mathematics-vi · pdf fileusing bodmas 55 ÷ 5 × (18 – 7) = 55 ÷ 5...

3Playing with number

CHAPTER-1: Playing with number

FORMATIVE ASSESSMENT

Oral-Based Questions 1. 1000; 2. 9999 3. Thousand 4. zero 5. Thousand 6. hundred 7. 1,00,000 8. 63000 9. L 10. No

Fill in the Blanks 1. mother did not cry much

2. (i) 100 (ii) 110

(iii) 1000

3. (i) 1000 (ii) 1000 (iii) 110 00 000, ,

4. 68000 5. 62,34,570 6. 56,643,175: Fifty six million six hundred forty three thousand one 7. 5235, 6024, 6234, 8100 8. 845 9. 6420, 2046 10. Litre

True/False 1. False: as M stands for 1000, C for 100 & L for 50 So, MCCL = 1000 + 100 + 100 + 50 = 1250 2. True 3. False: 3400 + 4700 = 8100 4. False: Metre is standard unit of length 5. True: as 1 kg = 1000 gm 6. False: It is 6 × (8 – 4) 7. False: Roman numeral for 97 is XCVII where as CXVII = 117. 8. False: Using Bodmas 55 ÷ 5 × (18 – 7) = 55 ÷ 5 × 11 = 11 × 11 = 121 9. True: Successor of 999999 = 999999 + 1 = 1,00,000 10. False: Place value of 5 is 500 and face value is 5 sum = 505 not 1000.

MATHEMATICS-VI

teacher’s manual Question bank mathematics-Vi4

Crossword

Project/Activity 1. 2.

SUMMATIVE ASSESSMENT

Multiple Choice Questions 1. (d) 2. (a) 3. (c) 4. (d) 5. (a) 6. (c) 7. (b) 8. (b) 9. (a) 10. (a)

Match the following (i)—(d) (ii)—(c) (iii)—(b) (iv)—(a) (v)—(f)

Very Short Answer Type Questions 1. MMCCXLV 2. 3500 3. (a) 45700 (b) 46000 4. 6 cm 25 cm = 6.25 m 5. 250 ml 6. 10,00,000 mg 7. 7,653,384 : Seven million six hundred fifty three thousand three

hundred eighty four. 8. 500 9. 6 × (9 – 3) 10. 10,000.

Short Answer Type Questions 1. 5067, 5076, 5607, 5670, 5706, 5760, 6057, 6075 6507 6570, 6705, 6750, 7056, 7065, 7506, 7560, 7605, 7650 2. 381, 382, 383, 384, 379, 378, 377, 376, 375 3. (i) 23900 (ii) 23000

5Playing with number

4. (i) 35 (ii) 720000 5. (i) DXCV (ii) CMXCVI (iii) CCXXVIII (iv) CDXLVI 6. 37 gm 7. 24 L200ML/24L 8. Ascending order is 5,40,360, 540720, 560005

Saving : ‘A GIRL CHILD IS LIKE SAVING DIAMOND’

/ ‘SAVE A GIRL CHILD SAVE YOUR COUNTRY’

9. 6078, 6087, 6708, 6780, 6807, 6870 10. 5312, 5321 11. 9915 12. 378 bottles 13. 399600 14. 235 15. 25 16. CLX 17. (1234 + 6789) + (2345 + 5678) + (3456 + 4567) = 8023 + 8023 + 8023 = 24069

Long Answer Type Questions 1. 12 : People can communicate very easily and very fast Drawback

is misuse of it like sending unnecessary posts to others. 2. ` 5967.5 3. 9 kg 4. 28 5. 42110 6. (i) 400000 (ii) 374400 7. 43 frocks, 55 cm Hots:

8 1

7

6

3

4 9 2

5

Nos, along rows are 816, 357, 492 Nos, along columns are 834, 159, 672 Nos, along diagonals are 852, 654 Largest number is 852 Smallest number is 159


2. 4 pyjamas 3. 87 cm; 13 cm 4. (a) 18750 m i.e., 18 km 750 m, (b) ` 78.75% 5. ` 5900

Multiple Choice Questions (a) 1. Kalahari Desert: Indian system Five lakh eighty thousand

sq km International System: Five hundred eighty thousand sq km 2. Australian Desert : Indian Twelve lakhs fifty thousand sq km International : One million two hundred fifty thousand sq km 3. Gobi Desert: Indian: Thirteen lakh square km International: One million, three hundred thousand sq km 4. Arabian Desert: Indian Eight lakh fifty thousand sq km International: Eight hundred fifty thousand sq km. 5. Sahara Desert: Indian Eight lakh sq km International: Eight million eight hundred thousand sq km (b) Kalahari Desert, Arabian desert, Australian desert, Gobi desert,

Sahara Desert (c) Sahara Desert (d) Arabian Desert

Value Based Questions 1. 190L; suggestion to the family is Instead of washing car, it could

have been wiped off with wet cloth instead of washing terrace it could be moped to save water

2. Cloth used is 3750 cm i.e., 3m 750 cm. Jyanti used paper if paper get spoiled it will thrown whereas if

cloth is used it can be washed and reused. 4. letter or signs 5. Greeks

CHAPTER-2: whole numbers


Oral-Based Questions 1. Natural numbers 2. Whole numbers 3. one 4. Zero 5. No; as every natural number & whole number has its successor 6. Yes

7whole numbers

7. Yes, Yes, commutative prop of multiplications 8. Zero 9. One 10. No

Fill in the Blanks 1. One 2. 2 3. whole numbers 4. 21 5. 49 6. additive 7. multiplicative 8. 2 × 15 9. 15 10. 10000

True/False 1. False 2. False 3. True 4. False 5. True 6. True 7. False 8. True 9. False 10. True

Crossword



Multiple Choice Questions 1. (a) 2. (d) 3. (b) 4. (a) 5. (b) 6. (a) 7. (b) 8. (d) 9. (d) 10. (d)

Match the following (i)—(d) (ii)—(a) (iii)—(b) (iv)—(c) (v)—(e) (vi)—(f)

Very Short Answer Type Questions 1. Zero 2. One 3. 16 + 15 = 15 + 16 4. 625 × (200 + 10) = 12500 + 6250 = 1.31250


5. 6124 6. 5251 7. 49 8. 4050 9. 55 10. 36

Short Answer Type Questions1.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A B

OR

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BA

B represents, 7 + 6 = 13 = B.2.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B A

16

B represents 15 – 73.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

7 7

17 18

Quotient 2, Remainder 24.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

3 3 3 3 3

3 × 5 = 15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

5 5 5

5 × 3 = 155. 78 × 999 + 78; 78(999 + 1) = 78006. (625 × 4) × (18 × 5); 2500 × 90 = 2250007. 36 as

4 × 9 Rectangle Triangle Square

9whole numbers

8. (a) 625 + 99 = 725 – 1 = 724 (b) 625 – 99 = 525 + 1 = 5269. 16

Short Answer Type Questions 2. 162 × 18 + 162 × 74 + 162 × 8 = 162 × [18 + 74 + 8] = 162 × 100 = 16200 3. (i) 1454 – 9 = 1444 + 1 = 1445 (ii) 1454 – 99 = 1354 + 1 = 1355 (iii) 1454 – 999 = 454 + 1 = 455 4. 485 × 995 = 485 × (1000 – 5) = 485000 – 2425 = 482575 5. 1

2

3

4

5

6

7

8

T

36 6 × 6 = 36

6. 15 × 15 + 15 × 5 + 15 × 3 = 15 [15 + 5 + 3] = 345 Total monaj spent = ` 345% 7. ` 15625 8. 999 + 1999 + 2999 = 1000 – 1 + 2000 – 1 + 3000 – 1 = 6000 – 3 = 5997 9. 2784 students can board bus. Suggestion for students who come

by private vehicle is to either use school bus or cycle or can walk down to school as it will help in lowering fuel consumption traffic jam and also pollution

10. Weight of each carton = 1040 tons.

Long Answer Type Questions 1. (a) 795 (b) 885 (c) 1785 (d) 10785 2. (a) 18878 (b) 18788 (c) 17888 (d) 8888 3. (a) 3085 (b) 15175 (c) 103375 (d) 570625 4. (a) 300 (b) 60 (c) 12 (d) 200 5. (a) 7578 (b) 182358 (c) 585414 (d) 5419458 6. (a) 65145 (b) 523523 (c) 4870487


7. 1099989, 10999989 8. (a) a and b are reciprocal of each other (b) At least one of a and b is zero (c) a and b are equal but not equal to zero (d) a is zero, b is any number

Higher Order Thinking Skills

1. 78 and 43 as 78 + 43 = 121 78 × 43 = 3354

2. 83 3. 99975 4. 127, 255

Value Based Questions 1. 56250 × 4 – 12825 × 16 = 25 × 2250 × 4 – 25 × 513 × 16 = 100 × (2250 – 513 × 4) = 100 × (2250 – 2052) = 100 × 198 = 19800 2. 450 × 999 = 450 × (1000 – 1) = 450000 – 450 = 449550. 3. ` 10,500: No he was not right he should have requested to help his

friend.

Multiple Choice Questions Ans. 57418

True/False with Justifications 1. False e.g., 2 ÷ 3 is not a natural number 2. False: 6th triangular number is 21 3. True: 6th square no. is 6 × 6 = 36 4. True as 1 is square number as well triangular no. 5. False 625 × 147 = 91875 + 625 × 53 = 33125 = 125000 625 × (147 + 53) = 625 × 200 = 125000 \ 625 × 147 + 625 × 53 = 625 × (147 + 53) 6. True: Zero is an additive identity 7. False: Successor of 1 million is 1000001 8. True 9. True 10. True

11Playing with numbers

CHAPTER-3: Playing with numbers


Oral-Based Questions 1. Factor of a number is a number which divides given number

exactly. 2. Multiple of a number is a number which is exactly divisible by a

given number. 3. 1 and number itself are always factors of the given number. 4. Number itself is always a multiple of itself 5. Nos. whose unit digit is one of 0, 2, 4, 6, 8. 6. Nos. which are divisible by only one & itself are prime numbers. 7. Smallest prime number is 2 8. No, as 78 (no. formed by last two digits) is not divisible by 4. 9. Two prime numbers whose difference is 2 are called twin prime

numbers. 10. Two numbers whose H.C.F. is 1 are called coprime nos.

Fill in the Blanks 1. Multiple/factor 2. One and number itself 3. 2 4. 1 5. Twin-prime 6. their product 7. 1 8. 9 9. L.C.M. 10. 9 & 5 both

True/False 1. False: e.g., 9 is odd but not a prime number. 2. False: e.g., 1 is a square number but not composite no. 3. True 4. False: 2 is a prime number as it has only two factors 1 & 2. 5. True: 6 + 7 + 8 = 21, 21 is divisible by 3 but not by 9. 6. True: because 100 and 101 are coprime numbers 7. True: because 158 and 159 are consecutive numbers 8. False: 1 is neither prime not composite number 9. True: 2 + 3 is divisible by 5 but 2 and 3 are not divisible by 5. 10. True: Product of two nos. = product of H.C.F. and L.C.M.


Crossword



Multiple Choice Questions 1. (c) 2. (c) 3. (b) 4. (c) 5. (d) 6. (b) 7. (b) 8. (d) 9. (c) 10. (b)

Match the following (i)—(c) (ii)—(c) (iii)—(c) (iv)—(e) (v)—(d)

Very Short Answer Type Questions 1. 2 2. 1, 97 3. 17, 34, 51, 68, 85 4. 2, 3, 5, 7, 11, 13, 17 5. 3 + 4 + 5 = 12, 12 ÷ 3 = 4, 4 + 5 + 6 = 15, 15 ÷ 3 = 5, 5 + 6 + 7 = 18, 18 ÷ 3 = 6 6. 221 7. 1 8. Sum of digits = 7 + 8 + 9 + 2 + 3 = 29 not div. by 3 9. 6854 24 no. formed by last two digits is 24 and 24 ÷ 8 = 3 \ given no. is divisible by 8 10. 782 5 : Unit digit is one of 0 or 5 hence divisible by 5.

Short Answer Type Questions 1. 101, 131, 141 2. 90, 91, 92, 93, 94, 95, 96 3. 2 + 5 + 89

13Playing with numbers

4. 56728 : No. formed by last three digits is 728 which is divisible by 8

)8

8

)918 728

72

×

5. 1, 2, 3, 17, 51 6. 45, 90, 135 7. 342, 33, 84, 5976 8. (a) 4 (b) 7 9. 90 10. 25

Short Answer Type Questions 1. 1080 2. 9 3. 3795 4. 53904 [Hint for a no. to be divisible by 8 if should be div by 2 & 4] 5. 46020 = 2 × 2 × 3 × 5 × 7 × 11 6. 420

Long Answer Type Questions 1. 36, 108 2. (10, 150); (30, 50) 3. 54 4. 7 m 5. 60 limes 6. 17 7. 1205 8. 960

Hots: 1. 7 2. 7561 3. (2, 2), (5, 2), (8, 2), (1, 6), (4, 6), (7, 6) 4. 4199

Value Based Questions 16 min 48 sec past 9 a.m.

True/False 1. False it should be div by 3 & 4 both 2. True 3. True 4. True 5. True 6. True 7. False 2 & 3 both are prime & are consecutive 8. False P.F. of 6 is 2 × 3 9. True 10. True

Life Skills 1. Minimum no. of tiles is 240 ticls, ` 3600 2. 3150 cm, No. of Jumps of A, B, C are 45, 42, 35 resp.


CHAPTER-4: basic geometrical ideas


Oral-Based Questions 1. Plane is a flat surface which can be extended indefinitely in all

directions e.g., table top. 2. Line segment is a part of line with two fixed end points and cannot

be extended at all. 3. Circle is a collection of points which are at equal distance from a

fixed point is called centre of the circle and equal distance is called radius.

4. One 5. No 6. Two or move points which lie on a line are called collinear points. 7. Three or more lines are concurrent if they all pass through the same

point. 8. twice the radius 9. Infinite tines 10. Lines in a plane which are not parallel are intersecting lines.

Fill in the Blanks 1. Adjacent 2. Parallel 3. Diameter 4. Point 5. Line 6. Chord 7. 35 8. Circumference 9. Diagonal 10. Semi-circles.

True/False 1. False: as M stands for 1000, C for 100 & L for 50 So, MCCL = 1000 + 100 + 100 + 50 = 1250 2. True 3. False: 3400 + 4700 = 8100 4. False: Metre is standard unit of length 5. True: as 1 kg = 1000 gm 6. False: It is 6 × (8 – 4) 7. False: Roman numeral for 97 is XCVII where as CXVII = 117. 8. False: Using Bodmas 55 ÷ 5 × (18 – 7) = 55 ÷ 5 × 11 = 11 × 11 = 121 9. True: Successor of 999999 = 999999 + 1 = 1,00,000 10. False: Place value of 5 is 500 and face value is 5 sum = 505 not 1000.

15basic geometrical ideas

Crossword

1

6

7

9

4

2

3

5

10

8



Multiple Choice Questions 1. (b) 2. (b) 3. (d) 4. (b) 5. (d) 6. (b) 7. (d) 8. (d) 9. (c) 10. (b)

Very Short Answer Type Questions 1. 14 cm 2. Yes

3. AB is line segment; ΑΒ→

is a line AB 4. No; A & B lie outside circle. 5. No; Polygon is a simple closed curve 6. 42 cm 7. 10 cm 8. No; Since radius is 8 cm so distance of any point lying inside the

circle from centre will be less than 8 cm

9. arms BA→

, BC→

vertr B 10. AOC , BOC= =3 1 11. Three DSTO, DSOU, DSTU.


Short Answer Type Questions 1. Six 2. Pentagon ABCDE no. of diagonals = 5

3. Yes D C

BA

4. Six

5. (a) CD (b) AD→

(c) AD↔

6. (a) Line does not have any fixed point where as a ray has a fixed end point

(b) Line can be extended indefinitely in both directions but ray cannot be extended at all.

7. Yes. This is a simple curve 8. No, not a simple curve 9. 18 10. Sides AQ, QR, PR Angles: ∠P, ∠Q, ∠R; Vertices P, Q, R

Short Answer Type Questions1.

a b

Zero point of intersection

2.

a

b

Maximum number of point of intersection = 4

3. (a) l

m

n

minimum point of intersection is zero

17basic geometrical ideas

(b) maximum number of point of intersection is 3

4. (a)5.

O

P

R

Q

S

B

C

A

6. (i) OA, OB, OC (ii) BC (iii) PQ, BC (iv) AOC & BOA (v) CAB, CPB� � (vi) CPQ�

(vii) PAQ�

7.

O

A

D

Q

C

P

B

X

Y

6

8. 13 9. 3 cm

10. (i) l || m (ii) (q, l); (q, m); (r, l), (d, m), (p, l), (p, m) (iii) A, F, B (iv) A, F, B, C, D (v) lines r, q, l, m; pt of convenience C

Match the following (i)—(d) (ii)—(e) (iii)—(f) (iv)—(a) (v)—(c) (vi)—(b)

Value Based QuestionsOn Diwali, Rakhi, Bhai Doj etc.


True/False 1. False: AB represents a line A B

2. False: A

B C

Triangle is a last sided polygon

3. True: O

r r BA AB = r + r = 2r

4. True: A

5. True: l

m

6. True: l

m n

l is || l to n but m in not parallel to n

7. True 8. False: 4 8 8 3

2( )−

= 4 × 5 = 20

9. True:l

m

180°

10. False: polygon is formed by line segments

CHAPTER-5: understanding elementary shaPes


Oral-Based Questions 1. 90° 2. more than 0° but less than 90° 3. No 4. No 5. F + V – E = 2 6. A triangle having no two sides equal is called scalene triangle. 7. Equiangular triangle. 8. A line bisecting line segment at right angle. 9. Three 10. One

19understanding elementary shaPes

Fill in the Blanks 1. Hexagon 2. 1, 2 3. Zero 4. Square pyramid 5. equilateral triangle 6. acute 7. Square 8. 7 9. Perpendicular bisector 10. half revolution

True/False 1. True 2. False 3. False 4. True 5. True 6. True 7. True 8. False 9. 135° 10. False

Crossword



Multiple Choice Questions 1. (c) 2. (c) 3. (d) 4. (b) 5. (a) 6. (b) 7. (c) 8. (d) 9. (b) 10. (b)


Match the following (i)—(e) (ii)—(d) (iii)—(b) (iv)—(c) (v)—(a)

Very Short Answer Type Questions 2. Zero/1080° 3. equilateral triangle 4. 45° each 5. scalene/obtuse 6. F – 6, 5 – 12, V = 8 7. F + V – E = 2 8. 9. Square

10. Rectangle

Short Answer Type Questions 1. Cube and Triangular Pyramid 2. 60°

3. 45° 4. (a) PQ→

(b) PS→

5. (a) A BO

(b) A B

6.

P

B

CD

E

A

a cm

a cm

a cm

a cm

a cm

7. (b)

8. (a) Cuboid (Operator shows a book) (b) Cube (Show a dice)

Short Answer Type Questions 1. They are perpendicular bisector. 2. a = Acute a = b = 90° a = acute, b = obtuse, c = acute Fig. A Fig. E Fig. K

a = acuteb = reflex

a = acuteb = acute

p = acuteq = obtuse M Z Y

3. Hour hand = 30°, Minute hand = 360° 4. ?? 5. ?? 6. Yes 7. Yes

21understanding elementary shaPes

8.

R

P Q

40 m

30 m Isosceles triangle 9.

Long Answer Type Questions 1. (i) Cone (ii) Cone (iii) sphere (iv) cube (v) Pyramid 2. ?? 3. A B C D

C mid point of BD ⇒ BC = CD (i) AC = AB + BC = CD + BC = BD (ii) AD = AB + BC + CD = AB + CD + CD C mid point of BD = AB + 2CD = AB + 2AB = 3AB (iii) CD = AD – AC = AC + CD – (AB + BC) = AC + CD – AB – BC = AC – AB as CD = BC 4.

A B

CD

(i) AB || CD (ii) D = 90° (iii) 180° 5. (i) 90°; right angle (ii) 120°; obtuse angle (iii) 180°; straight angle (iv) acute angle = 60°

Hey Do You Recognize Me (i) Equilateral triangle (ii) Trapezoid (iii) Regular Nonagon (iv) Hexagonal Prism (v) Pentagonal Pyramid

True/False (with Justification) 1. False, e.g.,

A B

l here line l is perpendicular butdoes not bisect AB


2. True : 3. True:

4. True 5. False: If length and breadth of a cuboid are equal then only it is a

cube otherwise not.

Multi-Disciplinary Questions 2. Central Chamber

Regular OctagonMain buildingMinaret circle

3. Octagon

CHAPTER-6: integers


Oral-Based Questions 1. Collection of whole numbers and negatives of natural nos. form

collection of Integers i.e., – – –, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, .... 2. No 3. Absolute value of an integer is its numerical value regardless of

its sign e.g., | – 5 | = 5, | 5 | = 5. 4. Zero is neither negative nor positive integer. 5. Immediately to the right of the integer. 6. Non-negative integers. 7. As every integer has its successor. 8. – 7 & 7, – 6 & 6, – 15 & 15 there are numerous pairs of integers

whose sum is zero. 9. Yes 10. Yes

Fill in the Blanks 1. Non-negative 2. – 1 3. negative 4. 1 5. Zero 6. 1 & 3 7. – 2 & – 3 8. 4, 3 9. – 107 10. – 4

23integers

True/False 1. True 2. False 3. True 4. False 5. False 6. True 7. False 8. False 9. False 10. True

Crossword

Project/Activity 1.


Multiple Choice Questions 1. (c) 2. (a) 3. (d) 4. (d) 5. (c) 6. (b) 7. (c) 8. (a) 9. (c) 10. (b)

Match the following (i)—(f) (ii)—(a) (iii)—(b) (iv)—(d) (v)—(e) (v)—(c)

Very Short Answer Type Questions 1. – 3, – 2, – 1, 0, 1, 2, 3 2. – 3, – 2, – 1, 0 {there are many more} 3. – 14, – 15, – 16, – 17 {there are many more} 4. – 4, – 3, 0, 2, 6 5. 17, 3, – 2, – 18, – 20, – 53 6. – 6, – 5, – 4, – 3, – 2, – 1, 0, 1 7. – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4 8. – 99, – 98, – 97, – 96 9. – 12 10. (8, 4); (10, 5) many move 11.

0 1 2 3 4 5

| – 5|


Short Answer Type Questions 1. – 12, – 7; – 16, – 11, many more 2. (a) – 26 & – 38 (b) – 24 & 0 (c) 45 & 0 (d) 43 & 34 3. (a) – 5, – 4, – 3, – 2, – 1, 0, 1 ; no. of integers = 7 (b) – 6, – 5, – 4 ; no. of integers = 3 4. (a) – 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2 ; no. of integers = 9 (b) – 7, – 6, – 5, – 4, – 3 ; no. of integers = 5 5. (a) 9 (b) – 3 (c) – 10 (d) 16 6. Zero; Successor is 1; – 1 & 1 are additive predecessor is – 1 inverse

of each other. 7. (a) 16 (b) – 20 (c) – 0 (d) – 14 8. (a) 29 (b) 30 (c) 8 (d) 0 9. (a) – 12 (b) + 20 (c) – 18 (d) + 15,000 10. (a) 60 (b) – 5

Short Answer Type Questions-II 1. (a) 740 (b) – 26 (c) 257 (d) 400 2. (a) zero (b) 600 3. – 2, – 1, 0, 1, 2; yes these are countable 4. – 11, 11 5. – 226 6. 140 7. – 149 8. 220 9. 2016 – 14 = 2002 10. (a) 14 * 20 = 14 – 20 – 2 = – 6 – 2 = – 8 (b) 100 * 85 = 100 – 85 – 2 = 13

Long Answer Type Questions 1. (a) 35 (b) 135 (c) 160 (d) 0 2. (a) Zero (b) – 2 3. (a) < (b) > (c) = 4. (a) – 2 (b) – 12 5. (a)

0–1–2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Ans. 9 (b)

–19–20–21 –18–17–16–15–14 –13 –12–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3

Ans. – 7

25integers

6. – 365 7. 260 8. (a)

–14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0

Ans. – 12 (b)

–4 –3 –2 –1 0 1 2 3 4 Ans. – 2 (c)

–6 1 2 3 4 5 6 7 8 9 10 11 12–5 –4 –3 –2 –1 0

Ans. – 4 (d)

14131211109876543210–1

Ans. 11

HOTs 1. 4 minutes 2. (a) 5°C (b) 5°C 3. 405 × (1 + 20 – 2) = 405 × 19 = 7695

True/False 1. True; Predecessor means number to the left and to left of any

negative integer is always a negative integer. 2. True; Abs value is only numerical value it is regardless of sign

(+, –) 3. False e.g., sum of – 4 & 6 is – 4 + 6 = 2 not |– 4| + |+6| = 10 4. False; No we move to right only if no. to be added is +ve and to

left if no. to be added is –ve. 5. True

Multi-Disciplinary Questions 1. (a) Rise in water level (b) Deposit of ` 100 (c) log 5/defeat by 10 runs (d) 5°C rise in temperature. 2. d


CHAPTER-7: Fractions


Oral-Based Questions 1. Fraction represents a part of a whole or a group. 2. a is numerator, b is denominator. 3. Like fractions are the fractions with same denominator. 4. If denominators of fractions are not same i.e., they are unlike then

fractions are called unlike. 5. A fraction having numerator smaller than denominator is called

proper fraction. 6. Improper fractions. 7. When improper fraction is written as a combination of whole

number and a proper fraction then this is called mixed numeral. 8. Whole number q is quotient, r is remainder & d is denominator. 9. Improper Fraction 10. Yes

Fill in the Blanks 1. Improper 2. proper 3. Unit 4. Mixed 5. 48 6. 35 7. 42 8. < 9. > 10. <

True/False 1. False 2. True 3. True 4. True 5. True 6. True 7. False 8. True 9. False 10. False

Crossword

27Fractions

Project/Activity 1.


Multiple Choice Questions 1. (a) 2. (a) 3. (b) 4. (a) 5. (d)

6. (b) 7. (d) 8. 58

9. (a) 10. (a)

Match the following (i)—(c) (ii)—(a) (iii)—(b) (iv)—(e) (v)—(d)

Very Short Answer Type Questions

1. 49

2.

3. 0 1

3/5

4. (a) 607

(b) 434

5. 87, 95 6. 14

7. 30 8. 58

glass 9. 1317

734

>

10. 2517

Short Answer Type Questions

1. 116

2. 3210

18/7

187

= 247

3. 25

34

2320

+ = 4. 16235

5. 34955

6. 12

7. 49

is not equivalent to 23

8. 47

9. 25

10. 712


Short Answer Type Questions-II

1. (a) 2068

517

= (b) 6565

(c) 6825

2. x = 55, y = 55 3.

210

1—4

5

4. (a) 169182

(b) 156168

5. 23

1318

79

1112

< < <

6. 3518

2 23

1 512

1 16

> > > 7. 15

th

8. Younger one got 1940

Youngest one got biggest share so she loves

the youngest grand child the most

Long Answer Type Questions

1. 375 2. 49

3. 160

, ` 3446 23

, Yes it is a good drop

4. 115

; she is a hardworking girl and 5. 60 m

6. ` 575

= ` 11.40

HOTs

1. 16

2. no. of quadrilaterals

no. of triangles = 6

1212

=

Value Based Questions

1. Each will get 23

of sandwiches

True/False (With Justification) 1. True 2. True

3. True; 77121

711

2133

= =

4. 5769

1923

3846

= = No lowest form is 1923

not 3846

29decimals

5. 447

597

1037

14 57

+ = = True 6. True

7. True ; Numerator is less than denominator

8. True ; as 17

27

37

, , have same denominator

9. True; 62 > 54 10. False ; 49

415

>

Life Skills 1. School is at 10 km distance, No we should not take lift from

stranger.

2. Bought 25

of CDS and 35

of CDS as gift

3. Amrita worked for more no. of hours, by 78

hrs. 4. English = 30, Hindi = 40, Both = 10 40 people do not read any news paper. Hindi is read more.

5. 97

m, Smallest 48

, largest 208

6. 48

208

808

× = = 10

7. ??

CHAPTER-8: decimals


Oral-Based Questions 1. Decimal numbers having same number of decimal places is

called decimal number.

2. 35100

720

= 3. 2.4

4. Forty two point three five 5. Place decimal after three digits from right

6. 1 × 10 + 7 × 1 + 2 × 110

1 1100

5 11000

+ × + ×

7. 2.8 8. 8.5 9. 4.23 10. 1.070 kg


Fill in the Blanks

1. 58

2. .425 3. 24

4. 2.5 5. .160 6. .75 7. = 8. unlike decimals 9. 36.202 10. 6.025

True/False 1. False; decimal will be after two places from right 2. False; 25P = ` .25 3. True 4. False; 3.96 not 3.60 5. True 6. False; It is read is zero point two five. 7. True 8. False 9. True 10. False; as they are unlike decimals.

Crossword

Project/Activity 1.


Multiple Choice Questions 1. (c) 2. (c) 3. (c) 4. (b) 5. (b) 6. (b) 7. (a) 8. (c) 9. (d) 10. (d)

Match the following (i)—(f) (ii)—(a) (iii)—(c) (iv)—(e) (v)—(d) (vi)—(b)

31decimals


1. 0 14

2. 320

3. Fifteen point zero two five 4. 1.09 5. 0.05

6. Tens Ones Tenth Hundredth1 9 0 6

7. 7 rupees 30 paise 8. 0.077 km

9. 2 × 10 + 2 × 1100

5 11000

+ × 10. pt. B

Short Answer Type Questions 1. 215.505 2. 0.94 ml 3. 0.0215 < 0.2015 < 0.2115 < 0.215 4. ` 50.50 5.

6. (a) 400 + 3 + 6100

= 403.06 (b) 8 + 351000

= 8.035

7. 0.089 8. 2.968 9. 6.5 m ; 487.50 m 10. (a) 3.008 (b) 8.025 (c) ` 500.05

Short Answer Type Questions-II 1. ` 25.55 2. 35.5 m 3. ` 68.40

Long Answer Type Questions 1. ` 14.40 2. Total weight with her is 9 kg 100 g. She can carry 5 kg 900 g more 3. 5 climbs 4. Gain is ` 4313.60 5. Meenakshi drove 155.175 km in total she drove 24 kg 940 m more

on Monday than on Tuesday.

HOTs 1. ` 54.50

Value Based Questions 1. 6 kg 700 g of fruit was distributed. Sunita is good by heart and

want to help blind children.


2. 1 kg 750 g paper was wasted in recycling the used paper. It will not call it as wastage rather it is use of paper. We mash save paper since paper is made from trees so saving paper means saving a tree.

True/False 1. Yes, because to right side of any decimal number we can annex

any number of zeros as are required. 2. No there are not like decimals because decimal places are not same. 3. False; as 10 m 5 cm = 10.05 ml 4. True; 1l = 1000 ml, .060 l = 60 ml

5. False; 5.608 = 5 610

81000

+ + 6. False; as it is 2403400

7. False; because 1.005 > 0.1005 8. False; as Paisa = ` 0.01 9. False; because sum is 1.30 m 10. False because 2350 g = 2.35 kg

11. False; it represents 1100

Life Skills 1. ` 313.40 2. 9 m 3. 2 kg 820 gm

CHAPTER-9: data handling


Oral-Based Questions 1. Data is information collected in the form of numbers or fact. 2. Data presented as collected is called raw data Arranged data. 3. Arrayed data 4. bar graph 5. Frequency is number of times an observations repeats itself. 6. Each entry of data is called an observation. 7. When data collected by someone else is used thus it is called

secondary data. 8. Scale is : 1 cm represents 40 units. 9. Observations, Tally marks, frequency. 10. No. of observations of a type or a group.

Fill in the Blanks 1. Primary 2. Arrayed 3. Primary 4. Secondary 5. Pictograph or bar graph

33data handling

6. Frequency 7. Total number of observation 8. Origin 9. Uniform 10. 20 students present on a day.

True/False 1. True 2. False 3. True 4. False 5. False 6. False 7. True 8. False

Crossword



Multiple Choice Questions 1. (d) 2. (c) 3. (d) 4. (a) 5. (b) 6. (c) 7. (a) 8. (c) 9. (a) 10. (b)

Match the following (i)—(c) (ii)—(d) (iii)—(b) (iv)—(a) (v)—(e)

Very Short Answer Type Questions 1. 1250 units 2. 240 3. * * * * * 4. 23 5.


Short Answer Type Questions 1. Arrange the information in tabular form.

Weightin kg

Tallymakrs

No. of Students(Frequency)

26 3

28 3

30 5

32 3

35 6

38 2

40 3

2. (a) May (b) August – 150 (c) April & July (d) Janurary, February, December 3. (a) Bar graph depicts no. of magazines A, B, C & D (b) Magazine D (c) Magazine C (d) 1000 (e) may vary (e.g. India Today) (f) By reading vocabulary, grammar, usage of language is

improved. 4. (i) English (ii) Foreign language (iii) Hindi 5. (a)

1750

4250

30002500

5000 5

2

2.52.2

1.5

3000

1800

1500

Buses

Population

Buses 20 cm = 1000 buses

for Population 20 cm = 1 million

35data handling

(b) State A 50005000000

= 11000

State B 25002 000 000, ,

= 1800

State C 32500

State D 42502 2 1 000 000. , ,×

= 178800

State E 35300000000

7

= 178800

(c) State E 6. Let * represents 10 old age home (a) TEV * * * * * * * * * * KOLKATA * DELHI * * * * * * * * * * * MYSORE * * * * * KERALA * * * * * * * * * * (b) Sandhya, Delhi (c) Yes more of old age homes are required (d) KA (e) 370 (f) ?? 7. (a) Information: No. of Internet user in various cities.

(b) Delhi (c) 10 00025 000

25

,,

= = 2:5

8. (a) Bar graph provides information of people below poverty line in rural area

(b) In 1995–96 & 1996–97 (c) 1990–91 (d) From 1990 & 1997 (e) No.

Short Answer Type Questions-II 1. (a) Bar graph represents wheat grown (in tonnes) in different

regions. (b) D (c) 150 tonnes (d) A & E (e) A & B 2. (a) In 1996–97 & 1997–98 export is at same level. (b) In 1995–96 & 1995–97; 2000 Crores (c) 1998–99 export is highest.


4. Let represents 420 tigers

(a) Bandipur

Corbett

Kanha

Meighat

Manas

Dudhwa

(b)

500

400

300

200

100

410

340310

190170

120

X0

Y

1 cm = 100 tigers

No

. o

f T

igers

B

A

N

D

I

P

U

R

C

O

R

B

E

T

T

K

A

N

H

A

MEIGBAT

MANAS

DUDHWA

Tiger Reserve

(d) Missing logo National Tiger ??? (e) By making people aware about saving Tiger through slogans,

placards, Advertisements etc.

37data handling

2. (a)

50

40

30

20

10

(40)(43)

(13)

(29)

X0

Y

1 cm = 10 unitsR

oll

ing

Sto

ch

RED

Y

E

L

L

O

W

B

L

U

E

BLUE

GREEN

Name (Terminals)DILSHAD

GARDEN

(23)

NOIDA

CITY

CENTRE

HUDACIT

YCENTRE

VIOLET

INDERLOK

VAISHALI ITO

(b) Blue (Noida City Centre) (c) Blue (Vaishali) (d) It has helped in reducing traffic jams and hence pollution. (e) To reduce number of vehicles on rood and to save natural

resource (Petrol, fuel).

True/False (With Justification) 1. True; = 5 girls \ three = 5 × 3 = 15 girls 2. False ; it represents 7 3. True; \ 1 unit = 20 tonnes, 5 units = (20 × 5) = 100 tonnes 4. False; 6 length vary as per numerical data (frequency) 5. False; Numerical data is represented by pictures and not by bars.

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

1. Observation Tally Marks Frequency

1 3

2 8

3 4


4 35 26 5

25

2. (i) 1 unit represent 10 marks. (ii) Mathematics (iii) Hindi (iv) English

Multidisciplinary

200

300

225

325

0

2 cm = 20 units

Exp

ort

in

th

ou

san

d t

on

nes

2

0

0

5

2

0

0

6

2

0

0

8

Year

200

2

0

0

9

300

400

220

240

260

280

320

340

360 350

2

0

0

7

400

2

0

0

4

2.

10

80

0

1 cm = 10 units

Po

pu

lati

on

(in

lak

hs)

M

U

M

B

A

I

KOLKATA

BANGLORE

City

45

CHENNAI

30

90

60

20

30

40

50

60

70

80

90

D

E

L

H

I

39mensuration

CHAPTER-10: mensuration


Oral-Based Questions 1. Perimeter is total distance along the boundary of any simple

closed curve in a plane. 2. Measurement of surface (or enclosed region) of a plane closed

figure is called Area. 3. Metre, Centimetre 4. Square cm, sq. m 5. 18 cm 6. 16 cm 7. 4 a units 8. s2 sq units 9. lb square units 10. 5 cm

Fill in the Blanks 1. Area 2. length 3. na 4. 210 sq/cm 5. 10000 6. 5000 7. 10,000 sq/m 8. 1 9. 40 cm 10. 3a units

True/False 1. True 2. False 3. False 4. True 5. False 6. False 7. False 8. False 9. False

Crossword

1

2

3

6

5

4

Project/Activity 1.



Multiple Choice Questions 1. (a) 2. (d) 3. (b) 4. (b) 5. (c) 6. (b) 7. (b) 8. (d) 9. (a) 10. (b)

Match the following (i)—(c) (ii)—(e) (iii)—(a) (iv)—(d) (v)—(b)

Very Short Answer Type Questions 1. 32 cm 2. 10 cm 3. 10 cm 4. 64 cm 5. 120 cm 6. 60000 7. 12a units 8. 8 square units 9. 125 m, 500 m 10. 12 m 11. 500 cm

Short Answer Type Questions 1. 48 m 2. 200 m 3. 28 m 4. 600 m 5. 30 6. 96 cm

7. 240 m × 600 m 8. 96 cm 9. 23

Short Answer Type Questions-II 1. ` 3600 2. 1500 sq-m 3.

4 cm Operator on a

square sheet draw

circle of radius 4 cm

Area is approximately 16 sq-cm

4. 78 cm2

5. (a) Area will become 4 times (b) Area becomes one-fourth 6. 80 tiles 7. 25 ha, ` 5,00,000 8. 300 sq-m 9. 24 cm 10. 20 cm 11. (a) 240 (b) 42

Long Answer Type Questions 1. (a) 15 cm (b) 20 cm (c) 12 cm (d) 10 cm

2. 65 m 3. 95 m2 4. 222 34

sq-m

5. 16 m2

41mensuration

HOTs 1. 128 m2 2. Area 13 sq cm 3. 1200 cm2

4. Possible dimensions are

Multi-Disciplinary Questions 1. 10 cm

True/False 1. False: Area is required 2. True: around the table cloth means perimeter 3. True: if side length is ‘a’ then perimeter = 39 and side length is ‘2a’ then perimeter = 6a 4. False: if becomes four lines 5. True 6. 2000 m 7. True; New perimeter = 2[L + B] = 2[l + 2 + b – 2] = 2 (l + b) = original perimeter. 8. False; we require area of both tile & wall 9. No ;

s When square sheet is divided into two halves then sum of

perimeters of these two rectangles

= 2 s ss s

+ + +

2 2

= 6s

Where as original perimeter = 4s 10. False; 7 square units.

Life Skills 1. 160 cm 2. 247500 sq m 3. 12 4. ` 4500, ` 13500

CHAPTER-11: mensuration


Oral-Based Questions 1. Literal : Alphabets used to represent number is called literal e.

age of son is x years.


2. Constant: Fixed value is called constant e.g., sum of angles of a quadrilateral is 360°. It does not change it has fixed value.

3. Algebraic expression: An expression formed by using literals, numbers and four mathematical expressions (+, ×, –, ÷) is called an algebraic expression e.g. 3x + 7y + 8.

4. Variable: If the literals used can vary i.e. can take different values, then it is called variable.

5. Perimeter of a square is 4s here s can take various values. 6. Measure of straight angle = 180°. 7. 10 8. 8 9. Let sister’s age be x years, required algebraic exp = x – 2 10. a + 7 = 16

Fill in the Blanks 1. algebraic 2. y = x + 5 3. 4 4. 4x 5. 2x – 5 = 6 6. ? 7. ` 5x 8. ` (15000 + 7x) 9. 6 and 7 10. a

True/False 1. False 2. True 3. False 4. False 5. False 6. True 7. True 8. True 9. True 10. True

CrosswordDOWN 1. Literal 2. Constants 3. Algebra

ACROSS 4. Trial 5. Solution 6. Variable

Project/Activity 1.

T

E

R

A

L U T I O N

S

T

A R I A

L

G

E

B

R

A

B L EV

N

T

O

C

OS

S

I

L

R I A L

1

4

5

2

6

3

43mensuration


Multiple Choice Questions 1. (c) 2. (b) 3. (a) 4. (a) 5. (b) 6. (b) 7. (a) 8. (d) 9. (b) 10. (a)

Match the following (i)—(c) (ii)—(a) (iii)—(b) (iv)—(e) (v)—(d)


1. 2x + 7 2. 3x – 7 3. 13

(17x)

4. 16 – 3y = 4 5. 14

y + 5 = 2 6. 6y + 2 = 14

7. x = 4 8. 7 9. Co-efficient of 2x is 2 Coefficient of – 2y is – 7

Coefficient of 83

z is 83

10. d = 14 cm.

Short Answer Type Questions 1. 5x + 1 2. 4x + 1

3. P = 2 x x+

43

where x = breadth

4. (a) 2y – 5 (b) 27

x + 4

5. Let x = 1, 2 × 1 + 7 = 9 ≠ RHS, Not a solution x = 2, 2 × 2 + 7 = 11 = RHS, True is a solution

6. Let x = 1, 13

9+ = 283

≠ RHS Not a solution

x = 2, 23

9+ = 293

≠ RHS Not a solution

x = 3, 33

9+ = 303

10= ≠ RHS Not a solution

x = 5, 53

9+ = 32 ≠ RHS Not a solution

x = 9, 93

9+ = 12 ≠ RHS True is a solution


7. – 10 8. 6a × a or 6a2 sq units 9. 6a units 10. 10a units 11. 12a 12. r raws 9r, 8 raws 8r, 10 raws 10r


1. x = 7 2. x = – 3 3. 134

4. 18 5. 6

Long Answer Type Questions 1. (a) Yes (b) No (c) No 2. (a) 7, 23 + 8 ≠ 15; 10 + 8 ≠ 15 3. (b) 13, 2 × 6 – 7 = 5 ≠ 19; 2 × 10 – 7 = 13 ≠ 19

(c) 18, 2 × 423

14

+ 8 = 38 ≠ 20, 23

323

8× + = 643

8 83

+ =8 ≠ 20

4. (a) ` 15,000 re (b) 12

15re −

years

5. (a) Monu’s age is 7 years less than twice his brother Sonu’s age re . rc.

(b) length of a rectangle is 3 more than its breadth i.e. P. (c) Puneeta has 7 make than half the number of ` 100 notes i.e.

(m) Sunita has 6. (a) (P + 10) years (b) (P – 5) years (c) (P + 25) years (d) (2P – 10) Kg

7. x

5 km/hr 8. ` (4 m + 3 n)

9. (a) (x + 10) (y + 10) Sq. cm, (b) 2(x + y + 20) cm

10. 320

x2

Value Based Questions 1. Diwali 2. Price of petrol = ` (x + 2) Yes diesel contributes more towards pollution.

3. ` ( )aP

− 2000

Loves for her father and understands her Social responsibility.

45ratio ProPortion oral Questions

True/False (with Justification) 1. False; No, as 6 × 2 + 7 = 19 ≠ 28. 2. True; as 1 m = 100 cm. 3. False it 5 – 3x 4. False as area = 4 × side sq. cm = 16 sq. cm of a square 5. True as Perineter of an equilated triangle is 3 × side = 3a units. 6. False as an equation is a statement of equality and not inequality. 7. False 6x + 7 = 5 is a statement of equality, so is an equation and

not an algebraic expression. 8. True as a cuboid has 12 edges 9. True as there are number of prime numbers after < 100.

CHAPTER-12: ratio ProPortion oral Questions


Oral-Based Questions 1. (a) by subtraction (b) by division 2. When tow 3. In the nation a : b, when the antecedend a i.e. a and consiequent

i.e., b do not have any common factor other than 1 we say that the ratio a : b is in its simplest form.

4. When a, b, c and d are in proportion.

5. Simplest form of 20 : 25 = 2025

45

= = 4 : 5

6. d 7. d 8. d 9. In the ratio a : b the first term a is the antecedent. 10. In the ratio a : b the second term b is the consequent?

Fill in the Blanks 1. ratio 2. lowest or simplest 3. means 4. extremes 5. third term 6. proportion 7. a = b 8. 5 : 7 9. 50 : 7 10. π

True/False 1. False 2. True 3. True 4. False 5. True 6. False 7. False 8. False 9. True 10. False


CrosswordDOWN 1. Proportion 2. Fourth 3. means 4. extremes

ACROSS 5. ratio 6. Invertendo 7. alternendo

Project/Activity 1.


Multiple Choice Questions 1. (c) 52 : 12 or 13 : 3 Ans. (c) 2. (b) 4 80 000

3 60 000, ,, ,

= 43

= 4 : 3

Ans. (b) 3. (c) Girls 2

2 5+ × 1400 =

27

× 1400 = 2 × 200 = 400

Ans. (c) 4. (c) Let women be

54

= X900

⇒ 54

9002

450 225

× = x

⇒ x = 1125 Ans. (c) 5. (a) r : d = r : 2r =

rr

L2 2

= = 1 : 2 Ans. (a) 6. (b) Speed of Car A = 180

3 = 60 km/hr

5 61 P R O P O R T I O N

A N2 F U U R T H V 7

3 M E A W S AR LT T

6 E X T R E M E 5N RD NO E

NDO


Speed of Car B = 1404

= 35 km/hr

Ratio of speed of car A to car B = 6035

127

= = 12 : 7.

Ans. (b) 7. (c) 1st angle =

22 3 5+ +

× 180 = 210

× 180° = 36°

2nd angle = 310

× 180° = 54°

3rd angle = 510

× 180° = 90°

Ans. (c) 36°, 54°, 90°

8. (a) Expenditure = 23

of income = 23

× ` 60 00020 000,,

= ` 40,000 Savings = ` 60,000 = ` 40,000 = ` 20,000

Lat is of savings to income = 20 00060 000

13

,,

= = 1 : 3.

Ans. (a) 9. (a) 8 : 12= 2 : 3 Ans. (a) 10. (b) Number or vertices of a cuboid = 8 Number of edges = 12 and Ratio 8 : 12, 2 : 3 Ans. (b) 2 : 3

Match the following (i) 75 : 27 = 25 : 9 Ans. (c) (ii) 6 : 14 = 3 : 7 = 21 : 49 Ans. (a) (iii) 1 hr : 15 mm ⇒ 60 min : 15 min, 4 : 1 Ans. (b) (iv) 10 : 100 = 1 : 10 Ans. (e) (v) 1 yr : 146 days = 365 days : 146 days 5 : 2 Ans. (d)


1. 116 : 174 = 11617487

5887

58=


2. 30 : 365 = 6 : 73 3. 115161

135243

, 115 × 243; 135 × 161, 27945; 21735

4. Number of girls 33 5

48 38

486

+× = × = 18

5. Let the ratio constant be x length = 5x and breadth = 4x P = 2(L + B) ⇒ 180 = 2 (5x + 4x) ⇒ 90 = 9x ⇒ x = 10 ⇒ Length = 5x = 5 × 10 = 50, Breadth = 4x = 4 × 10 = 40 6. A right angle = 90°, a complete angle = 360°

⇒ 90360

14

°°= = 1 : 4

7. Vertices of a square fryramid = 5, edges of a square fryramid = 8 Ratio 5 : 8 8. ?? 9. AB : AC = 4 : 7

ABAC

= 47

⇒ ABAB+ BC

=+

=44

47x

⇒ 4 + x = 7 is x = 3

If BC ⇒ ABBC

= 43

⇒ BC = 9

⇒ AB9

43

= ⇒ AB = 12 cm

10. 2 kg 350 gm = 2350 gm, 4 kg 700 g = 4700 gm

Ratio 23504700

235470

7510

12

= = = = 1 : 2

11. 246

:: x5

⇒ 246

= x5

⇒ x = 244

56×

= 20 ⇒ x = 20

12. 73 : 365 = 1 : 5

Short Answer Type Questions 1. Ram ; Shyam = 1 : 5

Ram’s share = 16

× 60 = 10

Shyam’s share = 56

× 60 = 50


2. 999999999

111111111

111111

111

= = 111111 : 111

3. Area of a square of side 4 cm = 16 cm2

Area of a square of side 5 cm = 25 cm 2 Ratio = 16 : 25 4. Ratio of the actual distance to sketch map

= 10000000

2

5000000

1

= 5000000 : 1

5. 1830

= 13500x

⇒ x = 13500 30

182

1500750

× = 22500

Ans. ` 22,500 6. Let the consequent be x

38

24=x

⇒ x = 243

× 8 = 8 × 8 = 64

7. 1 score = 20 ⇒ 2 scores = 40 Let cost of 100 aranges be y

40100

90=y

⇒ y = 90 10040

9 1004

× = × = 9 × 25 = 225

Ans. ` 225

8. 14 : 16 = 7416

78

= = 7 : 8 and 35 : 40 = 3540

78

= = 7 : 8

as 7 : 8 = 7 : 8 ⇒ 14 : 16 and 35 : 40 are in proportion.

9. Kriti’s Share = ` 11 2+

× 60 = 13

× 60 = ` 20

Kiran’s Share = ` 23

× 60 = ` 40


Short Answer Type Questions-II 1. (a) 20

9 = 20 : 9 (b) 16

9 = 16 : 9

2. (a) Father’s age : Apoorvas age = 50 : 20 = 5 : 2 (b) 45 : 15 = 3 : 1 ( ) 60 : 30 = 2 : 1

3. (a) 1442160

16240

230

= = = 1 : 15 (b) 104 to 143 = 104143

(c) 5490

610

35

= = = 3 : 5

4. 2124

78

5664

98112

= = =

5. (a) Tube to margo = 30 : 16 = 15 : 8

(b) Neem : Total = 20100

= 1 : 5

(c) Hibiscus : Pire = 286

143

= = 14 : 3

6. (a) Religion to English drama = 20001400

107

= = 10 : 7

(b) Religion to total = 20002900

= 20 : 29

(c) English drama to Hindi drama = 14001500

= 14 : 15

7. (a) 603 2 5

= x ⇒ 60 23 5× = x ⇒ 40 = x

5 ⇒ x = 200 km

(b) 7560

32

756070

32

154

12

158

× = × = × =

8. Speed of Bullock cart = 10 km/h Speed of auto rickshaw = 45 km/h Ratio of speed = 10 : 45 = 2 : 9 No it is not good to use animals for this purpose as this leeds to

animal crmeltry. 9. Cost of 1 score = 20 pens = ` 180 Cost of 1 dozen = 12 pencils ` 150

Ratio of cost of pen to cost of pencils = 180150

= 6 : 5


10. 20 men – 24 days

205

= x24

⇒ 20 24

5×

= x ⇒ 4 × 24 = x

⇒ x = 96 days

11. Utkarsh share = 25

× 500 = ` 200

Srishtis share = 35

× 500 = ` 500

No she was not fare as she did not give them equal animals.

12. Cost of 1 pen = ` 18012

02

= = ` 15

Cost of 1 ball pen = 568

= ` 7

Rate = 15 : 7

13. Ratio of ages Shreya 15=

Bhoomika 12 = 5 : 4

Shreyas’ share = 59

× 36 = ` 20

Bhoomikas’ share = 49

× 36 = ` 16

Long Answer Type Questions 1. Smalles 4312 largest divisible by 1324 smallest

Rate 43121324

2156662

1028331

= = = 1028 : 33!

2. Area of 1 flower bed = (2.5)2 m2 = 6.25 m2

Area land = 20 × 10 m2 = 200 m2

Area of 4 flower beds = 4 × 6.25 = 25.00 m 2

(a) 25200

= 1 : 8 (b) 25175

17

= = 1 : 7

3. Sonu’s share = 29

× 9,00,000 = 2 × 1,00,000 = ` 2,00,000

Monu’s share = 39

× 9,00,000 = ` 3,00,000

Tonu’s share = 49

× 9,00,000 = ` 4,00,000


4. 69

= 3 30 000, ,

x ⇒ x =

3 30 0001 65 000

93

62

, ,, ,

× = ` 4,95,000

69

= 4 50 000, ,

y ⇒ y =

4 50 000 93

2 25 000

62

, ,

, ,

× = ` 6,75,000

5. Children = 320 – (114 + 110) = 320 – 224 = 96

(a) Women : men = 114110

5755

= = 57 : 55

(b) Children to total = 96320

1240

310

= = = 3 : 10

(c) 110320

= 11 : 32

Company owner lacks ethics as be has employed children and hence is encouraging child labour and runing their childhood.

6. Number of students who opted for outdoor sports = 3200 – (800 + 1500) = 3200 – 2300 = 900

(a) SwimmingIndoor

= =8001500

815

or 8 : 15

(b) 1500900

159

53

= = = 5 : 3 (c) 9003200

932

= = 9 : 32

7. Truck covrs 135 km is 5 hr. (a) Let it takes x hrs to cover 81 km

⇒ 13581

5=x

⇒ x = 51

819

13527 3

× = 3 ⇒ x = 3 hrs.

(b) Time = 1 hr + 20 min.

= 1 + 2030

1 23

= hrs = 53

hrs.

Let D = x km

x135

= 5 35

⇒ x135

53 5

13

=×

= ⇒ x = 13

× 135 = 45 km

Distance = 45 km.


8. (a) Present age of FatherPresent age of Son

= 4214

= 4 : 1.

(b) Son 12 yrs. old = (14 : 2) yrs. Father 42 – 2 = 40 yrs

Father ageSons age

= =4012

103

= 10 : 3.

(c) After 10 yrs father’s age = 42 + 10 = 52 yrs. After 10 yrs Son’s age = 14 + 10 = 24 yrs.

Age of FatherAge of Son

= =5224

136

= 13 : 6

(d) Father 30 years del = 42 – 12 Son 14 = 12 = 2 yrs old

Age of FatherAge of Son

= 302

= 15 : 1

9. D = 90 km, T = 212hrs = 5

2hrs.

(a) Let time for 30 km be × hr.

x30

5 290

= ⇒ x = 5

2 90× × 30 =

515

hr.

= 515

604

× min = 20 min.

(b) Let distance in 2 hr be y km.

y2

905 2

= ⇒ y2

90 25

= × ⇒ y = 9018

51

2 2× × = 72 km

HOTs

1. x : y = 2 : 3 ⇒ xy

= =23

1015

y : z = 5 : 7 ⇒ yz

= =57

1521

⇒ x : z = 10 : 21 2. Let the number be 3x and 5x is According to the question.

3 +105 +10

=57

xx

⇒ 21x + 70 = 25x + 50 ⇒ 20 = 4x ⇒ x = 5 Number are 3 × 5 = 15 and 5 × 5 = 25 3. CXV = 115, XCV = 95


Ratio = 11595

2319

= = 23 : 19

Value Based Questions 1. Let xl of juice contains 120 mg

x660

120144

3036

56

= ⇒ x = 56

× 660 = 5 × 110 = 550 ml

2. Time taken manars = 1 hr. 60 min Time taken by Vidisha = 20 min (a) ratio 60 : 20 = 3 : 1 (b) Both are health conscions and also care about the environment.

True/False (with Justification) 1. False; as 1 m = 1000 mm, \ ratio is 1000 : 1

2. False; as a : b = c : d ⇒ ab

cd

= ⇒ ad = bc.

3. True ; 204

377

76133

= ⇒ 4 × 133, 7 × 76, 532, 532, as 532 = 532

4. False; If a : b = c : d, then using invertends b : a = d : c. 5. True ; using altemend a : b = c : d = is 3 are as a : c = b : d

Life Skills

108594 1650

= x ⇒

2121085946611 1

1650150

× = x

⇒ x = 300 litres

55symmetry

CHAPTER-13: symmetry


Oral-Based Questions 1. A figure is said to be symmetrical if it can be divided into parts of

save shape and size. 2. The live which divides a figure into parts of same shape and size

is called its axis of symmetry. 3. Maximum infinite Minimum Zero 4. Nine 5. 10 letters 6. 3 7. A Rhembus and a rectangle 8. Circle 9. Square

Fill in the Blanks 1. 2 2. n 3. no 4. 1 5. no 6. 8 7. 3 8. A live of symmetry 9. infinite 10. Parallelogram.

True/False 1. False 2. False 3. True 4. False 5. True 6. False 7. False 8. False 9. True 10. False

CrosswordDOWN 1. Hexagon 4. One 5. Semi circle

ACROSS 2. Symmetry 3. Two 6. infinite 7. square

Project/Activity 1. yes 2. yes 3. fold 4. yes 5. love for environment and matter.



Multiple Choice Questions 1. (c) 2. (c) 3. (a) 4. (b) 5. (d) 6. (b) 7. (b) 8. (c) 9. (b) 10. (b)

Match the following (i)—(e) (ii)—(a) (iii)—(g) (iv)—(a) (v)—(d) (vi)—(d) (vii)—(b) (viii)—(e) (ix)—(b) (x)—(g)

Very Short Answer Type Questions 1. Yes 2. No 3. 3 4. angle bisector 5. One

Short Answer Type Questions

1. 2. Yes, M

3. 4.

5. k

Short Answer Type Questions-II 1. M A T H E I C S

1 1 1 2 1 1 0 0

2. more then 1 none no line of symmetry S, R

3.

57symmetry

4.

5. (a) (b)

6.

HOTs 1. No as the parts are of same shape and size but different colours

i.e. they are not identical. 2. None 3. Yes, as the two parts are identical. 4. only horizontal line as the two are minor images of each other.


1. Yes


2. Yes Bangladesh

3. Yes Japan

4. Pakistan No 5. China No

6. Finlard 7. Canda

8. Italy wave

Life Skills

Answers may vary sample answer

CHAPTER-14: Practical geometry


Oral-Based Questions 1. Compass, scale, pencil, eraser, and square. 2. 72°, 15°, 30°, 45°, 75°, 90°, 105°, 120°, 135°, 150°, 165° and 180° 3. Angles like 30°, 60°, 45°, 90° a multiples of 15° 4. One 5. One 6. It is used for comparing line segments

Fill in the Blanks 1. 45°

2. 180°, If we are using 180° protactor and 360° If we are using 360° protactor 3. Same 4. One 5. 30°, 60° and 90°

True/False 1. False 2. False 3. True 4. False

59Practical geometry

CrosswordDOWN 1. Three 3. ?

ACROSS 2. One 4. Bisector 5. ? 6. Ninety

Project/Activity 1.


Multiple Choice Questions 1. (d) 2. Set–Square 45° – 90° – 45° Ans. (c) 3. 1Ans. (b) 4. ProtractorAns. (b) 5. Set-square with 30° – 90° – 60° as Isna triangle side opposite to

the 30° angle is half the hypotenuse.Ans. (d)

Match the following (a)—(ii) (b)—(iv), (ii) (c)—(vi), (i) (d)—(i) (e)—(vi) (f)—(iv), (i)

Very Short Answer Type Questions 1. 2.

3.


4. 5. 6.

7. 8.

9. 10. <

Short Answer Type Questions 1. 2. 3.

4. 5.

6. 7.

8. 9.


10.


1. 2.

3. BC = 3.6 cm 4. AC = d AB, AC = 6.3 cm BC = 2.1 cm

5.

6. Yes MN and MP are equal.

Yes it passes through the centre. Yes it contains another diameter.



1. They angles bisector of AB and AC intersect at the centre of the circle.

2. PA = PB and QA = QB We observe that any part on the perpendicular bisector of a line segment is equidistant from its end parts.

3. Yes the line l passes through the point m

4. Yes QQ = QBYes –ANQ and –BNQ are equal.

We observe that any point on the angle bisector of an angle is equidistant from its arms.


5. CD = 8 cmwe get a quadrilatiral speical name of this quadrilaterial is rectangle.

True/False 1. False; It can be drawn using compasses and scale. 2. False; We can make angles and parallel likes also. 3. True; as all 30°, 45°, 60°, 90° etc. are multiples of 180. 4. True; a line parallel to a given line can be drawn using scale

compuss or scale and set square.

5. True; First using perpendicular bisector find 12

of a line segment

then further find 12

of one of the parts this will five one four the.

6. True;

As the set square is an isosceles triangle and angle bisector of the angle formed by two equal sides i.e. the vertical angle is also the perpendicular bisector of the base. Hence when folded along this line the two parts overlap each other.

WORKSHEET-1

Chapter knowing our numbers: 1. (i) (d) 2. (ii) (c) 3. (i) True (ii) False (iii) False 5, 8, 6, 9, 5, 3 76 5 crores eighty six lakhs ninety five thousand three hundred

seventy six. 4. 1l = 1000 ml, So, 4l 500 ml = 4500 ml. Number of glasses = 18


5. Diameter of Jupiter, 142,800,000 m One hundred forty two million eight hundred thousand. 6. Largest number of seven digits 999999 Smallest number of eight digits 1,00,00,000 difference 1,00,00,000 – 99,99,999 = 1 7. least number of six digits = 204567 greatest number of six digits = 765420 Sum 765420 + 204567 969987

8. (a) 900 + 500 = 1400 (b) 800 + 400 = 1200 (c) 11200 + 3500 = 14700 (d) 17700 + 13600 = 31300

WORKSHEET-2

Chapter whole numbers: 1. (i) (d); (ii) (d); (iii) (a); (iv) (b) 2. (i) 19 × (12 + 1) (ii) 786 × (3 + 7) = 7860

(iii) 24 × 25 = 24 × 1004

= 600

3. 837 + 208 + 363 = (837 + 363) + 208 = 1200 + 208 = 1408. 4. Total weight that can be carried by both the vehicles. 482 × 15 + 518 × 15 = (482 + 518) × 15 = 1000 × 15 = 15000 5. 5 × 12 × 500 mg weight of 1 box

= 60 × 500 mg = 30,000 mg = 300001000

g = 30 g

weight of 32 boxes = 32 × 30 g = 960 g 6. (a) 33 Sum = (33 + 48) + 54 + 69 (b) 48 = 81 + 54 + 699 (c) 54 = (81 + 69) + 54 (d) 69 = 150 + 54 = 204


7. 8732 × 102 = 8732 × (100 + 2) = 8732 × 100 + 8732 × 2 = 873200 + 17464 = 890664

WORKSHEET-3

Chapter—Playing with numbers: 1. (i) True (ii) False (iii) False (iv) True 2. (i) 1 (ii) perfect (iii) Composite number. (iv) 25 (v) 5 or 0 (vi) 2 3. LCM of 3, 4 and 5 = 60, 2 more then 60 = 62 4. 896; 672

Square tile of side 224 cm.

no. of tales

4224896 67222456 1

×

= 2688 (a) Sum of the digits = 6 + 7 + 2 = 15 as 15 is not divisible by 9 therefore 672 is not divisible by 9 (b) Sum of the digits = 5 + 6 + 5 + 2 = 18 as 18 is divisible by 9 therefore 5652 is divisible by 9.

WORKSHEET-4

Chapter—Basic Geometric Ideas 1. Ray has one end point and extends indefinitely in one divection. 2. (i) angle (ii) Infinite


3.

4. (i) ET and KI or EK and TI (iii) EK, KI; KI, IT; IT, TE; TE, EK. 5. (i) U, P, Q, S (ii) R (iii) A, B, C, T, S, R. 6. Namber of so in a hexagon diagenals in a polygon

= n n( ) ( )− −3

26 6 3

2 = 9

7. Two

8. AC = 6 cm OA = 3 cm

OA = 12 AC or AC = 2OA

WORKSHEET-5

Chapter—?? 1. Protractor 2.

3. (i) False (ii) True (iii) Ture (iv) False 4. (i) b (ii) (c) (iii) (a) (iv) (d) 5. (c) Acute triangle Obtuse triangle Right triangle (d) Scalene triangle Isocscles triangle Equilateral triangle


6.

No. of Vertices

No. ofedges

No. offaces

7. Triangular prism 6 9 5Square prism 8 12 6Pentagonal 10 15 7

8.

WORKSHEET-6

Chapter— 1. decreasing speed by 10 km/hr. 2. < as (– 23) – (45) = – 68 and – 45 – (– 23) = – 45 + 23 = – 22 and – 68 < – 22 3. – 6 – (– 8) = – 6 + 8

So, – 6 + 8 = 2 4. – 250 – 180 = – (250 + 180) = – 430 5. (i) additive inverse of (– 5 + 10 = 5) is – 5


(ii) 8 less than – 3 is – 3 – 8 = – 11 (iii) ________ – 8 = – 26 ⇒ _______ = – 26 – (– 8) = – 26 + 8 = – 18 6. 160 – (– 50) – (– 35) = 160 + 50 = 35 = 160 + 85 = 245 7. Simplify – 28 + (– 60) – (– 30) + (– 40) – (+ 30) = – 28 – 60 + 30 – 40 – 30 = – 28 – 60 – 40 = – 128 8. (i) Prime numbers less than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Unit digit of the product is 0 as 2 × 5 = 10 and product of primes 2 × 5 × 3 × 7 × 11 × 13 × 17 × _________ × 47 = 10 (3 × 7 × 11 × 13 × 17 × ________ × 47) (ii) Sun of the integers is 75 One integer is – 28 Other integer = 75 – (– 28) = 75 + 28 = 103

WORKSHEET-7

Chapter—Fractions

1. 14

, 14

, 14

, 14

, 12

, 34

, =1

2. Answers may varry sample answer.

3. (i) 578

(ii) 1 38124

4. (i) 1220

35

= (ii) 1881

29

=


5. LCM of the denominator < is 5, 10, 15 and 20 is

15

, 310

, 615

, 720

= 1 125 12

3 610 6

6 415 4

7 320 3

××

××

××

××

, , ,

= 1260

1860

2460

2160

, , ,

arranging in as cerding order

1260

1860

2460

2160

, , , = 15

310

720

615

, , ,

6. Weight of the tank = weight of tank filled with wheat weight of

wheat 60 15

kg

= 75 14

– 60 14

= 3014

2414

−

= 604

= 15 kg

7. (i) 35

3 75 7

= ××

, 21 ÷ 3 = 7

= 2135

(ii) 47

4 157 15

= ××

= 60105

, 105 ÷ 7 = 15

(iii) 4560

= 45 ÷ 545 ÷ 5 , 60

12 = 5

= 912

34

=

8. (i) – 527

= 53

⇒ = 53

= 527

= 45 527

5027

+= = 1

2327

(ii) 65

23

78

+ − = 144 80 105

120+ −

= 119120

9. 67

= 67

xx

and 6x + 7x = 91, 13x = 91,

= 6 77 7

4249

××= x = 91

13 = 7

5 5, 10, 15, 202 1, 2, 3, 4

1, 1, 3, 2

= 5 × 2 × 3 × 2 = 60


WORKSHEET-8

Chapter—Decimals 1. Thirty seven point two eight three

2.

3. (i) 16 mm = 1610

cm = 1.6 cm

(ii) 874 g = 8741000

kg = 0.874 kg

4. (i) 3.75 + 14.458 = 18.208 (ii) 105.230 – 67.852 = 37.378 5. Suhani benght shoes for ` 759.50 Gave ` 1000 Money shopkeeper will return to her = 1000.100 – 759.150 240.50

6. (i) 58

125125

´ = 6251000

= 0.625

(ii) 6.284 = 62841000

1571250

=

(iii) 88 ml = 881000

l = 0.088l

7. (i) 13.8, 13.256, 13.67, 13.09 descending order = 13.8, 13.67, 13.256, 13.09 (ii) 652 = 257 Place value 5 appearing at tens place = 50

Place value 5 appearing at hundredth place = 5100

= .05

Sum 50 + 0.05 = 50.05 8. length of the ribbon = 5 m 60 cm length of one pieces = 1 m 20 cm length of second piece = 3 m 15 cm Total length of the two pieces = 4 m 35 cm lengths of the third piece = total length of the ribbon – length of the two pieces = 5 m 60 cm – 4 m 35 cm = 1 m 25 cm


WORKSHEET-9

Chapter—Data Handling 1. Class Number of students I

II

III

IV

V

2.

3. Number of bulbs sold in the month of July = 5 × 50 = 250 Number of bulbs sold in the month of August = 4 × 50 = 200 Number of bulbs sold in the month of Sept. = 3 × 50 = 150 Number of bulbs sold in the month of October = 7 × 50 = 350 Number of bulbs sold in the month of Nov. = 9 × 50 = 450


(i) Total number of bulbs sold during the give time ? = 250 200 150 350 + 450 1400 (ii) Number of bulbs sold more in the month of october than

September = 350 – 150 = 200 (iii) Number of bulbs sold in November = 450 (iv) L.E.D bulb consumes less electricity than the normal bulb. 4. (a) Number of students who want to play football = 40 (b) Game of circket is liked by maximum number of the students. (c) Game of football is played by the least number of student. (d) Number of students who like to play Badminten is 70 5.

WORKSHEET-10

Chapter—Mensuration 1. Perimeter of an equilateral triangle of side of length 16 cm = 3 ×

side = 3 × 16 cm = 48 cm 2. Perimeter of the shape AC + BC + BG + EG + DE + DF + AF = (3 + 3 + (BG + AF) + 5 + 1 + 5) cm = (17 + (AB – FG) = 17 + (3 – DE) = [17 + (3 – 1)] cm as FG = DE opposite sides of a rectangle = [17 + 2] cm = 19 cm


3. (i) Perimeter of a square = 4 × side = 4 × 7 = 28 cm. (ii) Perimeter of a regular hexagon = 6 × side = 6 × 7 cm = 42 cm. 4. Number of full squares = 8 Area 8 cm2

Number of d squares = 1 Area = 0.5 cm2

Number of squares more than 12

= 4 Area = 4 cm2

Number of squares less than 12

= 4 Area 0 (as area of squares less

than 12

is to be ignored

So, total area = 8 + 0.5 + 4 = 12.5 cm2

5. Sides of square gare less = 5 km Adjacent side = 4 km Length = 2 × 5 km = 10 km

Breadth = 12

× 5 km = 52

km = 2.5 km

New figure is a rectangle and its perimeter is = 2 (L + B) = 2(10 + 2.5) = 2 × 12.5 = 25 cm 6. Area of a rectangle = 810 sq. cm One side = 30 cm

⇒ other side = 81030

cm = 27 cm

P = 2(L + B) = 2(30 + 27) cm = 2 × 57 cm = 114 cm. 7. L = 3 m, B = 1 m 75 cm = 1.75 m Area of cloth required = 3 × 1.75 m2 = 5.35 m2

length of lace required = P of he table cloth. = 2(L + B) = 2(3 + 1.75) = 2 × 4.75 cm = 9.50 m


WORKSHEET-11

Chapter—Alegebra 1. 4 6 8 10 2 x

1 2 3 4 5 x-22

2. Kuber’s age = x – 12

yrs. = x = 72

yrs.

3. (i) – 9 – 16 (ii) 7p (b – 2) 4. Perimeter of parallelogram = 2(a + b) When b is 3 less than ‘a’ ⇒ b = a – 3 Perimeter will be = 2(a + a – 3) = 2(2a – 3) = 2(2a – 3) or 4a – 6 5. Cost of 1 dozen bananas = ` 40 Cost of a dozen bananas = ` 40a Cost of 1 kg oranges = ` 30 Cost of b kg oranges = ` 30b Total cost of oranges and bananas = ` 40a + ` 30b

6. a 1 26a – 5 1 7

When a = 1, 6a – 5 = 6 × 1 – 5 = 6 – 5 = 1 When a = 2; 6a – 5 = 6 × 2 – 5 = 12 – 5 = 7 When a = 3; 6a – 5 = 6 × 3 – 5 = 18 – 5 = 13 When a = 4; 6a – 5 = 6 × 4 – 5 = 24 – 5 = 19 When a = 5; 6a – 5 = 6 × 5 – 5 = 30 – 5 = 25 When a = 6; 6a – 5 = 6 × 6 – 5 = 36 – 5 = 31 Mona’s present age = ‘a’ yrs. 7. (i) her age 10 years age = (a – 10) yrs. (ii) Mona’s mothers age = (a + 25) years. (iii) Mona’s grand mother’s age is = (3a – 4) yrs. 8. (i) 7 times p = 7p 6 taken away from 7 times p = 7p – 6 (ii) 9a – 2b if a = – 9, and b = 5 is 9 × (– 9) – 2 × 5 = – 81 – 10 = – 91


(iii) Let the numbr be a half of a = 12

a

6b taken away from the = 12

a – b

Number of cards in a pack of card = 52

⇒ 12

a – 6 = 52

⇒ 12

a = 58 ⇒ a = 116

WORKSHEET-12

Chapter—Ratio proportions 1. Radiv : diameter = 1 : 2

2. Raghav’s share = 2

2 3+ × ` 100

= 25

× 100 = 2 × 20 = ` 40

Madhav’s share = 32 3+

× 100 = 35

× 100 = 3 × 20 = ` 60

3. x : 77 : : 91 : 49

x77

= 9149

x = 9149

77

13

7

11´ = 143

4. Length : breadth is 4 : 5Length (in m) 60 m 80 m 60 m 52 mBreadth (in m) 75 m 100 m 75 m 65 m

60x

= l = 60 m lb

= 45

= 60x

⇒ x = 60 54

15

´ = 75

l = 80 m lb

= 45

= 80x

⇒ x = 80 5

4

20

× = 100

b = 75 m 45

= y75

⇒ 45

× 85 = y ⇒ y = 4 × 15 = 68 y = 6 cm.


b = 65 m 45 65

=y ⇒ y =

45

6513

× = 52 m

5. (i) 60 cm : 2.5 cm

= 602 5

60025

24

1.= = 24 : 1

(ii) 450 ml to 3 litres 1 l = 1000 ml

4503000

= 45300

960

320

= = = 3 : 20

WORKSHEET-13

Chapter—Symmetry

1. (a) None (b)

(c) (d)

(e) None (f )

2.


3.

4. True as when the parts are identical this means they are of same shape and same size. So the like is a line of symmetry.

5.

6. Infinite number of lines of Symmetry can be drawn in a circle.

Every diameter of the circle is a line of symmetry.

WORKSHEET-14

Chapter—Practical Geometry 1. (i) (ii)

2. (i) (ii)

PL ^ AB


3. OR−−→

bisects POQ QOP = POR = 43°

4. AB ^ PQ and PC = QC = 4 cm

5. Yes, it passes through the centre of the circle.

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