Vedanta Excel in Mathematics Book 9 Final Re_CTP

Revision and Practice Time

Trigonometry D
90°–α
1. From the given figure, find the trigonometric ratios of sinα C
and cosθ.
A 90°–θ
2. From the given figure, find the values of sinθ, cosθ, tanθ, B
sinα, cosα and tanα. D
α C
θ
12 cm 3 cm

3. In the following figures, find the values of sinθ and cosα. A 4 cm B

a) A b) P
θ

12 cm 3 cm D 25 cm 20 cm
B 12 cm QA
4 cm
θ C α
R

4. In the adjoining figure, O is centre of circle. AB the diameter and P O
X is the mid-point of the chord PQ. If AB = 20 cm, PQ = 16 cm and
∠ PQB = q, find the value of tanq. XqQ
B
5. If tanq = 1 , show that sinq – 2cosθ = – 3
2 sinq + 2cosθ 5

6. If ntana = m, prove that msina – ncosa = m2 – n2
msina + ncosa m2 + n2

C

7. In the given D ABC, ∠ B = 90° and ∠ CAB = 45°. If AB = x cm, 45° A
prove that cos45° = 1 . x cm
2
A
B

8. In the adjoining equilateral D ABC, AD ⊥ BC and AC = 2a units.

Prove that sin60° = 3 .
2

BC

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 347 Vedanta Excel in Mathematics - Book 9

Answers

1. Sets

Exercise : 1.1

1. a) P ∪ Q b) P ∩ Q c) P – Q d) Q – P e) P

f) Q g) P ∪ Q h) P ∩ Q g) P – Q

2. a) A ∪ B b) A ∪ B c) A ∩ B d) A ∩ B e) A – B

f) Y – X g) (A ∪ B ∪ C) h) P ∩ Q ∪ R

3. a) (i) A ∪ B = {1, 2, 3, 5, 6, 7, 9} , A ∪ B = {4, 8, 10}

(ii) A ∩ B = {1, 3}, A ∩ B = {2, 4, 5, 6, 7, 8, 9, 10}

(iii) A – B = {5, 7, 9}, A – B = {1, 2, 3, 4, 6, 8, 10}

(iv) B – A = {2, 6}, B – A = {1, 3, 4, 5, 7, 8, 9, 10}

b) (i) P ∪ Q ∪ R = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15}

(ii) P ∩ Q ∪ R = {6} (iii) P ∪ Q ∪ R = {7, 11, 13, 14}

(iv) P ∩ Q ∩ R = {1, 2, 3, 4, 5, 7, 8, ..., 15} (v) (P ∪ Q ) ∩ R = {3, 6, 12}

(vi) (P ∩ Q) ∪ R = {2, 3, 4, 6, 9, 12, 15}

4. a) (i) A ∪ B = {a, b, e, h, l, n, p} Ae a tbuh B (ii) A ∩ B = {a, n} Ae a tbuh B
pl n pl n

(iii) A – B = {e, p, l} A pe l an tbuh B (iv) B – A = {b, h, u, t} Ae a tbuh B
pl n
P
56
b) (i) P ∪ Q = {1, 2, 3, 4, 5, 6, 7, 8, 9} 3 41Q82 7 (ii) P ∩ Q = {1, 2, 4, 8} P
9 56
3 41Q82 7
9
P P
56
(iii) P – Q = {3, 5, 6, 7, 9} 3 56 7 (iv) Q – P = φ 3 41Q82 7
41Q82 9 9

c) (i) M ∪ N = {11, 13, 15, 17, 19, 23} M N (ii) M ∩ N = {17, 19} M N
11 11 23
17 17
13 19 23 13 19
15 15

(iii) M – N = {11, 13, 15} M11 N (iv) N – M = {23} M N
23 11 23
17 17
13 19 13 19
15 15

5. a) and b) Show to your teacher. 6. a) (A – B) ∪ (B – A) = {1, 2, 6, 10}

b) (i) A D B = {a, d, e, h, i, n, r, t} (ii) P D Q = {1, 2, 7}

7. a) (i) A = {2, 4, 6, 8, 10} (ii) B = {1, 4, 6, 8, 9, 10} (iii) A ∪ B = {1, 2, 4, 6, 8, 9, 10}

(iv) A ∩ B = {4, 6, 8} (v) A ∪ B = {4, 6, 8} (vi) A ∩ B = {1, 2, 4, 6, 8, 9, 10}

(vii) A = {1, 3, 5, 7, 9} (viii) B = {2, 3, 5, 7}

b) (i) A = {1, 3, 5, 7, 9, 11, 13, 15} (ii) A ∪ A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

(iii) A ∩ A = φ (iv) U = φ

Vedanta Excel in Mathematics - Book 9 348 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

8. a) (i) P ∪ Q = {1, 2, 3, 4, 5, 6, 8} P ∪ Q = {7, 9, 10}
PQ PQ

(ii) P ∩ Q = {2, 4} P ∩ Q = {1, 3, 5, 6, 7, 8, 9, 10}
PQ PQ

(iii) P – Q = {1, 3, 5} P – Q = {2, 4, 6, 7, 8, 9, 10}
PQ PQ

(iv) Q – P = {6, 8} Q – P = {1, 2, 3, 4, 5, 7, 9, 10}
PQ PQ

(v) P ∪ Q = {1, 3, 5, 6, 7, 8, 9, 10} (vi) P ∩ Q = (7, 9, 10)
PQ PQ

b) (i) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 15} A ∪ B ∪ C = {8, 10, 13, 14}

(ii) A ∩ B ∩ C = {3} A ∩ B ∩ C = {1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

(iii) (A ∪ B) ∩ C = {3, 6, 9} (A ∪ B) ∩ C = {1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15}

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 349 Vedanta Excel in Mathematics - Book 9

Answers A ∩ (B ∪ C) = {2, 4, 6, 8, 10, 11, 12, 13, 14, 15}
(iv) A ∩ (B ∪ C) = {1, 3, 5, 7, 9}

(v) (A – B) ∪ C = {3, 6, 9, 11, 12, 15} (A – B) ∪ C = {1, 2, 4, 5, 7, 8, 10, 13, 14}

(vi) A ∪ (B – C) = {1, 2, 3, 4, 5, 7, 9, 11} A ∪ (B – C) = {6, 8, 10, 12, 13, 14, 15}

9. a) and b) Show to you teacher.

10. a) (i) P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R) (ii) P ∩ (Q ∪ R) = (P ∩ Q) ∪ (P ∩ R)

(iii) P – (Q ∪ R) = (P – Q) ∩ (P – R) (iv) P – (Q ∩ R) = (P – Q) ∪ (P – R)

b) Show to you teacher. 11. a) and b) Show to you teacher.

12. Complete your project work in a group or individually. Discuss the outcomes in the class.

1. Show to your teacher. Exercise : 1.2

2. a) 9 b) 3 c) 4 d) 5 e) 2 f) 4 g) 6 h) 5 i) 1 j) 2
(iii) 8 (iv) 25
3. a) (i) 53 (ii) 12 (iii) 35% (iv) 30%
(iii) 75 (iv) 13
b) (i) 85% (ii) 20%

c) (i) 45 (ii) 40

4. a) (i) b) (i) c) (i) 35
NN CF
T M

200 200 150 325 450 525 100 35 115

200
50

(ii) 50 (iii) 200 (iv) 150 (ii) 200 (ii) 215

d) (i) 5. a) (i) 145 (ii) 300 b) (i)

CA (iii) BA T C
70% 10% 20% 135 145 165

275 325 175


(ii) 10% (iii) 20% 55 125
(ii) 325 (iii) 450

Vedanta Excel in Mathematics - Book 9 350 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

6. a) (i) 57 FC b) (i) 625 (ii) 125 (iii) 385 (iv) PS
(ii) 7 20 7 30 260 125 240
(iii) 27
(iv) 37 18 125

7. and 8. Complete your project work in a group or individually. Discuss the outcomes in the class.

2. Taxation

Exercise: 2.1
1. a) Rs 5,50,000 b) Rs 4,20,000 c) Rs 3,85,292 d) Rs 10,04,640

2. a) Rs 3,054 b) Rs 4,020

3. a) Rs 38,000 b) Rs 2,90,000 c) Rs 35,000 d) Rs 1,02,500

4. a) Rs 13,387 b) Rs 11,100 c) Rs 54,500 d) Rs 5,01,600

5. a) Rs 57,000 b) Rs 15,200 c) Rs 1,50,780 d) Rs 27,850

6. a) Rs 20,000 b) Rs 4,000

7. a) Rs 5,301.76 b) Rs 13,690 c) Rs 11,150 d) Rs 44,000

8. a) Mrs. Pandey pays Rs 4,300 more tax b) Rs Sumesh pays Rs 2,500 more tax

9. Complete your project work in a group or individually. Discuss the outcomes in the class.

y Exercise: 2.2
x
1. a) R% of Rs x b) × 100% c) Rs P + R% of Rs P d) Rs (x – y + z)

2. a) (i) Rs 2,860 (ii) Rs 4,550 (iii) Rs 4,000 b) (i) Rs 4,500 (ii) Rs 7,500 (iii) Rs 66,000

3. a) Rs 390 b) Rs 1,950 c) Rs 3,705 4. a) Rs 1,808 b) Rs 4,520 c) Rs 209

5. a) Rs 3,600 b) Rs 9,700, Rs 1,455 c) Rs 3,042 6. a) 14% b) 13% c) 13%

7. a) (i) Rs 25,425 (ii) Rs 38,420 (iii) Rs 82,603 (iv) Rs 1,16,616 b) Rs 3,051 c) Rs 4,972

d) Rs 2,92,896 8. a) Rs 21,696 b) Rs 6,215 c) Rs 64,975

9. a) Rs 870.10 b) Rs 1,118.70 10. a) Rs 2,400 b) Rs 20,000 c) Rs 66,000

11. a) Rs 80 b) Rs 5,000 12. a) Rs 3,456 b) Rs 819 c) Rs 510 13. a) 13% b) 13%

14. a) 25% profit b) 20% profit 15. a) Rs 40,000 b) Rs 50,000 16. a) 10% b) 10%

17. a) Rs 63,280 b) Rs 3,82,844 c) Rs 88,592 18. a) 4% b) 3% c) 10.33% profit

19. Complete your project work in a group or individually. Discuss the outcomes in the class.

3. Commission, Bonus and Dividend

Exercise: 3.1
1. a) Rs 60,500 b) Rs 3,60,000 c) Rs 1,20,000

2. a) (i) Rs 3,75,000 (ii) Rs 2,46,25,000 b) (i) Rs 37,500 (ii) Rs 12,12,500

3. a) Rs 1,62,900 b) Rs 1,10,000 c) Rs 1,85,00,000 d) Rs 3,50,000

4. a) 2.5% b) 5.5% 5. a) Rs 70,930 b) Rs 33,250 c) (i) Rs 1,215 (ii) Rs 2,375 (iii) Rs 4,392

6. a) (i) Rs 30,300 (ii) Rs 6,50,000 b) Rs 23,100 c) 1% 7. a) Rs 47,53,000 (b) Rs 2,28,300

Exercise: 3.2
1. a) Rs 50,000 b) Rs 9,75,000 c) Rs 18,16,100 2. a) Rs 9,180 b) Rs 40,000

3. a) Rs 23,12,500 b) Rs 3,60,00,000 4. a) 12% b) 20%

5. a) (i) Rs 34,560 (ii) Rs 2% (iii) Rs 50,00,000 b) (i) Rs 20,000 (ii) 2% (iii) Rs 3,90,62,500

6. a) Rs 20,832 (b) Rs 28,000

7. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 3.3
1. a) (i) Rs 12,50,000 (ii) Rs 48,00,000 (iii) Rs 78,93,000 b) (i) Rs 1,200 ii) Rs 490 (iii) Rs 560

2. a) Rs 960 b) Rs 2,304 3. a) 20% b) 20% 4. a) Rs 1,12,00,000 b) Rs 48,60,000

5. a) Rs 36,210 b) Rs 1,26,360 6. a) 22% b) 27% 7. a) Rs 1,48,00,000 b) Rs 1,25,40,000

8. Complete your project work in a group or individually. Discuss the outcomes in the class.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 351 Vedanta Excel in Mathematics - Book 9

Answers

4 . Household Arithmetic

Exercise: 4.1
1. b) 145 units c) 4 units d) t = xy + z 2. a) Rs 30 b) Rs 30

3. a) Rs 162 b) Rs 149 4. a) Rs 142.50 b) Rs 175 c) Rs 136

5. a) Rs 29.40 b) Rs 119.70 c) Rs 187 d) Rs 306.25 6. a) Rs 1,097.50

b) (i) Rs 1,075.55 (ii) Rs 1,097.50 (iii) Rs 1,152.38 (iv) Rs 1,207.25 (v) Rs 1371.88

7. a) Rs 1,102.50, 6.67% b) 10.91% 8. a) 90 units b) 130 units 9. a) Rs 320 b) Rs 321.20

Exercise: 4.2
1. a) Rs 621.50 b) 15.54 c) Rs 124.30 2. a) 500 calls b) 485 calls

3. a) Rs 960.30 b) Rs 9,882 c) (i) Rs 2,342.55 (ii) Rs 2,415 (iii) Rs 2,898 (iv) Rs 3,622.50

4. a) Rs 446 b) Rs 885 5. a) 5 km b) 10 km

6. and 7. Complete your project work in a group or individually. Discuss the outcomes in the class.

Unit 5 Mensuration-I (Area)

Exercise: 5.1

1. a) (21i)sx(2sy4–ccamm) 2( 2s – b) ((bsi)i–)21c8)m4cmcnm2c 2m 2 (icgi))i)149430 x2 cm2 d) q 4p2 – q2 cm2 e) x + y+z cm
4 +r – cm2 2
f) (p + q + r) (p + q – r) (p q) (q + r – p)
2. a) b) 210 ft2.
cm2 (iv) 360 cm2 c) 16,296 m2

d) 168 cm2 e) 4 3 cm2
3. a) 168 cm2 b) 336 cm2 c) 126 cm2 d) 192 cm2 e) 240 cm2 f) 222 cm2

4. a) 180 m2 b) 2,340 m2 c) 216 m2 d) 0.96 hectare

5. a) 54 cm2 b) 336 cm2 c) 60 m d) 108 m 6. a) 6 cm, 8 cm , 10 cm

b) 8 ft,. 15 ft, 17 ft. c) 30 m, 40 m, 50 m 7. a) Rs 806.40 b) Rs 1320 c) Rs 3,024

Exercise: 5.2
1. a) 16 Aana b) (i) 4 Paisa (ii) 64 Paisa c) (i) 4 Daam (ii) 16 Daam (iii) 256 Daam

d) 20 Kattha e) (i) 20 Dhur (ii) 400 Dhur f) 13.31 Ropani

2. a) 3 Paisa b) 5.9 Dhur c) 2.64 Aana d) 3.11 Bigha 3. a) 511.25 sq.ft. b) 361.3 m2

4. a) 117.94 Ropani b) 20.67 Bigha 5. a) Rs 1,00,00,000 b) Rs 5,24,879.66 profit

6. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 5.3
1. a) Equal b) Equal 2. a) (i) xy m2 (ii) xy m2 (iii) 2xy m2 (iv) 2xz m2

(v) 2yz m2 (vi) 2z (x + y) m2 (vii) xy +2z (x + y) m2 (viii) xy +2z (x + y) m2

b) PQ m2 c) 4xy m2 d) 5a2 ft2 e) (2A+B) m2

3. a) 100 m2 b) 625 ft2 c) 576 m2 d) 144 m2 e) 300 sq. ft. f) 240 ft2 g) 209 m2

4. a) (i) 150m2 (ii) 150m2 (iii) 150m2 (iv) 100m2 (v) 250m2 (vi) 550 m2

b) (i) 288 m2 (ii) 240 m2 (iii) 528 m2 c) (i) 450 ft2 (ii) 900 ft2 (iii) 1,350 ft2

5. a) 5m b) 20 ft. c) 9.6 ft. 6. a) 128 m2 b) 300 sq. ft.

7. a) 102 m2 b) 276 m2 c) 3170 ft2 8. a) (i) 124 m2 (ii) 31 b) (i) 13 (ii) 200

9. a) 29 b) 605 10. a) 10 ft. b) 4 m

11. Complete your project work in a group or individually. Discuss the outcomes in the class.

Unit 6 Mensuration-II (Prism)

Exercise: 6.1

1. Answer the given questions yourself and discuss in the class. Then show to your teacher.

2. a) 540 cm3 b) 480 cm2 c) 255 cm2 d) 648 cm2

3. a) 150 cm2 b) 64 cm3 c) 6 cm, 516 cm2 d) 4 cm e) 50

4. a) 96 cm2 , 288 cm2 , 480 cm2 , 576 cm3 b) 38 cm2 , 170 cm2 , 246 cm2 , 190 cm3

c) 48 cm2 , 204 cm2 , 300 cm2 , 288 cm3 d) 32 cm2 , 150 cm2 , 214 cm2 , 160 cm3

e) 69 cm2 , 240 cm2 , 378 cm2 , 345 cm3 f) 600 cm2 , 3,600 cm2 , 4,200 cm2 , 18,000 cm3

5. a) (i) 2,16,000 cm3 , 60 cm (ii) 21,600 cm2 b) (i) 10 m2 (ii) 3,000 l (iii) Rs 12,000

c) (i) 960 (ii) 10 cm 6. a) 6 cm b) 20 cm c) 20 cm d) 27 7. a) 9.6 l b) 10 cm, 4 l

Vedanta Excel in Mathematics - Book 9 352 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise: 6.2

1. a) (i) 1 xy (ii) (x+y+z)×l (iii) xy+(x+y+z)×l (iv) 1 xyl
2 2
1
b) (i) 4 (p + q + r) (p + q – r) (p + r – q) (q + r – p) (ii) (p+q+r)×h

(iii) 1 (p + q + r) (p + q – r) (p + r – q) (q + r – p) + (p+q+r)×h
2

(iv) 1 (p + q + r) (p + q – r) (p + r – q) (q + r – p) ×h
4

c) (i) 3 a2 cm2 (ii) 3ah cm2 (iii) ( 3 a2 + 3ah) cm2 (iv) 3 a2h cm3
4 2 4

2. a) 24 cm2 b) 36 cm2 c) 270 cm2 d) 20 cm e) 366 cm2 f) 288 cm2

3. a) 410 cm3 b) 180 cm3 c) 8 cm

4. a) (i) 750 cm3 (ii) 270 cm3 (iii) 1200 cm3 (iv) 1080 cm3 (v) 1200 cm3

(vi) 3840 cm3 b) (i) 128 cm2, 147.6 cm2 (ii) 103.2 cm2,113.4 cm2 (iii) 360 cm2 , 408cm2

(iv) 900 cm2 , 960 cm2 (v) 450 cm2, 536.6 cm2 (vi) 380 cm2, 414.1 cm2

5. a) 8 cm b) 18 cm c) 30 cm 6. a) 24 cm b) 10.5 cm

7. a) (i) 1650 cm3 (ii) 1232 cm2 b) (i) 2160 cm2 (ii) 2412 cm2 c) (i) 432 cm2 (ii) 432 cm3

8. a) (i) 230 3 cm2 (ii) 450 cm3 b) (i) 152 sq2, 96 ft3 9. a) 5 m b) 10 m

10. a) 146.83 ft3 b) 8 inch

11. Complete your project work in a group or individually. Discuss the outcomes in the class.

7. Mensuration-II (Cylinder and Sphere)

Exercise: 7.1
1. a) (i) 2πxy cm2 (ii) 2πx(x +y) cm2 (iii) πx2y cm3 b) (i) 2πb (A + a) cm2 (ii) 2π(A+a)(b+A-a) cm2
(iii) πb (A+a)(A-a) cm3 c) (i) πpq cm2 (ii) pq(π+2) cm2 (iii) pq(π+2) + πp2 cm2 (iv) 1 πp2q cm3
c) 770 cm3 2
a) 440 cm2 b) 330 in2
2.

3. a) (i) 1100 cm2 (ii) 1408 cm2 (iii) 3850 cm3 b) (i) 1056 cm2, 1282.29 cm2, 3168 cm3

c) (i) 880 cm2, 1188 cm2, 3080 cm3 d) (i) 5500 cm2, 7425 cm2, 48125 cm3

4. a) (i) 6600 cm2, 9372 cm2, 69300 cm3 b) (i) 55 in2, 74.25 in2, 48.125 in3

5. a) 3080 l b) 269.5 l c) 30.8 m3 6. a) 297 cm2 b) 2013 cm2

7. a) 68750 cm3 b) 20944 cm3 c)264 cm2 d) 1188 cm2

8. a) 2156 cm3 b) 179.67 cm3 9. a)4620 cm3 b) 3080 cm3 c)1188 cm2

10. a) 720cm2, 874 cm2, 1540 cm3 b) 5400 cm2, 6786 cm2, 34650 cm3 c) 297 m3

11. a) 1760 cm3 b) 352 cm3 c) 2.112 kg d) 13.31 kg 12. a) 25 cm b) 5600

13. a) Bucket-B can hold 4.048 l more water than bucket-A

b) Tank-Y can hold 4455 l more water than tank-X.

14. a) 35,200 l b) 19.25 l 15. a) 2904 m2 b) 8.8 m3

16. Complete your project work in a group or individually. Discuss the outcomes in the class.

1. 1(i4i3) 734.3π3x3cmcm3 3 Exercise: 7.2 2 πp3 cm3 c) 12.57 cm2, 4.19 cm3
2. a) (i) 4πx2 cm2 b) (i) 2πp2 cm2 (ii) 3πp2 cm2 (iii) 3 (iii) 5544 cm2, 38808 cm3
a) (i) 616 cm2, (ii) 498.96 cm2, 1047.82 cm3

(iv) 221.76 cm2, 310.46 cm3 b) (i) 2772 cm2, 4158 cm2, 19404 cm3

(ii) 1232 cm2, 1848 cm2,5749.33 cm3 (iii) 443.52 cm2, 665.28 cm2, 1241.86 cm3

(iv) 49.28 cm2, 73.92 cm2, 45.99 cm3

3. a) 154 cm2, 179.67 cm3 b) 1386 cm2, 220.5 m3 c) 21999494092 km3

4. a) 11.21 kg b) 4365.9 cm3 c) 154 cm2 d) 1386 cm2

5. a) 1039.4 cm2, 2425.5 cm3 b) 27.72 cm2, 19.404 cm3 6. a) 718.67 cm3 b) 3850 cm2

7. a) 1.22 cm3 b) 462 cm2 c) 1527.43 cm3 8. a) 924 cm2 b) 8316 cm2

9. a) 3 cm b) 7 cm c) 21 cm 10. a) 38808 cm3 b) 5544 cm2

11. a) (i) 2772 cm2 (ii) 4158 cm2 (iii) 19404 cm3 b) (i) 1232 cm2 (iii) 5749.33 cm3

c)693 cm2, 1039.5 cm2 12. a) 3 times b) (i) 16:1 (ii) 64:1 c) (i) 2:3 (ii) 4:9

13. a) 9 cm b) 12 cm c) 4 cm 14. a) 6.5 cm b) 0.63 cm c) 16

15. a) 14.4 m b) 2 cm c) 5

16. a) (i) 77.44 kg (ii) 11088 cm2 b) (i) 6.41×1024 kg (ii) 3.61 ×108 km2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 353 Vedanta Excel in Mathematics - Book 9

Answers

1. a) Rs xy b) Rs PQ Exercise: 7.3
c) Rs AB d) Rs 21,600 e) Rs 39,000

2. a) Rs 35,100 b) Rs 6,600 c) Rs 4,500 3. a) (i) Rs 13,500 (ii) Rs 12,750

(iii) Rs 12,000 b) (i) Rs 10,800 (ii) Rs 10,000 (iii) Rs 11,520

4. a) Rs 16,900 b) Rs 18,900 c) Rs 11,520 5. a) Rs 8,100 b) Rs 25,050 , Rs 22,545

6. a) 5m b) Rs 11,520 c) Rs 7,200 d) 5 m e) 6 m

7. a) Rs 10,800 b) Rs 9,200 8. a) Rs 10,800 b) 4 m c) Rs 6,480 d) Rs 6,336 e) 4.5 m

9. a) Rs 8,100 b) 4.2 m

10. Complete your project work in a group or individually. Discuss the outcomes in the class.

8. Sequence and Series

Exercise: 8.1
1. Answer the questions yourself and discuss in the class.
5 6
2. a) 24, 29 b) 8, 5 c) 16, 32 d) 6, 3 e) 25, 36 f) 36 , 49

3. a) 5, 8, 11, 14 b) –2, 3, 8, 13 c) 2, 6, 12, 20 d) –2, 3, –4, 5 e) 1, 3, 6, 10

f) 0, 13, 21, 53 g) 41, 13, 156, 275 h) –1 , 2 , 1–33, 4
3 7 21
4. a) 4n, 24, 36 b) 5n+1, 31, 46 c) 13 – 4n, –11, –23 d) n2, 36, 81 e) (–1)n+1.2n, –64, 512

f) n n 1, 67, 190 g) (n n2 1)2 , 36 , 18010 h) n2 + 2, 38, 83
+ + 49
5. a) 3, 6, 12, 24, 48 b) 4, –3, 1, –2, –1, –3 c) 15, 101

6. a) (i) (ii) 3n+2 (iii) 32 b) (i) (ii) 3n – 2 (iii) 28

c) (i) (ii) n2 (iii) 100 d) (i) (ii) 4n+2 (iii) 42

Exercise: 8.2

1. Answer the questions yourself and discuss in the class.
2. a) sequence b) series c) sequence d) series

3. a) 5 + 10 + 15 + 20 + 25 b) 1 – 2 + 4 – 8 + 16 c) –7 – 3 +1+ 5 + … d) 1+f) 126+ 1 + 81g+) .4..
4. a) 5 b) 4 c) 5 d) 8 c) 42 d) 62 e) 138 4
5. a) 50 b) 120

6. a) 3 b) –3 7. a) 6, 10, 4 b) 20, 35, 15
6 65
(3n – 1) (4n – 14) 3n
8. a) tn = 3n –1, b) tn = 4n – 14, n = c) tn = 3n, n =
n=1 1 1
9 10 12
4n ( –1)n 1.n (–1)n.2n
d) tn = 4n–1, – 1 e) tn = (–1)n+1.n , + f) tn =(–1)n.2n ,
1 1 1
n = 7 n = n =
n =1 n n 9 n 2nn++11 , 8 n+1
g) tn= n + 1, n n + 1 h) tn = (n + 1)2, n =1 (n + 1)2 i) tn = n =1 2n + 1

5n 10 5n 7
+ 1)2 , + 1)2 n(n + 1)
j) tn = (–1)n (n (–1)n (n k) tn = n(n+1),
n =1
10 n =1

l) tn =n2 + 2n + 3, n =1 (n2 + 2n + 3)

Exercise: 8.3
1 Answer the questions yourself and discuss in thedc)lNasost. an2A. a.P). tn = a+(n-1)d b) t6 = a+5d
3. a) A.P. b) A.P. c) Not an A.P.

4. a) 2n+1 b) 4n – 9 c) 17 – 7n d) 1 – 3n 5. a) 21 b) 61 c) 55

6. a) 3 b) 4 c) -5 d) 13 7. a) 16 b) 37 c) 40

8. a) 19th b) 21st 9. a) Yes b) Yes c) No

10. a) 2, 3, 50 b) 7, 4, 63 c) -28, 3, 29 11. a) 3+8+13+18+… b)50+47+44+41+…

Vedanta Excel in Mathematics - Book 9 354 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

12. a)12th b) 15th 13. b) 0 14. a) Rs 23,000 b) Rs 164 c) 50

15. a) Offer B b) (i) 170, (ii) B.S.2086 16. a) 7 b) 10th day c) 21 years d) 16 days

17. Complete your project work in a group or individually. Discuss the outcomes in the class.

1 yourself and Exercise: 8.4 an2G. a.P). tn
3. Answer the questions b) G.P. discuss in the class. = arn–1 b) t4 = xy3
a) G.P. c) G.P. d)
81, -1 12 Not
4
4. a) 2, 6, 18 b) –9, –27, –81 c) , d) 27, 9, 3 5. a) 384 b) 1 c) 144

6. a) 2 b) 4 c) 3 d) 1/2 7. a) 7 b) 5

8. a) 9th b) 8th 9. a) Yes b) Yes 10. a) 1536 b) 1458 c) 16

11. a) 5 + 15 + 45 + 135 + ... b) 9 + 18 + 36 + 72 + ...

12. a)512 b) 324 c) (i) 40 (ii) 160

13. a) Rs 87,846 b) Rs 20,480 c) 8,09,112 d) Rs 2,45,650

14. Answer yourself and discuss in the class.

15. Complete your project work in a group or individually. Discuss the outcomes in the class.

9. Factorisation of algebraic expressions

1. a) x (x + 1) Exercise: 9.1
b) x (x + 2) c) (x+ 2) (x + 1) d) (a + 3) (a + 3)

2. a) 2x (a + 2b) b) 2p(p – 3) c) 3ab (2a + 3b) d) 2px (x – 2 + 3p)

e) 3x2 y2 (2x + 3y – 1) f) (2x + 3y) (a + b) g) (3a – 1) (x – y) h) (x + 3) (x + 2)

i) (t – 1) (2t – 1)

3. a) x2 + 5x + 6 = (x + 3) (x + 2) b) (x2 + x – 6) = (x + 3) (x – 2)

c) x2 – 7x + 12 = (x – 4) (x – 3) d) 2x2 + 7x + 3 = (2x + 1) (x + 3)

e) 2x2 + x – 6 = (2x – 3) (x + 2) f) 2x2 – 5x + 3 = (2x – 3) (x – 1)

4. a) (a + b) (x + y) b) (m + n) (p – q) c) (a + b) (a + c) d) (x2 + y2 ) (m – n)

e) (x – 2) (y + 3) f) (x + 4) (x + 3) g) (p – 8) (p – 1) h) (4x – 1) (4x – 1)

i) (a – c) (a – b) j) (x – y) (x + 3) k) (pr – q) (qr – p) l) (x + y + z) (y + z)

5. a) (x + 1) (x + 3) b) (x – 8) (x + 1) c) (a – 15) (a – 12) d) (x + 2) (2x + 3)

e) (p – 3) (3p + 2) f) (x – y) (2x + 5y) g) (a – b) (3a – 13b) h) abx (3a + 5b) (3a – b)
((3ib)a +4)5()4bam–, xym– 3(xiyi)) ((xy4x++xy1) 6)
i) + 5) j) ( k) (x + y + 1) (2x + 2y + 7) l) (x –y – 2) (3x – 3y – 4)
6. a) (x (x + 3) m b) (i) (x + 8) m, (x + 5) m (ii) (x2 + 9x + 18) sq. m.

c) (2x2 + 13x + 6) sq. m.

7. Complete your project work in a group or individually. Discuss the outcomes in the class.

1. a) (3x + 2) (3x – 2) Exercise: 9.2
b) (5ab + 1) (5ab – 1) c) 3a (4x + 5y) (4x – 5y)

d) (x2 + y2 ) (x + y) (x – y) e) xy(4x2 + 9y2 ) (2x + 3y) (2x – 3y)

f) (25a2 + 16b2 ) (5a + 4b) (5a – 4b) g) (2 + m – n) (2 – m + n)

h) (1 + a – b) (1 – a + b) i) (4 + 5p – 5q) (4 – 5p + 5q) j) 3(a – b) (a + b)

k) (a + b + c) (a + b – c) l) (p + q + r) (p – q – r) m) (a + b – 2) (a – b + 2)

n) (4a2 + 2a + 1) (4a2 – 2a – 1) o) (x + y) (ax – ay – 1) p) (a – b) (a + b – x)

2. a) 96 cm2 b) 216 cm2 c) 299 m2 d) 392 m2 e) 544 sq.ft. f) 756 m2

3. a) (x + y + 5 (x – y + 1) b) (a + b – 2) (a – b – 8) c) (p + q – 14) (p – q + 2)

d) (x2 + y – 5) (x2 – y + 13) e) (3a + 4x – 4) (3a – 4x – 6) f) (25y + z – 2) (25y – z + 18)

g) (4p – 8q + 3r) (4p – 10q – 3r) h) (5x + 3y – z) (5x – 7y + z)

4. a) (ac + ab – bc + bd) (ac – ad + bc + bd) (b) (xy + x + y – 1) (xy – x – y – 1)

c) (3p + 2q + pq – 6) (3p + 2q – pq + 6) d) (30 – xy + 10x + 3y) (30 – xy – 10x – 3y)

5. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 9.3
1. a) (x2 + 2x+2)(x2 – 2x+2) b) (2a2 + 2a+1)(2a2 – 2a+1)

c)(p2+4pq+8q2)(p2 – 4pq+8q2) d) (9m2+6mn+2n2)(9m2 – 6mn+2n2)

e) (8a2+12ax+9x2)(8a2 – 12ax+9a2) f) (25b2+10bd+2d2)(25b2 – 10bd+2d2)
((mx22++mxy++21y)2()m(x22––mxy++12y) 2) ((a120+c2+2a2+t+4t5)2()a(21–0c22a–+24t)+t52 )
g) h)
2. a) b)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 355 Vedanta Excel in Mathematics - Book 9

Answers

c)(6p2+3p+1)(6p2 – 3p+1) d) (3m2+4mn+5n2)(3m2 – 4mn+5n2)

e) (2x2+5xy+3y2)(2x2 – 5xy+3y2) f) (15x2+11xy+4y2)(15x2 – 11xy+4y2)

g) 2(4x2+xy+y2)(4x2 – xy+y2) h) 5(2b2+by+3y2)(2b2 – by+3y2)

(i) 3mn(4m2 +5mn + 3n2) (4m2 – 5mn + 3n2)

3. a) (2x2+2x – 3)(2x2 – 2x – 3) b) (3p2+2p – 4)(3p2 – 2p – 4)

c)(5a2+3a – 1)(5a2 – 3a – 1) d) (y2+3yz – 2z2)(y2 – 3yz – 2z2)

e) (9a2+3ax – 5x2)(9a2 – 3ax – 5x2) f) (11p2+pq – 6q2)(11p2 – pq – 6q2)

g) x (2x2+6xy – 5y2)(2x2 – 6xy– 5y2) h) 3p(3b2+bp – p2)(3b2 – bp – p2)

(i) 15ab(2a2 +2ab – 3b2) (2a2 – 2ab – 3b2)

4. a) (x+1)(x – 1)(3x+4)(3x – 4) b) (y+1)(y – 1)(2y+1)(2y – 1)

c)(m+1)(m – 1)(5m+2)(5m – 2) d) (a+b)(a – b) (3a +5b)(3a – 5b)

e) 25(c + d)(c – d) (2c + d)(2c - d) f) (p+q)(p – q)(13p +14q) (13p – 14 q)
x2 x x2 x a2 b2 a2 b2 1 1
5. a) y2 + y + 1 y2 – y + 1 b) b2 + a2 + 1 b2 + a2 – 1 c) x+1+ x x–1+ x

d) x2 + 3x + 1 x2 – 3x + 1 e) m2 + 5m – 2 m2 – 5m – 2 f) b2 + b – 10 b2 – b – 10
y2 y y2 y n2 n n2 n d2 d d2 d

6. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 9.4
3. a) (2x + 5)3 b) (3a + 4)3 c) (4y – 5)3 d) (7m – 6)3 e) (10a – 3b)3 f) (2x + 11y)3

4. a) (2a + 3) (2a + 3) (2a + 3) b) (5x + 1) (5x + 1) (5x + 1) c) (3p – 4) (3p – 4) (3p – 4)

d) (9w – 8) (9w – 8) (9w – 8) e) (6m – 5n)(6m – 5n)(6m – 5n)

f) (13e + 7g) (13e + 7g) (13e + 7g)

5. a) (2x + y) (4x2 – 2xy + y2) b) (1 + 3a) (1 – 3a + 9a2) c) 2t(4t – 1)(16t2 + 4t + 1)

d) y(x – 4y)(x2 + 4xy + 16y2) e) (a2+b) (a4 – a2b+ b2) f) (4x2y - 5) (16x4y2 + 20x2y+25)

g) (a+2)(a – 2) (a2 + 2a + 4) (a2 – 2a + 4) h) (3x + y)(3x– y) (9x2 + 3xy+ y2) (9x2 – 3xy + y2)

6. a) (a+b+1)(a2+2ab+b2 – a – b + 1) b) (x – 1) (x2 + 7x + 19) c) –(x+3y)(7x2 + 6xy + 3y2)

d) p+ 1 p2 – 1 + 1 e) a – b a +1+ b a –1+ b f) x x+ 1 x2 – 1 + 1
p p2 b a b a b a x x2

g) y y+ 1 y– 1 y+1+ 1 y–1+ 1 y2 – 1 + 1 h) p p– q p2 + q + q2
y y y y y2 q p p2

7. a) (3x + 4y) (9x2 – 2xy + 16y2) b) (2 + 3a) (4 – 9a + 9a2) c) (4m – 5n) (16m2 + 13mn + 25n2)

d) (p – 2) (2p2 – 3) (p2 + 2p + 4) e) (2a – 1) (5a2 + 2) (4a2 + 2a + 1)

f) (x -1) (2x – 1) (x2 + x + 1)(4x2 + 2x + 1)

8. a) (i) (2a +1) ft., (a +1) ft., (a – 1) ft. (ii) (2a2 + 3a + 1) sq. ft. b) (i) 27 cm3 (ii) (x3 – 27) cm3

9. Complete your project work in a group or individually. Discuss the outcomes in the class.

10. H.C.F. and L.C.M.

Exercise: 10.1
1. Answer the questions yourself and discuss in the class.

2. a) 2x (x + 2) b) 2xy (x – 1) c) 3a2b2 (2a + 3b) d) 4a2b2(a + b – 2) e) p – q

3. a) a + b b) a (a – 2) c) x + 3 d) x + y e) 4 (x + 5)

f) x (x + 2) g) a – b – 1 h) x2 + 2xy + 4y2 i) p +2 j) x2 + 2xy + 2y2

4. a) a2 + a + 1 b) p2 – 2p + 4 c) 4x2 + 2x + 1 d) 9a2 – 3a + 1 e) 18x (x – 3y)

f) 10 (x – 10y) g) x2 + 5x + 12 h) a2 + 4a + 10 i) a + 1 j) x – 1

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

f) m – 1 g) x – 4y h) x (x + 5) i) 4x2 – 6xy + 9y2 j) x2 – xy + y2

6. a) x2 + x + 1 b) p + 2 c) a – b d) a2 + ab + b2 e) a + b + c

f) 3x + 2y + 2z g) x – y + 1 h) a – b + 1 i) 4x2 + 2x + 1 j) 9x2 +3x + 1

7. a) (x + 15) m b) (x – 2) m

8. Complete your project work in a group or individually. Discuss the outcomes in the class.

Vedanta Excel in Mathematics - Book 9 356 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise: 10.2
1. Answer the questions yourself and discuss in the class.

2. a) 6x2 (x2 – 1) (x + 3) b) 12x2(x + 2)(x2 – 9) c) 24a2b2(a + b) (a3 – b3) d) (x2 – 4) (x2 – 9)

e) (a – 3) (a – 4) (a – 5)

3. a) 6x2 (x + 2) b) ax (x2 – 1) c) 10x4y4(2x + y) d) xy (x2 – y2)

e) 2x (4x2 – 1) f) a3 – b3 g) (x + 3) (x2 – 4) h) 3 (x2 – 9) (x2 – 3x + 9)

i) a2b2 (a2 – b2) (a2 + ab + b2) j) (x2 – xy + y2)(x3 – y3) k) (a2 +ab + b2) (a3 + b3)

l) 2x(2x – 1) (27x3 + 1)

4. a) 4 (x3 + 125y3) (x2 + 5xy + 25y2) b) 6a (8a3 – 27b3) (4a2 + 6ab+ 9b2)

c) (1 – 8x3)(1 + 2x – 4x2) d) (2a + 1) (8a3 – 1) (4a2 – 2a – 1)

e) x (x2 + 5x + 9)(x2 – 5x + 9) f) y (10y2 + 4y – 1)(10y2 – 4y – 1)

5. a) (a+2)2 (a3 – 8) b) (a – 3)2 (a3 + 27) c) a (a – 1)2 (a2 – 4)

d) (x + y)(x2 + y2)(x3 – y3) e) 2x2(2x – 1) (3x – 2) (x3 + 8) f) x2 (x + 1)(x + 3)(x3 – 27)

g) a2 (a +1)(a +2)(a3 – 8) h) a (a3 – 1) i) (x – y)(x2 + y2)(x3 + y3) j) (x +1)(x +2)(x+3)

6. a) (a + b + c) (a + b – c) (b + c – a) (c + a – b) b) (x + y + z) (x – y – z) (y – z – x) (z – x – y)

c) (3x + 2y + 2z) (3x -2y + 2z) (3x – 2y – 2z) (2z – 3x – 2y)

d) (x2 – a2)(x2 – b2) e) (x2 – 1)(x2 – 4) f) a (a + b + 5) (a + b – 5) (a – b +1)

g) xy (x + 3y + 11)(x – 3y + 11)(x – 3y – 3)(x – 3y – 11) 7. a) 4a (a – b)2 b) x3 + 1

8. Complete your project work in a group or individually. Discuss the outcomes in the class.

11. Indices

Exercise: 11.1 c) 1211 d) 125 e) 116 f) 12

1. a) am + n b) 1 c) 1 d) 2 2. a) 8 b) 5

g) 8116 h) 1143 i) 12 j) 25 k) 7 l) 52 m) 21 n) 32 o) 10 p) 3
c) 25 d) 23 9 16 25 d) 5
3. a) 1 b) 1 c) 1 d) 1 4. a) 4a2x2 b) 25p2q2 c) 7



5. a) 1 b) 1 e) 1 f) 1 g) 1 h) xy
ab x2 + y2
7. a) 16 25 f) 1
8. a) 15a2b b) 1 c) 2 d) 2 e) 6m2n f) (a
e)
b) a2 c)1 d) 2p 1 b)2 g) 1 y)2 h) (a – b)
q + (2x –

9. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) x 2a j) a a+b
10. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 y b

12. Simultaneous Equations
Exercise: 12.1

1. a) 1 b) –4 c) y = –2, x = 2 d) 4 e) 6

2. a) (5, 2) b) (1, 4) c) (–3, 1) d) (3, 5) e) (5, 2)

3. a) x = 3, y = 2 b) x = 4, y = 1 c) x = 1, y = 3 d) x = 2 , y = 1
h) x = 3, y = –2
e) x = 3 , y = –1 f) x = 2, y = –1 g) x = –1, y = 1 l) x = 1, y = 1

i) x = 5, y = 0 j) x = 1, y = 0 k) x = 1, y = 1 d) x = 6, y = 4
h) x = 5, y = 2
m) x = 2, y = 3 n) x = 3, y = –2 o) x = 10, y = 3 l) x = 3, y = 0

4. a) x = 3, y = 6 b) x = 2, y = 10 c) x = 1, y = –4

e) x = 2, y = –1 f) x = 1, y = 4 g) x = 2, y = 1

i) x = 3, y = 2 j) x = 3, y = –2 k) x = 4, y = 1

m) x = 5, y = 7 n) x = 4, y = 6 o) x = 5, y = 5

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 357 Vedanta Excel in Mathematics - Book 9

Answers

1. a) 35, 25 b) 20, 10 Exercise: 12.2
c) 33, 26 d) 18,6 e) 9, 5
f) Rs 325, Rs 175 g) 30 years, 8 years h) 42 years, 7 years i) 36 years, 12 years
j) 35 m, 25 m
2. a) Rs 75, Rs 45 b) 3, 2 c) 5, 6
7 4 3
3. a) 9 b) 9 c) 8 d) Rs 25,000, Rs 15,000 e) Rs 8,000, Rs 6,000

4. a) 40 years, 15 years b) 32 years, 12 years c) 42 years, 12 years.
d) 14 years, 10 years e) 47 years, 7 years f) 45 years, 13 years
g) 29 years, 5 years h) 58 years, 25 years i) 29 years, 5 years.
j) 45 years, 15 years k) 34 years, 6 years r) 50 years, 30 years
m) 15 years, 21 years n) 19 years, 15 years.
5. a) 97 b) 46 c) 63 d) 39 e) 27 f) 84
g) 38 h) 59 i) 76 j) 72 k) 36 l) 45
6. a) Rs 30, Rs 15 per km b) Rs 25, Rs 5 per day 7. a) 5, 7 b) Rs 60, Rs 90
8. a) 12 : 00 b) 65 km/hr, 60 km/hr 9. a) 17 m, 9 m b) 180

10. Complete your project work in a group or individually. Discuss the outcomes in the class.

13. Geometry: Triangle

Exercise: 13.1
1 and 2 Answer the questions yourself and discuss in class. Then show to your teacher.

3. a) 23o, 46o, 111o b) 40o, 60o, 80o c) 30o, 35o, 115o d) 72o, 36o, 72o

4. a) a = 60o, b = 50o b) 90o, 140o c) 28o, 112o d) 80o, 120o, 160o

e) x = 100o, y = 40o, z = 140o f) x = 50o, y = 40o g) x = 55o, y = 165o h) x = 20o

i) x = 50o 5. a) 50o, 30o, 100o b) 15o, 30o, 135o c) 50o, 80o, 50o

Exercise: 13.2

1. a) (i) longest side AB shortest side AC (ii) longest side EF shortest side DE

(iii) longest side PQ shortest side PR

b) (i) Greatest angle ∠ Y Smallest angle ∠ Z (ii) Greatest angle ∠ A Smallest angle ∠ B

(iii) Greatest angle ∠ F Smallest angle ∠ E

c) Longest side BC Shortest side AB d) Longest side QR Shortest side PQ

e) Greatest angle ∠ Y Smallest angle ∠ X

2. Answer the questions yourself and discuss in class. Then show to your teacher.

3. a) 3 cm < AC < 13 cm b) 2 cm < c

< 10 cm

4. a) S.S.S., ∠ A = ∠ P, ∠ B = ∠ R, ∠ C = ∠ Q b) R.H.S., DF = ZX, ∠ F = ∠ Z, ∠ E = ∠ Y

c) S.A.S., BC = QR, ∠ C = ∠ R, ∠ B = ∠ Q d) A.S.A., ∠ F = ∠ S, EF = RS, GF = TS

5. a) S.S.S., a = 70°, x = 50°, b = y = 60° b) A.S.A., x = 6.4 cm, y = 5.8 cm, a = 30°

8 and 9 Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 13.3

1. Answer the questions yourself and discuss in the class. Then show to your teacher.

2. a) 70°, 70°, 40° b) 130° c) 60°, 60° d) 20° e) 110° f) 69°, 69°, 111°

g) 70°, 140° h) 65°, 130°, 65° i) 37°, 106° j) 60°, 90° k) 30°, 60° l) 70°, 40°

3. a) 75°, 75°, 30° b) 60°, 70°, 40°, 80° c) 110°

5. a) x = 2, y = 3 b) x = 4 cm, y = 3 cm 6. b) 75°

13. Complete your project work in a group or individually. Discuss the outcomes in the class.

1. a) 8 cm b) 2 cm Exercise: 13.4 d) 12 cm e) 2 cm

2. a) 4.5 cm b) 7.5 cm, 4.5 cm c) 10 cm, 9 cm d) 3.2 cm, 2.4 cm e) 6 cm
3. a) 18 cm b) 43.01 in
c) 9 cm, 5 cm
c) 72 ft.

Vedanta Excel in Mathematics - Book 9 358 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

14. Geometry: Parallelogram
Exercise: 14.1

1. Answer the questions yourself and discuss in the class. Then show to your teacher.

2. a) 10 cm b) 45° c) 40° d) 30°

3. a) w = y = 2x = 72°, z = 3x° = 108° b) a = 4y = 80°, b = 5y = 100°

c) p + 10° = 2p – 50° = 70°, p + q = r = 110° d) x = 20°, 2x = 40°

e) y = 65°, x = 50° f) x = 125° g) a = 40°, b = 140° h) x = 70°, y = 110°

4. a) 70° b) 70° c) 120° d) 25°, 65°

5. a) 140° b) 33° c) 60°, 120° d) 62°, 28° e) 25°, 115° f) 30°, 60° g) 65°

6. a) x = y = 4 cm b) x = 15, y = 5 c) a = 5, b = 1 d) 8 cm e) p = 3 cm, q = 6 cm

7. a) 75°, 15° b) 15°, 75°

14. Complete your project work in a group or individually. Discuss the outcomes in the class.

15. Geometry: Construction
Exercise: 15.1

Complete the construction of quadrilaterals yourself and compare with your friends. Then show to
your teacher.

7. Complete your project work in a group or individually. Discuss the outcomes in the class.

16. Geometry: Circle

Exercise: 16.1
1, 2, 3. Answer the questions yourself and discuss in the class. Then show to your teacher.

4. a) 12 cm b) 8 cm c) 24 cm d) 4 cm 5. a) 2 cm b) 10 cm

6. a) 6 cm b) 14 cm c) 6 cm 7. a) (i) 1 cm (ii) 7 cm b) 2.5 cm c) 13 cm

15. a) 10 m b) 48 ft. c) 160 m

16. Complete your project work in a group or individually. Discuss the outcomes in the class.

17. Statistics (I): Classification and Graphical representation of data

Exercise: 17.1
1. Answer the questions yourself and discuss in the class. Then show to your teacher.

2 and 3 Draw the cumulative frequency table yourself and discuss in the class. Then show to your

teacher.

4. a) p = 4, q = 25, r = 5 b) a = 25, b = 20, c = 100

5, 6, 7 Draw the cumulative frequency table yourself and discuss in the class. Then show to your

teacher.

8. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 17.2
1. Answer the questions yourself and discuss in the class. Then show to your teacher.

2. a) (i) 20 (ii) 65 (iii) 30 b) (i) 60 (ii) (30 – 40), 60 (iii) 100

3 and 4 Draw the histograms yourself and discuss in the class. Then show to your teacher.

5. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 17.3
1. Answer the questions yourself and discuss in the class. Then show to your teacher.

2. Draw the histograms and frequency polygons yourself and discuss in the class. Then show to your

teacher.

3 and 4 Draw the frequency polygons yourself and discuss in the class. Then show to your teacher.

5. Complete your project work in a group or individually. Discuss the outcomes in the class.

Exercise: 17.4
1. a) (i) 50 (ii) 20 (iii) 20 b) (i) 30 (ii) 10-20 (iii) 5

2 a) (i) 20 (ii) 16 b) (i) 75 (ii) 30

2. Draw the histograms and frequency polygons yourself and discuss in the class. Then show to your

teacher.

3. Draw the ogive curves yourself and discuss in the class. Then show to your teacher.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 359 Vedanta Excel in Mathematics - Book 9

Answers

4, 5, 6, 7 Draw the ogive curves yourself and discuss in the class. Then show to your teacher.
8. Complete your project work in a group or individually. Discuss the outcomes in the class

18. Statistics (II): Measures of central tendencies

Exercise: 18.1

1. a) 34 b) Rs 450 c) 13 years d) 67 2. a) 10 years b) 7 c) 7

3. a) 120 b) 27, 93 c) 5 d) 25

4. a) 66 b) 10.8 years c) 63.44 kg d) 62.2 cm

5. a) 28 b) 7 c) (i) 35 (ii) 100 d) (i) 11 (ii) 50

6. a) 11 b) 20 c) 5 d) 10

Exercise: 18.2

1. Answer the questions yourself and show to your teacher.

2. a) (i) 20 (ii) 28 (iii) 30 (iv) 24 (v) 13 b) 50 kg c) 34 years d) 32

3. a) (i) 12 (ii) 10 (iii) 10 b) (i) 39 (ii) 34 (iii) 70

4. a) 25 b) 158 c) 6 d) 7 5. a) 18 b) 172
c) 3 d) 7

6. a) (i) 7 (ii) 21 kg b) 18 years c) Rs 36 d) 8 to 12 e) Rs 1,500

to Rs 2,000 f) (i) c (ii) f g) 7 h) Rs 150

7. a) (i) 120 cm (ii) 95 cm (ii) 25 cm b) 59 c) 50

8. a) 34.5 years b) Rs 542.85 9. a) 50 b) 20 c) Rs 65 d) 40 kg

10. a) 36 b) 80 c) 27, 37 d) Q1 = 100 cm, Q2 = 120 cm, Q3 = 130 cm

11. Complete your project work in a group or individually. Discuss the outcomes in the class.

19. Probability

1. a) P {a certain event} = 1 Exercise: 19.1 b) P (E) = n (E)
n(S)
P {an impossible event} = 0

c) (i) {HH, HT, TH, TT} (ii) {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

(iii) {1, 2, 3, 4, 5, 6}

(iv) {(1, 1), (1, 2), (1, 3) (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2),

(3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5),

(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

d), e), f) and g ) Answer the questions yourself and discuss in the class. Then show to your teacher.

2. a) 16 b) 51 c) 35 d) 1 e) 5 f) 21 g) 1
8 6 13

h) 1 i) 31 j) 51 k) 95 l) 13 m) 71 n) 2
26 3

3. a) (i) 1 (ii) 121 (iii) 2 (iv) 1110 (v) 10 (vi) 9
11 11 11 11

b) 1 , 12 c) (i) 113 (ii) 512 (iii) 1 d) (i) 1 (ii) 1 (iii) 1
13 13 26 8 2 4

(iv) 3 (v) 34 (vi) 3 4. a) 2 b) 171 c) 12 d) 4
8 4 3 13

Vedanta Excel in Mathematics - Book 9 360 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

e) 5 f) 1
6 4

5. a) 0.562 b) 0.001 c) 870 d) (i) 0.27 (ii) 0.38 e) (i) 0.82 (ii) 0.965 (iii) 0.08

6. and 7. Complete your project work in a group or individually. Discuss the outcomes in the class.

20. Trigonometry

Exercise: 20.1
AB BC ABCB PQ PR PQ
1. a) sinθ = AC , cosθ = AC , tanθ = b) sinα = QR , cosα = QR , tanα = PR



c) sinβ = YZ , cosβ = ZX , tanβ = YZ 2. a) sinθ = 3 , cosθ = 4 , tanθ = 3
XY XY ZX 5 5 4


b) sinα = 3 , cosα = 4 , tanα = 43 c) sinβ = 12 , cosβ = 5 ,tanβ = 12
5 5 13 13 5

3. a) sinα = CQ , tanθ = CAAB b) sinβ = BY , cosθ = AC
PC BX BC


c) tanα = PR , cosθ = QPRR d) sinα = QPRR , cosq = TR
PQ QR

4. a) 1 – cos2A b) 1 – sin2θ c) Sinθ d) 1 – cos2α e) 4 f) 12
1 – sin2θ cosα 5 13

g) 54 h) 5 i) 21 j) 4 k) sinα = AB l) cosθ = AB
12 29 3 CA CA

5. a) sinθ = 5 , tanα = 3 b) cosα = 3 , tanθ = 12 6. a) 3 , 3 b) 12 , 5
13 4 5 5 5 4 13 12

7. a) 4 , 3 b) 3 , 3 9. a) 16152 b) 112 10. a) 3 b) 12 , 5 c) 4 , 4
5 5 5 4 65 5 13 12 5 3

1. a) 43 b) 21 c) Exercise: 20.2 e) 32 f) 0 g) 41

3 d) 0

h) 1 i) 1 j) 5 k) 1 l) 12 m) 12 n) 1
2

o) 41 p) 3 q) 0 r) 1 s) 3 t) 1 u) 1
4 2
y) 2 z) 0
v) 1 w) 1 x) 3 4. 6.4 cm 3. a) 15 cm, 8.7 cm b) 8 cm,
11.3 cm
c) 13.9 cm, 6.9 cm 5. a) 60°, 30° b) 30°, 60°

c) 45°, 45° 6. a) 61.5 m b) 65.82 m 7. a) 10 3 m, b) 25 2 ft., 25 ft. c) 15 m

8. a) 60° b) 30° c) 45°

9. and 10. Complete your project work in a group or individually. Discuss the outcomes in the class.

Revision and Practice Time

Set

1. (i) P∪Q = {21, 23, 25, 27, 29, 31, 37} P Q (ii) PQ = {23, 29} PQ
P (iv) Q – P = {21, 25, 27}
31 2239 21 31 2239 21
37 25 37 25
27 27

Q PQ

(iii) P – Q = {31, 37} 3371 2239 21 31 23 21
25 37 29 25
27 27

2. A∆B = {1, 5, 6, 7, 8, 10, 16, 25}

3. (i) A = {5, 7, 8, 9, 10, 11} (ii) B = {1, 2, 4, 5, 7, 8, 10, 11}

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 361 Vedanta Excel in Mathematics - Book 9

Answers

(iii) A ∪ B= {1, 2, 4, 5, 7, 8, 9, 10, 11} (iv) A ∩ B= {5, 7, 8, 10, 11}

(v) A ∪ B = {5, 7, 8, 10, 11} (vi) A ∩ B = {1, 2, 4, 5, 7, 8, 9, 10, 11}

(vii) A – ( A ∩ B ) = {3, 6, 12} (viii) (A ∪ B) – B= {1, 2, 4, 5, 7, 8, 10, 11}
4. (i) A∪B∪C = {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14} (ii) A∩B∩C =φ
(iii) A – (B∪C) = {1, 3, 5, 7} (iv) B ∪ (C∩A) = {2, 4, 6, 10, 12, 14}

5. (i) P – (Q∪R) = {2, 11} (ii) P ∪ Q ∪ R = {6, 8, 10, 12}

(iii) P – (Q∩R) = {4, 6, 8, 9, 10, 12} (iv) (P∩Q)∪R = {4, 6, 8, 9, 10, 11, 12}

6. (i) (A – B) ∪ (B – A) = {a, c, g, h, i, o, r, s, y} and (A∪B) – (A∩B) = {a, c, g, h, i, o, r, s, y}

(ii) (A – B) ∪ (B – A) = (A∪B) – (A∩B)

7. (i) H – T = {2, 4, 8} and T – H = {2, 4, 8} (ii) Yes

9. (i) 13 I C 10. (i) Z
(ii) 37 25 2 13 (ii) 50 32 G
(iii) 10 35
(iii) (iv) 47 10

37

11. (i) AO M E
(ii) 25 (iii) 15 12. , 25%

25 25 15 20% 40% 15%

15 25%

1. Rs 11,000 2. Rs 1,99,500 Taxation 4. Rs 6,728.20
3. Rs 34,000

5. Rs 1,29,944 6. Mrs. Dhital pays Rs 2,500 more tax. 7. Rs 3,238.40

8. Rs 6,000 9. Rs 4,000 10. Rs 225 11. 15%

12. 15% 13. Rs 4,000 14. 40% 15. 20%

16. Rs 1,800 17. Shop-A is1.87% more expensive than shop-B

18. Mr. Gupta, Rs 22.60 less 19. Rs 40,680, 17% 20. Rs 60,000; Rs 1,014

21. Rs 4,29,400 22. Rs 10,31,503.55

Commission, Bonus and Dividend
1. Rs 10,000 2. Rs 5,00,000 3. Rs 24,82,500 4. Rs 5,700 5. Rs 26,250

6. Rs 16,000 7. 2% 8. Rs 30,000 9. Rs 11,170 10. Rs 98,000

11. Rs 6,01,800 12. Rs 35,156.25 13. 12% 14. Rs 1,50,00,000

Household Arithmetic
1. a) Rs 162 2. Rs 1,302 3. a) 130 units

4. (i) 15 units, 27 units, 45 units (ii) Rs 73.50, Rs 152.39, Rs 289.10 (iii) 89.71%

5. Rs 728.44 6. a) 224 b) Rs 309.50 7. R 758.23 8. 425 calls 9. Rs 1,140

10. Rs 14,301 11. Rs 230 12. 2 km 13. 6 km

1. a) Rs 4,536 2. Rs 2,939.40 Mensuration
4. Rs 6,450 5. Rs 10,080
8. Rs 3,600 9. Rs 3,360 3. (i) 8.3 Aana (ii) 1.24 Kattha (iii) 19.40 Dhur
6. Rs 16,875 7. 5 cm

10. (i) 61,200 (ii) Rs 74,340 11. (i) 1,44,000 cm3 (ii) 12,000 cm2 (iii) 19,200 cm2

12. 4 m 13. 360 cm2, 360 cm3 14. 35 cm 15. 42 cm 16. 9 cm

Vedanta Excel in Mathematics - Book 9 362 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

17. 7 m 1 18. 4,620 cm3 19. 11,000 cm2 , 57750 cm3 20. 5 cm 21. 2,640 cm2

22. (i) Rs 11,880 (ii) 707.85 kg 23. 12,320 cm3 24. 3,850 cm3 25. 962.5 m3

26. 192.5 l 27. 24,750 l 28. 18 cm 29. 1,386 cm2, 4,851 cm3

30. 216 31. 12 cm 32. 3,696 cm2 33. 4,851 cm3 34. 31.5 cm

Sequence and Series

H HHH

5 2. (i) H C C C C H (ii) tn = 2 (n +1) (iii) 22

1. 3n
n =1

H HHH

3. a) 19 b) 8th 4. 8+6+4+2+… 5. 3, 5, 7, 9, … 6. Rs 561 7. 9 weeks

8. Rs 5,120 10. 5,000 m

1. a) (x + y + 3)(x + y – 3) Factorisation
b) (a + b + c) (a + b – c) c) (p + q + r) (p – q – r)

d) (4x2 + 2x – 1) (4x2 – 2x + 1) e) (a – b + c + d) ( a – b – c – d) f) (x – a) ( x – b)

g) (ab + a –b + 1) (ab – a + b + 1) h) (a2 b-2 + ab-1 + 1)( a2 b-2 – ab-1 + 1)

i) (x2 + xy + y2 ) (x2 – xy + y2 ) (x4 – x2 y2 + y4) j) (b – d) (b2 + b + bd + d + d2 )

k) (p + 1) (p2 + p + 1) l) (2m + 1)(2m – 1) (4m2 + 2m + 1) m) (4 – 3x)3

n) (a – 1) (a – 2) (a – 3) (a – 4) o) (a + b + c) (a2 + b2 + c2 – ab – bc – ca)

p) (x – y – z) (x2 + y2 + z2 + xy – yz + zx)

HCF and LCM (Class 10 ko 370 & 371 ma xa)

1. a) HCF : x(x + 2) b) HCF : 3x(x – 5) c) HCF : (a + b – 6)
LCM : x (x2 – 4) LCM : 3x(x2 – 25) LCM : b(a – b) (a + b – 6)
d) HCF : (m – n – 1)
e) HCF : p(p + 1) f) HCF : ab(3a – b)

LCM : mn(m + n) (m – n – 1) LCM : p(p – 1) (p + 1)2 LCM : 6ab (3a + b) (3a – b)2

g) HCF : (a + b) h) HCF : (x – 2)

LCM : ab(a + b)2 LCM : 2ax(x + 2) (x – 2) 2

i) HCF : 3x(x + 1) j) HCF : ab(ab – 2)

LCM : 18x(x – 1) (x3 + 1) LCM : ab (ab + 2) (a3b3 – 8)

k) HCF : (x – 1) l) HCF : (a + 1)

LCM : (x – 1) (x2 + 1) (2x2 + x + 2) LCM : (a + 1) (a2 – 4) (2a2 – 3a + 2)

m) HCF : (4a2 – 2a + 1) n) HCF : (4x2 + 2x + 1)
LCM : (8a3 + 1) (4a2 + 2a – 1) LCM : (1 – 8x3) (1 + 2x – 4x2)

o) HCF : (p2 – 2p + 4) p) HCF : (4a2 – 2ab + b2)
LCM : (p3 + 8) (p2 + 2p + 4) LCM : (2a + b) (16a4 + 4a2b2 + b4)

q) HCF : (x2 + 5x + 13) r) HCF : (3k2 + 4k + 5)
LCM : x(x4 + x2 + 169) LCM : 2k(9k4 + 14k2 + 25)

s) HCF : (x – 1) (x – 3) t) HCF : (x + 1) (x + 2)
LCM : (x2 – 1) (x2 – 9) LCM : (x2 – 1) (x2 – 4)

u) HCF : v) HCF : (x + y – 11)
LCM : LCM : (x + y – 11) (x – y + 1) (x – y + 11)

w) HCF : (xy – x + y +1) x) HCF : (xy + 3x + 2y – 6)

LCM : (1 – x) (xy – x + y + 1) (xy + x – y + 1) LCM : (x – 2) (xy + 3x + 2y – 6) (xy – 3x – 2y – 6)

y) HCF : 6x(2x + 1) z) HCF : x4 + x2y2 + y4

LCM : 180x (x – 1) (8x3 + 1) LCM : x(x6 – y6)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 363 Vedanta Excel in Mathematics - Book 9

Answers

2. a) HCF : 1 b) HCF : y(2x – 1)

LCM : 72ab(a + 1) (a – 3) (a2 – 4) LCM : 60xy(2x + 1) (3x – 1) (8a3 – 1)

c) HCF : mn(2m + 3n) d) HCF : x(2x + 1)

LCF : mn(2m – 3n) (4m – 5n) (8m3 + 27n3) LCM : x(2x – 1) (8x3 + 1)

e) HCF : x(x2 + x + 1), LCM : x(x6 – 1) f) HCF : p(p2 – p + 1), LCM : p (p3 + 1) (p2 + p + 1) )

g) HCF : x2 + xy + y2 , LCM : x(x2 – xy + y2) (x3 – y3) h) HCF : (y2 + y + 1), LCM : y6 – 1

i) HCF : (a2 – a + 1), LCM : a6 – 1 j) HCF : (x + y + z), LCM : (x + y + z) (x – y – z) (y – z – x) (z – x – y)

k) HCF : (3m + 2n + r) LCM : (3m + 2n + r) (3m – 2n – r) (r – 3m – 2n) (3m + r – 2n)

Indices x2 x
f) a2(p2 – n2) g) – x)x y
1. a) 1 b) 1 c) 1 d) 1 e) 1 (a h) i) 1 j) 1

3. a) 21 b) 1 c) 0 d) 2 e) 0 f) 1 g) 1 h) 13 i) ± 2 j) 0, 2
2
Simultaneous Equations
1. a) x = 29, y = 5 b) x = 4, y = 7 c) x = -3, y = 9 d) x = 2, y = 2 e) x = 5, y = 5 f) x = 1, y = 5

2. 2 l, 3 l 3. 4, 2 4. 375, 25 5. 12 years, 33 years 6. 13 years, 16 years
1
7. 11 years, 36 years 8. 15 years, 21 years 9. 21 years, 8 2 years 10. 25 years, 55 years

11. 30 years, 70 years 12. 10 years, 30 years 13. 15 years, 60 years

14. 7 years, 14 years 15. 1,992 16. 2,000, 2,010 17. 25 years, 15 years

18. 54 19. 24 20. 73 21. 52 22. 57 23. 27 24. 28

25. 27 26. 5, 8 27. 41 km/hr, 49 km/hr 28. 10 p.m. 29. 4 km/hr, 6 km/hr

30. 10 m, 8 m 31. 10 km/hr, 40 km/hr

Geometry-Triangle
5. 54 ft. 6. 101 m 7. 8cm

1. a) 1 cm b) 17 cm Circle

1. Show to your teacher. Statistics
2. Show to your teacher.

3. a) 33.5, 30, 30 b) Rs 800, Rs 800, Rs 800 4. a) 11 b) 8 c) 9, 11 d) 6, 4 e) 8

5. a) Q1 = 20, Q2 = 30, Q3 = 50 b) Q1 = 10, Q2 = 20, Q3 = 25

Probability

1. 41 2. 4 3. 2 4. A 1 , B 1 , C 1
17 25 2 4 4

5. (i) 1 (ii) 1 (iii) 1 (iv) 1 (v) 2 (vi) 4 (vii) 51
13 52 4 2 13 13 52

(viii) 3 (ix) 3 (x) 3
4 4 13

6. (i) 4 (ii) 5 (iii) 4 (iv) 4 (v) 2 (vi) 1
9 9 9 9 9 3

7. (i) 2 (ii) 3 (iii) 5 (iv) 1
5 5 9 3

8. 7 (i) 6 (ii) 2 (iii) 9 9. 2
26 25 5 25 3

Trigonometry
CD ABCC 4 35, 34, 153, 1132, 5
1. a) sinα = BD , cosθ = 2. sinθ = 5 , cosθ = tanθ = sinα = cosα = tanα = 12

3. a) sinθ = 3 , cosα = 12 b) sinθ = 3 , cosα = 45 4. 21 10. 30° 11. 45°
5 13 5
12. 45° 13. 8 cm 14. 3 cm

17. a) 30° b) 45° c) 30° d) 30°

Vedanta Excel in Mathematics - Book 9 364 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 365 Subject: Compulsory Mathematics Specification grid Time: 3 hours
Secondary Level (Class 9) Total Remarks

Full Marks: 100 4
14
Cognitive Units KCA HA
domain -

Subject area 1×5

1 Set 1 Set - - 1×4

2 Taxation

2 Arithmetic 3 Bonus and dividend 1×1 2×2 1×4

4 Household arithmetic

5 Area of plane surface 1×1 3×2 1×4 1×5 16
3 Mensuration 6 Prism

7 Cylinder and sphere

8 Sequence and series

9 Factorisation

4 Algebra 10 H.C.F. and L.C.M. 1×1 5×2 2×4 1×5 24

11 Indices

12 Simultaneous equations

Vedanta Excel in Mathematics - Book 9 13 Triangle

5 Geometry 14 Parallelogram Construction 2×1 3×2 3×4 1×5 25
15 Construction

16 Circle

17 Graphical Representation 1×1 1×2 1×4 -7
of data
7 Statistics
18 Measure of Central
Tendency

8 Probability 19 Probability - 2×2 - -4
-6
9 Trigonometry 20 Trigonometry - 1× 2 1 ×4 4 37
20 100
Total no. of question 6 17 10

Total marks 6 34 40

MODEL QUESTION SET Maximum Marks: 100
Time: 3 hrs.
Class: IX
Subject: Compulsory Mathematics

Attempt all the questions

Group-A (6 × 1 = 6 )
1. (a) Write down the formula for finding the rate of VAT when VAT amount and selling
price are given.

(b) What is the curved surface area of cylindrical object having the radius of base x

cm and height y cm? A
2. (a) What is the value of (9xo), for x ≠ 0?

(b) Define histogram.

3. (a) In ∆ABC, AB = AC and ∠BAD =∠CAD, write down the
relation between AD and BC.
BDC
YS

(b) O is the centre of the given circle. If OX⊥PQ, OY⊥RS and PQ = RS, R O

write the relation between OX and OY. P XQ
Group-B (17 × 2 = 34)
4. (a) Mr. Shakya is an agent. He gets 1.25 % commission while selling a house for two
crore rupees.

(i) How much commission did the agent get?

(ii) How much amount will the house owner get after paying the commission?

(b) Mrs. Thapa travelled 5 km by a taxi. The minimum fare of Rs 14 appeared

immediately after the meter was flagged down, then the fare went on at Rs 7.20

per 200 meters. Calculate the total fare paid by her.

5. (a) The sketch of a park is given alongside. Calculate its area. 51 m 30cm
53 m 30cm
52 m

(b) A hemispherical bowl has diameter 10.5 cm. if the bowl is completely filled with
vegetable soup, find the volume of the soup.

(c) The following figure shows a closed victory stand. 30cm
Find its lateral surface area.

30cm 30cm
40cm
6

6. (a) Evaluate (5n – 1) by expanding.
n=3

(b) Resolve into factors: 9a4 +14a2x2 + 25x4. A
7. (a) Find the H.C.F. of y3 – y a nd y4 – y
2x
(b) Find the L.C.M. of u2 + uv – 6v2 and u3v – 4uv2

(c) Simplify: 7n + 2 + 4 × 7n 7x–30° 3x+10°
7n + 1 × 8 – 3 × 7n DC
8. (a) From the figure given alongside, find the size of ∠ABC. B

(b) In the given figure, HEAD is a parallelogram. H ND 25°
If AM⊥HE, AN⊥HD and ∠NAD = 25°, find the M
measure of ∠MAE and ∠MAN.

EA

Vedanta Excel in Mathematics - Book 9 366 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Model Question Set

(c) In the given circle, O is the centre and OP ⊥ AB. If OA= 50 cm and O
AB = 48 cm, find the length of OP.

9. (a) In the given figure; find the trigonometric ratios of sinθ A AP B
and tanα in terms of sides of triangles. C
P
q a
B Q

(b) In a discrete data; the mean is 50, Σfx = 100n + 150 and
N = 4n – 15, find the values of n and N.

10. (a) Define sample space. A bag contains 20 marbles of same shape and size. Out
of them 8 are green and the rest are black. If a marble is taken from the bag at
random, what is the probability that the marble so chosen is black?

(b) A card is drawn from a well shuffled deck of 52 plying cards. What is the
probability that the card drawn will be a faced card?

Group-C (10 × 4 = 40)

11. A and B are the subsets of a universal set U. If U = {x: 10 < x < 30, x∈ N}, A = {y: y
is an odd number, 10 < y<20} and B = {z: z is a prime number, 15 < z < 30}. Verify
that: n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

12. The rate of electricity charge up to 20 units is Rs 3 per unit and Rs 6.50 per unit from
21 to 30 units. If the meter reading of a household with 5A meter box was 01046 units
on 1 Baishakh and 01072 units on 1 Jestha, find the charge of consumption of electricity
with Rs 50 service charge.

13. A rectangular room is 10 m long, 8 m wide and 5 m high. 5 m
It contains two windows of size 2 m × 1.5 m each and a
door of size 1 m × 4 m. Find the cost of painting its walls
and ceiling at Rs 60 per sq. metre. 8m 10 m

14. Simplify: xa ×a2 + ab + b2 xb ×b2 + bc + c2 xc c2 + ca + a2
xb xc xa

15. A year hence, a father will be 5 times as old as his son. Two years ago, he was three
times as old as his son will be four years hence. Find their present ages.

16. In a circle with centre O, AB is a chord and OP⊥AB. Prove that AP = BP.
17. Verify experimentally that the angle opposite to the longer side is greater than the

angle opposite to the shorter side in triangle. (Two figures of different measurements
are necessary)
18. Construct a quadrilateral ABCD in which AB = 5.2 cm, BC = 4.8 cm, DA = 4.1 cm,
∠ABC = 75o and ∠BAD = 60o.

A

19. In the given figure, ABC is a right angled triangle and BCDE is a 62cm
rectangle. Find the length of AE.

E 45°
D

B 60m C

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 367 Vedanta Excel in Mathematics - Book 9

Model Question Set

20. Find the lower and upper quartiles of the following data.

Ages (in years) 22 27 32 37 42 55

Number of people 35 42 40 30 24 16

Group-D (4 × 5 = 20)

21. The present rate of income tax is fixed by Inland Revenue Department (IRD) is given
below.

For an individual For couple

Income slab rTaatxe Income slab rTaatxe

Up to Rs 4,00,000 1% Up to Rs 4,50,000 1%

Rs 4,00,001 to Rs Rs 5,00,000 10% Rs 4,50,001 to Rs Rs 5,50,000 10%

Rs 5,00,001 to Rs Rs 7,00,000 20% Rs 5,50,001 to Rs Rs 7,00,000 20%

The monthly salary of Binisha, an unmarried cashier in a bank, is Rs 35,000 and her
annual income is equivalent to her salary of 15 months. Similarly, the monthly salary
of Chandan, a married civil servant is Rs 42,000 and his annual income is equivalent
to her salary of 13 months including festival expense. According to the above rates of
tax, who pays the more income tax and by how much?

22. Assuming that the earth is a sphere with radius 6400 km.

(i) If the average density of the earth is 5500 kg per cubic meter, estimate the mass of
the earth.

(ii) If 70% of the earth is covered by water, find the earth’s surface area covered by the
land.

23.. A man joined a company as the manager. The company gave him a starting salary of
Rs 80,000 and made an agreement to increase his salary by 10% annually.

(i) What will be his salary after 5 years?

(ii) By what constant amount should his salary be increased to get the same salary in
5 years?

24. In a parallelogram PQRS, T is the mid-point of side PS. If RT and the diagonal QS
intersect at O, prove that: (i) OQ = 2 OS (ii) OR = 2 OT

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Vedanta Excel in Mathematics - Book 9 368 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur