourite English Maths Science b) Events Sports Music Quiz Debate

Subjects

No. of 10 12 8 No. of 55 20 30 10
students
participants

Number of students Favourite Subject Inter-house Events
Number of students1260
11 55

10 50
9 45
8 40
7 35
6 30
5 25
4 20
3 15
2
1 10
0 5
0
English Maths Science
Sports Music Quiz Debate
Subjects
Events
Section B

4. a) Class 5 students conducted a survey about which game they like the
most. The table given below shows their responses.

Games Football Cricket Basketball Volleyball
No. of students
15 12 10 6

Let's draw a bar graph to show the above information.

b) The average monthly attendance of class 5 in the irst 4 months of a
new academic session is given in the table.

Months Baishakh Jestha Asar Shrawan
Attendance
15 25 30 28

(i) Let's draw a bar graph of the given data.

(ii) In which month the average attendance was minimum or
maximum?

(iii) In which month the average attendance was less than 25?

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Statistics

c) The table given below shows the number of votes received by 4
candidates of School prefect in a school.

Candidates A B CD

No. of votes 40 75 90 45

(i) Let's draw a bar graph of the data given.

(ii) Who won the election and how many votes did she/he receive?

(iii) Who is the nearest competitor in the election. By how many votes
was she/he defeated?

5. It's your time – Project work!

a) Let's conduct a survey inside your classroom and ind the number of
students who secured the grades A, B, C, and D while promoting from
class 4 to class 5. Write the numbers in a table and draw a bar graph to
show the information.

b) Working on your own, or with a partner, or in a group, investigate the
following for the pupils in your class. Collect the statistics in a table and
then illustrate them in bar graphs.

(i) Their favourite vegetables (ii) Their career choices

(iii) How do they usually come to school, by walking, by school bus, by
public vehicles, or by own vehicles?

17.3 Measurement of temperature – Review

Temperature shows the hotness or coldness of
objects. Thermometer is an instrument which is
used to measure the temperature.

Degree Celsius (°C) and Degree Fahrenheit
(°F) are two common units of temperature that
we use in our daily life.

Water boils at 100°C or 212°F and freezes at
0°C or 32°F.

Mercury is used in thermometers. Mercury is a liquid metal. Its level rises
inside a tiny tube in thermometer with the rise of temperature. Its level falls
when the temperature decreases.

Do you know?

The average normal body temperature of human is 98.6°F which is 37°C.

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Statistics

EXERCISE 17.3
Section A - Classwork
1. Let's say and write the temperature shown by these thermometers.

a)
b)
c)
d)

2. Let's say and write our body temperature in °F shown by these digital
thermometers.

a) 98.6°F b) 97.8°F c) 102°F

Section B

3. a) De ine temperature. What is the instrument used to measure
temperature ? Write the common units of temperature.

b) How many degree Fahrenheit (°F) are there in 0°C ?
c) How many degree Celsius (°C) are there in 212°F ?
d) What is the average normal body temperature of human in °F and in °C ?

4. a) In a winter morning, the temperature of air is measured to be 12.5°C. At
the noon, it is 28.7°C. In the evening, it is 21°C. Calculate the rise and fall
of temperature.

b) The room temperature of water is 20.5°C. When it is heated for
2 minutes in an electric kettle, its temperature rises by 25.8°C. Find the
temperature of hot water.

c) The room temperature of water in a beaker is 21.7°C. By how much
should the temperature be increased to boil it?

d) The temperature of water in an ice-tray is 18.6°C. By how much should
it be cooled down to convert into ice-cubes?

e) Sarada is being suffered from fever. When her mother measures her
body temperature she inds it to be 101.5°F. By how much does her body
temperature increase from the normal temperature?

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Statistics

It's your time – Project work!
5. a) Let's visit to the available website such as www.google.com and search

the current temperatures of the following places.

(i) Muktinath (ii) Biratnagar (iii) Birganj (iv) Nepalganj

Show these temperature by drawing a bar graph.
b) Can you ind the current temperature of your place by searching from

the website ? Let's try it.
c) Let's take a digital or clinical thermometer, and measure your and family

members' body temperature. Does everybody has normal temperature?

17.4 Ordered pairs – Review
Let's study the capitals of a few given countries.

Nepal – Kathmandu We can write these countries and their
India – New Delhi capitals in pairs. For example,
China – Beijing (Nepal, Kathmandu), (India, New Delhi),
Bhutan – Thimpu (China, Beijing) and (Bhutan, Thimpu).

In each of these pairs, the irst member is always a country and the second
member is it's capital. Therefore, the countries and capitals are in the ixed
order. Such pairs are called ordered pairs.
The members of an ordered pair are enclosed in a small brackets and they
are separated by comma.

17.5 Coordinates – Introduction

Let's ind the position of each of R1 Sita Ram Laxmi
the following students by making
ordered pairs in terms of Rows and Geeta Gopal
Columns (R,C).
Bhola Rita
Sita → (R1 , C1) → (1, 1) R2 Hari C2 C3
Ram → (R1 , C2) → (1, 2)
Laxmi → (R1 , C3) → (1, 3) R3 Shova
Hari → (R2 , C1) → (2, 1) C1
Rita → (R3 , C3) → (3, 3)
and so on.

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Statistics

In the given graph, a horizontal lin OX and a Y
vertical line OY are intersecting at O. Here,
OX is called X-axis and OY is called Y-axis. 10
The point of intersection O is called origin.
9
From origin (O), the number of squared
rooms along X-axis and Y-axis are 1, 2, 8
3, 4, … respectively.
7
Now, let's find the positions of some points
in terms of their ordered pairs. Y-axis 6

a) When we run 3 rooms along OX and 5
jump 4 rooms along OY, we reach to the
point P. 4

3

2

1

O1 2 3 4 5 6 7 8X
Origin X-axis

? Coordinates of P is (3, 4)

Similarly, Y

b) Coordinates of Q is (7, 8) 10

c) Coordinates of R is (8, 2) 9

In this way, the ordered pair of numbers Jump along OYo 8 Q(7, 8)
that shows the position of a point in a 7
graph is called the coordinates of the
point. The number of rooms counted 6
along X-axis is X-coordinate. The
number of rooms counted along Y-axis is 5
Y-coordinate. Therefore, coordinates of 4 P(3, 4)
a point are (x-coordinate, y-coordinate).
3 Jump R(8, 2)
2

1 Run

O 1 2 3 4 5 6 7 8 9 10 X

Run along OX o

EXERCISE 17.4
Section A - Classwork
1. Let's say and write the ordered pairs of these animals and their babies.

a) Cow – Calf b) Bat–Pup

c) Bear – Cub d) Deer–Fawn

e) Dog – Pup f) Cat – Kitten

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Statistics

2. Let's say and write the position of children in the ordered pairs of
(Row, Column) i.e. (R, C).

Mira → (R2 , C3)
a) Tashi →
R1 Tashi Maya Shiva

b) Abdul →

c) Maya → R2 Durga Abdul Mira
d) Dolma →

e) Shiva → R3 Aaron
C1
f) Aaron → Dolma Alima
C2 C3

3. Let's say and write the positions of fruits in Y
8
terms of ordered pairs of numbers.
7

a) Apple → 6
5

b) Guava → 4
3

c) Orange → 2
1

d) Mango → O 1 2 3 4 5 6 7 8 9 10 X

4. Let's study the given graph, then tell Y
and write the answers in the blank spaces. 10
9

a) The horizontal line OX is called 8

7

b) The vertical line OY is called 6Q

c) The point of intersection O is called 5

d) The coordinate of the point P is 4 P
3

e) The x-coordinate of the point P is 2R
1
f) The y-coordinate of the point P is
O 1 2 3 4 5 6 7 8 9 10 X
g) The coordinates of the points 5Y

(i) Q is (ii) R is

5. Let's plot the following points in the given 4
graph. 3
2

a) A (2, 4) b) B (4, 2) 1
c) C(6, 3) d) D (9, 1)
O 1 2 3 4 5 6 7 8 9 10 X

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Statistics

Section B
6. Let's write any 5 ordered pairs for each of the following cases.

a) The irst member is an animal and the second is its home.

b) The irst member is an even number and the second is its double.

c) The irst member is a square number and the second is its square root.

d) The irst member is an odd number and the second is 2 more than the odd
number.

7. Let's copy the following points with their coordinates. Then, write the
x-coordinate and y-coordinate separately.

a) P(3, 5) b) Q (7, 2) c) R(4, 6) d) M(2, 1)

e) N(1, 2) f) A (8, 9) g) B(9, 8) h) C(6, 4)
8. Let's write the coordinates of the vertices of each igure given in the

following graphs.
a) Y b) Y

L

RC

DB HP A
Q IG E
P
N
A EF

O XO X

9. Let's plot the coordinates of the following points in squared graphs. Join
the points in order and name the igures so formed.

a) A(1, 1), B(4, 1), C(1,5) b) D(5, 2), E(9, 4), F(6, 7)

c) P(2, 2), Q(5,2), R(5, 5), S(2, 5) d) K(1, 3), L(6, 3), M(6, 7), N(1, 7)

e) N(1, 2), E(4, 2), P(2, 4), A(4, 4), L(1, 7)
It's your time - Project work!
10. a) Let's arrange your 9 friends in 3 rows and 3 columns. Write the position of

each friend in the ordered pairs of (Row, column).

b) Let's write the position of your 10 friends in the ordered pairs of (Row,
column) inside your classroom. What is the ordered pair of your position?

c) Let's draw a triangle, a rectangle and a square in graphs by using ruler.

Write the coordinates of the vertices of each igure.

"

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Unit Set

18

18.1 Set – Looking back

Classwork - Exercise

1. Let's list the members of these sets in curly brackets.

a) e n a b) 1 3 5
pl 79

A= B=

2. Let's say and write any three members of the following sets inside curly
brackets.

a) A set of National Symbols of Nepal.

N=

b) A set of prime numbers less than 11. P =

c) A set of factors of 12. F =

18.2 Set– A well –defined collection

In the given collection of stationery items, pen is shorter than pencil but it
is longer than eraser. Once it belongs to the collection of 'long stationery
items', but again it does not belong to the collection of 'long stationery
items'. Thus, the collection of long stationery items is not well - de ined

and it is not called a set. However, it can be a set of stationery items.

Similarly, the collection of tall children in your class, the collection of delicious
food items, etc. are not well de ined collections. Therefore, these collections
are not sets.

On the other hand, in the given collection of 2 6
48
even numbers less than 10, it de initely includes

the members 2, 4, 6 and 8. Therefore, it is a
well-de ined collection and it is called a set.

In this way, a set is a collection of well-de ined
objects.

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Set

18.3 Membership of a set

Let's take a set of natural numbers less 6.
N = {1, 2, 3, 4, 5}
Here, 1, 2, 3, 4, and 5 are the members (or elements) of the set N. Each
member of this set belongs to the set N.

1 belongs to the set N and we write it as 1  1

belongs to the set N and we write it as 2  1 and so on.

We use a symbol '' to show the membership of members of a set.
18.4 Methods of writing members of a set

Let's study the following illustrations and learn about four main methods
of writing the members of a given set.

(i) Diagrammatic method 2 5
37
In this method, we write the members of a set
inside a circular or oval diagram.

(ii) Descriptive method

In this method, we describe the common property (or properties) of
the members of given sets. For example:

The set of prime numbers less than 11.

The set of vowels in English alphabets, and so on.

(iii) Listing method

In this method, we list the member of sets inside the curly brackets { }.
The members are separated by commas (,) and we can name the set by
a capital letter. For example:

The set of prime number less than 11 → A = {2, 3, 5, 7}

Set of vowels in English alphabets → % ^ a, e, i, o, u}

(iv) Set-builder or Rule method

In this method, we represent the members of a set by a variable
(x, y, z, p, …) Then, the common property (or properties) of the members
are described by the variable inside curly brackets.

For example:

A = {2, 3, 5, 7} → A = {x : x is a prime number less than 11}

We read it as 'A is a set of all values of x such that x is a prime number
less than 11.'

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Set

B = {a, e, i, o, u} → B = {p : p is a vowel in English alphabets}
We read it as 'B is a set of all values of p such that p is a vowel in
English alphabets.'

EXERCISE 18.1

Section A - Classwork

1. Let's tick (√ ) to the well-de ined collections.

a) A collection of intelligent students in your class.

b) A collection of intelligent students who got A+ grade in your class.

c) A collection of high mountains of Nepal.

d) A collection of mountains of Nepal higher than 8000 m.

e) A collection of some food items.

f) A collection of some delicious food items.

2. A = {2, 4, 6, 8} is a set of even numbers less than 10. Let's insert the
appropriate symbol '' or '' in the blanks.

a) 6 A b) 9 A c) 2 A

d) 10 A e) 8 A f) 5 A

Section B
3. Let's answer these questions.

a) What is a set?

b) Can we call a collection of sweet fruits a set? Express this collection as a
set.

c) Write four methods of writing members of a set.

d) How do we write the members of a set in listing method?
4. Let's write the members of the following sets in diagrammatic method.

a) A set of 3 gases in air

b) A set of the irst four letters in Nepali Barnamala.

c) A set of natural numbers less than 5.

d) A set of square numbers less than 20.

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Set

5. Let's write the members of these sets in listing method.

a) A set of four plants closer to the sun in solar system.
b) A set of the last four letters in Nepali Barnamala.
c) A set of whole numbers less than 5.
d) A set of cube numbers less than 100.
6. Let's express the following sets in descriptive method.

a) A = {a, b, c, d, e} b) B = {1, 3, 5, 7, 9}

c) C = {4, 8, 12, 16, 20} d) D = {1, 2, 5, 10}

7. Let's write the members of the following sets in listing method.

a) A = {x : x is a natural number less than 10}

b) B = {y : y is an even number less than 10}

c) C = {p : p is a square number less than 50}

d) D = {x : x is a factor of 12}

8. Let's express the following sets in set-builder form.

a) P = {0, 1, 2, 3, 4} b) Q = {1, 2, 3, 4}

c) R = {3, 6, 9, 12, 15} d) S = {1, 2, 3, 6, 9, 18}

It's your time - Project work!

9. a) Let's observe around your class room and select any four objects as

the members of a set. Then express the sets in four different methods:

(i)diagrammatic (ii) listing

(iii) descriptive (iv) set-builder.

b) Let's write whole numbers from 0 to 20. Select the appropriate numbers to
form the following sets in listing and set-builder forms.

(i) Set of multiples of 5 (ii) Set of factors of 20
(iii) Set of prime numbers (iv) Set of composite numbers
(v) Set of square numbers (vi) Set of cube numbers

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Set

18.5 Types of sets

Depending on the numbers of members of sets, there are three types of sets.

(i) Empty set ( or null set)

An empty set does not contain any member (or element). It is also called a
null set. For example:

The set of rectangles with 5 sides. A={}

The set of odd numbers between 3 and 5. B={}

The set of even numbers between 2 and 3. C={}

The set of natural numbers less than 1 and so on. D = { }
We write an empty or null set by using a symbol { }.

(ii) Unit set

A unit set contains exactly one member (or element). For example:

The set of the highest peak of the world. A = {Mount Everest}

The set of star in Solar System. B = {Sun}

The set of the square number between 5 and 10. C = {9}

The set of factor of 1, and so on. D = {1}
A unit set is also called a singleton set.

(iii) Finite set

A inite set contains a certain number of members that can be counted. For
example:

The set of Mathematics teachers in a school.

The set of whole numbers between 0 and 100. W = {0, 1, 2, 3,..., 100}

The set of odd numbers less than 50. A = {1, 3, 5, …, 49}

The set of prime numbers between 1 and 100, and so on. B = {2, 3, 5, …, 97}

(iv) In inite set

An in inite set contains uncountable number of members. The counting of
members of an in inite set is never-ending. For example:

The set of natural numbers more than 10. N = {10, 11, 12, …}

The set of even numbers more than 1, and so on. E = {2, 4, 6, …}

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EXERCISE 18.2

Section A - Classwork

1. Let's say and write whether these sets are empty, unit, inite or in inite
sets.

a) A set of multiples of 5 less than 30.

b) A set of prime numbers between 6 and 10.

c) A set of odd numbers between 3 and 5.

d) A set of multiples of 2.

2. Let's say and write whether the following sets are empty, unit, inite or
in inite sets.

a) A = { 7 } b) B = { }

c) C = { 1, 2, 3, …} d) D = { 1, 2, 3}
Section B

3. Let's answer the following questions.

a) What type of set is P = { } ? Why?
b) What type of set is Q = { 9 }? Why?
c) What type of set is N = {1, 2, 3, 4, 5}? Why?
d) What type of set is M = {1, 2, 3, 4, 5, …}? Why?

4. Let's list the members (elements) of these sets. Then, state whether they
are empty, unit, or inite sets.

a) The set of even numbers between 2 and 4.
b) The set of square numbers less than 3.
c) The set of English months starting with 'J' letter.
d) The set of multiples of 7 between 10 and 20.
e) The set of prime factors of 10.
f) The set of cube numbers between 30 and 40
It's your time - Project work!

5. Let's write the following types of sets of your own in descriptive method.

(i) Two empty sets (ii) Two unit sets

(iii) Two inite sets (iv) Two in inite sets

"

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Answers

1. Number System
Exercise - 1.1

Section B Face value Place name Place value
8. 5 Thousands 5,000
6 Ten-thousands 60,000
Numerals 7 Lakhs 7,00,000
a) 95731 Hundreds-thousands 700,000
b) 62915 5 Ten - lakhs 50,00,000
c) 2753460 Millions 5,000,000
8 Crores 8,00,00,000
d) 5816209 Ten-millions 80,000,000
3 Ten-crores 30,00,00,000
e) 82413596 Hundred-millions 300,000,000
7 Crores 7,00,00,000
f) 314702600 Ten-millions 70,000,000
4 Arabs 4,00,00,00,000
g) 770038002 Billions 4,000,000,000

h) 4162030575

9. a) 17,05,394 Seventeen lakh five thousand three hundred ninety-four.

b) 36,05,18,050 Thirty-six crore five lakh eighteen thousand fifty.

c) 4,07,62,33,917 Four arab seven crore sixty-two lakh thirty-three thousand nine hundred seventeen.

d) 2,150,712 Two million one hundred fifty thousand seven hundred twelve.

e) 50,958,207 Fifty million nine hundred fifty-eight thousand two hundred seven.

10. a) 5 × 1000000 + 2 × 100000 + 6 × 10000 + 3 × 1000 + 4 × 100 + 8 × 10 + 7 × 1

b) 2 × 10000000 + 4 × 100000 + 7 × 10000 + 1 × 100 + 5 × 10 + 5 × 1

c) 6 × 100000000 + 4 × 10000000 + 3 × 10000 + 5 × 1000 + 2 × 100 + 9 × 1

d) 3 × 100000000 + 5 × 1000000 + 2 × 10000 + 7 × 100

11. a) 925740 b) 6032108 c) 21049600 d) 330502005

12. a) 1 million b) 3 million c) 7 million d) 10 million e) 40 million f) 90 million

13. a) 10 lakh b) 40 lakh c) 80 lakh d) 1 crore e) 5 crore f) 7 crore

14. a) Four lakh thirty-nine thousand three hundred thirty-six.

b) Three crore two lakh sixty thousand two hundred forty-four.

c) One arab forty-two crore forty-five lakh forty-eight thousand two hundred sixty-six.

d) Two crore fifty-three lakh ninety-eight thousand one hundred seventy-seven.

15. a) 1,47,181 sq. km. b) Rs 32,04,900 c) Rs 1,12,06,000 d) Rs 16,09,05,700

16. a) Rs 2,50,000 Two lakh fifty thousand rupees

b) 30,48,900 Thirty lakh forty-eight thousand nine hundred

c) 1,79,87,520 km One crore seventy-nine lakh eighty-seven thousand five hundred twenty kilometre

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Answers

d) 14,96,00,000 km Fourteen crore ninety-six lakh km

e) Rs 2,05,04,00,000 Two arab five crore four lakh rupees

17. s_ !%),))) Ps nfv krf; xhf/ v_ @%$&^(* kRrL; nfv ;t\rfnL; xhf/ 5 ;o cG7fgAa]

u_ #%)))))) tLg s/f]8 krf; nfv

18. a) 89999 b) 1099999 c) 86931 d) 9666678
19. and 20. Please complete your project works and compare with your friends. Then discuss in your class.

Exercise - 1.2

Section B

2. a) (i) 480 (ii) 500 b) (i) 540 km (ii) 500 km

c) (i) Rs 1,800 (ii) Rs 2,000 d) (i) 8,400 (ii) 8,000

e) (i) Rs 27,800 (ii) Rs 28,000 (iii) Rs 30,000

f) (i) Rs 2,45,300 (ii) Rs 2,45,000 (iii) Rs 2,50,000

3. a) 490, 500 b) 2,800, 3,000 c) 9,000, 10,000

4. and 5. Please complete your project works and compare with your friends. Then discuss in your class.

2. Fundamental Operations

Exercise - 2.1

Section B

4. a) 1,280 students b) 9,430 people c) Rs 2,770 d) 3,545 men e) Rs 280 f) Rs 350
c) 3375, 8012
5. a) 7115, 4658 b) 9220, 5325 b) (i) 25,724

6. a) (i) Rs 6,625 (ii) Rs 925 (ii) 416 c) 1,022

d) (i) Rs 1,03,450 (ii) Rs 7,050 gain e) (i) 45,350 (ii) 22,450

7. and 8. Please complete your project work individually or in groups. Then discuss in your class.

Exercise - 2.2

Section B

9. Compare your answers with your friends. Then discuss in the class and show to your teacher.

10. a) 4,760 b) 29,452 c) 15,25,400 d) 24,09,225 11. a) (i) 112 (ii) Q = 1,377, R = 1

(iii) Q = 323, R = 3 (iv) 7,081 b) (i) Q = 135, R = 5 (ii) Q = 51, R = 5 (iii) 21 (iv) Q = 310, R = 20

12. a) Rs 810 b) Rs 85 per kg c) Rs 5,600 d) Rs 5,100 e) 816 g f) 72 calories

13. a) 540 km b) 576 c) 486 14. a) 65 b) 277

15. and 16. Please complete your project work. Compare your outcomes with your friends and discuss in the

class. Then show to your teacher.

Exercise - 2.3

Section B

6. a) 1 b) 4 c) 25 d) 26 e) 32 f) 6 g) 7 h) 15 i) 56 j ) 3

k) 27 l) 5 7. a) 23 b) 7 c) 50 d) 12 e) 13 f) 16 g) 70 h) 0

8. b) {5 × (6 + 3)} ÷ 5 c) 4 + {(12 – 5) × 3} d) 18 ÷ {2 × (4 + 5)} e) 8 × {(27 – 6) ÷ 7}

9. a) 50 b) 42 c) 6 d) 6 e) 3 f) 15

10. a) 15 b) Rs 100 c) 14 d) Rs 570 11. a) 210 ml b) 72 km c) Rs 3,150 d) 2

12. Please complete your project works and compare your outcomes with your friends. Then show to your

teacher.

3. Properties of Whole Numbers

Exercise - 3.1

Section B

2. Answer the questions yourself. Discuss your answers with friends. Then show to your teacher.

3. a) …, 155, 157, 159, 161, … b) …, 182, … 186, 188, 190, …

c) …, 321, …, 325, 327, 329, … d) …, 598, 600, 602, 604, …

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Answers

4. a) Answer the questions yourself. Discuss your findings with friends and teacher in the class.
5. Please complete your project works. Compare your outcomes with your friends.

Exercise - 3.2

Section B

7. Answer the questions yourself and show to your teacher.

8. Answer the questions yourself. Discuss about yours and others answer in the class. Then show to your

teacher.

9. a) 5, 10, 15, 20, 25 b) 7, 14, 21, 28, 35 c) 8, 16, 24, 32, 40 d) 9, 18, 27, 36, 45

e) 10, 20, 30, 40, 50 f) 12, 24, 36, 48, 60 10. a) 1, 2, 4, and 2 b) 1, 2, 3, 6 and 2, 3

c) 1, 2, 4, 8 and 2 d) 1, 3, 9 and 3 e) 1, 2, 5, 10 and 2, 5 f) 1, 2, 3, 4, 6, 12 and 2, 3

g) 1, 2, 7, 14 and 2, 7 h) 1, 3, 5, 15 and 3, 5 i) 1, 2, 4, 8, 16 and 2 j) 1, 2, 3, 6, 9, 18 and 2, 3

k) 1, 2, 4, 5, 10, 20 and 2, 5 l) 1, 2, 3, 4, 6, 9, 12, 18, 36 and 2, 3

11. a) 2 × 3 × 3 b) 2 × 5 c) 2 × 2 × 3 d) 2 × 7 e) 3 × 5

f) 2 × 2 × 2 × 2 g) 2 × 2 × 5 h) 2 × 2 × 2 × 3 i) 5 × 5 j) 3 × 3 × 3

k) 2 × 2 × 7 l) 2 × 3 × 5 m) 2 × 2 × 2 × 2 × 2 n) 2 × 2 × 3 × 3 o) 2 × 2 × 2 × 5

p) 2 × 3 × 7 q) 2 × 2 × 11 r) 3 × 3 × 5 s) 2 × 2 × 2 × 2 × 3 t) 2 × 5 × 5 u) 2 × 3 × 3 × 3
12 c) 16
12. a) 8 b) 2× 8

2× 4 2× 6

2 × 2× 2 2 × 2× 3 2 × 2× 4

2 × 2× 2 × 2

d) 18 e) 20 f) 24
2× 9 2 × 10 2 × 12

2 × 3× 3 2 × 2× 5 2 × 2× 6

2 × 2× 2 × 3

13. a) Please complete your project works. Compare your outcomes with your friends and discuss in the
class. Then show to your teacher.
Exercise - 3.3

Section B

5. a) 2 b) 3 c) 4 d) 6 e) 5 f) 7 6. a) 6 b) 12 c) 9 d) 24 e ) 1 0

f) 20 7. a) 4 b) 6 c) 5 d) 4 e) 10 f) 6 g) 8 h) 9 i) 15 j) 8

8. a) 12 b) 24 c) 8 d) 18 e) 40 f) 36 g) 30 h) 20 i) 48 j) 72

9. a) 12 b) 24 c) 20 d) 45 e) 36 f) 42 g) 60 h) 48 i) 54 j) 60

10. a) 6 b) 8 c) 10 11. a) 24 b) 36 c) 30

12. and 13 Please play the H.C.F. and L.C.M. games with partners and learn more about H.C.F. and L.C.M.

Exercise - 3.4

Section B

7. Answer the questions yourself and compare your answers with friends. Then show to your teacher.

8. a) 121 b) 144 c) 169 d) 196 e) 225 f) 256 g) 289 h) 324 i) 361

j) 576 k) 625 l) 1296 m) 14400 n) 16900 o) 19600 p) 22500 q) 10000 r) 40000

9. a) 4 b) 5 c) 6 d) 8 e) 9 f) 10 g) 12 h) 14 i) 15

j) 16 k) 18 l) 21 10. a) 64 b) 81 c) 100 11. a) 8 b) Rs 30 c) 12

12. Please complete your project works and compare your outcomes with your friends. Then show to your

teacher.

Exercise - 3.5

Section B

5. Answer the questions yourself and discuss in the class. Then show to your teacher.

6. a) 125 b) 216 c) 343 d) 512 e) 729 f) 1331 g) 1728 h) 3375 i) 27000

j) 64000 k) 216000 l) 1000000

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Answers

7. a) 2 b) 3 c) 4 d) 5 e) 6 f) 7 g) 8 h) 9 i ) 1 4
j) 20 k) 30 l) 50 8. a) 14 b) 15 c) 5 d) 21
g) 6 h) 0 i) 9 9. a) 8 cm3 b) 64 cm3 c) 1000 cm3 d) 64 e) 29 f) 17

10. a) 4 cm b) 6 cm c) 5

4. Fraction

Exercise - 4.1

Section B

5. Answer the questions yourself and discuss in the class. Then show to your teacher.

6. a) 2 , 3 , 4 b) 2 , 3 , 4 c) 4 , 6 , 8 d) 4 , 6 , 8 e) 6 , 9 , 12
4 6 8 6 9 12 6 9 12 10 15 20 8 12 10

f) 6 , 9 , 12 g) 8 , 12 , 16 h) 4 , 6 , 8 i) 6 , 9 , 12 j) 10 , 15 , 20
10 15 20 10 15 20 14 21 28 14 21 28 12 18 24

7. a) 1 b) 2 or 1 c) 1 d) 2 e) 3 f) 4 g) 3 h) 4 or 2 i) 2 j) 6 or 2
2 4 2 3 3 4 5 5 6 3 3 9 3

8. a) 2 b) 3 c) 1 d) 2 e) 2 f) 2 g) 3 h) 4 i) 2 j) 2
3 4 4 3 5 3 4 5 3 3

9. a) 2 b) 3 c) 1 d) 2 e) 4 f) 3 g) 3 h) 5 i) 1 j) 2
3 4 3 3 5 4 4 6 2 3
10. Please complete your project works. Compare your outcomes with your friends and discuss in the class.

Then show to your teacher.

Exercise - 4.2

Section B

6. Answer the questions yourself and discuss in the class. Then show to your teacher.
7.

Ascending order Descending order

a) 1 , 2 , 3 , 4 4 , 3 , 2 , 1
5 5 5 5 5 5 5 5

b) 2 , 3 , 5 , 7 7 , 5 , 3 , 2
8 8 8 8 8 8 8 8

c) 3 , 6 , 7 , 9 9 , 7 , 6 , 3
10 10 10 10 10 10 10 10

8. a) 2 , 1 b) 2 , 1 c) 6 , 3 d) 3 , 4 e) 5 , 6 f) 8 , 3 g) 3 , 2 h) 3 , 4
4 4 6 6 8 8 6 6 10 10 12 12 12 12 18 18

9. a) 3 < 4 b) 5 > 4 c) 6 > 5 d) 6 < 7
6 6 10 10 8 8 10 10

10. a) 132 b) 213 c) 212 d) 153 e) 241 f) 316 11. a) 4 b) 9 c) 7 d) 12 e) 15 f) 19
3 4 2 5 4 7

12. Please complete your project works. Compare your works with your friends. Then show to your teacher.

Exercise - 4.3

Section B

6. a) 223 b) 365 7. a) 113 b) 115 8. a) 3 b) 5 c) 212 d) 423 e) 2
5 8 7

f) 3 g) 132 h) 251 9. a) 2 b) 5 c) 3 d) 121 e) 191 f) 2190
10 5 7 8

10. a) 5 b) 5 c) 5 litre 11. a) 4 b) 4 c) 353 m
9 8 7 6 6
12. Please complete your project works and compare with your friends. Then show to your teacher.

Exercise - 4.4

Section B

5. a) 3 b) 114 c) 7 d) 1152 e) 9 f) 1145 g) 11 h) 1254 i) 112
4 12 10 12

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Answers

j) 383 k) 5152 l) 5158 6. a) 1 b) 5 c) 1 d) 1 e) 1 f) 1 g) 1 h) 5 i) 2
6 12 10 4 4 6 12 24 3

j) 194 k) 14 l) 1 7. a) 1112 b) 7 c) 1 d) 1172 e) 3 f) 1 g) 13 h) 285 i) 1
15 20 12 4 20 6 14 24

8. a) 1152 cups b) 9 c) 2612 m 9. a) 2 litre b) 1 c) 3
10 15 8 5

10. Please complete your project works and compare with your friends. Then show to your teacher.

Section B Exercise - 4.5 g) 3 h) 4 i) 6 j) 15
7. a) 1 b) 1 c) 1 d) 1 e) 1 f) 2

8. a) 1 b) 1 c) 1 d) 3 e) 2 f) 2 g) 15 h) 412 i) 232 j) 712
6 3 2 5 3 7 16

9. a) Rs 12 b) 6 kg c) 20 km d) 7 l e) Rs 27 f) 20 girls g) 45 boys h) 60 students

10. a) 412 b) 1312 m c) 1 d) Rs 5114 e) 1 f) 1
3 4 3

11. a) (i) 20 (ii) 10 b) (i) 21 (ii) 14 c) (i) 300 ml (ii) 450 ml d) 700 l e) 24 km

12. Please complete your project works and compare with your friends. Then show to your teacher.

Exercise - 4.6

Section B

5. Answer the questions yourself and discuss in the class. Then show to your teacher.

6. a) 6 b) 6 c) 8 d) 8 e) 15 f) 15 g) 3 h) 4 i) 10 j) 512

7. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 2 h) 1 i) 1 j) 1
6 6 8 15 3 4 5 10 8 15

8. a) 112 b) 2 c) 1 d) 1 e) 2 f) 2 g) 112 h) 2 i) 1 j) 112
3 2 2 2

9. a) 6 b) 10 c) 8 days 10. a) 1 b) 1 11. a) 2 b) 4 c) 3
4 12

12. Please complete your project works and compares with your friends. Then show to your teacher.

5. Decimal

Exercise - 5.1

Section B

6. Answer the questions yourself and discuss in the class. Then show to your teacher.

7. a) 0.1 = 1 b) 0.001 = 1 c) 0.0005 = 5 d) 0.38 = 38 e) 0.074 = 74 f) 0.409 = 409
10 1000 10000 100 1000 1000

8. a) zero point five b) zero point zero five or decimal zero five c) zero point zero zero five

d) zero point seven two or decimal seven two e) zero point zero four six f) zero point three zero eight

9. a) 0.3 6 b) 0.0 7

tenths = 0.3 tenths = 0.0

hundredths = 0.06 hundredths = 0.07

c) 0.195 d) 0.004

tenths = 0.1 tenths = 0.0

hundredths = 0.09 hundredths = 0.00

thousandths= 0.005 thousandths= 0.004

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Answers

e) 0.281 f) 0.999

tenths = 0.2 tenths = 0.9

hundredths = 0.08 hundredths = 0.09

thousandths= 0.001 thousandths= 0.009

10. a) 0.8 > 0.6 b) 0.42 < 0.45 c) 0.7 > 0.68 d) 0.09 < 0.1 e) 0.03 > 0.006 f) 0.296 < 0.33
11 .
Descending order
Ascending order 0.2, 0.12, 0.02, 0.002
0.542, 0.54, 0.5, 0.054
a) 0.002, 0.02, 0.12, 0.2

b) 0.054, 0.5, 0.54, 0.542

12. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 3 h) 1 i) 1 j) 1
10 100 1000 5 50 500 10 25 4 8

k) 112 l) 252 m) 421 n) 3110 o) 721 13. a) 0.5 b) 0.2 c) 0.4 d) 0.6

e) 0.8 f) 1.5 g) 2.5 h) 1.4 i) 2.8 j) 0.25 k) 0.75 l) 1.25 m) 2.75 n) 0.05
d) 0.8 e) 0.375
o) 0.28 p) 0.06 q) 1.04 r) 2.15 14. a) 0.25 b) 0.75 c) 0.2

f) 0.166 g) 1.5 h) 2.5 i) 0.333 j) 0.666 k) 1.333 l) 3.666

15. Please complete your project works and compare with your friends' work. Then show to your teacher.

Exercise - 5.2

Section B

7. a) 0.8 b) 0.08 c) 0.008 d) 2.2 e) 2.11 f) 4.5 g) 6.96 h) 4.012

i) 26.219 j) 37.079 k) 35.505 l) 28.383 8. a) 0.3 b) 0.75 c) 0.795 d) 0.8

e) 1.61 f) 1.691 g) 0.85 h) 1.78 i) 5.92 j) 6.933 k) 6.918 l) 13.775

9. a) 0.6 b) 0.2 c) 0.09 d) 0.5 e) 1.555 f) 1.62 10. a) 0.7 b) 0.17

11. a) Rs 326.20 b) (i) Rs 186.25 (ii) Rs 13.75 c) Rs 1,000 12. a) Rs 29.77 b) 364.32 kb c) Rs 59.50

13. a) Please complete your project works and compare with your friends' work. Then show to your teacher.

b) Play decimal cards matching with partners and learn more about addition and subtraction of decimal
numbers.

Exercise - 5.3

Section B

6. a) 0.6 b) 0.6 c) 0.8 d) 0.09 e) 0.008 f) 1.2 g) 2.4 h) 0.25 i) 3.6

j) 10.4 k) 48.9 l) 126.63 7. a) 2.4 b) 0.52 c) 0.09 d) 60 e) 80 f) 7

g) 0.5 h) 300 i) 500 j) 40 k) 2 l) 296 8. a) 0.08 b) 0.06 c) 0.12

d) 0.18 e) 0.26 f) 1.04 g) 3.6 h) 7.84 i) 12.48 j) 22.05 k) 29.184 l) 60.408

9. a) 3 b) 3 c) 3 d) 5 e) 5 f) 5 g) 16 h) 235 i) 0.08

j) 0.35 k) 0.014 l) 0.054 10. 1.5 l b) 1.8 kg c) 16 l d) 14.4 g e) 10.5 l f) Rs 115

11. a) 0.24 sq. m. b) (i) 7.5 cm (ii) 14.4 cm (iii) 13 cm

12. Please complete your project works and compare with your friends' work. Then discuss in the class and

show to your teacher.

Exercise - 5.4

Section B

7. a) 0.1 b) 0.2 c) 0.1 d) 0.3 e) 0.4 f) 0.3 g) 0.4 h) 0.3 i) 0.9 j) 0.5

8. a) 0.3 b) 0.2 c) 0.04 d) 0.03 e) 0.03 f) 0.12 g) 0.14 h) 0.12 i) 0.6
j) 0.5 k) 0.8 l) 1.2 m) 1.3 n) 1.5 o) 1.4
9. a) 20 b) 20 c) 10

d) 8 e) 20 f) 2 g) 2 h) 6 i) 5 j) 7 10. a) 3.2 b) 5.4 c) 1.3
d) 3.31 e) 14 f) 21 g) 1.2 h) 2.4

11. a) Rs 7.50 b) 7 minutes c) 2.5 m d) 10 12. a) 5 b) 0.2 c) 4 d) 0.5

13. Please complete your project works and compare with your friends' works .Then show to your teacher.

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Exercise - 5.5

Section B

5. a) 1.3 b) 4.7 c) 5.8 d) 8.4 e) 10.5

6. a) 2.17, 2.2, 2 b) 5.48, 5.5, 6 c) 6.71, 6.7, 7 d) 9.44, 9.4, 9 e) 12.65, 12.7, 13

7. a) Rs 0.65 b) Rs 0.50 c) 25 p d) 0.7 cm e) 5 mm f) 0.54 m g) 75 cm h) 0.25 km

i) 685 m j) 0.415 kg k) 268 g l) 0.75 l m) 375 ml n) 50 cm o) 0.5 km

8. Please complete your project works. Are the exchange rate of the given currencies similar among all the
students?

6. Percent

Exercise - 6.1

Section B

5. Answer the questions yourself and discuss in the class. Then show to your teacher.

6. a) 1 b) 1 c) 1 d) 1 e) 3 f) 1 g) 1 h) 3 i) 2 j) 1 k) 3 l) 9
50 25 20 10 20 5 4 10 5 2 5 10

7. a) 0.03 b) 0.08 c) 0.18 d) 0.29 e) 0.35 f) 0.47 g) 0.52 h) 0.66 i) 0.7

j) 0.81 k) 0.9 l) 0.99 8. a) 50% b) 25% c) 20% d) 75% e) 80% f) 70%

g) 15% h) 16% i) 18% j) 1% k) 9% l) 12% m) 27% n) 33% o) 56%

p) 75% q) 80% r) 90% 9. b) (i) 75% (ii) 25% c) (i) 80% (ii) 20% 10. b) 90% c) (i) 60%

(ii) 40% 11. a) English - 80%, Nepali - 80%, Maths - 100%, Science - 80% b) Maths c) 85%

12. and 13 Please complete your project works and discuss about the outcomes in the class. Then show to your
teacher.
Exercise - 6.2

Section B

2. b) (i) 18 (ii) 12 c) 72 d) (i) Rs 12,000 (ii) Rs 18,000 e) 12,000, 13,000

3. a) (i) Rs 150 (ii) Rs 1,350 b) Rs 960 4. a) (i) Rs 2,400 (ii) Rs 10,800

(iii) Rs 13,200 (iv) Rs 10,800 b) (i) 140 (ii) 210 (iii) 350 (iv) 350

5. a) English - 60, Nepali - 60, Maths - 72, Science - 39 b) 77%

7. Buying and Selling

Exercise - 7.1

Section B

4. Answer the questions yourself. Discuss about your answer in the class. Then show to your teacher.

5. a) profit Rs 20 b) loss Rs 20 c) profit Rs 130 d) loss Rs 150 e) profit Rs 290 f) loss Rs 180

6. a) profit 10% b) loss 20% c) profit 12% d) profit 12% e) loss 5% f) profit 20%

7. a) 16% b) 5% 8. a) (i) profit Rs 80 (ii) 10% b) (i) loss Rs 50 (ii) 4%

c) (i) profit Rs 800 (ii) 20% 9. b) Rs 160 c) Rs 75

8. Unitary Method, Simple Interest

Exercise - 8.1

Section B

4. Answer the questions yourself. Discuss about your answer in the class, then show to your teacher.

5. a) Rs 30 b) Rs 15 c) Rs 300 d) Rs 80 6. a) Rs 120 b) Rs 40 c) Rs 1,600 d) 1 US dollar = Rs 110

7. a) (i) Rs 50 (ii) Rs 200 b) (i) Rs 120 per kg (ii) Rs 1,200 c) (i) Rs 40 per kg

(ii) Rs 200 d) (i) 10 l per km (ii) 300 km e) (i) 60 minutes (ii) 300 minutes

8. a) Rs 630 b) 3 kg c) Rs 1,080 d) 5 l e) Rs 3,000 f) 4 days g) 450 km h) 10 l

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9. a) 6 pencils for Rs 48 b) 6 kg of potatoes for Rs 150 c) 9 sweets for Rs 135 d) 8 kg of grapes for Rs 720

10. b) (i) Rs 80 (ii) Rs 20 c) (i) Rs 90 (ii) Rs 45 d) (i) 60 km (ii) 20 km

11. and 12. Please complete your project works and compare your outcomes with the outcomes of your
friends. Then show to your teacher.

Exercise - 8.2

Section B

3. Answer the questions yourself and discuss about your answer in the class. Then show to your teacher.

4. a) Rs 20 b) Rs 35 c) Rs 80 d) Rs 270 5. a) Rs 10 b) Rs 18 c) Rs 44 d) Rs 75

6. a) Rs 108 b) Rs 300 c) Rs 400 7. a) Rs 24 b) Rs 75 c) Rs 56

8. a) (i) Rs 90 (ii) Rs 180 b) (i) Rs 100 (ii) Rs 300 c) (i) Rs 350 (ii) Rs 1,400 d) (i) Rs 975 (ii) Rs 5,850

9. Please complete your project works and compare your outcomes with the outcomes of your friends.
Then show to your teacher.

9. Ratio
Exercise - 9.1
Section B
4. Answer the questions yourself. Discuss about your answer in the class and show to your teacher.

5. b) p : q = 3 : 1 c) q : p = 1 : 3 d) a : b = 4 : 1 e) b : a = 1 : 4
f) 1 : 2 g) 3 : 5 h) 1 : 2 i) 3 : 4
6. a) 3 : 4 b) 3 : 2 c) 2 : 5 d) 9 : 7 e) 3 : 4

7. a) 3 : 2 b) 1 : 3 c) 1 : 2 d) 5 : 2 e) 3 : 20 8. a) (i) 8 : 3 (ii) 3 : 5 b) 1 : 2

9. Please complete your project works. Compare your outcomes with the outcomes of your friends, then

show to your teacher.

10. Time, Money, Bill and Budget

Exercise - 10.1

Section B

6. a) 14 : 10 b) 1 : 25 p. m. c) 15 : 30 d) 3 : 05 p. m. e) 16 : 45 f) 5 : 50 p. m.

g) 19 : 20 h) 8 : 55 p. m. 7. a) 130 min b) 90 min c) 180 min d) 1 h 15 min

e) 1 h 30 min f) 1 h 45 m g) 70 s h) 135 s i) 1 min 40 s

8. a) 30 days b) 6 weeks 3 days c) 18 months d) 32 months e) 1 year 8 months f) 3 years 6 months

g) 100 days h) 2 months 15 days i) 156 weeks j) 730 days

9. a) 6 h b) 5 h c) 5 h 15 min d) 7 h 30 min e) 8 h 40 min f) 10 h 35 min

10. a) (ii) 2016 (iv) 2020 (vi) 2024 b) 2024

11. Please complete your project works and compare your outcomes with the outcomes of your friends.

Then show to your teacher.

Exercise - 10.2

Section B

3. a) 4 h 5 min b) 6 h 25 min c) 2 h 50 min d) 2 h 30 min e) 4 years 1 months f) 8 years 7 months
g) 2 years 11 months h) 3 years 7 months i) 10 months 15 days j) 4 months 25 days

4. a) 9 : 15 a. m. b) 7 : 20 p. m. c) 1 : 10 p. m. d) 4 : 30 p. m. e) 5 : 45 a. m. f) 1 : 35 p. m.

g) 8 : 20 a. m. h) 8 : 00 a. m. 5. a) 5 : 30 p. m. b) 12 : 15 p. m. c) 7 : 15 a. m. d) 10 : 30 a. m.

e) 11 : 40 a. m. 6. a) 5 h 15 min b) 3 h 45 min c) 40 min d) 2 h 45 min

7. a) 45 min b) 1 h 15 min c) 3 h 30 min d) 13 h 40 min 8. a) 9 h 55 min b) 12 : 45 p. m. c) 14 h 45 min

9. a) 1 year 5 months 10 days b) 11 months 9 days c) Please find how old are you today?

10. a) 4 h 30 min b) (i) 2 h 40 min (ii) 11 : 45 a. m. c) 52 h 30 min d) 6 month 15 days

11. a) 45 min b) 6 h 30 min c) 52 weeks 1 day d) 2 months 10 days

12. Please complete your project works and compare your outcomes with the outcomes of your friends.
Then show to your teacher.

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Exercise - 10.3

Section B

3. a) Rs 28.10 b) Rs 91.20 c) Rs 29.85 d) Rs 59.85 e) Rs 186 and 40 p or Rs 186.40

f) Rs 1,065 and 40 p or Rs 1,065.40 g) Rs 324 and 65 p or Rs 324.65 h) Rs 349 and 95 or Rs 349.95

4. a) Rs 21.20 b) Rs 49.50 c) Rs 47.00 d) Rs 129.00 e) Rs 273.00 f) Rs 20.15

g) Rs 16.10 h) Rs 16.75 i) Rs 30.05 5. a) (i) Rs 156.25 (ii) Rs 343.75 b) (i) Rs 332.70

(ii) Rs 667.30 c) (i) Rs 329.70 (ii) Rs 2,307.90 6. a) Rs 147 b) Rs 363 c) Rs 3.45 d) Rs 110.50

7. Please complete your project works. Compare your findings with the findings of your friends. Then show
to your teacher.

Exercise - 10.4

Section B

2. Prepare the bills yourself and compare with the bills prepared by your friends. Then show to your
teacher.

3. a) Answer the questions yourself and show to your teacher.

b) Prepare the budget yourself and compare with the budgets of your friends. Then show to your teacher.

4. Please complete your project works and discuss about your outcomes in the class. Then show to your
teacher.

11. Algebra - Algebraic Expressions

Exercise - 11.1

Section B

7. Answer the questions yourself and discuss in the class. Then show to your teacher.

8. a) x + 2y b) 3a – b c) 6pq d) x+y e) 2 × (l + b) f) 3 × (m – n)
2
9. a) (x + 5) years b) (y – 2) years c) (x – 7) years d) 4y years e) x + 5 f) p – 4 g) 2x + 3

10. a) (i) 7 (ii) 7 (iii) 4 (iv) 1 b) (i) 10 (ii) 8 (iii) 2 (iv) 6

c) (i) 10 sq. cm (ii) 24 sq. cm (iii) 70 sq. cm d) (i) 14 cm (ii) 25 cm (iii) 26 cm

e) (i) 40 cu. cm (ii) 90 cu. cm (iii) 864 cu. cm

11. a) (i) 4y, 8 (ii) 3y, 6 b) (i) 2a, 6 (ii) 5a, 15 12. a) 10 units b) 17 units c) 12 units

13. Please complete your project works and compare with the project works of your friends. Then show to
your teacher.

Exercise - 11.2

Please actively take part in the classwork and show the best performance.

Exercise - 11.3

Section B

8. a) 5x b) 2x2 c) 6y d) 4y2 e) 2ab f) 7xy g) 2p2q2 h) 3a2b2
i) 3x j) x2 k) 5y l) 2y2 m) 3xy n) ab o) 7a2b2 p) 3p2q2

9. a) 2x + 5 b) 2x2 + 4 c) 3y + 10 d) 4y2 + 3 e) 5a + 4b
h) 8p2 + 11 i) 3x + 4y + 7 j) 5a + 6b + 7
f) 5a2 + 3b2 g) 5p + 14

10. a) 2x + 3 b) 3x2 + 2 c) y + 3 d) 2y2 + 3 e) 5a – 6

f) 3p2 – 1 g) 2x + y + 3 h) 2a + 3b + 1 i) p + 2q – 3r j) x – y – z

11. a) 2x + 2 b) 3x2 – 2 c) 2y + 3 d) 5x + 3y e) 2a2 – 3b2 f) x2 – y2 g) 4x2 + 3x + 4 h) 3a2 – 2a – 7

12. a) 2x b) 4a2 c) p + 1 d) 2x + 2 e) 2a f) 3p2 g) 2x + 2

13. a) (2x + 9) cm, 15 cm b) (4x + 12) cm, 24 cm c) (2x + 8) cm, 14 cm

14. Please completer your project works and compare with the project works of your friends .Then show to
your teacher.

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Exercise - 11.4

Section B

5. a) x2 b) a2 c) y2 d) 4x2 e) x3 f) p3 g) 8m3 h) 27x3

6. a) 6x2 b) 12y2 c) 8a2 d) –6p e) –10x2 f) x2 g) 2y2 h) –15ab

i) –9xy j) 12pq k) 3b3 l) –5x3 7. a) 2x + 4 b) –2x – 4 c) –2x + 4 d) x2 + 3x

e) –x2 – 3x f) –x2 + 3x g) 2a2 + 8a h) –2a2 + 8a i) 3y2 – 6y j) x2 + xy k) x2 – xy l) –x2 + xy

8. a) x2 + 3x + 2 b) y2 + 3y + 2 c) p2 + p – 2 d) a2 + 2a – 3 e) x2 – 2xy + y2 f) a2 – b2

9. a) x2 + 3x + 2 b) x2 + 5x + 6 c) a2 + 7a + 12 d) y2 + 8y + 15 e) a2 + 2ab + b2 f) a2 – b2
g) a2 – 2ab + b2 h) p2 – 4p + 4 i) 2x2 – 5x – 3 j) 2y2 – 7y + 6 k) 2p2 + pq – q2 l) x2 – 3xy + 2y2

10. a) (9x2) cm2 b) (x2 + 4x + 4) cm2 c) (6x2) cm2 d) (a2 + 4a + 3) cm2

11. a) (25a2) m2 b) (x2 + 6x + 9) m2 c) (12a2) m2 d) (x2 + 8x + 15) m2 e) (64 x3) cm3 f) (125 x3) m3

12. Please complete your project works and compare with the project works of your friends. Then show to
your teacher.

Exercise - 11.5

Section B

3. a) 2x b) 2y c) 3y d) 2a2 e) 2a f) 2 g) 4a h) 3x2 i) 3x
j) 3 k) 4p2 l) 3p m) 2 n) 3xy o) 5xy p) 7a2b2
q) 2a2b2 r) 7ab

s) 2ab t) 2 4. a) 2x + 6 b) 2x – 6 c) –3x – 6 d) –3x + 6 e) a2 + 5a

f) –a2 + 5a g) 4y2 – 6y h) –9y + 6y2 i) 7x + 4 j) 3x – 4 k) 3x + 4 l) 3p

m) 2b n) 6y o) x + y 5. a) x + 1 b) 2a – 7 c) 2y d) –2b

6. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

12. Algebra- Equation

Exercise - 12.1

Section B

7. a) x = 4 b) x = 1 c) y = 5 d) y = 3 e) a = 2 f) a = 2 g) x = 2 h) y = 4

8. a) x = 3 b) x = 5 c) p = 10 d) a = 9 e) y = 11 f) y = 3 g) x = 6 h) a = 6

9. a) x = 1 b) a = 1 c) y = 3 d) p = 2 e) x = 4 f) y = 2 g) a = 4 h) x = 2

10. a) x = 2 b) a = 6 c) y = 12 d) x = 3 e) a = 4 f) y = 10 g) x = 12 h) x = 6

11. a) x = 4 b) x = 9 c) y = 4 d) a = 9 e) x = 8 f) a = 3 g) x = 4 h) x = 10

12. a) x = 1 b) x = 8 c) y = 3 d) y = 2 e) x = 0 f) a = 8 g) y = 1 h ) x = 6

13. a) x = 2 b) x = 4 c) x = 2 d) x = 4 e) x = 2 f) x = 6 g) x = 2 h) 4

14. a) x = 6 b) x = 12 c) x = 5 d) x = 3 e) a = 3 f) a = 9 g) y = 6 h) x = 6

15. a) x = 2 b) x = 2 c) x = 2 16. a) x = 5 cm b) x = 3 cm, 2x = 6 cm

17. a) x = 6 cm b) x = 2 cm, 2x = 4 cm c) 2x = 4 cm, 3x = 6 cm

18. Please complete your project works and compare with the project works of your friends. Then show to
your teacher.
Exercise - 12.2

Section B

3. a) x = 11 b) y = 20 c) a = 9 d) p = 24 e) x = 7 f) y = 27 g) x = 12 h) y = 18 i) p = 18 j) x = 12

4. a) 12 b) 27 c) 9 d) 50 e) 24 f) 28

5. a) 18 b) Rs 15,500 6. a) 14 b) Rs 34 c) 14 years d) 33 e) Rs 275

7. a) 4 cm b) 10 m c) 25 m d) 25 m 8. a) 12, 24 b) 120, 240 c) 15 years d) Rs 60

9. a) 76 km b) 165 km c) 2,000 l d) Rs 30,000

10. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

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13. The metric Measurement System

Exercise - 13.1

Section B

4. a) 34 mm b) 85 mm c) 5.7 cm d) 9.3 cm e) 150 cm f) 325 cm g) 2.18 m h) 4.7 m i) 1350 m

j) 2200 m k) 4.675 km l) 7.8 km

5. a) 0.1 cm, 0.4 cm, 2.5 cm, 6 cm, 13.6 cm b) 0.01 m, 0.05 m, 0.48 m, 0.8 m, 2.64 m

c) 0.001 km, 0.003 km, 0.058 km, 0.07 km, 0.645 km

6. a) 2 mm, 5 mm, 38 mm, 40 mm, 122 mm b) 1 cm, 7 cm, 25 cm, 70 cm, 350 cm

c) 1 m, 9 m, 36 m, 60 m, 800 m

7, 8, 9 and 10 Please complete your project works and compare with the project works of your friends. Then

show to your teacher.

Exercise - 13.2

Section B

5. a) 31 cm 5 mm or 31.5 cm b) 26 m 20 cm or 26.2 m c) 15 km 425 m or 15.425 km

d) 11 cm 7 mm or 11.7 cm e) 13 m 65 cm or 13.65 m f) 5 km 750 m or 5.75 km

6. a) 17.4 cm b) 12.51 m c) 13.42 km d) 7.6 cm e) 17.84 m f) 11.69 km

7. a) 12 cm 9 mm or 12.9 cm b) 18 m c) 10 km 800 m or 10.8 km d) 1 cm 6 mm or 1.6 cm

e) 1 m 20 cm or 1.2 m f) 3 km 185 m or 3.185 km

8. a) 22.4 cm b) 14.25 m c) 17.25 km d) 1.2 cm e) 2.41 m f) 780 m

9. a) 18 cm 5 mm (18.5 cm) b) 10.05 m c) 1 m 60 cm (1.6 m) d) 3 cm 8 mm (3.8 cm)

e) (i) 12 km 625 m (12.625 km) (ii) 1 km 125 m (1.125 km) (iii) 4 km 600 m (4.6 km)

10. a) 11 cm 2 mm (11.2 cm) b) 5.95 m c) 20.58 km d) 53.2 km

11. a) 1 cm 7 mm (1.7 cm) b) 15 cm c) 30 d) 8 km 500 m (8.5 km) e) 15.4 km

12. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 13.3

Section B

5. a) 1250 mg b) 3425 mg c) 1375 g d) 2560 g e) 2.115 g f) 7.78 g g) 3.42 kg h) 5.9 kg

6. a) 15 kg 200 g (15.2 kg) b) 33 kg 760 g (33.76 kg) c) 5 kg 600 g (5.6 kg) d) 7 kg 690 g (7.69 kg)

e) 16 kg 500 g (16.5 kg) f) 37 kg 600 g (37.6 kg) g) 1 kg 370 g (1.37 kg) h) 1 kg 400 g (1.4 kg)

7. a) (i) 6 kg 250 g (6.25 kg) (ii) 2 kg 750 g (2.75 kg) b) (i) 34 kg 30 g (34.03 kg)

(ii) 2 kg 470 g (2.47 kg) c) (i) 8 kg 850 g (8.85 kg) (ii) 66 kg 650 g (66.65 kg) d) 1 kg 790 g (1.79 kg)

8. a) 9 kg 450 g (9.45 kg) b) (i) 5.4 kg (ii) 5.95 kg c) (i) 2.7 kg (ii) 225 g

9. a) 13 g 300 mg (13.3 g) b) 190 g c) 2 kg 200 g (2.2 kg)

10. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 13.4

Section B

3. a) 1125 ml b) 2250 ml c) 1.475 l d) 3.5 l e) 345 ml f) 1700 ml g) 1.3 l h) 2.8 l

4. a) 13 l 300 ml (13.3 l) b) 25 l 320 ml (25.32 l) c) 4 l 900 ml (4.9 l) d) 11 l 750 ml (11.75 l)

e) 14 l 400 ml (14.4 l) f) 31 l 500 ml (31.5 l) g) 1 l 400 ml (1.4 l) h) 1 l 300 ml (1.3 l)

5. a) (i) 14 l 100 ml (14.1 l) (ii) 800 ml b) (i) 6 l 250 ml (6.25 l) (ii) 1 l 250 ml (1.25 l)

c) 15 l 500 ml (15.5 l)

6. a) 1 l 500 ml (1.5 l) b) 1 l 800 ml (1.8 l) c) 10 l 500 ml (10.5 l) d) 2 l 200 ml (2.2 l)

7. a) 360 ml b) 7 jars c) 200 packets d) 12 days e) (i) 15 l 400 ml (15.4 l) (ii) 140 cups

8. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

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14. Perimeter, Area and Volume

Exercise - 14.1

Section B

2. a) 12 cm b) 13.5 cm c) 20 cm 3. a) 14 cm b) 12 cm c) 11 cm d) 8 cm

4. a) (i) 21 cm (ii) 18 cm b) (i) 18 cm (ii) 28 cm c) (i) 28 cm (ii) 34.8 cm

5. a) (i) 81 m (ii) 243 m b) (i) 190 m (ii) 380 m 6. a) (i) 140 m (ii) 560 m b) (i) 200 m

(ii) 1000 m c) (i) 160 m (ii) 480 m 7. a) 50 m b) (i) 180 m (ii) 45 m c) 5 cm d) 80 m

8. a) (i) 4 (ii) 4 m, 8 m b) 20 m, 60 m c) 10 m, 5 m d) 12 cm, 4 cm

9. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 14.2

Section B

4. Answer the questions yourself and discuss in the class. Then show to your teacher.

5. a) 300 cm2 b) 36 cm2 c) 3500 cm2 d) 324 cm2 6. a) 27 cm2 b) 64 cm2 c) 37 cm2

d) 82 cm2 e) 144 m2 f) 187.2 m2 7. a) b = 5 cm b) l = 4 cm c) l = 9 cm

8. a) 1080 m2 b) 3 m2 c) 48 m2, 48 m2 d) 5625 m2 e) 225 m2 9. a) 7 cm b) 40 m c) 9cm d) 8 m

10. a) (i) 7 cm (ii) 49 cm2 b) 400 m2 c) (i) 6 cm (ii) 54 cm2 d) (i) 3 m (ii) 4.5 m2

11. a) 56 cm2 b) 28 m2 c) 24 cm2

12. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 14.3

Section B

2. a) 26 kattha b) 52 kattha c) 28 dhur d) 70 dhur e) 25 aana f) 36 aana

g) 1 bigha 5 kattha h) 2 bigha 15 kattha i) 1 ropani 4 aana j) 2 ropani 10 aana

3. a) (i) Rs 22,500 (ii) Rs 1,35,000 b) (i) Rs 20,000 (ii) Rs 1,60,000

c) (i) Rs 5,00,000 (ii) Rs 15,00,000 d) (i) Rs 4,80,000 (ii) Rs 19,20,000

4. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 14.4

Section B

4. Answer the questions yourself and discuss in the class. Then show to your teacher.

5. 21 cm3 b) 27 cm3 c) 27 cm3 6. a) 27 cm3 b) 39 cm3 c) 64 cm3 d) 30 cm3

7. a) 3,375 cm3 b) 8,050 cm3 c) 36,000 cm3 8. a) 27 cm3 b) 64 cm3 c) 125 cm3

d) 216 cm3 e) 512 cm3 f) 1,000 cm3 g) 1,728 cm3 h) 8,000 cm3 9. a) 30 cm3 b) 78 cm3

c) 150 cm3 d) 90 cm3 e) 168 cm3 f) 3 m3 g) 32 cm3 h) 2 m3 10. a) 729 cm3, 729 cm3

b) 512 cm3, 512 cm3 c) 600 cm3, 600 cm3 d) 2,160 cm3 11. a) 6 cm b) 3 cm c) 6 cm d) 2 cm

12. Please complete your project works and compare with the project works of your friends. Discuss in the

class and show to your teacher.

15. Geometry - Line and Angle

Exercise - 15.1

Section B

8. Answer the questions yourself and discuss in the class. Then show to your teacher.

h) x° = 55° i) y° = 70° j) p° = 105°

9. Construct the given angles and show to your teacher. 10. Follow the instructions and complete the

constructions. Then show to your teacher. 11. Show to your teacher.

12. Please complete your project works and demonstrate in your class. Then show to your teacher.

Exercise - 15.2

Section B

4. Answer the questions and discuss in the class. Then show to your teacher.

5. Answer the questions and discuss in the class. Then show to your teacher.

6. a) (i) 50° (ii) 35° (iii) 60° (iv) 15° b) (i) 130° (ii) 90° (iii) 70° (iv) 30°

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Answers

c) (i) 120° (ii) 100° (iii) 75° (iv) 45° 7. a) x° = 40° b) y° = 150° c) z° = 40°

8. a) x° = 50° b) x° = 20° c) x° = 115° d) x° = 30° e) y° = 50° f) y° = 20°

9. a) p° = 110° b) x° = 105° c) y° = 60° d) x° = 90° e) y° = 110° f) x° = 50°

g) x° = 90°, y° = 45° h) x° = 90°, y° = 40° i) x° = 30°, 2x° = 60°

10. a) x° = z° = 100°, y° = 80° b) p° = r° = 75°, q° = 105° c) a° = c° = 135°, b° = 45°

d) x° = 90°, y° = 120° e) a° = 110°, b° = 30° f) x° = 40°, y° = 140°, z° = 130°

11. Please complete your project works and compare with the project works of your friends. Discuss in the

class and show to your teacher.

Exercise - 15.3

Section B

3. Answer the questions and discuss in the class. Then show to your teacher.

4. Answer the questions and compare with the answers of your friends. Then show to your teacher.

5. a) x° = 70° b) a° = 60°, 2a° = 120° c) y = 40° d) x = 20° e) a = 65°

6. a) x° = 110° b) y° = 60°, x° = 120° c) x° = 45°, z° = 45°, y° = 135° d) x° = 140°

e) a° = 75° f) y° = 60° g) x° = 60°, y° = 60° h) p° = 35°

i) x° = 65° j) a° = 110° k) x° = 125°, y° = 55° l) p° = 100°, q° = 80°

7. a) a° = b° = 65° b) x° = y° = 120° c) a° = b° = 40°, c° = d° = 140°

d) w° = x° = y° = 130°, z° = 50° e) a° = b° = c° = 70°, d° = 110° f) x° = y° = w° = 85°, z° = 95°

8. a) a° = c° = 60°, b° = 120° b) x° = y° = z° = 105° c) a° = b° = c° = 110°, d° = e° = 70°

9. Prove the relations yourself and compare with the works of your friends. Then show to your teacher.

10. Please complete your project works and demonstrate in the class. Then show to your teacher.

16. Geometry - Plane Shapes

Exercise - 16.1

Section B

5. Answer the questions yourself and discuss in the class. Then show to your teacher.

6. a) x° = 50° b) a° = 30° c) y° = 35° 7. a) x° = 50° b) a° = 40° c) p° = 70°

8. a) x° = 35° b) a° = 40° c) y° = 85° d) y° = 50°, x° = 80° e) a° = 55°, b° = 70° f) x° = y° = 48°
g) x° = y° = 45° h) a° = 30°, 2a = 60° i) x° = 30°, 2x° = 60°, 3x° = 90° 9. a) x° = 75°, y ° = 60°
b) a° = 80°, b° = 40° c) x° = y° = 60°, z° = 60° d) a° = b° = 50°, c° = 80° e) x° = 80°, y° = z° = 50°
f) p° = 40°, q° = 50° 10. a) x° = y° = 50°, z° = 80° b) a° = b° = 55°, c° = 70° c) x° = 70°, y° = z° = 55°
d) a° = 60°, b° = c° = 60° e) x° = 30°, y° = 40° f) a° = b° = 65°, c° = 50° g) x° = a° = 70°, z° = 40°
h) a° = 50°, b° = 60°, c° = 70° i) x° = 105°, y° = 45°, z° = 30°

11. Please complete your project works and compare with the project works of your friends. Then show to

your teacher.

Exercise - 16.2

Section B

4. Answer the questions yourself and discuss in the class. Then show to your teacher.

5. a) x° = 60° b) y° = 50° c) x° = y° = 45° d) x° = 60°, y° = z° = 120°

e) a° = 110°, b° = c° = 70° f) x° = 55°, y° = z° = 125° 6. a) x° = 60° b) a° = 110° c) y° = 50°

d) x° = 70°, 2x° = 140° e) a° = 45°, 2a° = 90°, 3a° = 135° f) x° = 36°, 2x° = 72°, 3x° = 108°, 4x° = 144°

7. a) z° = 50° b) 40°, 80°, 80°, 160° 8. Please complete your project works and compare with the

project works of your friends. Discuss in the class and show to your teacher.

17. Statistics
Exercise - 17.1
Section B
3. Answer the questions yourself and discuss in the class. Then show to your teacher.
c) 5 : 00 p. m. d) 6 : 55 a. m. e) 12 h 45 min
4. Complete your works. Discuss in the class and show to your teacher.

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Answers

Exercise - 17.2

Section B

4. Answer the questions and compare with the answers of your friends. Discuss in the class and show to

your teacher.

5. Please complete your project works individually or in a group. Discuss the outcomes in the class and

show to your teacher.

Exercise - 17.3

Section B

3. Answer the questions yourself and discuss in the class. Then show to your teacher.

4. a) rises by 16.2° C and falls by 7.7° C b) 46.3° C c) 78.3° C d) cooled down by 18.6° C

e) 2.9° F

5. Please complete your project works and compare with the project works of your friends. Then discuss in

the class and show to your teacher.

Exercise - 17.4

Section B

6. Answer the questions yourself and discuss in the class. Then show to your teacher.

7. Answer the questions and show to your teacher.

8. a) P (1, 3), Q (4, 4), R (2, 8), A (8, 2), B (9, 5), C (6, 8), D (5, 5)

b) E (3, 2), F (5, 2), G (6, 4), H (4, 6), I (2, 4), N(7, 3), E(10, 3), P(8, 6), A(10, 6), L(7, 9)

9. Plot the points in the squared graphs. Then get the following shapes.

a) Right-angled triangle ABC b) Triangle DEF c) Square PQRS d) Rectangle KLMN

e) NEPAL, shape of national flag of Nepal.

10. a) Please perform the given activities in the class and discuss about the outcomes.

18. Set

Exercise - 18.1
Section B
3. Answer the questions yourself and discuss in the class. Then show to your teacher.
4. Show the members of the given sets in diagrams and compare with the answer of your friends. Then

show to your teacher.

5. a) P = {Mercury, Venus, Earth, Mars} b) A = {x, If, q, 1} c) W = {0, 1, 2, 3, 4} d) C = {1, 8, 27, 64}

6. a) A = {the first five letters of English Alphabets} b) B = {odd numbers less than 10}

c) C = {the first five multiples of 4} d) D = {factors of 10}
7. a) A = {1, 2, 3, 4, 5, 6, 7, 8, 9} b) B = {2, 4, 6, 8}
d) D = {1, 2, 3, 4, 6, 12}
c) C = {1, 4, 9, 16, 25, 36, 49} b) Q = {x : x is a natural number less than 5}
8. a) P = {x : x is a whole number less than 5}

c) R = {x : x is a multiple of 3 less than 16} d) S = {x : x is a factor of 18}

9. Please complete your project works and discuss in the class. Then show to your teacher.

Exercise - 18.2

Section B

3. Answer the questions yourself and discuss in the class. Then show to your teacher.

4. a) A = { }, empty or null set b) B = {1}, unit or singleton set

c) C = {January, June, July}, finite set d) D = {14}, unit or singleton set

e) E = {2, 5}, finite set f) F = { }, empty set

5. Please complete your project works and compare with the project works of your friends. Then discuss in

the class and show to your teacher.

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Evaluation Model

Group A (10 × 1 mark = 10 marks)

1. Tick the correct answers.

a) How many billions are there in 2 arab?

(i) 20 billion (ii) 2 billion (iii) 200 billion

b) Which one is the prime number in the following numbers?

(i) 91 (ii) 95 (iii) 97

c) What is the quotient of 72000 ÷ 900?

(i) 80 (ii) 800 (iii) 8

d) What is the lowest common multiple of 15 and 20?

(i) 5 (ii) 60 (iii) 120

e) Which one is the improper fraction equal to the mixed number 535 ?
13 75 28
(i) 5 (ii) 5 (iii) 5

f) What is the difference of 0.5 – 0.05?

(i) 0.45 (ii) 0.55 (iii) 0

g) What is the value of 20% of Rs 20?

(i) Rs 2 (ii) Rs 4 (iii) Rs 40

h) What is the product of 2x × x?

(i) 3x (ii) 3x2 (iii) 2x2

i) What is the sum of 4 cm 5 mm and 5 mm?

(i) 5.0 cm (ii) 9.5 cm (iii) 4.5 cm

j) What is the complement of 36°?

(i) 90° (ii) 54° (iii) 180°

Group B (25 × 2 marks = 50 marks)

2. a) The population of a country is three crore 7 lakh ten thousand seven hundred
eighty-six.

(i) Re-write the population in numeral
(ii) Round off the population to the nearest thousand.

b) Write the numeral 70020531 in the expanded form.

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Evaluation Model
3. a) Write the correct number in the blank spaces and find the product or quotient.

(i) ........... times ........... dots = ........... × ........... = ...........

(ii) ....... dots are shared in ....... groups = ....... ÷ ....... = .......

b) Find the square root of 324 by factorisation method.
c) Find the L.C.M. of 24 and 36 by division method.

4. Simplify:

a) 2 + 4 – 1 b) 3 ÷ 9
9 9 9 5 10

5. a) Find the product of 3.2 × 8 b) Find the quotient of 1.5 ÷ 0.3

6. a) Convert 7 kg 300 g into the decimal of kilograms. b) Add: 45 m 75 cm + 20 m 55 cm

c) Express:

(i) 6 : 45 p. m. in 24 hour-clock system. (ii) 22 : 30 hour in 12 hour-clock system.

7. a) Add: (3x + 2y) + (x + y) b) Subtract: 2a – 3 from 5a – 7.

8. Solve:

a) 3x – 5 = 4 b) 2x + 2 +1 = 3.
3

9. a) Find the perimeter of a square which is 9 cm long.

b) Find the area of a rectangle which is 12 cm long and 8 cm broad.

c) Find the ratio of 2 m to 75 cm.

10. a) Find the volume of the given solids.

(i) (ii)

b) A solid box is 15 cm long, 6 cm wide and 2 cm high. How much water does it
displace when it is immersed into water?

11. Construct the angles a) 75° b)120° by using a protractor.

12. Find the unknown angles represented by the letters.

a) b)

x° a° 65°

30°

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Evaluation Model

Group C (10 × 4 marks = 40 marks)

13. Simplify:

(i) 18 – 10 × {4 + (12 – 7)} ÷ 18 (ii) 4 – 2 3 + 1 3
4 8

14. a) Rewrite the following sets in listing method.

(i) A set of prime numbers less than 10. (ii) F = {x : is a factor of 18}.

Y

10

b) Write the coordinates of the vertices of the shape given 9
in the squared graph.
8D C
7

6

5

4 B
3
2A

1

O 1 2 3 4 5 6 7 8 9 10 X

15. Draw a bar graph to show the information given in the table.

Class I II III IV V
No. of Students 30 25 35 20 15

16. If the cost of 5 kg of rice is Rs 525, find the rate of cost of rice. Find the cost of 9 kg
of rice.

17. A stationer buys a story book for Rs 250 and sells it for Rs 300. Find his profit and
profit percent.

18. The perimeter of a rectangular garden of length 60 m is 200 m. Find the area of the
garden.

19. Find the greatest number that divides 16 and 24 without leaving a remainder.

20. There are 450 students in a school and 60% of them are girls. Find the number of
boys.

21. The cost of a mobile is 2 times and Rs 500 more than the cost of a watch. If the cost
of the mobile is Rs 4,500, find the cost of the watch by making an algebraic equation.

22. Find the unknown angles represented by the letters. x°

80°
50° y°

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