Maths Zone book 4 2077

5. List the members of the following sets within brackets.
a. A set of letters in the word 'apple'
b. A set of letters in the word 'Mathematics'
c. A set of letters in the word 'Missisippi'
d. A set of letters in the word 'Papaya'

6. Write the sets in diagrammatic method.
a. The set of eight alphabets.
b. The set of first five multiples of 3.
c. The set of days beginning with letter 'T'
d. The set of even numbers between 20 to 30.
e. A = {5, 10, 15, 20, 25}

7. A. Re-write the following sets in descriptive method.
a. b.

1 3

5 7 9

B. i. {ruler, compasses, protractor, setsquare}
ii. {Kantipur, Gorkhapatra, Annapurna post}
8.A. Re-write the following sets in listing method. and name

the sets.
a. b.

Jan, Feb
Mar, April

B. a. The set of first 4 planets.
b. The set of composite numbers less than 10.

Maths Fun

Draw the picture of any six flags of your favorite country and
color them and paste them in your book.

.................................................. ..................................................

.................................................. ..................................................

.................................................. ..................................................

Practice Zone

Group 'A'

Circle the correct option

1. Write whether each of the following collection are well-defined
or not.

a. The collection of handsome boys of your class.
b. The collection of colors of rainbow.
c. The collection of first five even numbers.
d. The collection of English alphabets.
2. Write 'T' for true and 'F' for false statements.
a. Tiger is the member of the set of wild animals.
b. 2 is the member of the set of prime numbers.
c. The earth is the member of the solar system.
d. January is the member of the set of days in weeks.

Group 'B'

1. Rewrite the following sets in listing method. Also write the name
of the sets.

a. The set of multiples of 4 less than 20.
b. The set of first 5 months of an English year.
2. Write the following sets in diagrammatic method
a. The set of first 5 prime numbers.
b. The set of first 5 letters of English Alphabet.
3. Rewrite the following sets in descriptive method.
a. A = {Triangle, Square, Rectangle, Parallelogram}
b. N = {2, 3, 5, 7, 11}

Answers of Unit 11

Exercise 11.1

1. Show to your teacher.
2. Well defined: a, d, g, h, Non-well defined: a, c, e f

Exercise 11.2

1. (a) {Sun, Mon, Tues} (b) {1, 2, 3, 4, 5}

(c) a, e, i, o, u}

B. (a) {Jan, Feb, Mar, April, may} (b) {2, 4, 6, 8, 10}

(c) {11, 13, 17, 19}

2. (a) {a, p l, e} (b) {m, a, t, h, e, i , c, s}

(c) {m, i, s, p} (d) {p, a, y}

3. a. T b. T c. F

d. F e. F

4.

a. b. c.
a e 3 6 Tuesday

i o u 9 12 15 Thursday

d. e.
20, 22
5, 10

24, 26, 28, 15, 20

30 25

5. A. (a) The set of domestic animals (b) The set of five odd numbers.
B. (a) The set of geometric instruments. (b) The set of notational magazine:
6. (a) M = {Jan, Feb, Mar, April}
(b) P = {Triangle, Square, Rectangle, Pentagon}
B. (a) P = {Mercury, Venus, Earth, mars}

(b) C = {4, 6, 8, 9}

12 Algebra

Specific Objective Prescribed by CDC

 To solve the addition and subtraction problems of including box notation
by inspection/hit and trial method.

Class Discussion
What are the numbers for the letters in the following number line?

0 1 2 3 4 a 6 7 b 9 10 c 12 d 14 15

Here, a = 5, b = ........, c = ........, d = ........

We use letter for number in Algebra. .................,
What will be the next three numbers? .................,
a. 2, 5, 8, 11, 14, ................., ................., .................,
b. 5, 10, 15, 20, 25, ................., .................,
c. 3, 6, 9, 12, 16, ................., .................,

Multiplying a letter by number

2+2+2+2+2=?
2 + 2 + 2 + 2 + 2 = 5 times 2 = 5 × 2
Similarly,
If x + x + x + x + x = ?
x + x + x + x + x = 5 times x = 5 × x = 5x

++

2 mango + 2 mango + 2 mango (2 is added three times)
= 3 × 2 = 6 mangoes
x mango + x mango + x mango (x is added 3 times)
= 3 × x = 3x mango
3x is 3 times x. 3 is called coefficient of x.
The unknown number x is called variable.
Short form of x + x + x = 3x, the expanded form of 3x = x + x + x.

Examples

Write in short form.
a. a + a + a + a + a + a = 6 × a = 6a

b. y + y + y + y = 4 × y = 4y
Write in expanded form.
a. 6x = x + x + x + x + x + x

b. 5p = p + p + p + p + p
When x = 3 find the value of 8x.
a. 8x = 8 × 3 = 24

Exercise 12.1

1. Write the following sum in short form

a. m + m + m + m

b. a + a + a + a + a + a + a

c. b + b + b + b + b + b + b + b

d. y + y + y + y + y + y + y + y + y + y + y + y

2. Write in expanded form.
a. 7x b. 3y c. 5x d. 7m e. 4b

3. When x = 2, find the value of the following.

a. 10x b. 15x c. 8x d. 9x e. 6x
8 g. 2x + 3x h. 5x + 3x

f. x

i. 8x – 4x

Like and Unlike terms

Class Discussion

Let's observe the figures.

5 l water 3 kg orange 1 l milk 2 l milk

xy xy

Unlike Like

5l water be added to 3 kg Milk of first bottle and milk
orange? of second jug are added each
other. What will be the result?

How much will be water? There will be 3l of
milk.

How much will be the We can add like objects.
orange?
Similarly, we can also
Are they increased? subtract like term.

Of course not. Umm ...
We can't add these things.

We can't add unlike objects

Similarly we can't subtract
unlike terms.

Concept of addition and Subtraction

Class Discussion

2 pens + 5 pens = 7 pens 5 balls + 3 balls = 8 balls
2x + 5x = 7x 5y + 3y = 8y

7 apples + 5 apples = 12 apples 6 rats + 5 rats = 11 rats
7a + 5a = 12a 6b+ 5b = 11b

While adding like terms, we add only coefficients.

8 mangoes – 5 mangoes = 3 mangoes 10 copies – 3 copies = 7 copies
8x – 5x = 3x 10y – 3y = 7y

9 cows – 6 cows = 3 cows 7 fingers – 2 fingers = 5 fingers
9a – 6a = 3a 7b – 2b = 5b

While subtracting like term, we subtract only coefficient.

Exercise 12.2

1. Add.

a. 2x + 3x b. 3x + 5x c. 8y + 2y
f. 9m + 7m
d. 3y + 8y e. 4z + 3z
c. 10x – 8x
2. Subtract. f. 6a – 2a

a. 8y – 3y b. 7y – 2y c. 7m + 9m – 8m
f. 6x + 2x – 4x
d. 7b – 2b e. 15z – 5z i. 8x – 9x + 3x

3. Simplify. b. 7y + 8y – 6y
a. 3x + 2x – x

d. 6m + 5m – 3m e. 2b + 7b – 5b

g. 7y – 3y + 2y h. 3x – 4x + 5x

Equation

Class Discussion

Statements : A definite or clear expression of something in speech or
writing.

Mathematical Statements: A statement of mathematical relation.

Mathematical sentences: Mathematical statements which may either

true or false but not both are called mathematical sentences.

Example : The sum of 2 and 5 is 7 – True statements

5 is greater than 6 – False statements

Mathematics is difficult subject (not sentence).

Open Sentence: Mathematical sentence containing the variable

becomes either true or false depending upon the value of variable is

called an open sentence.

Example : x + 2 = 7
It may be true or false depending on the value of x. If x = 1  1 + 2 =

3 false, & if x = 5, 5 + 2 = 7 is true.

Equation : An open sentence containing the sign '=' is called an

equation. Example : x + 4 = 9.

Every equation has two sides - L.H.S (Left hand side) and R.H.S (Right

hand side).

Letters involved in the equation are called variables. These are usually
denoted by letters of English alphabets.

Translating phrases into expressions with variables that suggest

Addition.
‰‰ The sum of a and b  a + b
‰‰ 9 more than x  x + 9
‰‰ The total of x, y and z  x + y + z
‰‰ y increased by 5  y + 5

Word that suggest subtraction:

‰‰ b subtracted from a  a – b

‰‰ 9 less than x  x – 9

‰‰ The difference of y and b  y – b

‰‰ z decreased by 5  z – 5

Word that suggest multiplication:

‰‰ The product of a and b  a.b
‰‰ 9 of x  9x
‰‰ twice z  2z
‰‰ y times 5  5y
Word that suggest Division:

‰‰ The quotient of a and b  a ÷ b

‰‰ 9 into x  x/9

‰‰ y divided by 5  y/5

Example 1

Rewrite the following sentence using mathematical
symbols. The sum of x and 5 is 12.

Solution:
The sum of x and 5 is 12 can be written as x + 5 = 12.

Example 2

Rewrite the following mathematical symbol in words.
x–4=9
Solution:

x – 4 = 9 can be written as the difference of x and 4 is 9.

Solution of Equation

Find the solution for the following open sentences.

Example 3

Find the solution for the following open sentences. x + 5
= 8.

Solution: x + 5 = 8

If x = 0, then 0 + 5 ≠ 8 x+5=8 x+5=8
If x = 1 then 1 + 5 ≠ 8 or, x + 5 – 5 = 8 – 5 or, x = 8 – 5
If x = 2 then 2 + 5 ≠ 8 ∴ x = 3 ∴ x = 3
If x = 3 then 3 + 5 = 8

Therefore, the solution for the open sentence x + 5 = 8 is 3.

Example 4

Solve the equation: 2x + 7 = 11 or, 2x + 7 = 11
Solution:
2x + 7 = 11 or, 2x + 7 – 7 = 11–7
If x = 0 then 2 × 0 + 7 ≠ 11
If x = 1 then 2 × 1 + 7 ≠ 11 or, 2x = 4

or, 2x = 4
2 2
∴ x = 4

If x = 2 then 2 × 2 + 7 = 11

Therefore, the solution for the equation 2x + 7 = 11 is 2.

Exercise 12.3

1. Which of the following sentences are true, false or open?
a. The sum of 5 and 4 is 9.
b. The difference of x and 5 is 10.
c. The product of 4 and 6 is 20.
d. x decreased by 7 is 12.
e. The quotient of 125 and 5 is 3.
f. The sum of 3 and 10 is 12.

2. Rewrite the following sentences using mathematical
symbol.

a. The sum of y and 6 is 12.

b. The difference of 12 and z is 2.

c. The product of 3 and y is 18.

d. y is divided by 5 is 2.

e. Three times y is 6.

f. 10 less than x is 7.
3. Rewrite the following sentences in words.

a. x + 3 = 5 b. y – 7 = 3 c. 4x = 20
xe.a re5txh–e2fo=l1lo8w ingfo. pexn5
4. d. 3x + 7 = 16 of =6 are
For what value sentences
true?

a. The sum of 4 and x is 9.

b. The difference of y and 7 is 8.

c. The product of z and 6 is 18.

d. The quotient of x and 2 is 5.
5. Choose the value of x from the whole numbers from 0 to

10 and find the value of x so that the following sentences
become true.

a. x + 4 = 7 b. y + 5 = 9 c. z – 4 = 6

d. x – 3 = 4 e. 4x = 12 f. 6x = 24
14 i. y2 =
g. 2x + 3 = 9 h. 4x – 2 = 4
jS. olv4e7xth=e4 following equations.
6.

a. x + 7 = 10 b. y + 8 = 12 c. z – 6 = 15
d. x – 8 = 17 x y
g. 2x = 14 e. 3 = 7 f. 2 = 5

j. 6x – 2 = 10 h. 4x = 20 i. 3x + 2 = 11

k. y – 2 = 4 l. 2x + 7 = 13
2 5

Maths Fun

Test this trick out on your family and friends.

Hey Kabil, Think of
any number and I
know the final answer

will be 15.

Hey, Aashish
Hamm .......... Ok

7

Steps

‰‰ Tick a number
‰‰ Multiply it by 3.
‰‰ Add 45
‰‰ Double it
‰‰ Divide the result by 6.
‰‰ Subtract your original number.

Practice Zone

Group 'A'

Circle the correct option.

1. The value of x in x = 3 is
6
a. 9 b. 2 c. 18

2. The expression 3x + 5y + z is

a. monomial b. binomial c. Trinomial

3. The expression for the mathematical statement 'x' is increasing
by 4 is

a. x – 4 b. x + 4 c. 4 – x

4. If x = 2, y = 1 and z = 0, then the value of 3x – 2y + z is equal to

a. 8 b. 4 c. – 1

5. If 6x = 24, what is the value of 'x'.

a. 4 b. 18 c. 30

6. Which is the like term with '3xy'.

a. 8x2y b. 4xy c. – xy2

7. Sum of the term 4x, 3x, 2y is

a. x + 2y b. 9xy c. 7x + 2y

8. Which are the next 2 terms of pattern 5, 10, 15, 20 .......

a. 21, 22 b. 30, 40 c. 25, 30

Group 'B'

1. Solve the following.

a. a – 18 = 4 b. x+3

c. x/5 = 7 d. 5x = 25

2. Solve: 2x + 7 = 19

3. Simplify: 5x – 6y + 4x + 8y

4. Find the value of the following expressions if x = 2, y = 3 and
z=1

a. 2x + 3y + 4z b. 3z – 4y + 5x

5. Find the perimeter of the adjoining quadrilateral.

4x

2x + 5 3x – 2

5x

6. Make equation and solve following problem.

a. 3 times of y is increased by 2, the result is 11. Find y.

b. x is divided by 3 and the result is 6. Find x. A
7. Find the remaining side of

triangle whose perimeter is 17y. 7y 4y


BC


8. 72 is divided by x which gives the quotient 9. Find x.

Answers of Unit 12

Exercise 12.1: Show to your teacher.

Exercise 12.2

1. a. 5x b. 8x c. 10y d. 11y e. 7z f. 16m

2. a. 5y b. 5y c. 2x d. 5b e. 10z f. 4a

3. a. 4x b. 9y c. 8m d. 8m e. 4b f. 4x

g. 6y h. 4x i. 2x

Exercise 12.3

1. a. T b. 0 c. f d. 0 e. f

2. a. y + 6 = 12 b. 12 – z = 2 c. 3y = 18
f. x – 10 = 7
d. y = 2 e. 3y = 6
5
3. a. The sum of x and 3 is 5.

b. The difference of y and 7 is 3.

c. Four times x is 20. The product of 4 and x is 20.

d. The product of 3 and x is added to 7 is 16.

e. Two is subtracted from the product of 5 and x is 18.

f. The quotient of x and 5 is 6. x divided by 5 is 6.

4. a. 5 b. 15 c. 3 d. 10

5. a. 3 b. 4 c. 10 d. 7 e. 3

f. 4 g. 3 h. 4 i. 8 j. 7

6. a. 3 b. 4 c. 21 d. 25 e. 21

f. 10 g. 7 h. 5 i. 3 j. 2

k. 12 l. 15

Subject : Mathematics Model Question Full Marks : 100
Examination Grade 4 (14 × 1 = 14)

Time : 3 hours (Group A)


Encircle 'o' the correct answer.
1. Which instrument do we use to measure the side of a triangle ?
a. Ruler b. Protractor
c. Compass d. Set-square
2. What is the nearest hundred for 740 while we round off it ?
a. 600 b. 700
c. 800 d. 900
3. Which is the prime factorization of 12 ?
a. 1× 12 b. 2× 3
c. 4× 3 d. 2× 2 × 3
4. Which of the following is not proper fraction ?
a. 1 b. 4
c. 7 d. 25
5. What is the algebraic expression of product of a and b ?
a. a ÷ b b. a – b
c. a + b d. ab
6. In 4(1 + 3) which operation is performed in between 4 and (1 + 3) ?
a. addition b. subtraction
c. multiplication d. division
7. What is the mathematical expression of 3 times of 5 ?
a. 3 + 5 b. 3 × 5
c. 5 – 3 d. 5 ÷ 3
8. Which of the following are unlike terms ?
a. y, 3y b. 2x, x2
c. x, 4x d. 2x, 2x

Fill in the blanks.
9. In simplification.............. is done first out of addition, subtraction,

multiplication and division.
10. There are……………days in a week.
11. One meter is equal to …………..... centimeters.
12. To change a decimal number into percentage it is multiplied by ………. .
13. {1,2,3,4,} of representing the set is called .................... method.

14. In + 7 = 9, the value of is ………. .

(14 × 2 = 34)
(Group A)

P

15. In the given ∆PQR, the angles QPR = 50° and ?
PQR = 60°, then find the measure of angle QPR.
Q
60° 50° R

16. How many tens are there in a lakhs ? Write it.
17. Write down the first and last prime numbers in between the numbers

11 to 40.
18. Find all the possible factors of 6.
19. Simplify : 24 ÷ 8 × 2
20. Simplify : 3 + (15 – 2)
21. If Anil has Rs. 7 and 60 paisa, then how much paisa he has.
22. Find out the perimeter of a rectangle having length 5 cm and breadth

3 cm.
23. Simplify : 6.405 - 4.235 + 7.75
24. Calculate the total cost of 10 oranges at the rate of Rs. 8.50 each.
25. There is 15000 population in a village. If 40% of them are male, find the

population of females.

26 Read the bill given below and answer the following questions.

Ananda Agro farm

Neelakantha - 6, Dhading

Bill No : 345 Date: 2073-08-25

Pan No: 2 0 0 1 3 5 2 0 1

Costumers' Name : Ananda Poudel Address: Syangja
Amount (Rs)
S.N. Particular Qty Rate (Rs)
1. Chicken 4 kg 560 2240
2500
2. Egg 5 sheet 500 150
360
3. Potato 3 kg 50 5250

4. Tomato 3 kg 120 Signature

Total

In word : Five thousand two hundred and fifty only.

Goods once sold will not be taken back.

a. What is the cost of 1 sheet egg?

b. What is the total amount of bill?
27. Write the coordinates of vertices of the quadrilateral given in the graph.

10

9

8

7
6A

5C B
4
3

2

1D

0 1 2 3 4 5 6 7 8 9 10

28. Express the set of English vowels by diagrammatic method.

29. Express the set V = {2,4,6,8,10} in words or statement method.

30. Simplify : 2xy – 4xy + 5xy

31. Solve : x -7 = 11

(Group C) (12 × 3 = 36)

32. Using protector measure the ∠ABC, ∠BAC D C
and ∠BCD of the given quadrilateral ABCD.
Write their measures.

33. Factorize the number 64 into prime factors. B
A

34. List all the prime numbers between 1 to 30?

35. If out of 12 pencils, one third are distributed as prize, then how many
pencils are left there now ?

36. How much expenditure does it require to purchase a copy costing Rs.
50 and an eraser costing Rs. 10 for 5 persons ?

37. Hari's house is 2km 500m far from school. If Pemba's and Hari's houses
are in the same direction from the school. The distance of Pemba's
house is one third than that of Hari's house from the school. Find how
far is Pemba's house from the school ?

38 The weight of a box is 5 kg 400 gram. Find out the weight of such 7
boxes?

39. If the cost of 50 copy is Rs. 200, find the cost of such 1 dozen copy.

40. Find the percentage of 12 out of 20.

41. Look at the price list of a shop and answer the following questions.

S.No. Items Quantity Price

1. Sugar 1 kg Rs. 80

2. Salt 1 kg Rs. 18

3. Oil 1 litre Rs. 150

If 1kg of salt and 2 litre of oil are purchased, then how much is returned
from Rs. 500 ?

42. Following table shows the temperature of Lumle of a week. Present it
on a bar graph.

Days Sunday Monday Tuesday Wednesday Thursday Friday Saturday
15 10 13 12 18 13
M i n i m u m 12
Temperature (°C)

43. If x = 3cm and y = 5 cm, find the perimeter of the y-2 x+y
adjoining triangle. x+3

Group D [4 × 4 = 16]

44 Observe the given figure and write the names of

i. a right angled triangle, E D C

ii. an acute angled triangle,

iii. an obtuse angled triangle and

iv. the largest quadrilateral. AB

45. Find the difference between the greatest and smallest numbers formed
by the digits 2, 0, 5, 3, and 8.

46. If a cake is 20 cm wide and 7 cm thick and it's volume is 7000 cm³. Find
the difference between its breadth and length.

47. Rajendra bought 1 1 m cloth from one shop and 2 3 m cloth from
5 5
another. What length of cloth did he buy in all?