Question bank

Chapter-1   Integers
Q-1

Arrange the following integers in descending order.

–12, –18, 14, 0, –109, –32, – 6, 12, 16, 32

Q-2 Fill in the blanks:
(a) One less than a given integer is called its __________.
(b) One more than the given integer is called its __________.
(c) ___________ is less than every positive integer.
(d) The integers on the number line form an _______ sequence.
Q-3 One word answer:
(a) Find the sum of –18, 14.
(b) Find the sum of –26, –3.
(c) Find the sum of 26, –26.
(d) Find the sum of –35, –29.
Q-4

Fill in the blanks :

(i) The greatest negative integer is _______.

(ii) 0 is greater than every _______integer.

(iii) The absolute value of an integer is either_______or _______than the integer but never_______than the integer.

(iv) The successor of –91 is _______ .

(v) The predesessor of –380 is _______.

Q-5

Use the sign of >, < or = in the box to make the statements true :

(i) (– 8) + (– 4)_____ (– 8) – (– 4)

(ii) (– 3) + 7 – (19) _____ 15 – 8 + (– 9)

(iii) 23 – 41 + 11 ____ 23 – 41 – 11

(iv) 39 + (– 24) – (15) _____ 36 + (– 52) – (– 36)

(v) – 231 + 79 + 51 ____ – 399 + 159 + 81

Q-6

Find the sum :

(i) –18, 14

(ii) –26, –3

(iii) 26, –26

(iv) –35, –29

(v) –52, 0

Q-7

Evaluate :

(i) 16 + (– 8)

(ii) (– 11) + 8

(iii) (– 13) + (– 15)

(iv) 11 + (– 19)

(v) (– 30) + (– 22)

Q-8

Subtract :

(i) 28 from – 42

(ii) – 36 from 8

(iii) – 53 from – 37

(iv) – 64 from 0

(v) 0 from – 64

(vi) – 29 from –83

Q-9 True or False:
(a) A list of numbers following a definite rule which goes on forever is called an infinite sequence.
(b) Each multiplication fact has two division facts.
(c) For subtracting an integer, add its opposites.
(d) 0 is the additive identity where as 1 is the multiplicative identity for integers.
Q-10

Replace each blank by < or > to make the statement true :

(i) – 8____ – 18

(ii) – 4____ 0

(iii) – 357____ – 537

(iv) – 71____ 17

Q-11

Arrange the following integers on the number line :

(i) 7, 3 , – 1 , – 5 , – 9 , – 13 , –17 

(ii) – 2 , – 4 , – 6 , – 8 , – 10 , –12 , –14 

(iii) 15 , 10 , 5 , 0 , – 5 , – 10 , – 15 

(iv) – 11 , – 8 , – 5 , – 2 , 1 , 4 , 7

Q-12

Fill in the blanks :

(i) The greatest negative integer is _______.

(ii) 0 is greater than every _______integer.

(iii) The absolute value of an integer is either_______or _______than the integer but never_______than the integer.

(iv) The successor of –91 is _______ .

(v) The predesessor of –380 is _______.

Q-13

Arrange the following integers in ascending order.

– 4, –2, 9, 4, –11, 0, 20, 13, –22 , 6.

Q-14

Use the sign of >, < or = in the box to make the statements true :

(i) (– 8) + (– 4)_____ (– 8) – (– 4)

(ii) (– 3) + 7 – (19) _____ 15 – 8 + (– 9)

(iii) 23 – 41 + 11 ____ 23 – 41 – 11

(iv) 39 + (– 24) – (15) _____ 36 + (– 52) – (– 36)

(v) – 231 + 79 + 51 ____ – 399 + 159 + 81

Q-15

Find the absolute value of :

(i) | – 31 |

(ii) | 0 |

(iii) | 15 |

(iv) |– 12|

Q-16

Complete each of the following pattern :

(i) –2, – 4, – 6, – 8, ____ , ____ , ____ ,

(ii) –11, –8, –5, –2 ____ , ____ , ____ ,

Q-17

Verify a – (–b) = a + b for the following value of a and b :

(i) a = 21, b = 18 

(ii) a = 28, b = 11 

(iii) a = 75, b = 84

Q-18

Write down a pair of integers whose

(i) Sum is –7.

(ii) difference is –10.

(iii) Sum is 0

(iv) difference is 5.

Q-19

Write the additive inverse of the following :

(i) – 6                           (ii) 9 

(iii) – 2                         (iv) 1 

(v) – 97                       (vi) 254 

(vii) – 324                   (viii) – 3

Q-20

Fill in the blanks to make the following statement true :

(i) (–5) + (–8) = (–8) + (____)

(ii) –53 + ________ = –53

(iii) 17 + ________ = 0

(iv) [13 + (–12)] + (____) = 13 + [(–12) + (–7)]

(v) (–4) + [15 + (–3)] = [–4 + 15] + ________

Q-21

Find the sum of :

(i) 153 and – 302

(ii) 105 and – 27

(iii) – 238 and 500

(iv) – 35 and 97

(v) – 84 and – 32

(vi) 96 and – 112

Q-22

Solve - 

1. If a = –5, b = –7, c = 2, verify (a + b) + c = a + (b + c)

2. Simplify: { –13 –(–27) } + {–25 –(–40)}

3. The sum of two integers is 65. If one of them is –27, find the other.

4. If a = – 9 and b = – 6, show that (a – b) ¹ (b – a)

Q-23

Find each of the following products :

(i) 3 × (–1)

(ii) (–1) × 225

(iii) (–21) × (–30)

(iv) (–316) × (–1)

(v) (–15) × 0 × (–18)

(vi) (–18) × (–5) × (–4)

Q-24

Simplify :

(i) (– 8) × 9 + (– 8) × 7

(ii) 9 × (– 13) + 9 × (– 7)

(iii) 20 × (– 16) + 20 × 14

(iv) (– 16) × (– 15) + (– 16) × (– 5)

(v) (– 26) × 72 + (– 26) × 28

(vi) (– 16) × (– 8) + (– 4) × (– 8)

Q-25

Verify the following :

(i) 18 × [7 + (– 3) = [18 × 7 ] + [ 18 × (– 3)]

(ii) (– 12) × [(– 9) + (– 6) ] = [ (– 12) × (– 9)] + [ (– 12) × (– 6)]

Q-26

Evaluate each of the following:

(i) (– 30) ÷ 10

(ii) 50 ÷ (– 5)

(iii) (– 36) ÷ (– 9)

(iv) (– 49) ÷ 49

(v) 13 ÷ [(– 2) + 1]

(vi) 0 ÷ (– 12)

Q-27

Verify and also name the property used :

(i) (– 445) + 315 = 315 + (– 445)

(ii) 17 × (– 12) = (– 12) × 17

(iii) [64 + (– 40)] + 16 = 64 + [(– 40) + 16 ]

(iv) 20 × [5 × (– 16)] = (20 × 5) × (– 16)

(v) (– 20) × [(– 3) + 9 ] = (– 20) × (– 3) + (– 20) × 9

Q-28

Simplify each of the following :

(i) (– 21) × [(+16) + (– 13)]

Q-29

Find each of the following products :

(i) 3 × (–1)

(ii) (–1) × 225

(iii) (–21) × (–30)

(iv) (–316) × (–1)

(v) (–15) × 0 × (–18)

(vi) (–18) × (–5) × (–4)

Q-30

Multiply each of the following:

(i) 17 by 8

(ii) 13 by (– 9)

(iii) 25 by (– 12)

(iv) (– 42) by 13

(v) (– 53) by 0

(vi) 0 by (– 47)

Q-31

Divide each of the following :

(i) (– 53) by (– 1)

(ii) (– 27) by 1

(iii) (– 11) by 11

(iv) (– 65) by 13

(v) 0 by (–19)

(vi) (– 72) by (– 4)

(vii) – 21 by –7

(viii) 75 ÷ 25

Multiple Choice Questions
Q-1 The word integer means ______ or intact.

(i)

whole

(ii)

partial

(iii)

full
Q-2 ________ is neither positive nor negative.

(i)

Zero

(ii)

One

(iii)

Two
Q-3 Every negative integer is _________ than every positive integer.

(i)

bigger

(ii)

larger

(iii)

smaller
Q-4 Every negative integer is _________ than every positive integer.

(i)

bigger

(ii)

larger

(iii)

smaller
Q-5 Every negative integer is to the __________ of every positive integer.

(i)

left

(ii)

right

(iii)

top
Chapter-2   Fractions
Q-1 True or False:
(a) An improper fraction can be converted into a mixed fraction.
(b) Equivalent fractions can be found by multiplying or dividing the numerator and denominator of a fraction by the same nonzero number.
(c) Fraction is a number expressed as a quotient, in which a denominator is divided by a numerator.
(d) The product of a non-zero number and its reciprocal is 0.
Q-2 One word answer:
(a) What is the LCM of 16 and 12.
(b) Simplify : 5/9 - 7/12 + 1/2.
(c) Find the sum of 5/9 + 3/9.
(d) Solve 2 - 3/5.
Q-3

Convert the following mixed fraction into improper fractions :

(i) 1*3/5

(ii) 2*3/2

(iii) 10*3/25

Q-4

Arrange the following fractions in ascending order :

(i) 3/4, 5/6, 7/9, 11/12

(ii) 4/5, 7/10, 11/15, 17/20

(iii) 2/3, 5/7, 12/21

Q-5

Arrange the following fractions in descending order :

(i) 7/8, 7/12, 17/24

(ii) 3/5, 7/10, 2/3

Q-6

Find the value of :

(i) 1 /2 of 32

(ii) 7 /2 of 1

(iii) 5/ 8 of 20

Q-7

Find the reciprocal of the following :

(i) 3/ 5

(ii) 7 /8

(iii) 11 /7

(iv) 3 /7

(v) 5/ 8

Q-8

Divide:

(i) 5/7 by 3/14

(ii) 35 by 7/4

(iii) 45 by 6*2/3

Q-9 Fill in the blanks:
(a) A fraction has _________ parts.
(b) A fraction in which the numerator is smaller than the denominator is called a __________.
(c) A fraction in which the numerator is greater than or equal to the denominator is called an ______________.
(d) A _____________ is always greater than 1.
Q-10

Convert the following improper fraction into mixed fractions :

(i) 7/3

(ii) 13/7

(iii) 17/8

Q-11

Compare the fractions :

(i) 5/8 and 7/12

(ii) 5/9 and 11/15

(iii) 11/12 and 15/16

Q-12

Simplify:

(i) 5 /9 - 7 /12+ 1 /2 

(ii) 3*1/5+ 1/10+ 1*1/2

Q-13

Numericals - 

1. Lipika reads a book for 1* 1/ 3 hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

2. Find the area of a square room if each of its side is 10 *3/ 4 m.

3. Potatoes are sold at ` 17* 3/ 4 per kg. What will be the cost of 8 *1/ 2 kg of potatoes?

4. Raj reads 1/ 4 of a book in an hour. How much part of the book will he read in 3* 1/ 5 hours?

5. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2* 3/ 4 litres of petrol?

Multiple Choice Questions
Q-1 _________ represents a part of a whole, consisting of a number of equal parts out of a whole.

(i)

Integer

(ii)

Fraction

(iii)

none of these
Q-2 A fraction is a number of the form _______.

(i)

p+q

(ii)

p-q

(iii)

p/q
Q-3 A fraction has _________ parts.

(i)

two

(ii)

three

(iii)

four
Chapter-3   Decimals
Q-1 True or False:
(a) When a decimal is divided by 10, the decimal point is shifted to the left by one place.
(b) When a decimal is divided by 100, the decimal point is shifted to the left by two places.
(c) When a decimal is divided by 1000, the decimal point is shifted to the left by three places.
(d) 25.78/100 is a decimal fraction.
Q-2 One word answer:
(a) Multiply the decimal numbers 5.8 × 2.5.
(b) Multiply the decimal number 4.64 × 0.5.
(c) Multiply the decimal number 9.5 × 0.04.
(d) Multiply the decimal number 5.68 × 0.145.
Q-3

Which one of the following are like decimals ?
Q-4

Add the following :

(i) 6.75, 4.3, 2.913

(ii) 0.872, 3.46, 4.009, 4.17

(iii) 16.32, 20.04, 5.207

(iv) 0.0804, 0.00924, 0.1072, 0.02065

(v) 35.6, 7.9, 8, 62.66 and 21.71

Q-5

Subtract the following :

(i) 41.97 from 82.39

(ii) 76.34 from 92.48

(iii) 5.347 from 10.001

(iv) 325.272 from 450.62

(v) 6.473 from 17.589

Q-6

Evaluate :

(i) (7.4 – 3.06) + (5.2 – 2.1)

(ii) (6.2 – 3.3) + (7.5 – 3.06)

(iii) 8.379 + (4.32 – 2.21),

(iv) (5.3 – 1.2) – (6.2– 4.3)

(v) (18.3 – 4.2) – (16.4 – 3.07)

Q-7

Multiply the following decimal numbers :

(iv) 5.68 × 0.145

(v) 2.94 × 0.3215

(i) 5.8 × 2.5

(ii) 4.64 × 0.5

(iii) 9.5 × 0.04

Q-8

Multiply each number by 10, 100 and 1000.

(i) 0.342

(ii) 0.7

(iii) 9.6

(iv) 0.0349

Q-9

Simplify :

(i) 19.5 ÷ 5

(ii) 8.8128 ÷ 4

(iii) 55.38 ÷ 30

(iv) 41.28 ÷ 16

Q-10 Fill in the blanks:
(a) The number which are written in Decimal form are called ____________.
(b) The decimal number which has the same number of decimal places are called _____________.
(c) The Decimal Numbers which have different number of different number of Decimal places are called ________________.
(d) The value of 25.75/100 is _____________.
Q-11

Which is greater ?

(i) 0.5 or 0.05

(ii) 0.7 or 0.5

(iii) 7 or 0.7

(iv) 1.37 or 1.49

(v) 2.03 or 2.30

(vi) 0.8 or 0.88

Q-12

Subtract the following :

(i) 41.97 from 82.39

(ii) 76.34 from 92.48

(iii) 5.347 from 10.001

(iv) 325.272 from 450.62

(v) 6.473 from 17.589

Q-13

Numericals - 

1. How much less is 28 km than 42.6 km ?

2. What is to be added to 36.85 to get 71 ?

3. Shyama bought 8 kg 300 g apples and 3 kg 250 g mangoes. Sarla bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits ?

4. Yogita wants to buy a doll which costs` 150.63. Yogita got ` 34.95 from her father and ` 6.80 from her mother. How much more money does she need to buy the doll ?

Q-14

Find the continued product :

(i) 3.4 × 1.5 × 2.6

(ii) 0.3 × 0.03 × 0.003

(iii) 3.1 × 0.31 × 0.031

Q-15

Divide :

(i) 0.0216 by 0.6

(ii) 3.28 by 0.4

(iii) 42.8 by 0.02

(iv) 23.94 by 6.3

(v) 1391 by 1.3

Multiple Choice Questions
Q-1 The above example ______ can be read as ‘five hundred and sixty four and eight tenths’.
Q-2 To multiply a decimal by ___________, shift the decimal point 1 place to the right.

(i)

10

(ii)

100

(iii)

1000
Q-3 The number which are written in Decimal form are called ___________ Numbers.

(i)

fractional

(ii)

decimal

(iii)

none of these
Q-4 (.) is called the ______.

(i)

decimal point

(ii)

fractional part

(iii)

none of these
Chapter-4   Rational Numbers
Q-1 Fill in the blanks:
(a) __________ are the numbers which are positive integers and includes numbers from 1 till infinity.
(b) Natural numbers including 0 are called _____________.
(c) Every natural number is a __________.
(d) __________ is a rational number.
Q-2 One word answer:
(a) Find 4/9 + (-5)/12.
(b) Add 3/8, (-7)/12 and 11/18.
(c) Subtract 7/8 from 5/12.
(d) Simplify 3/4 - 2/3.
Q-3

Write the following words expressing rational form in to the form p /q , where p and q are integers.

(i) Five-thirds

(ii) Two and one-half

(iii) Opposite of two-thirds

(iv) Zero

(v) Opposite of one.

Q-4

Rewrite the following rational numbers in the simplest form :

(i) −8/ 6

(ii) 25/ 45

(iii) −44 /72

(iv) −8/ 10

Q-5

Express −36 /48 as a rational number with :

(i) denominator as 12

(ii)numerator as 9.

Q-6

Write the following in the standard form :

(i) 33/ 55

(ii) −7 /84

(iii) 24 /36

(iv) 72 /84

Q-7

Which is greater in each of the following :

(i) 2/ 3, 5 /2

(ii) -5/6, -4/3

(iii) − 3 /4, 2 /-3

Q-8

Add the following :

(i) −3/ 4 +18 /20

(ii) -7/9+ -4/27

(iii) 2/5 + -3/10

Q-9

Simplify the following :

(i) 2/ 3 *4 /6* 7/ 3

(ii) 27/ 4 *26/- 9 × 21

Q-10 True or False:
(a) A rational number is said to be positive, if both the numerator and the denominator are either positive or negative.
(b) A rational number is said to be negative if either its numerator or denominator is negative.
(c) Equivalent rational numbers are equal in value.
(d) To reduce the rational number to its standard form, we divide its numerator and denominator by their HCF ignoring the negative sign if any.
Q-11

Write four more rational numbers in each of the following patterns :

(i) -3/5, -6/10, -9/15, -12/20

(ii) -1/4, -2/8, -3/12

Q-12

Rewrite the following rational numbers in the simplest form :

(i) −8/ 6

(ii) 25/ 45

(iii) −44 /72

(iv) −8/ 10

Q-13

Write the following in the standard form :

(i) 33/ 55

(ii) −7 /84

(iii) 24 /36

(iv) 72 /84

Q-14

Find five rational numbers between

-5/7, -3/8

Q-15

Subtract the following :

(i) 3 /5 from  2/ 3

(ii) -5/6 from -2/5

(iii) −5 /6 from 3/ 2

Multiple Choice Questions
Q-1 Natural numbers including 0 are called _________ numbers.

(i)

positive

(ii)

negative

(iii)

whole
Q-2 In p/q, p is the ______ and q is the denominator.

(i)

numerator

(ii)

denominator

(iii)

none of these
Q-3 The set of natural numbers is represented by the letter “_________”.

(i)

M

(ii)

N

(iii)

O
Q-4 Is zero a rational number?

(i)

yes

(ii)

No

(iii)

Maybe
Q-5 In p/q, p is the ______ and q is the denominator.

(i)

numerator

(ii)

denominator

(iii)

none of these
Chapter-5   Exponents and Powers
Q-1 Fill in the blanks:
(a) _____________ are shorthand for repeated multiplication of the same thing by itself.
(b) The word ____________ is usually omitted while reading the exponential form.
(c) Any number raised to power _____ given the same number.
(d) When we multiply two numbers having same base then powers should be _____________.
Q-2 One word answer:
(a) Express 3^2 x 4^2.
(b) Express (-2)^5 x (-3)^5.
(c) Express 2,173,600,000 in standard form.
(d) Explain 0.00453 in standard form.
Q-3

Fill in the blanks:
Q-4

Express the following in exponential form:
Q-5

Using law of exponents, simplify and write the answer in exponential form:
Q-6

Find the value of x:
Q-7

Simplify:
Q-8

Write the following numbers in the expanded form:

(i) 420621

(ii) 3006194

(iii) 6306173

(iv) 20068

(v) 279404

Q-9 True or False:
(a) Exponents are shorthand for repeated multiplication of the same thing by itself.
(b) The factor which is multiplied by itself again and again is the base and the number of times the factor appears is the exponent.
Q-10

Find the value of:

(i) 34

(ii) 63

(iii) 45

Q-11

Express the following numbers in the usual form :
Multiple Choice Questions
Q-1 Exponents and _____ both are related to each other.

(i)

powers

(ii)

fractions

(iii)

none of these
Q-2 The value of the ___________ is based on the number of times the base is multiplied to itself.

(i)

exponent

(ii)

powers

(iii)

none of these
Q-3 _________ is an expression that shows repeated multiplication of the same number or factor.

(i)

Factors

(ii)

Powers

(iii)

Value
Q-4 a^n is also called the nth power of _________.

(i)

n

(ii)

a

(iii)

none of these
Chapter-6   Algebraic Expressions
Q-1 True or False:
(a) For adding coefficients of like terms, the rules for addition of integers apply.
(b) A polynomial’s degree is the highest or the greatest power of a variable in a polynomial.
(c) A zero polynomial is the one where all the coefficients are equal to one.
(d) Unlike terms neither be subtracted nor added.
Q-2 One word answer:
(a) Add 5mn, – 6mn, 8mn, – 4mn.
(b) Add 4m – 6n, 2n–4m + 2, 2m – 3mn – 5.
(c) Simplify x + x + x + x + x + x.
(d) Simplify 3p + p – p + p – p.
Q-3

Identify like terms in each of the following:
Q-4

Identify the following as unlike terms :
Q-5

Add the following :
Q-6

Subtract :
Q-7

Numericals -

1. From the sum of 3x – y + 11 and – y – 11. Subtract 3x – y – 11.

2. Three sides of a triangle are 2x2 + 3x + 1, x2 + 7, and 3x2 – 2x + 3. Find its perimeter?

3. What should be added to 2x2 + xy + 2y2 to obtain 3x2 + 5xy ?

4. The two adjacent sides of a rectangle are 8a – 4b and 6a + 9b. Find its perimeter.

5. Rachna spends 3x + 4y rupees for a book and 7x – 8y rupees for a shirt. How much does she spend in all ?

Q-8 Fill in the blanks:
(a) A _________ value is not fixed.
(b) A constant has a ___________ value.
(c) A symbol that represents one for more numbers is called a ____________.
(d) A numerical factor of a term that contains a variable is a ____________.
Q-9

Classify as constants and variables :
Q-10

For each expression given below, state whether it is a monomial, binomial or trinomial:

(i) ax + 8                    (ii) 4x2 × 3x                     (iii) 6x ÷ y 

(iv) 3z ÷ x + 5            (iv) 12 + 5z – 8              (vi) 3a – b ÷ c

Q-11

Subtract :
Q-12

Complete the following multiplications:
Q-13

Simplify:
Q-14

Find the products given below:
Multiple Choice Questions
Q-1 __________ is the branch of Maths that uses alphabetical letters to find unknown numbers.

(i)

Fraction

(ii)

Algebra

(iii)

none of these
Q-2 The values which are known in the given expression such as numbers are called ___________.

(i)

variables

(ii)

constants

(iii)

none of these
Q-3 Alphabetical letters are also called ____________.

(i)

variables

(ii)

constants

(iii)

both of these
Q-4 _________ are represented by letters like a, y, p, m, etc.

(i)

Variables

(ii)

Constants

(iii)

none of these
Chapter-7   Comparing Quantities
Q-1 Fill in the blanks:
(a) The _________ is used to compare two quantities.
(b) When we compare two quantities the _________ must be same.
(c) _________ is an equation that defines that the two given ratios are equivalent to each other.
(d) The __________ proportion describes the relationship between two quantities in which an increase in one quantity leads to a decrease in the other quantity.
Q-2 One word answer:
(a) Express 1/2 : 1/6 in the simplest form.
(b) Express 8 : 64 in simplest form.
(c) Express 28 : 63 in simplest form.
(d) Express 27 : 9 in simplest form.
Q-3

Express each of the following in the simplest form:
Q-4

Solve - 

1. Find the ratio of 3 km to 300 m.

2. Divide 84 toffees between two children in the ratio 5 : 7.

3. Two numbers are in the ratio 20 : 26. If the difference between the numbers is 96, find the numbers.

4. If 2a = 4b = 5c, find a : b : c

5. Three numbers are in the ratio 2 : 3 : 4 and sum of these numbers is 720. Find the numbers.

6. If two numbers are in the ratio 10 : 13 and their difference is 33. What are the two numbers?

7. The cost of an eraser is 80 paise and the cost of a pencil is ₹ 2. What is the ratio of their costs in simplest form?

8. The cost of a dozen pens is ₹ 96 and the cost of one score pencil is ₹ 60. Find the ratio between the price of pens to the price of the pencils.

9. The ratio of income to the saving of a family is 7:3. If its monthly income be ` 27300, find its monthly saving.

10. (i) If A : B = 1.5 : 3.5 and B : C = 5 : 6, find A : C (ii) If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z

11. Show that the numbers 22, 33, 42, 63 are in proportion.

12. What number must be added to each of the numbers 10, 18, 22, 38, to get the numbers which are in proportion ?

13. The price of 18 articles is ₹ 216 .Find the price of 25 articles

14. What must be subtracted from each of the numbers 3, 4, 5 and 8 so that remainders are in proportion ?

15. If a train covers 120 km in 3 hours, how much time it will take to cover 150 km at the same rate ?

Q-5

Give two equivalent ratios for each of the following ratios :
Q-6

Find the value of x if :
Q-7 True or False:
(a) Proportions are denoted by the symbol ‘::’ or ‘=’.
(b) The ratio value does not affect when the same non-zero number is multiplied or divided on each term.
(c) The ratio should exist between the quantities of the same kind.
(d) “a” is called the first term or antecedent.
Q-8

Express each of the following in the simplest form:
Q-9

Solve - 

1. Find the ratio of 3 km to 300 m.

2. Divide 84 toffees between two children in the ratio 5 : 7.

3. Two numbers are in the ratio 20 : 26. If the difference between the numbers is 96, find the numbers.

4. If 2a = 4b = 5c, find a : b : c

5. Three numbers are in the ratio 2 : 3 : 4 and sum of these numbers is 720. Find the numbers.

6. If two numbers are in the ratio 10 : 13 and their difference is 33. What are the two numbers?

7. The cost of an eraser is 80 paise and the cost of a pencil is ₹ 2. What is the ratio of their costs in simplest form?

8. The cost of a dozen pens is ₹ 96 and the cost of one score pencil is ₹ 60. Find the ratio between the price of pens to the price of the pencils.

9. The ratio of income to the saving of a family is 7:3. If its monthly income be ` 27300, find its monthly saving.

10. (i) If A : B = 1.5 : 3.5 and B : C = 5 : 6, find A : C (ii) If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z

11. Show that the numbers 22, 33, 42, 63 are in proportion.

12. What number must be added to each of the numbers 10, 18, 22, 38, to get the numbers which are in proportion ?

13. The price of 18 articles is ₹ 216 .Find the price of 25 articles

14. What must be subtracted from each of the numbers 3, 4, 5 and 8 so that remainders are in proportion ?

15. If a train covers 120 km in 3 hours, how much time it will take to cover 150 km at the same rate ?

Multiple Choice Questions
Q-1 The ________ method is a method in which you find the value of a unit and then the value of a required number of units.

(i)

unitary

(ii)

alternative

(iii)

none of these
Q-2 Any number without a variable is a __________.

(i)

constant

(ii)

variable

(iii)

fraction
Q-3 A _______ expression has only one term.

(i)

monomial

(ii)

binomial

(iii)

trinomial
Q-4 Any expression which has one or more terms with the variable having non-negative integers as an exponent is a ________.

(i)

monomial

(ii)

binomial

(iii)

polynomial
Chapter-8   Percentage and its Applications
Q-1 Fill in the blanks:
(a) __________ means per hundred.
(b) The symbol for per cent is ____________.
(c) The loss and gain are always calculated on the ___________.
(d) The amount for which the product is sold is called the ________________.
Q-2 One word answer:
(a) The total money paid by the borrower to the lender is.
(b) The additional money paid by the borrower to the lender for having used his money is.
(c) The duration for which the principal amount is given to someone.
(d) What is the formula of simple interest.
Q-3

Find:
Q-4

Convert each of the fraction into a percentage.
Q-5

Convert each of the following into a fraction:
Q-6

Find the S.P when:
Q-7

Find the C.P when:
Q-8

Numericals - 

1. Rajneesh bought 4 dozen pencils at ` 10·80 a dozen and sold them for 80 paise each. Find the gain or loss percent.

2. A shopkeeper buys 6 fans at ` 2200 each. On account of slump in the market he is forced to sell them at a loss of 10%. Find the selling price of 6 fans.

3. By selling an A.C. for ` 18000, I loss 20% . What did I pay for it?

4. A farmer sells his product at a loss of 8% . If his S.P was ` 27600, what was his actual loss?

5. A shopkeeper sold an article at a gain of 5%. He had sold it for ` 30 loss, he would have loss of 10%. Find the cost price of the article.

6. Rawat sells a TV for ` 8400 making a profit of 20%. What was the C.P of the TV?

7. Mohit sold a watch to Karim at a gain of 10% and Karim sold it to Rahim at a gain of 4%. If Rahim paid ` 14300 for it, for how much did Mohit purchase it?

8. If the manufacturer gains 10%, the wholesale dealer gains 15% and the retailer gains 25% then what is the production cost of a washing machine whose retail price is ` 37950?

Q-9 True or False:
(a) Gain on Rs.100 is called gain per cent.
(b) Loss on Rs.100 is called loss per cent.
(c) The overhead expenses like GST, labour charges, cartage, etc., are included in the cost price.
(d) The money borrowed is called the principal or the sum.
Q-10

Find the S.P when:
Q-11

Find the simple interest when:

(i) P = ₹ 1500, R = 12% p.a. and T = 3 years 3 months

(ii) P = ₹ 600, R = 12 1 2 % p.a. and T = 5 years

(iii) P = ₹ 5000, R = 9% p.a. and T = 146 days

(iv) P = ` 6400, R = 6% p.a. and T = 2 years

Multiple Choice Questions
Q-1 A percentage is a number or ratio that can be expressed as a fraction of ___________.

(i)

10

(ii)

100

(iii)

1000
Q-2 0.23 in percentage is ________.

(i)

2.3%

(ii)

23%

(iii)

230
Q-3 The word per cent means per ___________.

(i)

10

(ii)

100

(iii)

1000
Q-4 Percent is represented by the symbol _________.

(i)

-

(ii)

+

(iii)

%
Chapter-9   Lines and Angles
Q-1 Fill in the blanks:
(a) A _________ is a straight one-dimensional figure.
(b) A _________ is a line which has one endpoint and endless from another side.
(c) A ___________ is a part of a line with two end-points.
(d) Vertically opposite angles are ___________.
Q-2 One word answer:
(a) Point where the arms meet.
(b) Two straight line segments form a vertex.
(c) Which is always equal to 90 degrees.
(d) Which lies between 0 degree and 90 degrees.
Q-3

Refer to figure given below:

(i) Name two angles adjacent to Ð4.

(ii) Name 4 pairs of supplementary angles.

(iii) Name two pairs of vertically opposite angles.

Q-4 True or False:
(a) Number of rays having a common initial point form angle at that point.
(b) If a line intersects two or more lines at different points then that line is called Transversal Line.
(c) The angles which are on the opposite sides of a transversal and do not form a linear pair are called alternate angles.
(d) The interior angles which are on the opposite sides of a transversal and do not form a linear pair are called alternate interior angles.
Q-5

Refer to figure given below:

(i) Name two angles adjacent to Ð4.

(ii) Name 4 pairs of supplementary angles.

(iii) Name two pairs of vertically opposite angles.

Q-6

Solve -

1. Find the angle which is equal to its supplement.

2. An angle is 2 /3 of its complement. What is it magnitude ?

3. Find value of x in each of the following figure, if AOB is a straight line and ray OC lies on it.

If Ð AOC = 64° and Ð BOC = x Find the value of x.

4. Find the value of x in the following figures :

5. Identify the linear pairs in the following figure :

6. An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

7. In the figure given below, two straight lines PQ and RS intersect at O. If ÐPOS = 114°, find the measure of each of the angles.

(i) ÐPOR (ii) ÐROQ (iii) ÐQOS

8. In the given figure, two straight lines AB and CD intersect at a point O. If ÐAOC = 42°, find the measure of each of the angles:

(i) ÐAOD (ii) ÐBOD (iii) ÐCOB

Q-7

Find the complement of each of the following angles :

(i) 35°

(ii) 47°

(iii) 60°

(iv) 73°

Q-8

State the property that is used in each of the following statements ?

(i) If a || b, then

(ii) If

(iii) If Q-9

Solve - 

2. Find the value of x in the following figures, if l || m.

2. Find the value of x in the following figures, if l ||  m.

4. In the given figure, p || q and r || s. Find the angles a, b and c.

1. In the figure given below, l || m and n is a transversal. If

3. In the given figure, prove that CD || EF.

5. In the given figure, show that AB || CD. Give reasons.

6. In figure given below, find the values of x, y and z, given that l || m || n and p || q.

7. In the figure AB || CD and transversal EF cuts AB and CD at G and H respectively. If GL and HM are bisectors of

8. In the figure given below, AB || CD, Multiple Choice Questions

Q-1 A __________ is a straight one-dimensional figure, that extends in the opposite directions infinitely.

(i)

circle

(ii)

line

(iii)

none of these
Q-2 A line can be drawn from _________.

(i)

left to right

(ii)

top to bottom

(iii)

both of these
Q-3 A line can be ____________.

(i)

vertical

(ii)

horizontal

(iii)

both of these
Q-4 A line segment is a part of a line with __________ end-points.

(i)

two

(ii)

three

(iii)

four
Chapter-10   The Triangle and its Properties
Q-1 True or False:
(a) An exterior angle of a triangle is greater than either of its interior opposite angles.
(b) The sum of any two sides of a triangle is greater than its second side.
(c) The difference of any two sides of a triangle is less than its second side.
(d) The sum of all three angle of triangle is 90°.
Q-2

Find the unknown lettered angle :
Q-3

Draw rough sketches for the following :

(i) In ABC, BE is a median. 

(ii) In PQR, Ð S and QT are altitudes of the triangle. 

(iii) In XYZ, YL is an altitude of the triangle.

Q-4

Find :

(i) ∠DBC 

(ii) ∠BDC

(iii)

(iv) Q-5

Find the value of the unknown exterior angle x in the following diagrams :

Q-6

Find the value of the unknown interior angle x in the following figures :
Q-7

Find the value of x in each case :
Q-8 Fill in the blanks:
(a) ________ is a closed curve made up of three line segments.
(b) Triangle has ________ sides.
(c) A triangle cannot have more than one ___________.
(d) A straight line that joins a vertex of a triangle with the mid-point of the side opposite to it is called _____________.
Q-9 One word answer:
(a) Which triangle has all side lenghts of different measures.
(b) Which triangle has lengths of two of the three sides are equal.
(c) Which triangle has all the lengths of the sides are equal.
(d) Which triangle is a triangle whose all the three interior angles are acute.
Q-10

Draw rough sketches for the following :

(i) In ABC, BE is a median. 

(ii) In PQR, Ð S and QT are altitudes of the triangle. 

(iii) In XYZ, YL is an altitude of the triangle.

Q-11

Is it possible to have a triangle in which there are

(i) two right angles ?

(ii) two obtuse angles ?

(iii) two acute angles ?

(iv) all angles more than 60° ?

(v) all angles less than 60° ?

(vi) all angles equal to 60° ?

Q-12

Solve - 

1. In a

2. In

3. If angles of a triangle are in the ratio of 1 : 2 : 3, find each angle of the triangle.

4. In the given figure , DE || BC. If

5. Find the alternative angles in the figure.

Multiple Choice Questions
Q-1 Triangle is a closed curve made up of __________ line segments.

(i)

two

(ii)

three

(iii)

four
Q-2 The angles of an equilateral triangle are _________.

(i)

same

(ii)

different

(iii)

none of these
Q-3 A triangle has ______ sides.

(i)

three

(ii)

four

(iii)

five
Q-4 In triangle, there are _____ angles.

(i)

three

(ii)

four

(iii)

five
Chapter-11   Congruence of Triangles
Q-1 True or False:
(a) The figures are congruent if one figure have exactly the same shape and size as the other.
(b) Two line segments are congruent if they do not have the equal lengths.
(c) Two rectangles are congruent if they have the same length and breadth.
(d) Two circles are congruent if they have the same radius.
Q-2 Fill in the blanks:
(a) Two squares are congruent if they have the same _______ length.
(b) Two triangles are congruent if pairs of corresponding sides and corresponding angles are ____________.
(c) There are ___________ congruence rules that proves if two triangles are congruent.
(d) Two squares are congruent if their sides are _________.
Q-3 One word answer:
(a) The integers on the number line form.
(b) If two angles have the same measure in degrees, they are.
Multiple Choice Questions
Q-1 If two figures have exactly same shape and size, they are said to be _____________ .

(i)

Congruence of Triangles

(ii)

congruent

(iii)

both of these
Q-2 Two angles are said to be congruent if their measures are ____________.

(i)

equal

(ii)

double

(iii)

triple
Q-3 The meaning of congruence in Maths is when two figures are similar to each other based on their shape and __________.

(i)

size

(ii)

side

(iii)

colors
Chapter-12   Simple Linear Equations
Q-1 True or False:
(a) x + 2y = 4 is a linear equation in two variables.
(b) 3x + 2y + z = 15 is a linear equation in three variables.
(c) When the LHS = RHS of an equation, then it is said to be a balanced equation.
(d) Changing the side of the number is called transposing.
Q-2

Check whether the value given in the brackets is a solution to the given equation or not :

(i) n + 5 = 19 (n = 1)

(ii) 7n + 5 = 19 (n = – 2)

(iii) 7n + 5 = 19 (n = 2)

(iv) 4P – 3 = 13 (P = 1)

Q-3

Convert the following equation into statements :

(i) (x – 7) = 10

(ii) 4x = 28

(iii) P/ 2 + 7 = 11

(iv) 15/ x = 4

(v) 3x + 5 = 7x

Q-4

Solve the following :

(i) 3x = 30

(ii) 4x = 60

(iii) 4x = 16

(iv) – 2x = 18

(v) – 10x = 100

(vi) 5t = – 20

Q-5 Fill in the blanks:
(a) A _____________ equation in one variable is an equation that can be written in the form ax + b = 0.
(b) An __________ is a statement of equality with contains one or more unknown quantities.
(c) A statement that does not have an equals (=) sign is called an ____________.
(d) Transferring terms from the LHS of an equation to the RHS and vice versa is known as ____________ of terms.
Q-6 One word answer:
(a) Solve the equation 8 = x – 3.
(b) Solve 3x + 1/5 = 2 – x
(c) Solve the equation 5a = 30.
(d) Solve 13a – 7 = 19.
Q-7

Rewrite the following statements in the form of equations

(i) Difference of m and 8 is 12 (m > 8).

(ii) The sum of thrice a number and (– 4) is 15.

(iii) A number x multiplied by itself gives 9.

(iv) Seven-eighth of P when subtracted from 10 is 20.

(v) The sum of twice x and 4 is 15.

(vi) Sum of 2 and thrice a number is 21.

Q-8

Convert the following equation into statements :

(i) (x – 7) = 10

(ii) 4x = 28

(iii) P/ 2 + 7 = 11

(iv) 15/ x = 4

(v) 3x + 5 = 7x

Q-9

Solve the following equations by transposition. Check your answer :

(i) x + 5 = 9

(ii) a + 10 = 12

(iii) x + 3 /5= 4/ 5

(iv) n + 1.8 = 3

(v) x – 7 = 4

(vi) 12 + a = 23

(vii) y – 9 = 9

Q-10

Solve - 

1. Thrice a number when increased by 5 gives 44. Find the number.

2. Twice a number when decreased by 7 gives 45. Find the number.

3. The sum of Ritu's age and Ashu's age is 25. Ritu is 12 years old. Write an equation to find Asha's age.

4. 7 times a number decreased by 3 equals 18. Find the number.

5. How old is Ramesh, if 10 years ago he was 25 years old?

6. Find the number which when divided by 13 gives 6.

7. The sum of two consecutive even numbers is 98. Find the numbers.

8. Ram's father is five times as old as Ram. If sum of their ages is 114 years, find their ages.

9. A number is multiplied by 3 and then 5 is added to it to get the answer 20. What is the number?

10. After buying a book, I am left with rupees 5 out of my fifty rupees note. What is the cost of the book?

11. The ages of Sonal and Manoj are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

12. The length of a rectangular field is twice its breadth. If the perimeter of the field is 150 metres, find its length and breadth.

13. In an examination, a student requires 40% of the total marks to pass. If Rupa gets 185 marks and fails by 15 marks, find the total marks.

14. A purse contains ₹75 which includes 25 paise and 50 paise coins. If the number of 25 paise coins is thrice the number of 50 paise coins, find the number of 25 p and 50 p coins in the purse.

15. Mamta's mother is three times as old as Mamta and four times as old as Mamta's sister Monika. Monika is three years younger than Mamta. How old are Mamta, Monika and their mother?

16. A man travelled 3/ 5 of his journey by rail, 1 /4 by a taxi, 1/ 8 by a bus and the remaining 2 km on foot. What is the length of his total journey?

17. Benny thinks of a number. Subtracted 18 from it and divided the difference by 3. The result is 4 . What is the number?

18. The length of a rectangular hall is 3 metres more than double of its breadth. If its perimeter is 66 meters, what is its length?

Multiple Choice Questions
Q-1 An _________ is a statement of equality with contains one or more unknown quantities.

(i)

statement

(ii)

equation

(iii)

expression
Q-2 A statement that does not have an equals (=) sign is called an ____________.

(i)

inequality

(ii)

quantities

(iii)

both of these
Q-3 The standard form of linear equations in one variable is represented as:

(i)

ax + b = 1

(ii)

ax + b = 2

(iii)

ax + b = 0
Q-4 A linear equation in one variable is an equation which has a maximum of one variable of order ________.

(i)

2

(ii)

1

(iii)

3
Chapter-13   Data Handling
Q-1 True or False:
(a) Data is organised and represented graphically so that it becomes easy to understand and interpret.
(b) The “pie chart” is also known as a “circle chart”.
(c) The total value of the pie is 50%.
(d) The graphical representation of data using bars of uniform width drawn vertically or horizontally with different lengths is called as bar graphs.
Q-2

Form a frequency distribution from the following scores :
Q-3

The height (in cm) of 90 plants in a garden are given below. Calculate their mean height :
Q-4

Organise the following mark in a class assessment, in tabular form :

4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7

(i) Which number is the highest?

(ii) Which number is the lowest?

(iii) What is the range of the data?

Q-5

Following are the margins of victory in the football matches of a league.

1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 

2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2.

Q-6

Find the mode of the following distribution.
Q-7

The daily maximum and minimum temperature of Delhi in one week in the month of July is given below. Construct a bar graph using this data.
Q-8

Solve - 

1. A coin is tossed hundred times in which head is obtained 55 times. On tossing a coin at random, find the probability of getting : (i) a head (ii) a tail.

2. There are 6 marbles in a bag with numbers from 1 to 6 marked on each of them. What is the probability of drawing a marble with number : (i) 2 ? (ii) 5 ?

3. In a survey of 100 persons, it was found that 36 like coffee while 64 dislike it. Out ofthese persons, one is chosen at random. What will be the probability that the chosen person : (i) Likes Coffee (ii) Dislikes Coffee?

4. A deck of 20 cards has five black cards and fifteen red cards. One card is drawn without looking at the cards. What is the chance that it is black? What is the chance that it is red?

5. Five girls put their names in a box. They are Anjali, Hazel, Ayushree, Ishita and Rashi. Rashi draws a name from the box. What is the chance that she draws her own name?

Q-9 Fill in the blanks:
(a) _________ is a collection of information gathered by observations, measurements, research or analysis.
(b) _____________ is the data that is collected for the first time through personal experiences or evidence, particularly for research.
(c) ______________ is a second-hand data that is already collected and recorded by some researchers for their purpose, and not for the current research problem.
(d) The number of times a particular observation occurs is called its _____________.
Q-10 One word answer:
(a) Which type of chart or graph that is used to show information that changes over time.
(b) Which can be defined as a set of rectangles with bases along with the intervals between class boundaries.
(c) The most common representative value of a group of data is.
(d) Which is defined as the difference between the highest and the lowest observation.
Q-11

The weights of new born babies (in kg) in a hospital on a particular day are as follows :

Rearrange the weights in descending order.

Q-12

Given below are the ages of 25 students of class VII in a school. Represent the given data in the form of a frequency distribution.
Q-13

Form a frequency distribution from the following scores :
Q-14

Given below are the marks obtained (out of 75) by 16 students in a class :

54, 50, 52, 54, 54, 50, 48, 52, 52, 52, 54, 50, 52, 54, 52, 52

Q-15

Solve -

1. The following table shows the weights (in kg) of 15 workers in a factory.

Calculate the mean weight.

2. Find the mean of 8.6, 7.8, 9.5, 10.4, 6.9, 10.1, and 5.7.

3. A dice was thrown 20 times and scores were recorded as 5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1. Prepare frequency table of the scores as the upper face of the dice and find the mean score.

4. If the mean of 6, 4, 7, P and 10 is 8, find the value of P.

5. Find the mean from the given table :

Q-16

Find the mode of each of the following data :

(i) 3, 4, 5, 3, 6, 7 

(ii) 24, 34, 44, 24, 34, 44, 54, 44, 44 

(iii) 1, 1, 2, 4, 3, 2, 1, 2, 2, 4 

(iv) 17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14

Q-17

Find the mean and median of the following data :

Using empirical relation, calculate its mode.

Q-18

The following table shows the weight of 15 players :

Find the median and mean weights using empirical formula, calculate its mode.

Q-19

The daily maximum and minimum temperature of Delhi in one week in the month of July is given below. Construct a bar graph using this data.
Q-20

The number of cycles produced in a factory during five consecutive weeks are given below.

Draw a bar graph representing the above information.

Q-21

A gift pack of chips contains 2 cheese and onion, 2 plain salted, 3 masala munch and 1 pudina. Tanya takes out a pack of chips without looking at the packs. What is the chance that she picks :

(b) Masala

(a) Plain salted

(c) Cheese and Onion

(d) Pudina

Q-22

An ordinary dice is rolled. What is the probability that the number of dots on its upper face is :

(a) 3

(b) less than 3

(c) an even number

(d) 7

Multiple Choice Questions
Q-1 ___________ data is the data that is collected for the first time through personal experiences.

(i)

Primary

(ii)

Secondary

(iii)

First
Q-2 _____________ data is a second-hand data that is already collected.

(i)

First

(ii)

Secondary

(iii)

none of these
Q-3 The number of times a particular observation occurs is called its _____________.

(i)

data

(ii)

frequency

(iii)

information
Q-4 Data is a collection of information gathered by observations, measurements, research or ___________.

(i)

collection

(ii)

research

(iii)

analysis
Q-5 _____________ data is a second-hand data that is already collected.

(i)

First

(ii)

Secondary

(iii)

none of these
Chapter-14   Symmetry
Q-1 Fill in the blanks:
(a) _________ is a geometrical concept that is found in most cases including nature.
(b) The axis of the shape which divides the shape into two identical halves, is called a ___________ line of symmetry.
(c) A circle has ________ lines of symmetry.
(d) A _____________ is an symmetrical polygon.
Q-2 True or False:
(a) Figures or objects without symmetry are called asymmetrical.
(b) A square is also regular because of all its sides are of equal length and each of its angles is a right angle.
(c) Line symmetry exists in nature.
(d) The word ‘raised’ is usually omitted while reading the exponential form.
Q-3 One word answer:
(a) Every object has a rotational symmetry of order 1 as it would be its original position always after one complete rotation of.
Multiple Choice Questions
Q-1 Symmetry is a geometrical concept that is found in most cases including ____________.

(i)

nature

(ii)

lines

(iii)

none of these
Q-2 The lines or axes may be any combination of vertical, __________and diagonal.

(i)

straight

(ii)

landscape

(iii)

horizontal
Q-3 The word ‘raised’ is usually omitted while ________________ the exponential form.

(i)

listening

(ii)

reading

(iii)

Writing
Q-4 Symmetry is a geometrical concept that is found in most cases including ____________.

(i)

nature

(ii)

lines

(iii)

none of these
Q-5 The axis of the shape which divides the shape into two identical halves, vertically, is called a _____________ of symmetry.

(i)

vertical line

(ii)

horizontal line

(iii)

diagonal
Chapter-15   Visualising Solid Shapes
Q-1 True or False:
(a) The line segment where the faces of three-dimensional figures meet each other is called the edge.
(b) A pyramid is a three-dimensional shape, with a polygonal base and flat triangular faces, which join at a common point called the apex.
(c) A pentagonal prism has 7 faces,15 edges and 10 vertices.
(d) The corners or points where the edges of the figure meet each other are called vertices.
Q-2 Fill in the blanks:
(a) A closed, two-dimensional or flat figure is called a ______________.
(b) A triangle is a ____________ sided polygon.
(c) __________ are the best example of a triangle shape.
(d) Shapes that can be measured in 3 directions are called ___________________.
Q-3 One word answer:
(a) Which pyramid is a two-dimensional geometric shape that has a square base and four triangular bases that are joined at a vertex.
(b) Oblique sketches are drawn on.
(c) Guessing the amount of space available inside a box without actually measuring.
(d) When we cut any 3D object horizontally or vertically, we get a 2D face of that figure.
Multiple Choice Questions
Q-1 Shapes that can be measured in 3 directions are called _______________ shapes.

(i)

three-dimensional

(ii)

first-dimensional

(iii)

two-dimensional
Q-2 The line segment where the faces of three-dimensional figures meet each other is called the ________________ of the shape.

(i)

vertices

(ii)

edge

(iii)

vertex
Q-3 A _______________ is a three-sided polygon (2-D Shape) which has three edges and three vertices.

(i)

Sphere

(ii)

Buckyball

(iii)

triangle
Q-4 The line segment where the faces of three-dimensional figures meet each other is called the ________________ of the shape.

(i)

vertices

(ii)

edge

(iii)

vertex
Chapter-16   Practical Geometry
Q-1 True or False:
(a) Angle is not a polygon, because it is not a closed shape.
(b) The lines which do not have a common meeting point in the same plane, and distance between lines remain same are known as parallel lines.
(c) The Pythagoras theorem is used to find the length of the hypotenuse.
(d) A triangle with sides 4 cm, 3 cm and 8 cm sides can be drawn.
Q-2 Fill in the blanks:
(a) The lines which do not have a common meeting point in the same plane, and distance between lines remain same are known as _____________.
(b) ___________ are equidistant at all points.
(c) The construction of triangles is based on the rules of _______________.
(d) When two lines are intersected by a transversal and the alternate angles are ___________.
Q-3 One word answer:
(a) Which of a line parallel to the given line at a certain distance.
Multiple Choice Questions
Q-1 The word ‘Geometry’ is derived from _____________ Latin words.

(i)

one

(ii)

two

(iii)

three
Q-2 Triangle is a polygon that has ___________ sides.

(i)

three

(ii)

two

(iii)

four
Q-3 Angle is not a polygon, because it is not a _________ shape.

(i)

open

(ii)

closed

(iii)

none of these
Q-4 Triangle is a polygon that has ___________ sides.

(i)

three

(ii)

two

(iii)

four
Chapter-17   Perimeter and Area
Q-1 Fill in the blanks:
(a) The measurement of the part of a plane figure or a region enclosed is called ____________.
(b) Perimeter of a shape is defined as the total distance around the shape is called its ___________.
(c) Square is a quadrilateral, with ___________ equal sides.
(d) The rectangle is a _____________.
Q-2

Find the diameter of a circle whose circumference is :

(i) 2.2 cm

(ii) 26.4 cm

(iii) 220 cm

(iv) 44 cm

(v) 0.88 cm

Q-3

Solve - 

1. Two rectangular pieces of paper strips, each of lenght 30 cm and width 3 cm, are pasted at right angles to make the shape of a cross. Find the perimeter of the cross.

2. A square has a side of 15 cm. If two such squares are placed next to each other so that their sides touch, find the perimeter of the resulting rectangle.

3. A round plate has a circumference of 145 cm. Among the diameters 57 cm, 24 cm and 49 cm, which could be that of the smallest box in which the plate could be packed?

4. Two circles have diameters in the ratio 1 : 3. Find the ratio of their circumference.

5. A cycle wheel has a radius of 28 cm. What distance will it travel in one revolution and in 24 revolutions?

6. A wire forming a rectangle of dimensions 9 cm and 6.4 cm, is stretched and bent again to form a circle. What would be the diameter of the circle?

7. A rectangular field is 54 m long and 40 m wide. Find its perimeter.

8. Find the width of a rectangular vegetable garden if its perimeter is 16.4 m and its length is 5 m.

9. The diameter of a circular placemat is 30 cm. Find the circumference to the nearest millimetre.

10. The perimeter of this isosceles trapezium is 92 cm. Find the value of x.

11. A circular swimming pool has a diameter of 35 metres. What is its circumference?

12. If the ratio of the circumference of one circle to that of the other, is 4 : 3, in what ratio will their radii be?

13. A length of rope is placed on the floor in the shape of an equilateral triangle of side 2.2 m. If this rope is spread out and a circle is formed out of it, what will be the radius of the circle?

14. The diameter of the wheels of a lorry is 98 cm. What is the distance it will travel in 1000 rotations?

15. Find the perimeter of this rectangle.

Q-4 True or False:
(a) Parallelogram is a simple quadrilateral with two pairs of parallel sides.
(b) Triangle is a __________ sided closed polygon.
(c) The circumference of a circle refers to the distance around the circle.
(d) π refers to the ratio of a circle's circumference to its diameter.
Q-5 One word answer:
(a) What is the area of triangle.
(b) What is the Area of parallelogram.
(c) What is the area of square.
(d) What is the Perimeter of square.
Q-6

Find the circumference of a circle whose radius is:

(i) 5.6 cm

(ii) 4.9 cm

(iii) 6.3 cm

Q-7

Find the circumference of a circle whose diameter is:

(i) 84 cm

(ii) 91 cm

(iii) 42 cm

(iv) 21 cm

(v) 56 cm

Q-8

Solve the following Questions - 

1. PQRS is a parallelogram of area 120 cm2 . If PS = 10 cm and PQ = 15 cm, find the measures of SM and altitude PM.

2. PQRS is a parallelogram with altitude PM and base SR. SN is the altitude on base QR. If SR = 8.2 cm, PM = 4.8 cm and SN = 6 cm, what is PS?

3. The longer side of a parallelogram is 15.5 cm and the corresponding altitude is 12 cm. If the altitude corresponding to the shorter side is 20 cm, find the length of the shorter side.

4. ABCD is parallelogram. E and F are the midpoints of AB and DC respectively. What are the areas of parallelograms AEFD and EBCF, in terms of the area of parallelogram ABCD?

5. In the figure given for Q (2), if the area of parallelogram is 45 cm2 , PQ = 9 cm and SN = 6 cm, find PM and QR.

6. The area of a parallelogram ABCD with side AB = 25 cm and the corresponding altitude = 10.5 cm is equal to that of another parallelogram EFGH with side EF = 12.5 cm. Find the altitude of EFGH corresponding to side EF.

7. The diagonal BD of a parallelogram ABCD is 4.2 cm long. The perpendicular distance from this diagonal to each of the vertices A and C is 2.5 cm. Find the area of the parallelogram.

8. A parallelogram has an area of 2700 sq.cm. If its two altitudes are of lengths 30 cm and 45 cm, find the lengths of the sides.

9. In the figure, if AB = 4.4 cm, AE = 3.5 cm and AD = 5.5 cm, find the length of the perpendicular from B to AD.

10. One side of a parallelogram is 30 cm, and its area is 540 cm2 . Find the height corresponding to the given side.

Multiple Choice Questions
Q-1 The measurement of the part of a plane figure or a region enclosed is called __________.

(i)

length

(ii)

area

(iii)

perimeter
Q-2 ____________ of a shape is defined as the total distance around the shape is called its perimeter.

(i)

Perimeter

(ii)

area

(iii)

both of these
Q-3 Perimeter of a regular polygon = Number of sides × length of __________side.

(i)

one

(ii)

two

(iii)

four