Vedanta Excel in Mathematics Book 6 Final (2078)

Answers
1. Set

Exercise : 1.1

Creative Section

5. Show to your teacher.

6. a) 9N b) uV c) 3  Z d) 7  {2, 4, 6, 8} e) e{n, e, p, a, l}

f) 8  {1, 3, 5, 7} 7. a) W = {0, 1, 2, 3, 4, 5} b) M = {4, 8, 12, 16, 20}

c) A = {M, A, T, H, E, I, C, S} d) P = {2, 3, 5, 7, 11, 13, 17, 19} e) B = {4, 6, 8, 9}

8. a) A = {first five letters of Devanagari alphabets} b) N = {natural numbers less than 10}

c) P = {prime numbers less than 10 } d) V = {vowels of English alphabets}

e) F = {factors of 14} f) D = {first four multiples of 4}

9. a) W = {x : x is a whole number, x < 5}

b) S = {x : x is a perfect square number, x < 26}

c) O = {y : y is an odd number, y < 10}

d) A = {y : y is the first five letters of English alphabets}

e) F = {x : x is a factor of 15}

f) M = {m : m is a multiple of 3, m < 20}

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

Creative Section Exercise : 1.2
6. a) A = { }, null set b) B = {2, 4, 6, 8, 10, 12, 14, 16, 18}, finite

c) C = {22, 24, 26, ...}, infinite d) D = {16}, singleton

7. a) A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, n(A) = 9 b) B = {1, 2, 3, 6, 9, 18}, n(B) = 6

c) C = {a, p, l, e}, n(C) = 4 d) D = {1, 4, 9, 16, 25, 36, 49, 64}, n(D) = 8

8. a) A = {0, 1, 2, 3, 4} and B = {1, 2, 3, 4, 5} are equivalent.

b) P = {2, 3, 5, 7} and Q = {7, 5, 3, 2} are equal.

9. a) A = {1, 2, 3, 4, 6, 12} and B = {1, 2, 3, 6, 9, 18} are overlapping

b) P = {4, 8, 12, 16, 20} and Q = {7, 14, 21, 28, 35} are disjoint.

10.a) A = {a, b, c, d, e}, B = {a, e, i, o, u}, set of common elements = {a, e}

b) P = {1, 2, 3, 4, 5}, Q = {1, 3, 5, 7, 9}, set of common elements = {1, 3, 5}

c) M = {2, 4, 6, 8, 10, 12}, N = {3, 6, 9, 12, 15}, set of common elements = {6, 12}

11.a) C = {2, 3, 5, 7} A B b) R = {4, 8} P Q
12
12 2 16
4 3 4
68 9 5
7 68
10

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

2. Operations on whole numbers
Exercise : 2.1

Creative Section

3. a) 7 is at ten-crore or at hundred million place, face value is 7, place value is 700000000.

3 is at ten-lakh or at million place, face value is 3, place value is 3000000.

Vedanta Excel in Mathematics - Book 6 268 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

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b) 4 is at ten-arab or at ten billion place, face value is 4, place value is 40000000000.
6 is at crore or ten million place, face value is 6, place value is 60000000.

4. Nepali system International system

a) 2,70,58,91,436: Two arab seventy crore 2,705,891,436: Two billion seven hundred

fifty-eight lakh ninety-one thousand five million eight hundred ninety-one

four hundred thirty-six. thousand four hundred thirty-six.

b) 50,39,87,02,416: Fifty arab thirty-nine 50,398,702,416: Fifty billion three hundred

crore eighty-seven lakh two thousand ninety eight million seven hundred two

four hundred sixteen. thousand four hundred sixteen.

c) 4,00,87,65,93,120: Four kharab 400,876,593,120: Four hundred billion eight
eighty-seven crore sixty-five lakh hundred seventy-six million five hundred
ninety-three thousand one hundred ninety-three thousand one hundred twenty.
twenty.

5. a) 6,45,79,35,000 b) 859,124,090,000

6. a) (i) Fifteen crore eighty-six lakh fifty-seven thousand rupees

(ii) One hundred fifty-eight million six hundred fifty-seven thousand rupees.

b) (i) Rs 28,542,000,000

(ii) Rs 28,54,20,00,000: Twenty-eight arab fifty-four crore twenty lakh rupees.

7. a) 40 lakh b) 2 crore c) 30 arab d) 50 million e) 7 billion

8. a) 5 × 102 b) 2 × 103 + 7 × 102 c) 3 × 105 + 5 × 103 + 2 × 102 + 6 × 101

d) 9 × 107 + 1 × 105 + 8 × 104 + 3 × 102 + 7 × 101

e) 6 × 108 + 3 × 107 + 8 × 106 + 4 × 104 + 2 × 103 + 9 × 102 + 5 × 101 + 7 × 100

9. a) 325 b) 70406 c) 20051090 d) 8000900370

10. a) 1099999 b) 8819721 11. a) 10x + y b) 100a + 10b + c

12. a) 5000005, 4999995 b) 700007000, 699993000 c) 9000900, 8999100

13. a) 187, 9 b) 847, 99 14. a) 3654013 b) 8966004321

15 and 16. Please complete your project work and compare with your friends. Then, show

to your teacher.

Exercise 2.2

Creative Section

7. a) 10 b) 37 c) 12 d) 17 e) 56 8. a) 43 b) 37 c) 79 d) 48 e) 77

f) 55 g) 60 h) 18 9. a) Rs 2 b) Rs 250 c) Rs 610 d) 14

10. Please complete your project work and discuss with your friends. Then, show to your

teacher.

Exercise 2.3

Creative section

4. a) 16 b) 54 c) 30 d) 12 e) 2 f) 28 g) 66 h) 50

i) 0 j) 14 k) 1 l) 3 5. a) 36 b) 28 c) 13 d) 4 e) 3

6. a) 450 ml b) 84 km c) Rs 3725 d) 2 e) Rs 90 f) 5

Creative Section 3. Operations on whole Numbers
Exercise : 3.1
6. a) Yes b) Yes c) Yes d) Yes e) No
c) No d) Yes e) No 7. a) Yes b) No d) 30
8. a) 4 b) 6 c) 8 d) 14 9. a) 24 b) 18 c) 24

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10. a) 12 = 2 × 2 × 3 b) 18 = 2 × 3 × 3 c) 24 = 2 × 2 × 2 × 3 d) 28 = 2 × 2 × 7

e) 40 = 2 × 2 × 2 × 5 f) 56 = 2 × 2 × 2 × 7

11. a) 36 = 2 ×2 × 3 × 3 b) 60 = 2 × 2 × 3 × 5 c) 84 = 2 × 2 × 3 × 7

d) 99 = 3 × 3 × 11 e) 180 = 2 × 2 × 3 × 3 × 5 f) 210 = 2 × 3 × 5 × 7

12. a) 8 b) 3 c) 4 d) 8 13. a) 4 b) 6 c) 10 d) 12

14. a) 18 b) 24 c) 48 d) 72

15. Play the game with your friends in groups.

Exercise 3.2

Creative section

4. a) 2 b) 4 c) 6 d) 9 e) 10 f) 8 g) 12 h) 14

5. a) 3 b) 5 c) 6 d) 7 e) 14 f) 15 g) 25 h) 24 i) 15 j) 24 k) 21 l) 35

6. a) 6 b) 7 c) 14 d) 24 e) 30 f) 36 g) 48 h) 50

7. a) 12 b) 18 8. a) 12, 2, 3 b) 15, 2, 3 c) 20 l d) 3 m

9. Play the game with your friends in groups.

10. Please complete your project work and discuss with your friends. Then, show to your

teacher.

Exercise 3.3

Creative section

4. a) 6 b) 12 c) 12 d) 24 e) 18 f) 40 g) 60 h) 60

5. a) 24 b) 30 c) 36 d) 60 e) 84 f) 144 g) 180 h) 270

i) 84 j) 72 k) 120 l) 360 6. a) 36 b) 60 c) 72 d) 90 e) 60

f) 120 g) 150 h) 180 7. a) 72 b) 60

8. a) 60 m b) Rs 180 c) 12 seconds 9. a) 2 hours, 11 : 00 am b) 9 p. m.

10. a) 3, 4 b) 3, 5

11. and 12. Please complete your project work and discuss with your friends. Then, show
to your teacher.

Exercise 3.4

Creative section

6. a) 196 b) 625 c) 1764 d) 8100 e) 13225 f) 80656

7. a) Yes b) Yes c) No d) Yes e) No f) Yes

8. a) 6 b) 9 c) 14 d) 15 e) 18 f) 20 g) 24 h) 27 i) 35 j) 42

k) 48 l) 55 9. a) 64 b) 343 c) 729 d) 1728 e) 15625 f) 46656

10. a) Yes b) No c) Yes d) No e) Yes f) Yes

11. a) 2 b) 3 c) 5 d) 6 e) 9 f) 12

12. a) 625 b) 1024 c) Rs 2025 13. a) 21 b) 24

14. a) 10 b) 6 cm 15. a) 2 b) 3 c) 5 d) 3 e) 7 f) 5

16. Please complete your project work and discuss with your friends. Then, show to your

teacher. 4. Integers

Exercise 4.1

Creative section

6. a) + 6 b) –8 c) +5 d) –6 e) +8 f) –9

7. a) 3 b) –2 c) –14 d) 9 e) –8 f) –11 g) –15 h) 24

i) –42 j) –3 k) –8 l) 9 8. a) 1 b) –1 c) 1

d) –8 e) 16 f) –32 g) 9 h) –27 i) 16 j) –64 k) 25

l) –125 9. a) 6 km b) 6 km c) 5 km d) 24 km

10. a) 6° C b) (i) 3° C (ii) –3° C (iii) –5° C (iv) –8° C

c) (i) 33° C (ii) 17° C (iii) 10° C (iv) 3° C

11. Play the game with your friends in groups.

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5. Fraction and Decimal

Exercise : 5.1

Creative Section

6. a) (i) 15 , 20 (ii) 9 (iii) 11 , 7 b) (i) 5 (ii) 7
35 35 35 15 20 12 12

7. a) 2 , 3 , 4 b) 4 , 6 , 8 c) 4 , 6 , 8 d) 6 , 9 , 12 e) 8 , 12 , 16 f) 16 , 24 , 32
4 6 8 6 9 12 10 15 20 8 12 16 14 21 28 18 27 36

8. a) 3 , 2 , 1 b) 4 , 24, 1 c) 6 , 4 , 2 d) 9 , 6 , 3 e) 10 , 4 , 2 f) 12 , 8 , 6
6 4 2 8 2 9 6 3 12 8 4 15 6 3 18 12 9

9. a) Yes b) No c) No d) Yes

10. a) 3 , 4 b) 15 , 12 c) 4 , 5 d) 15 , 14
6 6 20 20 6 6 20 20

11. a) 5 < 7 b) 8 > 6 c) 3 < 7 d) 2 > 3
9 9 11 11 4 8 5 10

12. a) 1 < 5 < 3 b) 2 < 7 < 5 c) 1 < 3 < 5 d) 1 < 3 < 2
2 8 4 3 9 6 3 4 6 4 10 5

13. a) 9 > 4 > 3 b) 5 > 7 > 2 c) 5 > 3 > 3 d) 7 > 11 > 5
10 5 4 6 12 9 6 4 8 12 24 16

14. a) On food b) By bus c) Bhuniya d) Wife
15. Please complete your project work and compare with your friends. Then, show to your

teacher.
Exercise 5.2

Creative Section

6. a) 134 b) 216 c) 354 d) 474 e) 583 f) 6170

7. a) 11 b) 23 c) 37 d) 67 e) 83 f) 69
4 7 8 9 8 10

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

k) 2 l) 1 9. a) 1 b) 3 c) 1 d) 2 e) 3 f) 3
15 15 10 20 4 5 5 4
10. Please complete your project work and compare with your friends. Then, show to your

teacher.

Exercise 5.3

Creative section

9. a) 116 b) 11 c) 183 d) 195 e) 113 f) 141 g) 512 h) 6110 i) 71134
15

j) 93170 k) 7 5 l) 32729 10. a) 1 b) 1 c) 1 d) 1 e) 9 f) 11
12 6 12 6 2 14 24

g) 11 h) 261 i) 318 j) 2190 k) 4 11 l) 22149 11. a) 1 1 b) 1178 c) 17
24 18 12 24

d) 7 e) 1 f) 7 g) 6 7 h) 731 i) 1343 j) 2118 k) 17 l) 174
18 30 24 8 24

12. a) Rs 912 b) 10112 km c) 2734 kg 13. a) 112 m b) 1432 kg 14. a) 1 b) 158 km
24
15. Please complete your project work and compare with your friends. Then, show to your

teacher.

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Exercise 5.4

Creative Section

9. a) 3 b) 272 c) 119 d) 6 e) 20 f) 843 g) 225 h) 8 i) 15 j) 1
5 15 32 2

k) 1 l) 4 m) 9 n) 2 o) 423
3 9 20

10. a) 6 b) 15 c) 1 d) 1 e) 2 f) 1 1 g) 2 1 h) 1 1 i) 2 1 j) 1 1
15 27 3 6 2 4 2 2
2 5 g) 373 1
11. a) 1 b) 3 c) 1 d) 114 e) 2 f) 8 h) 3 i) 421 j) 3
2 3 5 4
1
k) 1 l) 7 2 12. a) 121 b) 121 c) 1 d) 2 e) 121 f) 114
6 6 21 f) 35 km g) 120
13. a) Rs 20 b) Rs 80 c) 15 d) 300 kg e) 120 m h) 300 i) 60

14. a) Rs 10 b) Rs 6 c) Rs 100 d) 15 e) 225 f) Rs 300

15. a) 132 b) 2 2 c) 9 d) 20 16. a) Rs 855 b) 21 km 17. a) 1 b) (i) 1 (ii) 1
3 16 21 6 6 3

18. a) 1 b) (i) 1 (ii) 2 (iii) 2 c) 4 19. a) 20 b) 12
3 3 3 3 5

20. a) 2,187 b) Rs 10,000, Rs 8,000 c) Rs 5,000, Rs 8,000, Rs 13,000, Rs 7,000 d) 4 km

21. a) 9, 1 b) 54, 1 c) 2 , 3 d) (i) 121 , 121 (ii) 131 , 113 (iii) 114, 114
9 54 3 2

22. a) (i) 1 (ii) 5 (iii) 10 b) 3 , 6, 16
6 20

23 and 24. Please complete your project work and discuss with your friends. Then, show to

your teacher. Exercise 5.5

Creative Section

4. a) 0.6, 0.06, 0.006 b) 4.7, 0.47, 0.047 c) 25.6, 2.56, 0.256 d) 0.01, 0.12, 1.23

e) 0.0005, 0.055, 5.55 f) 0.0003, 0.034, 3.45, 345.6

5. a) 0.5 b) 0.25 c) 0.2 d) 0.75 e) 0.4 f) 0.6 g) 0.625 h) 0.4375 i) 0.15

j) 0.36 k) 0.325 l) 0.54 m) 1.5 n) 2.75 o) 4.4 p) 7.666 q) 9.714 r) 10.444
1 2 1 1 1 1 1 121 3 3
6. a) 1 , 1 , 500 , b) 5 , 25 , 250 c) 2 , 20 , 200 d) , 20 , 200
5 50

e) 1212 , 114 , 1 f) 22 12, 241 , 9 7. a) 0.03 b) 0.08 c) 0.25 d) 0.48 e) 0.56 f) 0.97
8 40

8. Please complete your project work and compare with your friends. Then, show to your

teacher. Exercise 5.6

Creative Section

4. a) 0.2 + 0.05 b) 0.6 + 0.04 c) 0.7 + 0.01 + 0.004 d) 0.4 + 0.07 + 0.006 + 0.0005

5. a) 0.62 b) 0.73 c) 1.49 d) 8.54 e) 16.105 f) 34.007 g) 0.18

h) 0.33 i) 0.744 j) 2.48 k) 4.155 l) 4.125

6. a) Show to your teacher 7. a) 1.8 b) 1.95 c) 1.475 d) 0.37 e) 1.88 f) 1.744

8. a) 7.848 b) 35.65 c) 49.995 9. a) Rs 103.85 b) 46.4 °C c) 8 km d) 12.75 l

10. a) 0.1697 b) 0.70918 11. a) 53.87 kg b) 0.369 km

12. a) 0.02 b) 0.7 c) 0.009 d) 41.77 e) 63.684 f) 33.5

13. Please complete your project work and compare and discuss with your friends. Then,

show to your teacher.

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Exercise 5.7

Creative section

8. a) 24 b) 45 c) 68 d) 105 e) 260 f) 540

g) 960 h) 1920 i) 0.07 j) 0.05

9. a) 0.3, 0.3, 0.03 b) 0.4, 0.4, 0.04 c) 0.6, 0.06, 0.006

10. a) 0.006 b) 0.019 c) 0.025 d) 0.364 e) 0.736 f) 0.987

11. a) (i) 25 mm (ii) 56 mm b) (i) 3.7 cm (ii) 8.4 cm

12. a) (i) 315 cm (ii) 680 cm b) (i) 2.25 m (ii) 0.755 m

13. a) (i) 450 p (ii) 825 p b) (i) Rs 2.50 (ii) Rs 7.45

14. a) (i) 1400 m (ii) 2750 m b) (i) 1.8 km (ii) 4.25 km

15. a) (i) 1250 g (ii) 3674 g b) (i) 1.5 kg (ii) 2.45 kg

16. a) (i) 4500 ml (ii) 8250 ml b) (i) 0.35 l (ii) 1.265 l

Exercise 5.8

Creative Section

1. a) 18.2 b) 31.32 c) 84.42 d) 117.44 e) 7.776 f) 1.836

g) 0.36 h) 8.64 i) 21.016 j) 16.6788 k) 0.438 l) 0.000228

2. a) 1.2 b) 1.41 c) 0.236 d) 0.21 e) 0.078 f) 0.0036

g) 5 h) 6 i) 13.8 j) 2.5 k) 0.5 l) 0.16

3. Show to your teacher 4. a) 1.4 b) 1.5 c) 0.4 d) 6

e) 1.56 f) 0.88 5. a) Rs 137.25 b) 8.1 m

6. a) Rs 18.81 b) 1.65 m 7. a) 42.12 cm2 b) 6.3 cm

8. a) (i) 860 .28 km (ii) 944.7 km b) (i) Rs 1,996.65 (ii) Rs 6,236.80

9. a) (i) Rs 140.50 (ii) 3.5 kg b) (i) Rs 144.50 (ii) 45.5 hours

10. a) Shadeep b) 1.1

11. Please complete your project work and discuss in the class. Then, show to your teacher.

Exercise 5.9

Creative Section

3. a) 3.4 b) 6.5 c) 17.1 d) 25.3 e) 0.4

4. a) 3.42 b) 8.32 c) 21.98 d) 0.17 e) 0.53

5. a) 5.102 b) 12.628 c) 15.476 d) 0.274 e) 0.09

6. a) 4.2, 4.21, 4.213 b) 10.7, 10.66, 10.658 c) 8.1, 8.11, 8.109 d) 0.4, 0.4, 0.398

e) 0.1, 0.095 7. a) 0.1416, 0.142 b) 0.95208, 0.095 c) 2.5272, 2.527

8. a) 3.3333, 3.33 b) 6.6667, 6.67 c) 8.3333, 8.33

d) 3.1428, 3.14 e) 2.0833, 2.08 f) 1.8667, 1.87

6. Unitary Method
Exercise 6.1

Creative Section

3. a) Rs 80 b) Rs 405 c) Rs 723 d) Rs 1887.50 4. a) Rs 12 b) Rs 24 c) Rs 55 d) Rs 55.50

5. a) 7 b) 14 c) 17 d) 26

6. a) 4 pens for Rs 56 b) 9 kg of rice for Rs 810 c) 1 dozen of eggs for Rs 120

7. a) Rs 144 b) Rs 6,000 c) Rs 600 d) Rs 11,520

8. a) (i) 30 km (ii) 120 km (iii) 100 km b) (i) 60 km/hr (ii) 420 km

9. a) 8 kg b) 9 books 10. a) 16 km b) Rs 5,400 11. a) 5,625 l b) 2 hours

12. a) 10 MB, 10 MBps b) 50 MBps

13. Please complete your project work and discuss in the class. Then, show to your teacher.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 273 Vedanta Excel in Mathematics - Book 6

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7. Percent
Exercise 7.1

Creative Section

3. a) 75% b) 80% c) 70% d) 45% e) 48% f) 86% g) 6% h) 33%

i) 45% j) 62% k) 75% l) 93%
1 1 9 16 3 4
4. a) 5 b) 4 c) 20 d) 25 e) 4 f) 5

5. a) 50% b) 40% c) 16% d) 80% e) 75% f) 25%

6. a) 20% b) 75% c) 20% d) 25%

7. a) (i) 40% (ii) 60% b) (i) 65% (ii) 35%

8. a) (i) 55% (ii) 45% b) 80% c) (i) 48% (ii) 52% d) 55%, 45%

9. 30%, 20%, 50%

10. (i) 80%, 92%, 72%, 100%, 84%, 76% (ii) 20%, 8%, 28%, 0%, 16%, 24%

11. a) English: 85%; Nepali: 75%, Maths: 90%, Science: 84%

12. Please complete your project work and discuss in the class. Then, show to your teacher.

Exercise 7.2

Creative Section

3. a) Rs 15 b) Rs 54 c) Rs 231 d) 252 e) 540 f) 1,485

4. a) Rs 400 b) Rs 640 c) 880 d) 700 e) Rs 4,400 f) Rs 3,600

5. a) 680 b) (i) 12 (ii) 28 c) 8 students d) (i) Rs 3,510 (ii) Rs 1,890 (iii) Rs 98,280

e) (i) Rs 8,640 (ii) Rs 12,960 (iii) Rs 1,55,520 (iv) Rs 1,24,416

6. a) Rs 180 b) (i) Rs 1,530 (ii) Rs 16,830 c) Rs 1,800 d) (i) Rs 22,500 (ii) Rs 4,27,500

7. a) (i) Rs 125 (ii) Rs 1,125 b) (i) Shoes: Rs 300, Rs, 1,200, (ii) T-shirt: Rs 230,

Rs 920 (iii) Mobile: Rs 1,000, Rs 4,000

8. a) Rs 24,000 b) 32 km c) 400 d) 40

9. a) (i) 300 (ii) 165 b) (i) 40% (ii) Rs 20,600 (iii) Rs 12,360

10. Pragya, 4% 11. No, 99% 12. a) 72 b) 90% 13. a) 30, 20 b) 15, 8 c) 23 d) 46%

14. a) Sahayata, Rs 2,000 more b) Sahayata, by Rs 7,200

15. Please complete your project work and discuss in the class. Then, show to your teacher.

8. Profit and Loss

Exercise 8.1

Creative Section

3. a) profit Rs 15 b) profit Rs 40 c) loss Rs 35 d) loss Rs 30

4. a) Rs 145 b) Rs 225 c) Rs 180 d) Rs 645 5. a) Rs 440 b) Rs 795

6. a) Rs 35 b) Rs 25 7. a) Rs 75 b) Rs 165

8. a) Rs 3,030 b) Rs 6,996 c) Rs 180 d) Rs 700

5. a) a) Loss Rs 100 10. Profit Rs 60 11. Rs 310 12. Rs 22 13. Rs 666

14. and 15. Please complete your project work and discuss in the class. Then, show to your

teacher. 9. Algebra

Exercise 9.1

Creative Section

5. Show to your teacher x + y
2
6. a) xy + z b) 3(x + y) + 5 c) 2(p – q) – 4 d) r – pq e) 5ab + x f) – 7

7. a) (i) (x – 2) years (ii) (x + 2) years (iii) 4x years b) (b + 5) m c) 2x, 4x
yourbp) r21oj(ebc×t who)rk
8. a) a + b + c and c) 4l in the d) l2 e) 2 (l + b ) f) l × b
9. Please complete compare class. Then, show to your teacher.

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Exercise 9.2

Creative Section

4. a) 9 b) 9 c) 9 d) 30 e) 13 f) 21 g) 2 h) 3

5. a) 2 b) 12 c) 27 d) 3

6. a) (i) 16 cm2 (ii) 49 cm2 (iii) 12.25 cm2 (iv) 17.64 cm2

b) (i) 24 cm (ii) 36 cm (iii) 34 cm (iv) 17.2 cm

7. a) (i) 28 cm2 (ii) 48 cm2 (iii) 30 cm2 b) (i) 20 cm (ii) 28 cm (iii) 20.2 cm

8. (i) 180 m2 (ii) 156 m2 9. a) (i) 154 cm2 (ii) 616 cm2 (iii) 1386 cm2

b) (i) 44 cm (ii) 88 cm (iii) 132 cm 10. a) (i) 8 cm3 (ii) 64 cm3 (iii) 125 cm3

b) (i) 54 cm2 (ii) 150 cm2 (iii) 216 cm2

11. a) (i) 60 cm3 (ii) 385 cm3 b) (i) 132 cm2 (ii) 248 cm2

12. a) 13 cm b) 15 cm 13. a) 25 cm b) 22 cm c) 23 cm

14. a) (i) 6, 7, 8 (ii) 1, 3, 5 b) 5, 9, 13 15. a) 9y, 27 b) 2b + 3, 9

16. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 9.3

Creative Section

4. a) 11x b) 14a2 c) 8xy d) 9abc e) 7p3 f) 5mn g) 5x2y h) xy2

5. a) 6a b) 10p2 c) 3x + 4y d) 2m + 3n e) 2xy – yz – 5

f) 7p2 – 5q2 6. a) 6x b) q c) 7a d) 2y

8. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 9.4

Creative Section

3. a) 2x + 5 b) 5x + 6 c) 7a + 3 d) 9 – 5a e) 10m – 9 f) 15 – 7n

g) 10a + 6b h) 9a – 8b i)3p2 + 4q2 j) 5a2 + 2b2 k) 3x2 + 5xy l) 3x2 – 4x + 5

m) 3ab + bc – 1 n) 4abc + 2ab + 5a

4. a) 4x + 3 b) 3x - 2 c) 3a + 9 d) 4a – 6 e) 2p – 5 f) 2p – 7

g) 2m – 5n h) 4p – 3mn i) 5x2 + 7y2 j) 5a3 – 6b3 k) 2x3 + 7x2 – 4x + 13

l) 2ax + 8by – 10 m) 2abc – 3ab + 4bc + 3ca n) 4xyz + 5xy + 3yz – 9

5. a) 3x + 10 b) 4a – 9b c) 5m – 8n d) 3x + 2y e) 2a + 10b – 4 f) 3x2 + 4y2 + xy

7. a) x + 2y b) 4a – 9b c) 3p + 4q d) 9a – 7x e) m – n – 6 f) 6a + 2t

g) 4b + z h) a + 5b – 4c 8. a) 6x + 2 b) 10x + 3y

9. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 9.5

Creative Section

5. a) x2 b) 6x2 c) 12x2 d) 2x3 e) 6y3 f) 6x2y2 g) 12a3b3

h) –20x2y2z2 i) –15x3y3 6. a) x4 b) 30a4 c) 12x2y2 d) 30p3q3

e) 24b5c5 f) 10x3y3z3 g) –6a2b3c2 h) 10p2q3r2 i) 18x4y5z3

7. a) 4x2 + 10x b) 6a2 – 12a c) 5x4 + 40x2 d) 2a2b – 3ab2 e) 5a3b – 3ab3

f) 30x3y2 – 20x2y3 g) –8x2 + 6x h) –2p2q + 3pq2 i) –6a3bc – 15ab2c2

8. a) 6x2 + 15x b) 20a2 –24x c) 48p3 – 6p d) 2y4 + 14y2 e) 12m2 – 18m4

f) 56b3 + 21b5 g) x2y – xy2 h) 4x2y + 6xy2 i) 6a3b – 8ab3 j) –6p2q – 15pq2

k) –14b2c + 6bc2 l) –25x3y + 20xy3 m) –4x3 + 8x2 – 4x

n) –15a3 – 15a2 + 25a o) –12x3y + 15x2y2 + 9xy3

9. c) –24 d) 6 e) 18 10. a) x2 + 3x + 2 b) x2 + 2x – 3
c) y2 + 3y + 2 d) 0 e) x2 + 2xy + y2 f) a2 – 2ab + b2

Creative Section b) a2 + a – 2 Exercise 9.6 d) a2 + 2ab + b2
2. a) x2 + 3x + 2
c) x2 – x – 6

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Answers

e) x2 – y2 f) 4p2 – 9q2 g) 3x2 + 5xy – 2y2 h) 12a2 – 29ab + 15b2

i) 7p2 + 26pq – 8q2 3. a) x2 + 3x + 2 b) x2 + 7x + 12 c) a2 + a – 2

d) a2 – 5a + 6 e) b2 – 25 f) p2 – 16 g) a2 + 2ab + b2 h) a2 – b2

i) a2 – 2ab + b2 j) 2x2 + 5xy + 3y2 k) 2x2 + xy – 3y2 l) 2x2 – 5xy + 3y2

m) 9x2 – 16y2 n) 25a2 – 4b2 o) 2x2 – xy – 15y2

4. a) x3 + 2x2 + 2x + 1 b) x3 – 4x2 + 7x – 6 c) 2x3 – 3x2 – 13x + 12

d) 2a2 + 4a + 3ab + 2b + b2 e) 6a2 – 15a – 8ab – 10b – 8b2

f)12a2 – 28a – 7ab + 35b –10b2 5. Show to your teacher

6. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 9.7

Creative Section

3. a) x b) y2 c) a2 d) 3x e) 2y f) 4x3 g) 3xy2 h) 6a2b

4. a) x b) a3 c) 3p d) 3m3 e) –3y2 f) –2x

g) ab h) x2y2 i) 3x3y3 j) –5x2y k) –4a2b2 l) –4x2y2

5. a) 2x2 – 3x b) x2 – 2 c) a + 1 d) x – 3 e) 2b + 3

f) 3c – 2 g) 4m – 3 h) 2n2 – 3n i) p2 – 2pq2 j) 3a3 – b3

k) x2y + 2xy2 l) 3p3q2 – 4pq3 m) 2a3x2 + 3a2x3 n) 5 – 2c2 o) 5x2z + 8xyz2

p) 3mnp – 7m4n2

6. a) x + 1 b) a + 2 c) m + 3 d) p + 4 e) a + 3 f) b + 5 g) x + 2

h) y + 3 7. a) 2a2b b) 2x – 5y c) (x + 3) units d) (x + 5) units

8. a) 6x2y2 b) and c) Show to your teacher.

9 and 10. Please complete your project work and compare in the class. Then, show to your

teacher.

10. Equation, Inequality and Graph

6. a) x + 5 = 9 b) x – 4 = 6 Exercise 10.1 e) x = 5
2
7. a) 3 b) 4 c) 7x = 21 d) 6x = 30
c) 5 d) 4

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

9. a) 8 b) 4 c) 6 d) 4

Exercise 10.2

Creative Section

2. a) 5 b) 7 c) 10 d) 9 e) 8 f) 16 g) 3 h) 9 i) –10 j) 5 k) 8 l) –9

3. a) 3 b) 4 c) 6 d) 6 e) 9 f) 7 g) 4 h) 5 i) 3 j) –3 k) 4 l) 3

4. a) 10 b) 35 c) 56 d) 12 e) 15 f) 21 g) 3 h) 4 i) 5 j) 12 k) 6 l) 6

5. a) 5 b) 11 c) 6 d) 3 e) 5 f) 9 g) 1 h) 26 i) 3 j) 6 k) 18 l) 4

6. a) 2x = x + 4, x = 4 b) 3a + 3 = 2a + 5, a = 2

c) 4y = 2y + 6, y = 3 d) 5x + 2 = 3x + 8, x = 3

7. a) 4, 4 cm b) 2, 6 cm c) 8, 10 cm 8. a) 4, 6 cm b) 2, 5 cm

c) 2, 4 cm 9. a) 2, 6 cm, 4 cm b) 3, 6 cm, 5 cm c) 5, 11 cm, 7 cm

10. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 10.3

Creative Section

3. a) 5 b) 11 c) 15 d) 20 4. a) 4 b) 3

5. a) 7, 9 b) 10, 12 6. a) Rs 5 b) Rs 25 7. a) Rs 400 b) Rs 75

c) Rs 200 d) 60 8. a) Rs 2,500 b) Rs 800 c) Rs 1,800 d) Rs 480

9. a) 40° b) 55° c) 100° d) 45°

10. a) 130° b) 60°, 120° c) 32°, 64°, 116°

11. a) 4 cm b) 14 cm, 7 cm c) 5 cm d) 9 cm

12. a) 8, 2 b) 18, 15 c) 22, 15 13. a) 40 years, 10 years b) 30 years, 5 years

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Answers

14. a) Rs 4, Rs 11 b) 13, 19

15. Please complete your project work and compare in the class. Then, show to your teacher.

Exercise 10.4

Creative Section

5. a) x > 6 b) y < 2 c) x = –4 d) m > 0 e) p < 0 f) k = 0

6. a) x > 5 , x 5 b) y < –3, y –3 c) z = 6, z ≠ 6

d) –p > –2, –p – 2 e) –x < –4, –x –4 f) x + 5 = 9, x + 5 ≠ 9

g) y – 8 > – 2, y – 8 –2 h) 7 – x < x – 7, 7 – x x – 7

Exercise 10.5

Creative Section

4. a) {1, 2, 3, 4} b) {2, 3, 4, 5} c) {1, 2} d) {2, 3, 4, 5}
5.
x<5 x < –3

x≤4 x ≥ –2

x<4

6. a) {…, –1, 0, 1, 2, 3}

b) {3, 4, 5, …} x>2

x≤6

c) {…, 2, 3, 4, 5, 6}

x≥1

d) {1, 2, 3, 4, …}

7. a) x < 6, {…, 1, 2, 3, 4, 5} b) x ≥ 3, {3, 4, 5, …}

c) x < –4, {…, –6, –5, –4} d) x > – 5, {–4, –3, –2, –1, 0, 1, …}

e) 1 < x < 6, {2, 3, 4, 5} f) –3 ≤ x ≤ 3, {–3, –2, –1, 0, 1, 2, 3}

8. a) x ≥ 15 b) 4x ≥ 20, x ≥ 5 c) 7x ≥ 350, x ≥ 50

11. Coordinates

Exercise 11.1

Creative Section A

5. Show to your teacher. 6. Show to your teacher.

7. a) triangle ABC b) square PQRS c) rectangle MATH d) rectangle LIKE

e) kite NICE f) kite BEST g) trapezium YEAR

8. a) M(3, 2) b) N(4, 4) 9. a) C(5, 3) b) N(–2, 3)

10. Please complete your project work and compare in the class. Then, show to your teacher.

12. Geometry Basic Concepts

Exercise 12.1

Show to your teacher

13. Geometry - Angles

Exercise 13.1

Creative Section

8. a) 30° b) 80° c) 120° d) 15° e) 65°

9. a) 60° b) 150° c) 15 minutes d) 35 minutes

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Answers

10. a) 60° b) 50° c) 115° d) 250° e) 60° f) 30° g) 30°, 60°

h) 90°, 270° i) 15°, 30°, 45° j) 50°, 100° k) 42°, 84°, 126° l) 80°, 120°, 160°

Exercise 13.2

Creative Section A

3. a) Yes b) No c) Yes d) No e) No f) No

4. a) Yes b) No c) Yes d) No

5. a) Adjacent angles: ∠AOC and ∠BOC, ∠AOC and ∠AOD, ∠AOD and ∠BOC,
∠BOD and ∠BOC

Vertically opposite angles: ∠AOC and ∠BOD, ∠BOC and ∠AOD

b) Adjacent angles: ∠PTR and ∠PTS, ∠PTS and ∠STQ, ∠STQ and ∠QTR,
∠QTR and ∠PTR

Vertically opposite angles: ∠PTR and ∠STQ, ∠PTS and ∠QTR

c) Adjacent angles: ∠AOE and ∠AOC, ∠AOC and ∠COF, ∠COF and ∠BOF, ∠BOF
and ∠BOD, ∠BOD and ∠DOE, ∠DOE and ∠AOE

Vertically opposite angles: ∠AOE and ∠BOF, ∠AOC and ∠BOD, ∠COF and ∠DOE

6. a) (i) 35° (ii) 70° (iii) 28° (iv) 60°

b) (i) 135° (ii) 70° (iii) 30° (iv) 120°

7. a) 55° b) 72°, 108° c) 40°, 50° d) 85°, 95° e) 45°, 45° f) 90°, 90°

8. a) 80° b) 125° c) 60° d) 75° e) 36°, 144° f) 90° g) 70° h) 56°, 56°

9. a) 140° b) 10° 10. a) 36°, 108° b) 68°, 102° c) 50°, 60°, 70° d) 25°, 35°, 120°

11. a) y = 85°, x = z = 95° b) z = 150°, x = y = 30° c) a = 70°, b = c = 110°

d) p = 50°, r = q = 130° e) x = y = 36°, 4x = z = 144° f) 2x = y = 60°, 4x = z = 120°

g) x = 40°, y = 80°, z = 100° h) x = 40°, y = 60°, z = 120°, 2x = 80°

12. a) 30°, 100°, 50°, 180° b) 40°, 95°, 45°, 180°

Exercise 13.3

Creative Section

3. a) 40° b) 30° c) 60° d) 105° e) 80° f) 110° g) x = y = 120°; z = 60°

h) a = b = c = 105° i) r = q = 95° ; p = 85° j) x = y = 60° ; 2x = z = 120°

k) a = c = 2x = 72° ; b = 3x = 108° l) x = p = r = 36° ; q = 4x = 144°

4. a) 45° , 135° b) 80° , 70° c) 75° , 105° d) x = w = 82°, y = z = 80°

e) a = b = 112° , c = 68° f) x = 100° , y = z = 80° g) p = q = r = 86° ; s = 94°

h) 30°, 40°, 290° i) 120°, 60°, 60° j) 15°, 30° k) 50°, 60°, 70° l) 65°, 115° , 115°

5. Show to your teacher 6. Show to your teacher

7. a) 60°, 50°, 70° b) 90°, 90° c) y = w = 55°, x = z = 125°

14. Geometry - Triangles and Polygons

Exercise 14.1

Creative Section

3. a) 50° b) 35° c) 30° d) 42° e) 30°, 60° f) 60° g) 45°, 45° h) 40°, 50°

4. a) 50° b) 65° c) 72° d) 65°, 65° e) 70°, 70° f) 72°, 72° g) 48°, 48° h) 40°, 40°

Exercise 14.2

Creative Section

2. a) 40°, 80° b) 30°, 60°, 90° c) 40°, 60°, 80° d) 50°, 60°, 70°

3. a) 80° b) 40° c) 45° 4. a) 80°, 80° b) 45°, 47° c) 130°

d) 140° e) 110° f) 80° g) 60° h) 82° i) 65°, 65°, 115°

j) 66°, 66°, 114° k) 72°, 72°, 36° l) 86°, 47°, 47° m) 80°, 40°, 60°

n) 50°, 70°, 60° o) 50°, 50°, 75° p) 62°, 78°, 78°, 40°

Vedanta Excel in Mathematics - Book 6 278 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise 14.3
Creative Section A
3. a) Quadrilateral ABCD, triangles: 'ABD and 'BCD

b) Pentagon PQRST, triangles: 'PQR, 'PRS and 'PST

Quadrilaterals: PQRS and PRST

c) Hexagon RAMESH, triangles: 'RAM, 'RME, 'RES, 'RSH

Quadrilaterals: RAME, RMES, RESH

Pentagons: RAMES, RMESH

4. a) 100° b) 50°, 100° c) 35°, 70°, 105° d) 48°, 72°, 96°, 144°

5. a) 95° b) 80° c) 55°, 110° d) 42°, 84°, 126° e) 140°, 80°, 52°
f) 66°, 49°, 98°, 147° g) 120°, 85°
h) 110°, 130°, 60°, 60° i) 90°, 140°, 60°, 70°

6. a) 540° b) 720° c) 900° d) 1080° 7. a) 100° b) 36°, 72°, 108°, 144°, 180°

c) 38°, 152°d) 42°, 84°, 126°, 168° 8. a) 100° b) 65°, 130° c) 80°, 160°, 120°

9. Show to your teacher

Exercise 14.4 (Show to your teacher)

15. Geometry: Construction

Show to your teacher.

16. Perimeter, Area and Volume

Exercise 16.1

Creative Section A

1. a) 500 cm b) 1800 cm c) 2025 cm d) 3740 cm e) 182.88 cm

f) 432.04 cm g) 15.24 cm h) 25.4 cm i) 160.02 cm j) 266.7 cm

2. a) 157.48 in b) 787.4 in c) 649.61 in d) 1899.6 in e) 84 in

f) 288 in g) 426 in h) 585 in i) 307 in j) 647 in

3. a) 49.2 ft b) 91.84 ft c) 131.86 ft d) 182.2 ft e) 12.5 ft

f) 2.5 ft g) 2 ft h) 5.5 ft i) 7.5 ft j) 28.25 ft

4. a) 12.6 m b) 35.25 m c) 10 m d) 16.25 m

e) 100 m f) 18.48 m g) 7.77 m h) 11.2 m
5. a) 66 in, 167.64 cm, 1.68 m b) 34.44 ft, 20.34 ft c) 29,024.26 ft, 28,162.02 ft

d) 67.3 m, 45.81 m 6. a) 0.25 ft b) 1.35 m c) 3.23 m d) 257.66 ft

7. Please complete your project work and discuss in the class. Then, show to your teacher.
Exercise 16.2

3. a) 9 cm b) 12 cm c) 13 cm d) 16 cm

e) 11 cm f) 14 cm g) 26 cm h) 28 cm

4. a) (i) 15 cm (ii) 13.5 cm (iii) 7.8 cm

b) (i) 16 cm (ii) 26 cm (iii) 28.8 cm

c) (i) 19 cm (ii) 22 cm (iii) 25 cm

d) (i) 15 cm (ii) 27 cm (iii) 52 cm

5. a) 6 cm b) 15 cm 6. a) 12 cm b) BC = 8 cm

7. a) 80 km b) 120 m 8. a) (i) 220 m, 440 m, 660 m b) 720 m

9. a) 1,600 m b) 792 m 10. a) 21 cm b) 10 cm c) 40 m

11. a) (i) 4 cm, 6 cm, 10 cm (ii) 4 cm b) (i) 40 m, 50 m, 20 m (ii) 30 m

12. a) Saurav, 2 cm b) 10 units, 14 units, 40% more 13. a) 5 cm b) 4 cm

14. Please complete your project work and compare in the class. Then, show to your teacher.

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Answers

Exercise 16.3

Creative Section A

5. a) 20 square units b) 12 square units c) 12 square units d) 14 square units

e) 18 square units f) 34 square units

6. a) 28 cm2 b) 9 cm2 c) 27 cm2 d) 11 cm2 e) 12 cm2 f) 40 cm2

7. a) 24 cm2 b) 76 cm2 c) 117.5 cm2 d) 164.16 cm2

8. a) 36 cm2 b) 30.25 cm2 c) 110.25 cm2 d) 262.44 cm2

9. a) 25 m2 b) 33 m2 c) (i) 85 m2 (ii) Rs 6375

10. a) (i) 7 cm (ii) 28 cm b) 56 m c) (i) 10 cm, 34 cm d) 10 m

11. a) (i) 6 cm, 3 cm (ii) 18 cm b) 24 m

12. a (i) 3 cm (ii) 9 cm2 b) 225 m2 c) (i) 6 cm (ii) 48 cm2 d) 96 m2
13. a) 36 cm2 b) 55 cm2 c) 61 cm2 d) 128 cm2 e) 150 cm2 f) 18 cm2

14. a) 4 ft b) 3 ft 15. a) 12 m b) 10 m 16. (i) No (ii) Square, 9 cm2, 12.5%

17. Please complete your project work and discuss in the class. Then, show to your teacher.

Exercise 16.4

Show to your teacher. Exercise 16.5

Creative Section A

3. a) 94 cm2, 60 cm3 b) 197 cm2, 180 cm3 c) 258 cm2, 252 cm3 d) 961 cm2, 1,975 cm3

4. a) 24 cm2, 8 cm3 b) 150 cm2, 125 cm3 c) 121.5 cm2, 91.125 cm3

d) 346.56 cm2, 438.976 cm3 5. a) 664 cm2, 960 cm3 b) 486 cm2, 729 cm3

c) (i) 3m3 (ii) 3m3 (iii) 3000 l d) (i) 2,40,000 cm3 (ii) 2,40,000 cm3 (iii) 240 l

6. a) (i) 2 cm (ii) 8 cm3 b) (i) 5 cm (ii) 150 cm2 c) 64 cm3 d) 54 cm2

7. a) 6 cm, 3 cm b) (i) 10 cm, 5 cm (ii) 220 cm2

8. a) 248 cm2 b) 9,000 l

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

17. Symmetrical Figures, Design of Polygons and Tessellation

Show to your teacher

18. Statistics

Exercise: 18.1

Show to your teacher

Show to your teacher Exercise : 18. 2
Exercise : 18.3

Creative Section

3. Show to your teacher.

4. a) 9 b) 27 c) 10 years d) 7 cm

5. a) 10 years b) 90 cm c) 26 d) Rs 77.50

6. a) 19 b) 4° C c) 50 d) Rs 154

7. a) 82.5 cm b) 105 mm c) Rs 350 8. a) 19 b) 95

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

Vedanta Excel in Mathematics - Book 6 280 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Government of Nepal
Ministry of Education, Science and Technology
Curriculum Development Centre, Sanothimi, Bhaktapur

Syllabus of Mathematics-Class 6

S. Content Content Working
N. Area hours

Geometry • Lines and Angles: Intersecting and parallel lines (pair of 19
1. lines), Perpendicular lines, Use of set –squares and compass,
Construction of bisector of angle and perpendicular bisector of
2. Arithmetic line segment by using compass, Construction of parallel and
perpendicular bisector by using set-squares, Classification of
angles (acute angle, obtuse angle, right angle, straight angle,
reflex angle), Construction of angles and measurements (angles
of 30o, 45o, 60o, 90o, 120o)

• Triangle, Quadrilateral and Polygons: Classification of 9
triangles according to the sides and angles, Introduction of
quadrilateral (rectangle, square, parallelogram, trapezium,
rhombus)

• Solid objects: Relation of number of faces, edges, and vertices 10
of cuboid and cube, skeleton of cuboid and cube

• Coordinates: Introduction of axes and coordinates, points on 7
quadrants

• Symmetry and Tessellation: Symmetrical figures, Tessellation 5
from rectangle and square

• Real numbers: 18
(a) Whole numbers: Introduction of whole numbers, Simplification

of whole numbers including four basic operations and
brackets, Test of divisibility (2, 3, 5, 7 and 11), prime factors of
the numbers up to three digits, factors and multiples, table of
square roots (0-100), H.C.F. and L.C.M. of numbers (by prime
factorization),
(b) Integers: Introduction of integers

• Fraction and Decimal: 15
(a) Fraction: Equivalent fractions, Comparison, addition and

subtraction of unlike fractions, Multiplication and division of
fractions
(b) Decimals: Multiplication of decimals, Division of decimal (by
integer), Rounding off decimal (up to three decimal places)

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• Percentage: Problem based on percentage (to find a unknown 4
quantity when any two out of total number, percentage and 4
number of percentage are given) 4
15
• Profit and Loss: Introduction of profit and loss, Problems
related to profit and loss without having percentage) 10
10
• Unitary Method: Value of more item based on unit value, Unit 20
value based on value of more items of same type 10

• Distance: Relation between inch and centimeter, foot and

centimeter, inch and meter, foot and meter, inch and foot

• Perimeter, Area and Volume: Area of square and rectangular

3. Mensuration surface (using formula), Area of regular and irregular objects

by using the number of square), Area of rectangle and square

(using formula), Volume of cuboid and cube, Circle and its

different parts

4. Set • Set: Methods of describing a set, Membership of a set, Types
of set (Empty set, Equivalent and equal sets, Finite and infinite
set)

5. Statistics • Statistics: Construction of frequency table by using tally bars
for the given or collected data, Construction of simple bar
graph with width 10 or 5.

6. Algebra • Expressions: Addition and subtraction of two algebraic
expressions each containing up to three terms, Multiplication
and division of algebraic expressions (Monomial or binomial
by monomial) , value of algebraic expressions

• Equation, Inequality and Graph: Linear equation of single
variable, signs of trichotomy (<, >, =)

Vedanta Excel in Mathematics - Book 6 282 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Evaluation Model Set

Attempt all the questions.

Group-A [5×(1+1) = 10] PR

1. (a) If PQ A AB and RS A AB, what is the relation between
PQ and RS?

(b) How many inches are there in 1 foot? AQ SB
2. (a) On what axis does the point (0, 5) lie?

(b) If the cost of 1 kg of sugar is Rs 80, what is the cost of 5 kg of sugar?

3. (a) If V = {a, e, i, o, u}, find the value of n (V).

(b) Whatisthatisthefrequencyof25inthedata20,25,30,25,35,25,20,35,40,
20?

4. (a) Multiply 4a2 + 3b2 by 2ab.

(b) Write the statement “x is greater than 5” by using appropriate trichotomy
sign.

5. (a) If x = 3, what is the value of 3x – 5?

(b) Find the value of 100 .

Group-B (17× 2 = 34)

6. (a) Find the values of y and unknown angle from the figure 105° 3y
given alongside.
A

(b) From the given figure, find the value of x. xD

35° C
B

(c) If V, E and F denote the number of vertices, edges and faces of a cuboid

respectively, find the value of V – E + F.

7. (a) Construct an angle of 600 and bisect it.

(b) A rectangular garden is 15m long and 10m broad. Find the length of
wire required to fence it with 3 rounds.

(c) A block is 20cm long, 12cm wide and 5cm high. Find the volume of
such 40 blocks.

8. (a) Write the possible number the axes of symmetry of the given
figure. Also, draw the axes of symmetry in the figure.

(b) What is origin? Write down the coordinates of origin.

(c) Write the set A = {1, 2, 3, 4} in descriptive and set-builder method.

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9. (a) In the polymerise chain reaction (PCR) test was done among 1,450
3
suspected people of a place, 10 of them were found having corona
positive.

(i) How many of suspected people had corona positive?

(ii) How many of suspected people had corona negative?

(b) Out of 40 students of grade VI, 80% of them are attending their virtual
classes in zoom regularly. Find the number of students who are not
attending the virtual classes regularly.

(c) The weights (in kg) of 15 children of a class are given below.

20, 25, 30, 25, 35, 25, 35, 40, 35, 20, 40, 30, 20, 35, 25

Present the data in a frequency table using tally bars.

10. (a) What should be added to 3u – 4v + 1 to get 8u + 5v – 6?

(b) Divide: (15p4q3 – 20p2q4) ÷ 5p2q2

(c) Solve: 3y – 1 = 2y + 3
11. (a) 5 7
If the cost of a dozen of banana is Rs 30 more than the cost of 7 bananas,
find the cost of a banana.

(b) If a = 3, b = 2 and c = -1, find the value of ab + bc + ca.

Group-C (14 × 4 = 56) z°
75°
12. Find the sizes of unknown angles from the given figure. 62°
w° y°
13. From the quadrilateral ABCD given alongside, A D
x°
answer the following questions.

(i) Measure the length of each side. BC
(ii) Measure the size of each angle.

(iii) Write down the relation between the opposite sides and the opposite
angles of the quadrilateral.

(iv) What is the type of this quadrilateral?

14. Plot the points A (1, 2) and B (5, 4) on a graph-paper and join them.

(i) Mark the mid-point M of segment AB and find the coordinates of mid-
point M.

(ii) Produce AB to the point N such that AB = BN and find the coordinates
of point N.

15. If A = {x: x is a factor of 18} and B = {y: y is a prime number, y < 15}.

(i) List the elements of each the sets.

(ii) Write with reasons whether the sets A and B are equal or equivalent.

(iii) Are they overlapping sets? Give reason.

Vedanta Excel in Mathematics - Book 6 284 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

16. The students of a school were participated in the rally on ‘Children’s Day’
with two banners of equal area. If the first banner is 8ft long and 3ft wide and
the second banner was 6ft long, what was the width of the second banner?
Find.

17. Simplify: 24 ÷ 2 [70 ÷ 5{4 + (12 – 18 ÷ 6 × 3)}]
18. Shashwat distributed 48 Snickers and 72 Cadburys equally to her friends on

her birthday.
(i) Find the greatest number of her friends.
(ii)How many Snickers and Cadburys did each get?
19. Mr. Chaudhary sold a jacket for Rs 2,250 and made a profit of Rs 450.
(i) Find the cost price of the jacket.
(ii)If he sold the jacket for Rs 1600, find his profit or loss.
20. Sunibha went to a grocery and bought 421 kg of wheat flour so called “Aata”.
(i) She used 3 kg of “Aata” for breakfast in 2 days. How much “Aata” was

left then?
(ii) If she used equal amount of “Aata” in each day and finished in 3 days,

how much “Aata” was consumed in a day?
21. There are 30 students in a class. The record of number of students who were

present from Monday to Friday in the last week is given in the table below.
Draw a bar graph to represent the data.

Days Mon Tue Wed Thurs Fri

No. of present students 20 25 28 30 24

22. Subtract 2x – 3y + 5z from the sum of 4x + 2y –z and x – y + 6z

23. If a = (2x – 3) and b = (2x + 3), show that: ab + 9 = x2
4
24. Divide: (x2 + 5x + 6) ÷ (x+ 3)

25. If the perimeter of the given rectangle is 36cm, make 2x cm
an equation and solve for the value of x. Also, find
the exact length and breadth of the rectangle.

(x + 6) cm

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 285 Vedanta Excel in Mathematics - Book 6

Q. No. Marking Scheme Mark

1. a) Answer 1
b) Group-A 1
1
2. a) PQ//RS 1
b) 1 foot = 12 inch 1
Y-axis 1
3. a) 5 ×Rs 80 = Rs 400 1
b) n (V) = 5 1
Frequency of 25 is 3. 1
4. a) 8a3b + 6ab3 1
b) x>5
3×3 – 5 = 4 1
5. a)
b) 10
Group-B
6. a)
(i) 105o + 3y = 180o
b)
(ii) y = 250 1
c) (i) x+350 = 90o 1

7. a) (ii) x = 55o 1
(i) V = 8, E = 12, F = 6 1
b)
(ii) V– E + F = 2 1
c) (i) Construction of 60o correctly 1

8. a) (ii) Construction of bisector correctly 1
(i) Perimeter = 2 (15m + 10m) = 50m 1
b)
(ii) Required length of wire = 3P = 3×50m = 150m 1
c) (i) Volume of brick = 20cm × 10cm ×5cm = 1000cm3

9. a) (ii) Volume of 40 blocks = 40 ×1,000cm3 = 40,000cm3 1
(i) No. of axes of symmetry = 2 1
b)
(ii) Correct drawing of axes of symmetry 1
c) (i) Point at which the x-axis and y-axis intersect. 1

(ii) Coordinates of origin = (0,0) 1
(i) ( natural numbers less than 5} 1

(ii) {x:x is a natural number, x<5} 1
1
(i) No. of people with corona positive = 3 × 1450 = 435
10 1

(ii) No. of people with corona negative = 1450 – 435 = 1015 1

(i) No. of regularly present students = 80% of 40 = 32

(ii) No. of irregularly present students = 40 – 32 = 8 1
Construction of frequency table with tally bars correctly. 1+1

Vedanta Excel in Mathematics - Book 6 286 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

10 a) (i) 8u + 5v – 6 – (3u – 4v + 1) = 8u + 5v – 6 – 3u + 4v – 1 1

(ii) 5u+ 9v – 7 1

b) (i) 15p4q3 – 20p2q4 1
5p2q2 5p2q2 1

(ii) 3p2q – 4q2

c) (i) 7 (3y – 1) = 5 (2y + 3) or, 21y – 7 = 10y + 15 1

(ii) 11y = 22 ∴y = 2 1

11. a) (i) Let the cost of 1 banana = Rs x. Then, 12x = 7x + 30 1

(ii) 5x = 30 ∴x = 6 1

b) (i) ab + bc + ca = 3(2) + 2(-1) + (-1)(3) 1

(ii) 6 – 2 – 3 = 1 1

Group-C

12. (i) w = 62o, x = 75o, y = 75o 1+1

(ii) x + w + z = 180o or, 75o + 62o + z = 180o ∴z = 43o 1+1

13. (i) Measurements of sides 1

(ii) Measurements of angles 1
(iii) Opposite sides are equal and opposite angles are equal 1
(iv) Parallelogram 1

14. (i) Plotting the points on the graph and joining them 1
(ii) Marking the point M as M (3, 3) 1
(iii) Extending AB to N such that AB = BN 1
(iv) N (9, 6) 1

15. (i) A = {1, 2, 3, 6, 9, 18} and B = {2, 3, 5, 7, 11, 13} 1

(ii) n (A) = 6 and n (B) = 6. So, A and B are equivalent sets. 1

(iii) Common elements = {2, 3} 1
(iv) Sets A and B are overlapping. 1

16. (i) Area of 1st banner = 8 ft×3 ft = 24 sq. ft 1
(ii) Area of 2nd banner = 6 ft ×b = 6b sq. ft 1
(iii) 6b = 24 1
(iv) b = 4 ft 1

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 287 Vedanta Excel in Mathematics - Book 6

17. (i) 24 ÷ 2 [70 ÷ 5{4 + (12-3 × 3)}]=24 ÷ 2 [70 ÷ 5{4 + (12-9)}] 1

(ii) 24 ÷ 2 [70 ÷ 5{4 +3}] = 24 ÷ 2 [70 ÷ 5{7}] 1

(iii) 24 ÷ 2 [70 ÷ 35] = 24 ÷ 2 [2] 1

(iv) 24÷ 4 = 6 1
18. (i) Required greatest no. of students = H.C.F. of 48 and 72 1

(ii) By prime factorization, 48 = 2×2×2×2×3, 72 = 2×2×2×3×3 1

(iii) H.C.F. = 2×2×2 = 8 1

(iv) Share of snicker = 48÷8 = 6, Share of Cadbury = 72÷8 = 9 1

19. (i) C.P. = S.P. – P 1

(ii) Rs 2250 – 450 = Rs 1800 1

(iii) C.P.>S.P. There is a loss 1

(iv) Loss = C.P. – S.P. = Rs 1800 – Rs 1600 = Rs 200 1
1
20. (i) Left quantity of “Aata” = 412 – 3 = 9 – 3 1
2
9 3 121 1
(ii) 2 – 3 = 2 = kg 1
4
(iii) Quantity of “Aata” for 1 day = 412 ÷ 3
9 1 3 = 112
(iv) 2 × 3 = 2 kg

21. Representing the data in a bar graph correctly

22. (i) Sum = (4x + 2y –z) + (x – y + 6z) 1
(ii) 5x + y + 5z 1
(iii) Difference = (5x + y + 5z) – (2x – 3y + 5z) 1
(iv) 3x + 4y 1

23. (i) ab = (2x + 3)(2x – 3) = 2x (2x-3) + 3(2x-3) 1
(ii) 4x2 – 6x + 6x – 9 = 4x2 – 9 1
(iii) ab + 9 = 4x2 – 9 + 9 = 4x2 1
ab + 9 4x2 1
(iv) LHS = 4 = 4 = x2 = RHS

24. (i) x + 3 ) x2 + 5x + 6 (x + 2 1+1
r x2 r 3x

(ii) 2x + 6
r 2x r 6
0 1+1

25. (i) 2 (l+ b) = P or, 2 (x + 6 + 2x) = 36 1
(ii) 2 (3x + 6) = 36 or, 3x + 6 = 18
(iii) 3x = 12 or, x = 4 1

(iv) Length (l) = (4+6) cm = 10 cm, Breadth (b) = 2×4 cm = 1
8 cm
1

Vedanta Excel in Mathematics - Book 6 288 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur