Math 3

7. Keep the following objects in the given graph (1 cm) and trace its
outline. Estimate the area.

Number of unit squares =

Area = square cm.

Number of unit squares =

Area = square cm.

Number of unit squares =

Area = square cm.

Number of unit squares =

Area = square cm.

Mathematics 3 Approved by CDC 251

Unit Revision Test

1. What is the area of the followings.
1cm 1cm

Area = cm2 squares
Area = + + +

= cm2

2. Count the squares each of 1cm2 and write the area.

Area = cm2 Area = cm2

3. Find the area of the following figures. (Each square is 1 sq. unit)

Area = Area =

4. Complete the unit squares by taking 1 cm length for each parts. Also
find the area of your school diary by tracing outline on the graph.

252 Approved by CDC Mathematics 3

9Unit

ADDITIONAL CHAPTER

Estimated periods - 12

Objectives

At the end of this unit, students will be able to:
keep the elements of a set in { }.
list the elements of a set.
count, add and write the numbers.
suppose the numbers with variable 'x' and can calculate.

Teaching Materials

Chart of days of the week
Chart of months of the year
Chart of letters of Devanagari

Activities

It is better to:
ask the students to write 7 days of the week in a set notation { }.
ask the students to make a list of members of his/her family and teach
them to keep them in set notation.

Mathematics 3 Approved by CDC 253

9.1 Set

See, feel and lean.

It is a collection of animals
It is a set of animals

belongs to the set.

is a member of the set.

doesn’t belong to the set.

is not a member of the set.

It is a collection of to the set. Mathematics 3
It is a set of of the set.
to the set.
is of the set.

is Approved by CDC

254

It is a collection of to the set.
It is a set of of the set.
to the set.
is of the set.

is

It is a collection of to the set. 255
It is a set of of the set.
to the set.
is of the set.

is Approved by CDC
Mathematics 3

It is a collection of
It is a set of

to the set.

is of the set.

to the set.

is of the set.
∴ Thus, set is a collection of well defined objects.

Member of sets

See, feel and learn.

It is a set of fruits.

Banana is a member of the set.
Grapes is a member of the set.
Apple is a member of the set.
Pineapple is a member of the set.
∴ A = {Banana, Grapes, Apple, Pineapple}.

We use capital letters A, B, C, ….. to denote the set.

B = the set of days of the week
= {Sunday, Monday,Tuesday, Wednesday,Thursday, Friday, Saturday}

C = Set of any four months of English year.
= {January, March, April, November}

Thus, to denote the sets, capital letter of English alphabet are used.
The members are written inside { }.
The members of the set are separated by comma.
Denoting the set, writing the members within { } is called the listing method.

256 Approved by CDC Mathematics 3

See, feel and do.

A. Write the members of the following sets.

A = {Set of any four days of the English week.} , }
}
= { , , }
}
B = {Set of any four birds} }
}
= { , , , }
}
X = {Set of any four fruits.}

= { , , ,

D = {Set of any four animals.}

= { , , ,

V = {Set of English vowel letters.}

= {

E = {Set of first six Nepali months in a year.}

= {

F = {Set of any six zones of Nepal.}

= {

H = {Set of even numbers less than 15.}

= {

B. Write ‘T’ for true and ‘F’ for false for the following statements.

4 is a member of the set of odd numbers.
Apple is a member of the set of vegetables.
Radish is a member of the set of vegetables.
Car is a member of the set of vehicles.
January is a member of the set of the months of English year.

Mathematics 3 Approved by CDC 257

9.2 Algebra

See, feel and lean.

Observe the following examples. What number should you
write in the box to make the
6 + ? = 10
sum 10?
If we write 1,
6 + 1 = 7, which is not true.
Similarly,
6 + 2 = 8, which is not true.
6 + 3 = 9, which is not true
6 + 4 = 10, which is true.

What number should you write in
the box to make the sum 10?

So, guessing is very
important in such type of

problem.

Similarly,
12 – ? = 8

What number should you
write in the box to get the

difference 8?

Guess, if we write 1, 2, 3, 4………… then

12 – 1 = 11, which is not true.

12 – 2 = 10, which is not true.

12 – 3 = 9, which is not true. ∴ The required number in
12 – 4 = 8, which is true. the box is 4.

258 Approved by CDC Mathematics 3

See, feel and do.

A. Fill in the boxes by inspection method or hit and trail method:

8 + = 12 + 16 = 30 − 25 = 22

25 + 14 = 32 + = 37 31 − = 25

9 + = 15 + 18 = 27 − 22 = 10

10 + 7 = −8=7 42 − = 31

27 + = 32 28 − = 18 33 – 21 =

B. Find the value of the letters by inspection method or hit and trail
method:

x+3=9 y + 4 = 15 y − 3 = 16 y + 2 = 14

∴x= ∴y= ∴y= ∴y=

x + 9 = 18 y + 20 = 28 17 – y = 4 12 − y = 3
∴x= ∴y= ∴y= ∴y=

x + 12 = 19 x − 6 = 14 Z – 9 = 17 7 + 9 = 14
∴x= ∴x= ∴z= ∴y=

9 + x = 27 x−7=4 36 − z = 12 y − 4 = 11
∴x= ∴x= ∴z= ∴y=

y + 14 = 16 x − 8 = 14 x + 8 = 18 x + 42 = 46
∴y= ∴x= ∴x= ∴x=

28 + y = 32 22 − x = 10 38 − x = 10 x − 3 = 12
∴y= ∴x= ∴x= ∴x=

Mathematics 3 Approved by CDC 259

Addition and subtraction of the same letters

See, feel and learn.

(i) How many pens are there?
(ii) How many balls are there?
(iii) How many pencils are there?
(iv) How many books are there?
(v) How many erasers are there?
(vi) How many sharpener are there?

x ya a x y a b c
zb z c x y a
b

(i) How many x are there in the box ?

(ii) How many a are there in the box ?

(iii) How many z are there in the box ?

(iv) How many c are there in the box ?

(v) How many d are there in the box ?

(vi) How many y are there in the box ?

(vii) How many b are there is the box ?

2 pencils and 3 pencils = 2 pencils + 3 pencils = 5 pencils

2x and 3x = 2x + 3x = 5x,
∴ Here x denotes pencils

260 Approved by CDC Mathematics 3

D. Add the following as in above example:

3 pens and 2 pens = pens + pens = pens
3x and 2x = x
x + x =

4 mangoes and 3 mangoes = mangoes + mangoes = mangoes
4x and 3x = x
x + x =

5 balls and 4 balls = balls + balls = balls
5y and 4y = y
y + y =

6 eggs and 7 eggs = eggs + eggs = eggs
6y and 7y = y
y + y =

7 apples and 5apples = apples + apples = apples
7a and 5a = a
a + a =

E. Perform the following task:

x + 2x = 2x + 4x = 5x + 4x =
7x + 3x = 4y + 3y = 14y + 6y =
10z + 6z = 5z + 12z = x + 3x + 4x =
3x + 7x+ 9x =
2y + 5y + 7y = 2a + 4a + 5a =

10x + 3x + 2x = 4y + 7y + 3y =
9a + 3a + 2a = 4b + 6b + 7b =

F. Study and learn:

Subtract 4 pens from 9 pens = 9 pens – 4 pens
= 5 pens

Similarly, subtract 4x from 9x = 9x − 4x
= 5x, here x denotes pens.

Mathematics 3 Approved by CDC 261

G. Subtract the following as in above example:

2 apples from 7 apples = apples − apples = apples
2x from 7x = x
x − x =

4 pencils from 12 pencils = pencils − pencils = pencils
4x from 12x = x
x − x =

5 sweets from 9 sweets = sweets − sweets = sweets
5a from 9a = = a
a − a

7 bananas from 15 bananas = bananas − bananas = bananas
7z from 15z = z
z − z =

6 breads from 18 breads = breads − breads = breads
6y from 18y = y
y − y =

H. Perform the following task: 12 y 22 z 12 a
+30 y +34 z +15 a
4x 8x 3x 5y
+3 x +5 x + 6 x +7 y 19 y 49 y 61 z
−13 y −27 y −30 z
7x

7 x 5 x 9 x 14 y
−3 x −2 x −7 x −6 y

See, feel and do.

If x = 3, y = 2, find the values of x + y and x − y.

x+y x−y

=3+2 =3−2

=5 =1

262 Approved by CDC Mathematics 3

I. Do the following as shown in the above examples.

If x = 2 and y = 5, then x + y = + =
If x = 3 and y = 7, then x + y = + =
If x = 7 and y = 9, then x + y = + =
If a = 12 and b = 5, then a + b = + =
If a = 22 and b = 17, then a − b = + =
If x = 5 and y = 12, then y – x = + =
If x = 17 and y = 11, then x – y = + =
If a = 30 and b = 12, then a – b = + =

See, feel and do.

Simplify (ii) 3a − 2b + 5a + 7b
= 3a + 5a + 7b − 2b
(i) 2x + 3x + 4x − 2x = 8a + 5b
= 9x − 2x
= 7x

J. Simplify as in above examples:

2x + 4x + 6x 3x + 5x − 2x 4x + 6x + 7x − 5x
= = =
= = =
3a − 2a + 7a − 4a
4y − 5y + 9y − 2y 2a − 3b + 7a + 5b =
= = =
= =
263
8x + 7y − 2x + 3y 4a + 9b − 2a − 3b
= =
= =

Mathematics 3 Approved by CDC

See, feel and do.

If a = 2, b = 5 and c = 6, find the value of:

(i) 2a + 3b (ii) 5a − 2b + 3c

Solution: (ii) 5a − 2b + 3c
(i) 2a + 3b = 5 × 2 − 2 × 5 + 3 × 6
= 2 × 2 + 3 × 5 = 10 − 10 + 18
= 4 + 15 = 28 − 10
= 19 = 18

K. Do the following:

If a = 2, b = 4, c = 6, x = 3 and y = 5, find the value of the following as in the
above examples:

(i) a + 3b − c (ii) 2a − 3b + 5c + x (iii) a + b − x + y

(iv) 3a + 2b − 2c + y (v) 3a − 4b + 2c + x (vi) a + b + 2c − y

(vii) 4a − 2a + 5b − x (viii) 4a − x + 2y (ix) 5a − 2b + 3c − x

264 Approved by CDC Mathematics 3