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\ 06-Jan-2025 Surender Singh Routhan Proof-2 Reader’s Sign _______________________ Date __________

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Quick Check 10. (a) 5 (b) 1 (c) 97 11. 14x – 25x + 2
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2
2
3 3
10 6
6 3
210k l ; 10a b ; 2100x y 12. (a) (x – 2y)y 3 2 2 (b) 5x + x y – xy (c) 10x + 2x y – 4y 2
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(d) x y – 2xy – x y
Practice Time 8B Maths Connect
7 5 6
3 2
2 2
4 3 3
1. (a) –28x y (b) –4a b c (c) –715a b c (d) 9 a b c (a) 3.4x + 31y (b) 26x + 9
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(e) 62400p q 2 Mental Maths
4 4 4
6 6 7
2. (a) 665x y z , 10640 (b) –1071x y z , –137088 1. 0 2. –16 3. –4x y 4. 2
3 3
3 2
5
2 3 2
3. (a) 1 p q r (b) 3.75x y (c) 3 x y z 5. (x + 3) 6. 2
2 28
2 3
3 4
4. –5.1a b – 10a b Chapter 9: Visualising Solid Shapes
Think and Answer Let’s Recall
10 × (2x + 5) 1. (a) HE (b) ABFE and HEFG (c) ABCD, ABFE, ADHE
Quick Check Quick Check
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3x + 13xy – 10y , 26.25 (i) Top view (ii) Front view (iii) Side view
Practice Time 8C Practice Time 9A
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1. (a) 3p + 3p q (b) 4.4a b – 9.68ab 1. (b) (i) Front view (ii) Top view (iii) Side view
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2
3 4 2
(c) –16x – 32xy (d) 6x y z – 7x y z 2. (c) (i) Front view (ii) Top view (iii) Side view
(iii) Top view
(a) (i) Front view (ii) Side view
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3 2
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(e) –15x y + 3x y – 9x y (f) 6 7 x + 6y 2 − 30z 2 (b) (i) Front view (ii) Top view (iii) Side view
7x
7x
(c) (i) Top view
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2. –5mn – 5n + 278, –282 Think and Answer (ii) Front view (iii) Side view
2 2
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4
3 2
3. (a) 4x – 7x y – 4x y + 7xy (b) x 2 − y 2 Map shows locations of airports in India.
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(c) 0.4p – 2.8p + 3p – 21 (d) 0.75p – 2.5pq + 2q 2 Quick check
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4. (a) 6x – 4x – 23x + 44x – 24 (b) 16x – 16y + 8x – 48y – 35 1. Faces—6: ABCD, BCFG, ABGH, ADEH, DCFE, EFGH
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5. (a) 3a + 15a b – ab – 5b + a b (b) 3x – y + 4xy Edges—12: AB, BC, CD, DA, EF, FG, GH, HE, AH, DE, BG, CF
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(c) –7x – 28x + 44x – 12 (d) –21a + 18a – 3a – 16a – 5a Vertices—8: A, B, C, D, E, F, G, H
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2
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Faces—4: ABC, BOC, AOB, AOC.
6. (a) 6p q – p q – 32pq (b) 7p q – 4pq + 24q 2. Edges—6: AB, BC, AC, OA, OB, OC.
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3
2
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7. –b + 2b + 7b – 13; 11 8. 10ab − 25 ac − 15a 2 + ;. Vertices—4: O, A, B, C
Practice Time 8D 2 2 2 3. Faces—5: PQR, ABC, APRC, APQB, RQBC.
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11pq r Edges—9: AB, BC, CA, PQ, QR, RP, AP, CR, BQ.
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1. (a) 4x (b) –6y (c) 6l m (d) 23 Vertices—6: A, B, C, P, Q, R.
xy z
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2. (a) 8x – 2 (b) 11a – 13b 2 (c) 5x – 3x Think and Answer
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2 2
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3. (a) 3p + 5p – 7 (b) x y + xy – y + 1 1. tetrahedron 2. 7 3. rectangular pyramid
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(c) x + 4 (d) 2m – 3m + 5 4. three 5. No
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4. (a) Q = 6a – 13a + 22a – 24, R = 29 (b) Q = x + 2, R = –8x – 6 Practice Time 9C
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5. Q = 6x + 11x + 15x + 12x + 14, R = 14x + 2 1. Solid Vertices Faces Edges Is F + V – E = 2?
Quick check (V) (F) (E)
1. 10609 2. 9975 (a) Cuboid 8 6 12 Yes
Practice Time 8E (b) Triangular prism 6 5 9 Yes
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1. (a) 49t + 126tu + 81u 2 (b) 4x – 20xy + 25y 2 (c) Square pyramid 5 5 8 Yes
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6
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(c) 36a – 144b (d) x – y 6 (d) Rectangular prism 8 6 12 Yes
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(e) x 4 − x y + y 4 (f) 64 p + 36 q + 96 pq (e) Pentagonal pyramid 6 6 10 Yes
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9 3 4 49 25 35
(f) Pentagonal prism 10 7 15 Yes
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2. (a) 25x + 60x + 36 (b) 36x + 12xy + 49y
49 5 25 2. (a) (b) (c) (d)
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4 2
2 4
2 2 2
(c) s t + t u – 2s u t (d) 0.81p – 0.9pq + 0.25q 2
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3. (a) x + 11x + 24 (b) u v w – 9uvw + 20 Faces 4 6 20 8
2 2 2
4 13 Vertices 6 8 12 6
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+
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(c) 81x – 9x – 110 (d) x + axa 2
9 9 Edges 8 12 30 12
4. (a) 2601 (b) 1010025 (c) 9984 (d) 9.975 3. No.
5. (a) 100 (b) 12 Chapter Assessment
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6. (a) 128a + 162b (b) 6a – 6b 2 (c) x y + y z (d) x – 256
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2 2
2
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(e) 6561x – 1 (f) 0 A. 1. (b) 2. (b) 3. (a) 4. (c)
7. 27 9. 49 B. 1. (a) 2. (b) 3. (b)
Brain Sizzlers C. 1. cone 2. Congruent 3. 1:5000000
4.
cube
5. 5
a = 5, b = 15 D. 1. False 2. False 3. True 4. False 5. True
Chapter Assessment E. 1. Yes 2. 30 3. 22
A. 1. (b) 2. (d) 3. (c) 4. (c) 5. (d) 4. X = 15, Y = 8, Z = 9, P = 8, Q = 6
6. (c) 7. (d) 8. (b) 6. (a) 6 (b) 7 (c) Cube or cuboid (d) 12
B. 1. (d) 2. (d) 3. (b) 4. (a) Mental Maths
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C. 1. 3a + ab + 7ac + 2b – 6bc – 4c 2. 7x(7x + 2) – 7x 2 1. Cone, cylinder, sphere 2. Square/rectangular pyramid
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3. x + 2xy + y , `144 4. 70000 units 5. 1 3. Triangular prism, cone, square, pyramid
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7. 102 8. 520 9. 2x + 3x – 10 4. 128 km
367 Answers