Vedanta Excel in Mathematics Book - 8 Final (2078)

Statistics

EXERCISE 22.4
General Section – Classwork

1. Let’s say and write the correct answers as quickly as possible.

a) Median of 4, 6, 9 is .....................

b) Median of 5, 8, 10, is .....................
c) Median of 6, 2, 5, 4, 8 is .....................

d) The first quartile of 2, 5, 6, 8, 10, 13, 15, is .....................
e) The third quartile of 3, 4, 7, 10, 12, 15, 17, is .....................

f) The observation which occurs maximum number of times in a data is
called .....................

g) The mode of 4, 5, 7, 5, 5, 4, 9, 7, 4, 5 is .....................

h) The difference between the largest and score the smallest score is called ............
g) The range of 10, 30, 20, 80, 40, 60, 50, 70 is .....................

Creative Section - A

2. a) Find the medians of the following sets of data.
i) 21, 18, 35, 46, 40
ii) 15, 30, 35, 25, 20, 45, 40
iii) 22, 16, 14, 26, 32, 30

b) The weights of five students are as follows. Find their median weight.
48 kg, 59 kg, 43 kg, 63 kg, 52 kg

c) Find the median age of a group of 8 people whose ages in years are as follows:
47, 61, 13, 34, 56, 22, 30, 20

3. a) If the following numbers are in ascending order and median is 4, find the value
of x.
x, x + 1, x + 2, x + 3, x + 4

b) The numbers x – 2, x – 1, x + 2, x + 3, x + 5 are in ascending order. If the
median is 10, find the value of x.

4. a) Find the first quartiles (Q1) of the following sets of data.
(i) 14, 12, 17, 23, 20, 16, 10
(ii) 16, 25, 10, 30, 35, 8, 12
(iii) 40, 20, 30, 10, 16, 12, 18, 24, 28

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Statistics

b) Find the third quartiles (Q3) of the following sets of data.
(i) 15, 9, 21, 33, 27, 39, 45

(ii) 18, 26, 14, 22, 30, 38, 34

(iii) 30, 20, 50, 80, 40, 60, 70, 90
5. a) Find the modes of the following distributions:

(i) 7, 9, 5, 7, 10, 9, 7, 12

(ii) 15 kg, 21 kg, 17 kg, 21 kg, 28 kg, 21 kg, 15 kg, 21 kg

b) In a class, there are 15 students of 16 years, 14 students of 17 years, and 16
students of 18 years. What will be the modal age of the class?

c) In a factory, number of labourers and their remuneration are as follows. Find the
modal class.

Remuneration (in Rs) 1500 – 2000 2000 – 2500 2500 – 3000

No. of labourers 220 215 120

d) Find the modal size of the shoes from the data given below:

Size of shoe 56789 10
No. of men 10 15 30 25 18 12

e) Find the mode from the following data.

Daily wages (in Rs) 70 90 110 130 150 170
No. of workers 4 12 15 18 20 12

Creative Section -B

6. Find the median marks from the data given below:

a) Marks 24 36 50 65 78

No. of students 2 4 12 11 6

b) Marks 10 15 20 25 30 35
No. of students 3 7 15 12 7 3

c) Wage in Rs 45 55 65 75 85 95
No. of workers 20 25 24 18 15 7

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Statistics

7. a) Calculate the first quartile (Q1) from the data given below.

Marks obtained 32 36 40 44 48 52

No. of students 259632

b) Compute the third quartile (Q3) from the following table.

Wages in Rs 50 60 70 80 90 100
No. of workers
6 10 15 13 8 3

c) Find the first quartile (Q1) and the third quartile (Q3) from the following
distribution

Ages in years 22 27 32 37 42
No. of people 35 42 40 30 24

8. a) The heights of 10 students of class 8 are given below.

95 cm, 110 cm, 120 cm 90 cm, 100 cm,
116 cm
105 cm, 98 cm, 115 cm, 112 cm,

(i) What is the height of the tallest student?

(ii) What is the height of the shortest student?

(iii) Find the range of the height.

b) Find the range of the following data.

25, 20, 38, 50, 45, 27, 36, 18

c) The marks obtained by 20 students in Mathematics are given below. Find the
range.

Marks 4 6 8 10 12 14

No. of students 2 3 5 7 2 1

It’s your time - Project work!

9. a) Let’s collect the marks obtained by any of your 9 friends and find:

(i) the median marks (ii) the first and third quartiles marks.

b) Let’s conduct a survey to find the number of students from class 4 to class 8
in your school. Show the number of students of different ages in a frequency
distribution table and compute the following:

(i) median age (ii) the first quartile age (iii) the third quartile age

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Answers

1. Sets

Exercise : 1.1

Creative Section

5. a) C = {4, 6, 8, 9, 10}, C = {x : x < 12, x is a composite number}

b) B = {2, 4, 6, 8, 10}, B = {x : x is a multiple of 2, x ≤ 10}

c) Z = {–1, 0, 1}, Z = {integers between –2 and 2}

d) P = {prime numbers less than 10}, P = {x : x is a prime number, x < 10}

e) A = {S, C, H, O, L}, n(A) = 5

f) B ={1, 2, 4, 4, 6, 12}, n(B) = 6

6. a) 2, {7}, I b) 4, {s}, {v}, {s, v}, I

c) 8, {a}, {e}, {i}, {a, e}, {e, i}, {i, a}, {a, e, i}, I

d) 16, {1}, {3}, {5}, {7}, {1, 3}, {1, 5}, {1, 7}, {3, 5}, {3, 7}, {5, 7}, {1, 3, 5}, {1, 3, 7}, {1, 5, 7},

{3, 5, 7}, {1, 3, 5, 7}, I

7. a) The set of students of class 8. b) The set of students of a school.

c) The set of natural numbers less than 10.

8. (a) No b) Yes c) Yes d) Yes e) Yes

9. and 10. Please complete your project work and compare with your friends. Then discuss in the class.

Exercise : 1. 2

Creative Section

3. a) A – B = {x : x  A but x  B} b) B ‰ C = {x : x  B or x  C}

c) C – A = {x : x  C, but x  A} d) A ˆ B = {x : x  A, and x  B}

e) A ‰ B ‰ C = {x : x  A, or x  B or x  C}

f) A ˆ B ˆ C = {x : x  A, x  B and x  C}

4. a) P U b) P U c) P U
Q Q Q

d) P U e) P U f) P U
Q Q Q

5. a) A ‰ B = {a, b, c, d, e, f, g, h, i} b) B ‰ C = {a, d, e, f, g, h, i, o, u}

c) A ˆ B = {d, e} d) A ‰ B ‰ C = { a, b, c, d, e, f, g, h, i, o, u}

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Answers

e) A ˆ B ˆ C = {e} f) B – C = {d, f, g, h}
g) C – A = {i, o, u}
i) (A ‰ B) ˆ C = {a, e, i} h) A ‰ (B ˆ C) = {a, b, c, d, e, i}

j) A – (B ˆ C) = {a, b, c, d}

6. a) (A ‰ B) ˆ C = {2, 3, 4, 6} b) (A ˆ B) ‰ C = {1, 2, 3, 4, 5, 6, 7, 12}

c) A ‰ B ‰ C = {11, 13, 14} d) (A ‰ C) ˆ B = {1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15}

e) A – (B ˆ C) = {2, 4, 8, 10, 12} f) (A ‰ B) – (B ˆ C) = {2, 4, 8, 9, 10, 12, 15}

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

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7. a) P ‰ Q = {2, 3, 4, 6, 8, 10, 12} b) Q ‰ R = {1, 2, 3, 4, 5, 6, 9, 12}

c) P ‰ R = {1, 2, 3, 4, 5, 6, 8, 10, 12} d) P ˆ Q = {6, 12} e) Q ˆ R = {3, 6}

f) P ‰ Q ‰ R = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12} g) P ‰ Q ‰ R = {7, 11, 13, 14, 15} h) P ˆ Q ˆ R = {6}

i) P ˆ Q ˆ R = {1, 2, 3, 4, 5, 7, 8, 9, 10..., 15} j) P ‰ (Q ˆ R) = {2, 3, 4, 6, 8, 10, 12}
l) P – (Q ˆ R)= {2, 4, 8, 10, 12} m) P= = {2, 4, 6, 8, 10,
k) (Q=Q ‰ R) ˆ P = {2, 4, 6, 12} 2, 3, 4, 5, 6} 8. and 9. Show to your teacher 12}
n) = {3, 6, 9, 12} o) =R = {1,

10. Please complete your project work and compare with your friends. Then discuss in the class.

Exercise : 1. 3

Creative Section

3. a) 9 b) 12 c) 18 d) 9
b)
4. a) U U c) U
A B A B
PQ

15 12 13 35 10 50 30 10 25

10 5 10
(i) 65 (ii) 10 (iii) 30 (iv) 25
(i) 40 (ii) 10 (iii) 15 (iv) 13 (i) 10 (ii) 5 (iii) 35 (iv) 50

d) (i) X U e) A U
Y B

21 9 11 43 20 52

13 20
M
(ii) 13 Ui) 135 (ii) 20 (iii) 43 (iv) 52
5. a) (i) 50 (ii) 22 (iii) D U
b) (i) I C (ii) 100 (iii) 10 (iv) 75

c) (i) B 24 26 6. a) F 25 25 50

22 10
U (ii) 15% U , 50, 70
C C

20% 35% 30% 180–x x 120–x

b) (i) 145 (ii) 15% U c) (i) S U (ii) 400 (iii) 95
R B M

130 145 155 40 20 55

56 285

7. Please complete your project work and discuss about your outcomes in the class.

2. Number systems in different Bases

Creative Section Exercise : 2.1
4. a) 2 × 102 + 7 × 101 + 6 × 100
b) 3 × 103 + 8 × 102 + 1 × 101 + 6 × 100

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Answers

c) 5 × 104 + 4 × 103 + 2 × 101 + 7 × 100 d) 8 × 105 + 9 × 103 + 5 × 100

e) 7 × 106 + 4 × 102 + 9 × 100

5. a) 10012 b) 10102 c) 10112 d) 11002 e) 100102

f) 1101112 g) 11111002 h) 110110002 i) 1011010012 j) 1111010102

6. a) 9 b) 10 c) 23 d) 42 e) 61 f) 87 g) 103 h) 203 i) 238 j) 443

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

Exercise : 2.2

Creative Section

4. a) 135 b) 205 c) 1025 d) 2425 e) 10215
f) 20125 g) 32345 h) 40315 i) 112325 j) 221245
b) 13 c) 23 d) 59 e) 116
5. a) 9

f) 238 g) 290 h) 586 i) 898 j) 1947

6. a) 245 b) 525 c) 2215 d) 10002 e) 10001112 f) 1100001012

7. a) 123105, 11101110112 b) 11110112 > 1435 ; 75 c) 110112< 3225; 60 8. Shashwat

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

teacher.

3. Integers

Exercise : 3.1

Creative Section

4. a) 11 b) 9 c) 22 d) 80 5. a) 44 b) 45 c) 34 d) 59
g) 70 h) –12 i) 44
e) 14 f) –30 d) 8 e) –1 f) 50 j) 14 k) 5 l) 6
g) 150
6. a) 3 b) 9 c) 20 7. a) Rs 205 b) 4 sweets c) Rs 200

4. Real Numbers System

Exercise : 4.1

Creative Section

4. a) 2.2• , 22.2• , 222.2• b) 3.3• , 33.3• , 333.3• c) 8.3• , 83.3• , 833.3•

d) 5.45• 4• , 54.5• 4• , 545.45• 4• e) 2.162• 16• , 21.62• 16• , 216.2• 16•

5. a) 13 b) 29 c) 4919 d) 383 e) 1372 f) 34343 g) 3523 h) 3537 i) 65 j) 145
6. a) Show to your teacher. b) Show to your teacher.

7. and 8. Please complete your project work and discuss in your class. Then show to your teacher.

Creative Section Exercise: 4.2
3. a) 3.24 × 108
b) 6.12 × 1011 c) 7.48 × 1010 d) 3 × 10–6 e) 5.4 × 10–8 f) 9.36 × 10–10

4. a) 1010 sq.cm b) 2 × 106 c.c c) 10–4 sq.m d) 10–10 sq.km e) 10–6 cu.m f) 2.592 × 106 seconds

5. a) 6371 km, six thousand three hundred seventy-one kilometres.

b) 1.48 × 108 km c) 9.46 × 1012 km

6. a) 2700 b) 45000 c) 756000 d) 8450000000

e) 0.025 f) 0.0056 g) 0.0000495 h) 0.0000000783

7. a) 4.4 × 103 b) 9.2 × 104 c) 1.1 × 106 d) 1.61 × 1010 e) 2.94 × 103

f) 2.4 × 103 g) 6.3 × 105 h) 1.405 × 107 i) 8.1 × 104 j) 2.78 × 10–4

k) 4.45 × 10–5 l) 5.314 × 10–3

8. a) 5.44 × 105 b) 1.053 × 108 c) 3.015 × 103 d) 1.944 × 10–12

9. a) 2.7 × 105 b) 8 × 10–3 c) 5.37 × 1012 d) 1.1 × 105 e) 3.2 × 102 f) 3.7 × 103

10. a) 1.86 × 104 litres b) 1.62 × 104 litres c) 1.2348 × 106 m d) 40 tanks

e) 1.076 × 109 km

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Exercise : 4.3

Creative Section

4. a) 7 2 b) 2 3 c) 6 3 d) 3 7 e) 5 6 f) 3 2 g) 11 2 h) 3
k) 4 2 l) 3 5 c) 8 10 d) 12 15
i) 21 2 j) 23 3 5. a) 2 6 b) 3 10

e) 2 3 f) 3 2 g) 2 2 h) 5 i) 2 5 j) 4 k) 6 3 l) 3 5

6. a) 3 10 b) 12 c) 1 d) 3 e) 4 f) 5 g) 22 h) 68

7. a) 2 b) 3 c) 32 d) 6 e) 30 f) 2 – 1 g) 3 + 1 h) 7 ( 3 – 2)
4 2 4
6 53 35 7 11 5
i) 3 + 2 j) 2 3 – 3 8. a) 6 b) 10 c) 4 + 2 3 d) 2 e) 2 f) 10
d) 19 3
g) 6 2 h) 33 –2 5 i) 5 9. a) 13 7 b) 9 2 c) 12 2 d) 720 m2 e) 3 3 f) 991 2
4 80 80
10. a) 16 2 cm b) 12 3 cm c) 1500 2 m2

11. a) (i) (16 + 4 3) cm, (18 + 8 3) cm2 (ii) (12 + 4 5) cm, (13 + 6 5) cm2

(iii) (34 + 6 2) cm, (74 + 24 2) cm2 b) (i) 9 cm2 (ii) 144 cm2 (iii) 75 cm2

5. Ratio, Proportion and Unitary Method

Exercise : 5.1

Creative section

4. a) 4 : 3 b) 2 : 1 c) 4 : 5 d) 1 : 25. a) (i) 2 : 1 (ii) 1 : 3 b) 5 : 4

6. a) 2 : 3 b) 3 : 10 c) 14 : 15 d) 5 : 2 7. a) (i) 2 : 3 (ii) 2 : 4 : 3 b) (i) 4 : 5 (ii) 4 : 6 : 5

8. a) 2 b) 3 c) 15 d) 14 9. a) 12 b) 100 m c) 12 boys d) (i) Rs 12,000 (ii) Rs 9,000

10. a) Rs 40, Rs 60 b) Rs 80,000 ; Rs 1,00,000 c) 600 g, 360 g 11. a) 4.5 km b) 3 cm

12. a) 30°, 60°, 90° b) 48, 72°, 96°, 144° c) 36°, 54° d) 60°, 120° e) 40°, 50°

13. a) Rs 200, Rs 100, Rs 50 b) Rs 48,000 ; Rs 24,000 ; 8,000 c) (i) 18, 30 (ii) 9 : 15 : 4 : 2

14. a) Rs 40,000; Rs 60,000, Rs 80,000 b) (i) Rs 45,000; Rs 90,000; Rs 1,35,000, Rs 1,80,000

(ii) Rs 18,000 ; Rs 36,000 ; Rs 54,000, Rs 72,000

15. a) 24, 30 b) 70, 50 16. a) 45 years, 15 years b) 12 years, 21 years c) 24 years , 18 years

d) 30 years, 8 years 17. a) 7 cm b) (i) 24 m (ii) 80 m (iii) 384 m2 c) (i) 36 m, 27 m (ii) 972 m2

d) (i) 15 cm, 12 cm (ii) 54 cm

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

Creative section Exercise : 5.2 d) 9
4. a) and c) are in proportion.
5. a) 6 b) 12 c) 6

6. a) (i) 8 (ii) 12 (iii) 18 (iv) 21 b) (i) 4 (ii) 15 (iii) 16 (iv) 36 c) (i) 7 (ii) 8 (iii) 5 (iv) 9

d) (i) 5 (ii) 20 (iii) 6 (iv) 8 7. a) (i) 9 (ii) 8 (iii) 7 b) (i) 24 (ii) 48 (iii) 15

8. a) Rs 810 b) 18 c) 7 hours 9. a) 12 passengers b) 15 passengers

10. a) 12 workers b) 30 days c) 10 hours d) 3 more e) 40 days f) 120 days g) 15 days

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

Exercise : 5.3

Creative section

4. a) (i) Rs 80, Rs 960 (ii) 3 kg b) (i) 8 hours (ii) 30 km/hr c) (i) 40 km/l (ii) 8l
1 1 6 3
5. a) (i) 14 (ii) 2 (iii) 7 parts of work b) (i) 4 parts of work (ii) 4 days
d)
c) (i) 2 hours (ii) 1 part (iii) 1 part (i) 1 (ii) 500l
120 4 3

6. a) (i) 48 km (ii) 32 km b) Rs 22,500 (ii) Rs 2,700 7. a) Rs 880 b) Rs 720

8. a) 54 minutes b) 8 days c) 10 days d) 4 workers e) 30 days f) 36 days g) 25 days

9. a) (i) 2400 MB (ii) 3 minutes b) (i) 2 minutes (ii) 15 MB per second

10, 11, 12. Please complete your project work and compare with your friends. Then show to your

teacher.

Vedanta Excel in Mathematics - Book 8 306 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

6. Percentage and Simple Interest

Exercise : 6.1

Creative section

5. a) Rs 40 b) Rs 400 c) 272 d) 432 6. a) 10% b) 20% c) 30 % d) 75%

7. a) Rs 4,800 b) Rs 50,000 c) 300 kg d) 1200 km.

8. a) (i) 66.67% (ii) 33.33% b) 20% 9. a) 85% b) (i) 40% (ii) 60%

10. a) 5% b) 25% 11. a) (i) Rs 325 (ii) Rs 2,925 b) Rs 984

c) zinc : 348 g, copper : 522 g d) (i) Food : Rs 6,300, House rent : Rs 7,875

fuel : Rs 3,150, miscellaneous : Rs 4,725. (ii) Rs 9,450

12. a) (i) Rs 20,350 (ii) Rs. 24,420 b) 15,87,600 c) 86,528 d) Rs 1,70,100

13. a) (i) 740 (ii) 481 b) Rs 27,800, Rs 16,680 c) (i) 60%

(ii) 40% (iii) Rs 67, 500 (iv) Rs 23,625, Rs 16,875

d) income: Rs 31,000, Food : Rs 9,300, Rent : Rs 4,650 ; other items : Rs 1,550

14. a) 900 b) 800 c) 200 d) Rs 6,720

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

Exercise : 6.2

Creative section

4. a) Rs 80 b) Rs 2,500 c) 4 years d) 12% e) Rs 1,500, Rs 300 f) Rs 3,000, Rs 2,250

5. a) Rs 11,484 b) Rs 20,250 c) Rs 11,853 6. a) 11% p.a. b) 10% c) 12%

7. a) Rs 3,500 b) Rs 6,400 c) 3 years 8. a) Rs 8,000 b) 7 years c) 6 months

9. a) Rs. 3,000 b) Rs 4,545 c) Rs 5,000 10. a) Rs 7,700 b) Rs 15,000

11. a) 3 years b) 2 years 12. a) 5% b) 4 years, 4% p.a.

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

7. Profit, Loss and Simple Interest

Exercise : 7.1

Creative section

3. Rs 48, 10% b) Rs 32, 5% c) Rs 690 d) Rs 1,872 e) Rs 1,750 f) Rs 2,100

4. a) (i) Rs 720 (ii) 10% b) (i) Rs 60 (ii) 4% c) profit : 10%

d) gain : 12.5% e) loss : 5% f) profit : 11.43% g) gain : 17.5%

5. a) (i) Rs 23 (ii) Rs 483 b) (i) Rs 152 (ii) Rs. 1,368 c) Rs 7,245 d) Rs 1,42,048

e) Rs 38 each f) Rs 108 each

6. a) Rs 400 b) Rs 700 c) Rs 75 each 7. a) (i) Rs 4,800 (ii) Rs 5,280

b) Rs 63,000 8. a) (i) Rs 9,200 (ii) Rs 10,000 b) (i) Rs 5,500 (ii) Rs 5,000

c) (i) Rs 2,160 (ii) Rs 1,800

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

Exercise : 7.2

Creative Section

4. a) 5% b) Rs 153, 10% c) Rs 47, Rs 893 d) Rs 45, 10% e) Rs 96, Rs 896

5. a) (i) Rs 96 (ii) Rs 864 b) Rs 2,125 c) Rs 2,720 6. a) Rs 200 b) Rs 600

7. a) (i) Rs 160 (ii) Rs 1,440 (iii) Rs 1,300 b) Rs 4,600 c) Rs 350

8. a) (i) Rs 300 (ii) Rs 1,200 (iii) Rs 156 (iv) Rs 1,356 b) Rs 1,695 c) Rs 4,400

9. a) (i) Rs 1,000 (ii) Rs 100 (iii) Rs 900 (iv) Rs 1,017 b) Rs 2,346 c) Rs 9,492

10. a) Rs 2,000 b) Rs 5,000

11. Please complete your project work and compare with your friends. Then discuss in the class.

8. Algebraic Expressions

Exercise : 8.1

Creative Section
4. Answer the questions yourself and show to your teacher.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 307 Vedanta Excel in Mathematics - Book 8

Answers

5. a) 3 b) 4 c) 2 d) 5 e) 3 f) 6

6. a) (i) 15 (ii) 16 b) (i) 400 (ii) 180 (iii) 340 c) (i) 154 (ii) 44 d) (i) 25, 25 (ii) 1, 1

(iii) 125, 125 (iv) 1, 1 v) 5, 5 (vi) 13 7. a) 20 b) 121 c) (i) 220 (ii) 528 (iii) 770

Exercise : 8.2

Creative Section

5. a) (x + 2)2 = x2 + 4x + 4 b) (x + 3)2 = x2 + 6x + 9 c) (x + y)2 = x2 + 2xy + y2

d) (x – 1)2 = x2 – 2x + 1 e) (x – 2)2 = x2 – 4x + 4 f) (x – y)2 = x2 – 2xy + y2

6. a) (x + 1) (x – 1) = x2 – 1 b) (x + 2) (x – 2) = x2 – 4 c) (x + y) (x – y) = x2 – y2
1 1
7. a) (i) 4a2 + 4a + 1 (ii) x2 – 6xy + 9y2 (iii) a2 – 2 + a2 (iv) x2 + 2 + x2

b) (i) p3 + 6p2 + 12p + 8 (ii) 8a3 – 12a2b + 6ab2 – b3 (iii) y3 + 3y + 3 + 1
c) (i) 9x2 – 6x + 1 (ii) 4y2 + y 1 y3
1 1 4y2
(iv) x3 – x + 3x – 27x3 2+

(iii) 8p3 + 12p2q + 6pq2 + q3 (iv) 27x3 – 9x + 1 – 1
x 27x3
8. a) (i) (x + 1)2 (ii) (a – 2b)2 (iii) (3p + 2q)2 b) (i) (x + 2)3 (ii) (2a – 3)3 (iii) (p – 3q)3

9. a) 8xy b) 4xy c) 6xy d) 20xy e) 42ab

10. a) 9x2 + 27x b) 3a2 + 3a c) 6x2 + 12x d) 9a2 + 27a e) 12x2y + 48xy2

11. a) a2 – 9 b) 4x2 – 1 c) 16 – 9p2 d) 4x2 – 9y2 e) x4 – y4

f) 4x4 – 25y4 g) a2 + 2ab + b2 – c2 h) x2 + 2xz + z2 – y2 i) p2– 2pr + r2 – q2

j) x4 – y4 k) x4 – 16 l) 16a4 – y4 12. a) 399 b) 2499 c) 6396 d) 9996

13. a) x3 + 8 b) x3 + 27 c) x3 – 1 d) y3 – 64 e) 8x3 + 27y3 f) 27a3 – 125b3

14. a) 19 b) 20 c) 7 d) 51 15. a) (i) 7 (ii) 5 b) (i) 23 (ii) 21 c) (i) 18 (ii) 20

d) (i) 38 (ii) 40 16. a) 180 b) 185 c) 52 d) 36 17. a) 8 b) 125 c) 27 d) 343

18. a) 2(a2 + b2) b) 4xy c) 8p2 + 18 d) 12xy e) 2(x2 + 1 ) f) –8
x2 a
19. a) 3 b) 2.2 c) 1.1 d) 4.5

20. Please complete your project work and compare with your friends. Then discuss in the class

and show to your teacher.

9. Laws of Indices

Exercise : 9.1

Creative Section

5. a) 26 b) 39 c) (5x)–5 d) (xy)–4 e) 3 (ax)7 f) x3 g) 35 h) 55
1 1 1
i) 24 j) y14 k) x l) p2(a+b)

6. a) x6 b) p4q6 c) 1 d) a3b3 e) x4y4 f) x g) y
x4y8 7. a) 64 b) 27 c) 5
x 1 3
h) xy i) ( y )3 j) x d) 7 e) 2 f) 2 g) 3

h) 4 i) 2 j) 1 k) 1 l) 4 m) 3 nid)))1351295 jo))1494 8. a) 2 b) 1
2 27 5 2 e) 5 4
c) 5 d) 4 1 4
m) 2 n) 2 e) 8 f) 2 g) 2 h) 3 k) 5 l) 2
4
o) 3 9. a) 8 b) 27 c) 4 f) 48 g) 9 h) 3

10. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) 1 j) 1 k) 1 l) 1

11. a) 1 b) 2 c) 4 d) 5 e) 3 f) 5 g) 10 h) 6 12. a) 16 b) 108

c) 3 d) 16 e) – 3 f) –27 g) –1 13. a) 8 b) 1024
8 4 48 9
14. Please complete your project work and compare with your friends. Then discuss in the class

and show to your teacher.

Vedanta Excel in Mathematics - Book 8 308 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

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

Exercise : 10.1

Creative Section

3. a) 2a (x + 2y) b) 3x (2x – 3) c) 4px2 (2x + 3) d) 2mx (2x + m – 3) e) 3b2y2 (3y – 2b + 5)

f) –3a2 (3a3 + 2ax2 + 5 ) g) (2x + 3) (x + 4) h) (y – 4) (2y – 3) i) (x + 2y) (7x + y)

4. a) 150 b) 800 c) 0.058

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

d) (x – 4) (x – 3) e) (3x + 2y) (2x – y) f) (x2 + y2) (a + b)

g) (x + y) (x2 + x + 1) h) (x – z) (x – y) i) (x + y) (a – 2x)

j) (x + 3) (x – y) k) (a – x ) (ax + b2) l) (ac – b) (bc – a)

6. a) 3ab and a + 2 b) x + 2 and x + y c) x + 3 and x + 4a

7. a) 2a and 2x + 3y b) (x + y), (2x + y), (6x + 4y) c) 4x + 10y

Exercise : 10.2

Creative Section

3. a) (x + 6) (x – 6) b) (a + 7) (a – 7) c) (5 + y) (5 – y)

d) ( 4 + 9p ) (4 – 9p) e) x(x + 4) (x – 4) f) 2 (a + 6) (a – 6)

g) 5p (p + 4) (p – 4) h) 3y (y + 3) (y – 3) i) 5a (a + 2b) (a – 2b)
j) 2x3y (2x + 3y) (2x – 3y) 1 1 1 1 1 1
k) (5x + 7 ) (5x – 7 ) l) ( 2x + 9 ) ( 2x – 9 )

4. a) (x2 + 4) (x + 2) (x – 2) b) (a2 + 9) (a + 3) (a – 3)

c) (x2 + y2) (x + y) (x – y) d) (4p2 + q2) (2p + q) (2p – q)

e) (9x2 + 25) (3x + 5) (3x – 5) f) 2 (4y2 + 9) (2y + 3) (2y – 3)

g) (a4 + b4) (a2 + b2) (a + b) (a – b) h) (16x4 + y4) (4x2 + y2) (2x + y) (2x – y)

5. a) (a – b + 3) (a – b – 3) b) (x + y + 5) (x + y – 5)

c) (a2 + b2 + 2) ( a2 + b2 – 2) d) (a2 + ab – b2) (a2 – ab – b2)

e) (4 + x + y) (4 – x – y) f) (7 + a – b) (7 – a + b)

g) (x + y + 5) (x – y + 1) h) (a + b – 1) (a + b – 9)

6. a) (x2 + xy + y2) (x2 – xy + y2) b) (x2 + x + 1) (x2 – x + 1)

c) (x2 + xy + 4y2) (x2 – xy + 4y2) d) (a2 + 3ab + b2) (a2 – 3ab + b2)

e) (x2 + 3xy + 3y2) (x2 – 3xy + 3y2) f) (a2 + 2ab + 5b2) (a2 – 2ab + 5b2)

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

i) (2a2 + 5ab + 3b2) (2a2 – 5ab + 3b2)

7. a) 400 b) 2160 c) 1820 d) 201 e) 2499 f) 6396 g) 9999 h) 9991

8. a) (x + 2) (x2 – 2x + 4) b) (y + 3) (y2 – 3y + 9) c) (2a + 1) (4a2 – 2a + 1)

d) (2x + 3y) (4x2 – 6xy + 9y2) e) (3a + 5b) (9a2 – 15ab + 25b2) f) (p – 2) (p2 + 2p + 4)

g) (3m – n) (9m2 + 3mn + n2) h) (a – 10b) (a2 + 10ab + 100b2)

9. a) 135 cm2 b) 299 cm2 c) 189 m2 d) 476 m2 e) 756 sq. ft. f) 1375 m2

Exercise : 10.3

Creative Section

4. b) (x + 2) (x + 2) = x2 + 4x + 4 c) (x + 3) (x + 1)=x2 + 4x + 3 d) (x + 3) (x + 2)=x2 + 5x + 6

5. a) 2, 5 b) – 3, – 6 c) 8, – 4 d) – 6, 5

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

d) (x + 3) (x + 5) e) (x + 2) (x + 4) f) (x + 4) (x + 5)

g) (x + 3) (x + 6) h) (x + 5) (x + 6) i) (x + 6) (x + 8)

7. a) (x – 1) (x – 2) b) (x – 2) (x – 3) c) (x – 1) (x – 5)

d) (x – 4) (x – 6) e) (x – 3) (x – 7) f) (x – 2) (x – 6)

g) (x – 4) (x – 9) h) (x – 3) (x – 10) i) (x – 7) (x – 8)

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

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d) (x – 3) (x + 6) e) (x – 2) (x + 7) f) (x – 5) (x + 8)
g) (x – 7) (x + 12)
9. a) (x + 1) (x – 2) h) (x – 5) (x + 9) i) (x – 6) (x + 10)
d) (x + 4) (x – 7)
g) (x + 4) (x – 11) b) (x + 2) (x – 3) c) (x + 3) (x – 5)
10. a) x (x + 7) (x + 8)
d) x2 (x – 5) (x – 9) e) (x + 2) (x – 6) f) (x + 5) (x – 8)
g) x3 (x – 6) (x – 12)
11. a) (x + y + 2) (x + y + 3) h) (x + 5) (x – 13) i) (x + 8) (x – 9)
d) (x – y + 2) (x – y – 11)
b) x(x + 3) (x + 14) c) x2 (x + 3) (x – 7)

e) x (x – 2) (x + 15) f) x2 (x – 2) (x + 4)

h) x3 (x – 6) (x + 17) i) x4 (x + 2) (x – 6)

b) (a + b + 11) (a + b + 3) c) (p – q – 6) (p – q – 5)

12. a)(a + 4) unit, (a + 2) unit, (4a + 12) unit b) (x2 + x – 42) sq. units

13. and 14. Please complete your project work and compare with your friends. Then show to your
teacher.

Exercise : 10.4
Creative Section

3. a) (x + 3)2 b) (x + 4)2 c) (x + 5)2 d) (a + 6)2 e) (a + 7)2 f) (a + 8)2
l) (x – 15)2
g) (x – 2)2 h) (x – 1)2 i) (p – 9)2 j) (p – 10)2 k) (p – 12)2
f) (4x + 3)2
4. a) (2a + 1)2 b) (2a + 5)2 c) (3a + 1)2 d) (3x + 2)2 e) (3a + 4)2 l) (12 – 5x)2

g) (3x – 4)2 h) (5x – 8)2 i) (4a – 5)2 j) (7p – 1)2 k) (6 – 5p)2

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

d) (x + 1) (3x + 1) e) (x + 1) (3x + 2) f) (x+ 3) (3x + 1)

g) (2x + 1) (2x + 5) h) (x + 1) (4x + 7) i) (x – 1) (2x – 1)

j) (x – 2) (3x – 4) k) 4 (x – 1) (x – 1) i) (2 – x) (4 – 9x)

m) (1 – x) (13 – 4x) n) (x – 2) (6x – 7) o) (a – 1) (3a – 17)

6. a) (x – 1) (2x + 3) b) (x – 2) (3x + 7) c) (x + 2) (4x – 3)

d) (x + 3) (5x – 2) e) (x + 2) (6x – 1) f) (x + 4) (7x – 3)

g) (2x + 3) (2x – 1) h) (2x + 5) (3x – 2) i) (a – 4) (2a + 3)

j) (a + 1) (3a – 8) k) (2a + 1) (2a – 9) l) (2a + 3) (a – 5)

m) (4x + 3) (2x – 7) n) (2x + 1) (3x – 7) o) (x – 3) (5x + 2)

7. a) (x + 2y ) (2x + y) b) (x + y) (3x + 2y) c) (x + y) (2x – 3y)

d) (2x + 3y) (4x – 5y) e) (3x – 4y) (5x + y) f) (4a – 3b) ( 6a – 5b)

g) (3a – 2b) (5a – 6b) h) 2(a – 2b) (7a – 5b) i) (a – 6b) (8a + 3b)

8. a) (5x + 5y)2 b) (7a – b7)2 c) (2x + 1 )2 d) (3p – 61p)2
2x
9. a) (a + b + c + d) (a + b – c – d) b) (p – q + r + s) (p – q – r – s)

c) (a + b + c) (a – b – c) d) (x + y – z) (x – y + z)

10. a) (x + y – 2) (2x + 2y – 5) b) (a + b – 2) (3a + 3b – 4)

c) (p – q – 3) (2p – 2q + 3) d) (2m – 2n + 1) (3m – 3n – 7)

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

Exercise : 10.5

Creative Section

3. a) 2xy b) 3a2b2 c) pxy d) 4x2 e) 3x2y2 f) 5abc

4. a) a + 7 b) a(a + b) c) x + 3 d) 2(x + 2) e) x(x + 2y) f) 2x – 3

g) a + 2 h) x + 1 i) (a + 3) j) 2x + 3 k) x – 5 l) 2x – 3

m) a + 2 n) a – 3 o) 2x – 3 p) 3x – 5 q) x (x – 5) r) x (x – 5)

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

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

Vedanta Excel in Mathematics - Book 8 310 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise : 10.6

Creative Section

3. a) 4x2y2 b) 6a3b3 c) 12x3y3 d) 6x4y4 e) 24x5y5 f) 84x3y3z3

4. a) a2x (x + 1) b) 2x2 (x +2) c) 6a2b (a + 2b) d) abx2 (a + b)

e) 6x2 (x + 2) f) 2 (a2 – 4) g) 6a (a2 – 1) h) xy (x2 – 25) i) 7a2x2 (a2 – x2)

j) xy (x2 – y2) k) 2x (4x2 – 1) l) (x2 – 4) (x + 3) m) (x – 2) (x2 – 9)

n) 2x (2x – 3) (x2 – 25) o) a (a + 3) (4a2 – 9) p) (x + 3) (x + 4) (x + 5)

q) (a + 3) (a – 4) (a – 5) r) (a – 2) (a – 6) (a + 7) s) (2a + 1) (a2 – 4)

t) (x2 – 16) (3x – 4) u) (x – 1) (3x + 1) (4x + 3) v) (x + 3) (4x2 – 12x + 9)

5. a) m(m2 – 4) (m + 1) b) 4(x2 – 25) (x + 2) c) (a2 – b2) (a + b) (2a – b)

d) (x + 2) (x2 – 4) (x + 6) e) (x – 3) (x2 – 9) (x – 7) f) (x + 2) (x + 4) (x2 – 9)

g) (a + 5) (a2 – 1) (a2 – 36) h) (2a + 1) (a2 – 4) (9a2 – 1)

6. and 7. Please complete your project work and compare with your friends. Then show to your teacher.

11. Rational Expressions

Exercise : 11.1

Creative Section 3 2a2 3p 4q3 –bc 3p2
4x d) 3b2 e) 2ab2 f) 4q g) 3p 3a 4q2r2
3. a) x b) c) x h) – 2x2 i) j)
2 2y 3z

4. a) 1 b) 1 c) x x 4 d) x 1 y e) x 3 3 f) a + b
2x 2y – – –

g) x 5 h) 5a i) x 1 2y j) a2 1 b2 k) 1
2x – 3b + + x+3

l) x m) a+2 n) a (a – 6) o) 2(a + 5) p) x – 7
– a– 7 a–3 a+9 x + 7
x 4

q) x+6 r) x – 4 s) x + 5 t) x+2 u) x – 3
x–1 x + 2 x – 3 x(2x + 1) x – 1

Exercise : 11.2

Creative Section 2xy 12xp a 20ab 4x2y2z2
3x3 5ab 5aby 4b 9xy 3pqr
2. a) 2y2 b) c) d) e) f)

3. a) x2b2 b) 3xz c) 2x4y4 d) 3a7
ayz2 ac 3a6b5 4xc

4. a) 2 b) 4 c) 1 d) 1 e) xy(2a + 3b) f) 5x + 4y
3 (x + 3) 2 (x – y) x+2

g) a (2x + 9y) h) a+2 i) (x + 2) (a – 4)
1 + 2a a–1 (x – 3) (a – 1)

j) 4xy – z2 k) – x (x + 2y) l) a(a + 4) (a – 2) m) a – 5
y (x + y) (a – 4) (a + 2) a – 1

Exercise : 11.3

Creative Section

2. a) 1 b) 3 c) 1 d) p + q e) x 1 y f) 1 g) x–2 h) 1 i) x x j) a – 1
b + a+b x+2 a+5 +2 a – 2

3. a) 2x b) (p – 1 – 1) c) 4a 1 d) ab (a2 + b2) x+y
x2 – 1 2) (p 4a2 – a2 – b2 e) x2y2

f) x 1 2 g) –x 1 h) – 10x i) x2 2 j) x 2 2
+ x2 – x2 – 25 – a2 +

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Answers

k) (x x2 + y2 y2) l) 6xy m) –1 n) –1 o) x+4
+ y) (x2 – 9x2 – y2 2a + 3b (a – b) (b – c) x2 – 1

p) (a 2– 7a – 4) q) 1 – 5a r) x+4 2)
+ 2) (a2 (a – 1) (a2 – 1) x (x + 1) (x +

4. a) 2 b) x2 1 1 c) 2x d) x+5
x (x + 1) (x + 2) – x+2 x+1

e) 8a + 1 f) 1 g) 1 h) 1 i) 6xy j) 8xy3
a2 – 1 x2 – y2 x4 – y4

5. a) 3 b) (x + 2) (x 9 3) (x – 4) c) 1 d) 0
(x – 3) (x – 5) – (x – 2) (x – 3)

e) 1 f) (x 3x –7 3) g) –1
(x – 2) (x – 3) – 2) (x – y–3

12. Equation, Inequality and Graph
Exercise : 12.1

Creative Section

3. Show the graphs of inequalities to your teacher.

4. a) {5, 4, 3, …} b) {5, 6, 7, …} c) {4, 3, 2, 1, …} d) {5, 6, 7, …} e) {3, 2, 1, 0, …}

f) {3, 2, 1, 0, …} g) {2, 3, 4, 5, …} h) {2, 3, 4, 5, …} i) {– 5, – 4, – 3, – 2, …}

j) {– 3, – 4, – 5, …} k) {7, 8, 9, ........} l) {2, 3, 4, 5, …} m) {3, 2, 1, 0, …}

n) {– 6, – 7, – 8, …} o) {0, –1, –2, –3, …} p) {2, 1, 0, –1, …}

5. a) {3, 4, 5} b) {2, 3, 4} c) {– 6, – 5, ..., 5, 6, 7} d) {0, 1, 2, 3} e) 3

f) {3, 4, 5, 6} g) {0, –1, –2...... , – 6} h) {5, 4, 3, 2, 1} i) {–1.5, –1, 0, 0.5}

j) {– 7, –6, ......... 0, 1, 2} k) {– 7, – 6, ......, – 2} l) {2, 3, 4, 5, 6}

6. a) {...,–20, – 17, – 14, – 11} b) {3, 1, – 1, – 3, – 5} c) {– 5, – 3, – 1, ...}

7. a) 4 b) 2 8. a) 4 b) 4

Exercise : 12.2

Creative Section f) 2 g) 12 h) 5 i) –2 j) – 7 k) –1 l) 2 m) – 1 n) 5 0) 0
4. a) 5 b) 2 c) 3 d) 1 e) 4 3

5. a) 18 b) 21 c) 22 6. a) 15, 17, 19 b) 24, 26, 28

7. a) 16, 21 b) 32, 24 c) 19, 25 d) Rs 55, Rs 80 e) Rs 60, Rs 130

f) Rs 40, Rs 100 g) Rs 45, Rs 60 8. a) Rs 18000 b) Rs 15,900

9. a) Rs 1920, Rs 2880 b) 45°, 60°, 75° c) 36°, 72°, 108, 144°

10. a) 22 m, 40 m b) 25 m, 75 m, c) 15 m, 18 m 11. a) Rs 680 b) Rs 550 c) Rs 1800

12. a) 12 years, 21 years b) 10 years, 40 years c) 10 years, 30 years

d) 12 years, 45 years e) 10 years, 22 years

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

Exercise : 12.3

Creative Section

3. a) (4, 3) b) (3, 5) c) (4, –2) d) (7, 3)

4. Solve the given equations graphically and show to your teacher. a) (3, 1) b) (2, 5) c) (4, 5) d) (7, 3)

e) (– 3, – 4) f) (2, 5) g) (5, 9) h) (1, – 2) (i) (3, 2) j) (5, 3)

k) (4, 3) l) (2, 1) m) (– 2, – 4) n) (6, – 3)

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

Vedanta Excel in Mathematics - Book 8 312 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise : 12.4

Creative Section

4. a) 2, 1 b) 3, 2 c) 6, – 1 d) 5, 1 e) 9, – 1 f) 6, 3 g) 3, 4 h) 2, 5

i) 8, 5 j) 4, 1 5. a) 3, 1 b) 4, 2 c) 3, 5 d) 4, 10 e) 8, 3 f) 4, 5

g) 7, 6 h) 5, 8 i) – 3, 7 j) 2, 5 6. a) 11, 7 b) 22, 17 c) 30, 24 d) 18, 12

7. a) 15, 21 b) Rs 75, Rs 25 8. a) 34 years, 6 years b) 12 years, 8 years

c) 36 years, 12 years d) 40 years, 8 years e) 39 years, 9 years f) 40 years, 15 years

9. a) 24 m, 12 m b) 35 m, 25 m

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

Exercise : 12.5

Creative Section

3. a) 2, 3 b) 1, 2 c) –3, 4 d) 4, –5 e) 9, 3 f) – 2, –11 g) 0, – 3 h) 0, 8 i) 0, 7

4. a) r1 b) r 2 c) r 3 d) r 4 e) r 5 f) r 6 g) r 7 h) r 8 i) r 9 j) r 10

k) r 3 l) r 5 m) r 7 n) r 10 o) r 8 p) r 11
2 4 6 9 3 8

5. a) 1, 2 b) 2, 3 c) 1, 4 d) 3, 4 e) r 6 f) r 2 g) 3, 6 h) – 2, – 3 i) – 4, – 3

j) – 2, – 7 k) – 6, – 7 l) – 9, – 5 m) 14, – 5 n) – 3, 13 o) 5, – 2

p) – 10, 4 q) – 15, 5 r) – 7, 4

6. pja)))206,,,–215223 b) 0, 1 c) 0, 1 d) 0, 3 e) 0. 4 f) 0, 5 g) – 1, – 1 h) 1, 21o)ir) –323, 7
7. a) 4, 8 k) 2, 3 4 2 2, 3 4 n) – 3, –213 2
q) – – 4 4 – 1
l) 2, 3 m) 3
4 3 r) –1
3 ,– 3 2 ,
2 3 2

b) 6, 9 c) 10, 6 d) 12, 7 e) 3, 6 f) 3, 4 g) 8, 5 h) 5, 7 i) 3 j) 4

8. a) 9 years, 5 years b) 4 years, 9 years 9. a) 12 m, 8 m b) 10 m, 7 m

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

13. Transformation

Exercise : 13.1

Creative Section

3. a) A' (– 6, – 3) b) P' (– 5, – 1) c) E' (– 6, 1 )

B' (– 2, – 1) Q' (– 3, – 6) F' (– 2, 1)

C' (– 1, – 6) R' (– 2, 0) G' (– 1, 4)

D' (1, – 4) K' (2, 1) H' (– 5, 5)

E' (5, – 2) L' (0, 4) P' (3, 6)

F' (7, – 6) M' (6, 3) Q' (1, 1)

R' (5, 2)

S' (7, 4)

4. a) A' (– 4, 6), B' (– 1, 4), C' (– 5, 2)

O' (0, 0) Q' (– 2, – 4), R' (– 6, – 3)

b) E' (6, 3), F' (2, 6) G' (3, 1)

K' (2, 0), L' (4, – 5), M' (1, – 3)

c) A' (5, 4) , B' (3, 1), C' (1, 3), D' (0, 6)

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Answers

P' (– 1, – 6), Q' (5, –9), R' (– 6, – 1) S' (– 2, – 2)
5. a) P' (3, – 6), Q' (5, – 9) , R' (4, – 2)
B' (3, – 3), C' (– 5, – 7)
b) A' (– 2, – 4) L' (– 6, 3), M' (– 2, – 4)
c) K' (– 1, 4), E' (2, – 6) , F' (4, 1)
d) D' (3, 5), B' (– 4, 7), C' (– 6, 3)
6. a) A' (– 1, 4), Q' (4, – 6), R' (5, 5)
b)P' (2, 3), F' (– 5, – 2), G' (0, – 3)
c) E' (– 3, – 7), Y' (– 4, – 5), Z' (– 2, 6)
d) X' (– 1, 4),

7. a) A' (0, 4), B' (– 3, 0), C' (2, – 5) b) P' (– 7, – 8), Q' (– 4, 6), R' (6, 2)

8. a) W' (4, – 2), X' (– 3, – 6), Y' (– 1, 4), W" (– 4, – 2), X" (3, – 6), Y" (1, 4)

b) R' (– 7, – 2), S' (4, – 5), T' (6, 3) R" (– 7, 2), S" (4, 5), T" (6, – 3)

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

Exercise : 13.2

Creative Section

2. Rotate the given figures through the given angles about the given centre of ration and show to your

teacher.

3. (i) Anti clock direction

a) A' (– 6, 1) B' (– 8, 4), C' (– 2, 2) P' ((21,1 – 1), Q' (3, – 4), R' (6, – 2)
b) D' (0, – 3), E' (– 4, – 1), F' (– 5, – 5) K' 2), L' (2, 5), M' (6, 3)

c) A' (2, – 3), B' (5, – 5), C' (4, – 1) E' (– 6, 4), F' (– 3, 0), G' (– 1, 3)

(ii) Clockwise direction

a) A' (6, – 1), B' (8, – 4), C' (2, – 2) P' (– 1, 1), Q' (– 3, 4) R' (– 6, 2)

b) D' (0, 3), E' (4, 1), F' (5.5) K' (– 2, – 2), L' (– 2, – 5), M' (–6, 2)

c) A' (– 2, 3), B' (– 5, 5), C' (– 4, 1) E' (6, – 4), F' (3, 0), G' (1, – 3)

4. a) A' (– 5, – 3), B'(– 1, – 5) , C' (– 2, – 1) P' (1, – 6), Q' (5, – 3), R' (2, – 2)

b) D' (4, – 4), E' (0, – 4), F' (2, – 1) K' (3, 0), L' (5, 4), M' (1, 3)

c) A' (– 1, 1), B' (– 2, 5), C' (– 5, 1) E' (– 5, – 5), F' (– 1, – 5), G' (– 3, –1)

5. a) (i) P' (– 2, – 4), Q' (– 7, 3), R' (6, – 1) (ii) P' (2, 4), Q' (7, – 3), R' (– 6, 1)

b) A' (5, 8), B' (– 2, 3), C' (2, – 9) 6. a) K' (4, – 1), L' (– 5, 3), M' (–2, –5)

K" (– 4, 1), L" (5, – 3), M" (2, 5) b) D' (1, – 4), E' (6, 0), F' (0, 5)

D" (1, 4), E" (6, 0), F" (0, – 5)

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

Exercise : 13.3

2. Displace the given figures and show to your teacher

3. a) A' (3, 7) b) B' (2, –1) c) C' (3, 2) d) D' (–7, –4)

4. a) P' (10, 11), Q' (13, 7), R' (12, 13) b) A' (–2, 11), B' (–6, 6), C' (–12, 10), D' (–9, 13)

5. a) 3 units right and 5 units up b) 5 units left and 3 units down

6. a) M' (–1, 2), M" (–7, 11) b) A' (3, 0), B' (5, –6), C' (–2, –9), A" (–2, 1), B" (0, –5), C" (–7, –8)

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

14. Geometry- Angle

Exercise 14.1

Creative Section - A

2. a) 130° b) 72°, 108° c) 42° d) 40°, 50° e) 36°, 144° f) 24°, 66° g) 75°, 105°

3. a) 122° b) 55° c) 20° d) 36° e) 20° f) 120° g) 144° h) 26°

4. a) 40°, 60°, 80° b) 30°, 60°, 90° c) 18°, 36°, 54°, 72° d) 88°, 88°, 92° e) 45°, 45°,

135°, 135° f) 90°, 120°, 150° g) 103°, 115°, 142° h) 35°, 105°, 40°, 40°, 65°, 75°

5. a) 60°, 120° b) 45°, 135° 6. a) and b) Show to your teacher

7. Show to your teacher

Vedanta Excel in Mathematics - Book 8 314 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Exercise : 14.2

Creative Section b) 100°, 100°, 80° c) 130°, 50° d) 100°, 80°, 80°, 100°
3. a) 75°, 75°, 75°

e) 85°, 95°, 95° f) 115°, 65°, 115°, 65°, 115° g) 112°, 112°, 78° 102°

h) 75°, 60°, 120°, 105°, 105°, 120° 4. a) 20° b) 25° c) 45° d) 50° e) 36° f) 60° g) 30° h) 35°

5. a) 88°, 92° b) 130°, 50°, 50° c) 70°, 70°, 70° d) 96°, 84°, 84°, 84°

e) 60°, 60°, 120° f) 90°, 90° g) 60°, 70°, 50°, 120°, 50° h) 40°, 80°, 60°

i) 50°, 70°, 60° j) 30°, 28° k) 64° l) 280° m) 70°, 290° n) 75° o) 52° p) 291°

6. a) 80°, 100°, 80° b) 110°, 70°, 70°, 70° c) 110°, 110°, 40°, 30° d) 75°, 55°, 50°, 50°

7. a) 70° b) x = 40° , y = 140°, z = 40° 8., 9. and 10. Show to your teacher

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

15. Geometry- Triangle

Exercise : 15.1

Creative Section

2. a) 100° b) 50°, 100° c) 45°, 60°, 75° d) 36°, 54°, 90° e) 30°, 60° f) 120°

3. a) 90° b) 35°, 105° c) 56°, 61°, 63° d) x = y = 64° e) a = b = 45°

f) x = 50°, y = z = 65° g) x = 72°, y = 108° h) x = 86°, y = 38°

4. a) a = 70°, b = 65°, c = 70° b) x = 58°, y = 52°, z = 70° c) x = 85°, y = 55°, z = 95°

d) x = 29°, y = 58° , 2x = 58° e) x = 65°, y = 55°, z = 60° f) x = 65°, y = z = 57.5°

g) x = 72°, y = 66°, z = 42° h) x = 105°, y = 45° i) x = 54°, y = 29°

j) p = q = r = 40° k) a = 50°, b = 40°, c = 90°, d = 30°, e = 150°

l) x = 90°, y = 80°, z = 43° 5. and 6. Show to your teacher

Exercise : 15.2

Creative Section 6. a) S.A.S. axiom, 5 cm b) A.S.A. axiom, 6.5 cm
4. and 5. Show to your teacher d) R.H.S. axiom, 45°

c) S.S.S. axiom, 50°

7. a) x = 3.2 cm, ‘A = ‘ P = 85°, ‘ B = ‘ Q = 35°,

AB = PQ = 4.5 cm, AC = PR = 3.2 cm , BC = QR = 5.5 cm

b) x = 2.5 cm, ‘ W = ‘ D = 20°, ‘ Y = ‘ F = 45° , ‘ X = ‘ E = 115°

XY = EF = 2.5 cm, XW = DE = 3.5 cm, WY = DF = 6 cm.

c) x = 2 cm, ‘ Q = ‘ K = 90°, ‘ R = ‘ L = 52°,

‘ P = ‘ M = 38°, QR = LK = 2.8 cm, RP = LM = 5.2 cm

QP = MK = 4.3 cm.

d) x = 4.5 cm, ‘ A = ‘ D = 64°, ‘ B= ‘ F = 86°,

‘ C = ‘ E = 30°, AB = DF = 3.1 cm, BC = EF = 6.5 cm, AC = DE = 7 cm.

8. Show to your teacher. 9. Please complete your project work and discuss in the class.

Exercise : 15.3

Creative Section

2. a) PQ = 6 cm, ‘ A = 75°, ‘ Q = 55° b) x = 16 cm, y = 20 cm

3. a) AB = 6 cm b) x = 5.6 cm c) AB = 37.5 cm, AE = 8 cm

d) BD = 2 cm e) ‘QXY = 80° , QX = 9 cm f) 3.2 cm.

Exercise : 15.4

Creative Section

2. Show to your teacher 3. a) (ii) x = 6 cm b) (ii) AC = 6 cm c) (ii) 16 m

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 315 Vedanta Excel in Mathematics - Book 8

Answers

16. Geometry - Quadrilateral and Regular Polygon

Exercise : 16.1

Creative Section

3. a) 55°, 125°, 125° b) 120°, 60°, 60° c) 105°, 105°, 75°, 75°

d) 70°, 110°, 110°, 70° e) 55°, 125°, 125° f) 80° 100°, 100°, 80°, 80°

g) 105°, 75°, 75° 75° h) 115°, 115°, 30°, 35° i) 80°, 80°, 100°

j) 45°, 105°, 105° k) 40°, l) 70°, 70°, 70°, 70°, 110° m) 75°, 75°, 105°

n) 110°, 70° o) 56°, 124°, 84°, 84° p) 45°, 135°, 30°, 15°

4. a) 10 cm, 17 cm, 17 cm b) 3 cm, 7 cm, 7 cm c) 2 cm, 7 cm, 7 cm

d) 5 cm, 10 cm, 10 cm. 5. and 6. Show to your teacher

7. and 8. Please complete your project work and discuss in the class.

Exercise : 16.2

Creative Section

2. a) 360° b) 540° c) 720° d) 900° e) 1080° f) 1260° g) 1440° h) 1800°

3. a) 90° b) 108° c) 120° d) 128.57° e) 135° f) 140° g) 144° h) 150°

4. a) 90° b) 72° c) 60° d) 51.42° e) 45° f) 40° g) 36° h) 30°

5. a) 5 b) 6 c) 7 d) 8 e) 10 6. a) 4 b) 5 c) 6 d) 8 e) 9

7. a) 5 b) 6 c) 8 d) 9 e) 10 8. a) 115° b) 70° c) 107° d) 115° e) 235° f) 79°

g) 97° h) 60° i) 111.67° 9. a) 150° b) 102° c) 36° d) 90°

10. Please complete your project work and discuss in the class.

17. Geometry - Construction

Exercise : 17.1

Show to your teacher
6. Please complete your project work and compare with your friends. Then show to your teacher.

18. Coordinates

Exercise : 18. 1

Creative Section

3. a) 5 cm b) 8 cm c) 5 cm d) 15 cm 4. a) yes b) yes c) no d) no e) yes f) no

5. a) yes b) no c) yes

6. a) 24 cm b) 20 cm c) 13 cm 7. a) x = 5 cm, y = 12 cm b) x = 5 cm, y = 10 cm

8. a) 8 m b) 12 m c) Shyam, by 20 m d) (i) 12 m (ii) 28 m

Exercise : 18. 2

Creative Section

2. a ) 2 2 units b) 5 units c) 2 10 d) 5 2 e) 10 units f) 4 units

3. a) 10 units b) 15 units c) 5 2 units 4. a) 2 units, 200 km b) 45 km
c) 4 5 units, 360 km d) 348.5 km

5. a) (i) 15 units (ii) 30 units (iii) Show to your teacher b) 20 units, Show to your teacher

6. Show to your teacher 7. Show to your teacher 8. a) a = 1 b) a = 12

9. and 10. Please complete your project work and discuss in the class. Then show to your teacher.

19. Circle

Exercise : 19.1

Creative Section

3. a) 44 cm, 154 cm2 b) 88 cm, 616 cm2 4. a) 22 cm b) 616 cm2 c) 44 m, 154 m2

Vedanta Excel in Mathematics - Book 8 316 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

5. a) (i) 440 m (ii) 15400 m2 b) (i) 110 m (ii) 962.5 m2

6. a) 2640 m b) 2420 m c) 3 rounds 7. a) 3.5 km b) 280 ft c) 70 cm

8. a) (i) 21 cm (ii) 1386 cm2 b) 61600 m2 c) 22 m d) 132 m

9. a) 7 cm b) 42 cm 10. a) 42 cm2 b) 1039.5 cm2 c) 286 cm2 d) 82 cm2

e) 42 cm2 f) 38.5 cm2 g) 87.43 cm2 h) 168 cm2 i) 462 cm2

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

20. Area and Volume

Exercise : 20.1

Creative Section

2. a) 35 cm2 b) 24 cm2 c) 63 cm2 d) 116 cm2 e) 81 cm2 f) 9 cm2

g) 9 3 cm2 h) 8 3 cm2 i) 192 cm2 j) 36 cm2 k) 100 cm2 l) 60 cm2

m) 24 cm2 n) 26 cm2 o) 45 cm2 p) 102 cm2 q) 66 cm2 r) 55 cm2

3. a) 100 cm2 b) 247.5 cm2 c) 540 cm2 d) 375 cm2 e) 357 cm2 f) 122.5 cm2

4. a) 40 cm2 b) 135 cm2 c) 96 cm2 d) 119 cm2 e) 360 cm2 f) 240 cm2

g) 108 cm2 h) 43 cm2 i) 88 cm2 j) 140 cm2 k) 84 cm2 l) 100 cm2

5. a) (i) 10 m (ii) 100 m2 (iii) Rs 7,000 b) Rs 50,000

6. a) (i) 1120 m2 (ii) Rs 1,00,800 b) (i) 25 m (ii) 800 m2 (iii) Rs 60,000

c) Rs 9000 d) Rs 16,000 e) Rs 28080 7. a) 2820 m2, Rs 3,10,200 b) 2184 ft2, Rs 24,024

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

Exercise : 20.2

Show to your teacher.
5. Please complete your project work and discuss in the class. Then show to your teacher.

Exercise : 20.3

Creative Section

2. a) 54 cm2 b) 288 cm2 c) 179 cm2

3. a) 154 cm2, 880 cm2, 1188 cm2 b) 616 cm2, 3080 cm2, 4312 cm2 c) 1386 cm2, 5280 cm2, 8052 cm2

4. a) 285 cm2, 309 cm2 b) 336 cm2, 384 cm2 c) 648 cm2, 756 cm2 5. a) 100 cm2

b) 2350 cm2, 1750 cm2 6. (i) 1188 cm2 (ii) 1881 cm2 7. 338 cm2 8. 408 cm2

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

Exercise : 20.4

Creative Section

3. a) 64 cm3 b) 300 cm3 c) 868 cm3 d) 1746.36 cm3 e) 4435.2 cm3 f) 24640 cm3

g) 600 cm3 h) 54 cm3 i) 336 cm3

4. a) (i) 125 cm3 (ii) 91.125 cm3 (iii) 512 cm3 (iv) 15.625 m3 b) (i) 60 cm3

(ii) 150000 cm3 (or 0.15 m3) (iii) 315000 cm3 (or 0.315 m3) (iv) 960000 cm3 (or 0.96 m3)

c) (i) 1540 cm3 (ii) 539 cm3 (iii) 6930 cm3 (iv) 18.48 m3

5. a) 1000 cm3 b) 15 cm, 225 cm2 c) 1.728 cu.m 6. a) 60 l b) 4200 l

7. a) 15 cm b) 50 cm c) 1.5 m d) 20 cm

8. a) 15 b) 225 c) 30,300 d) 10000

9. a) 136 cm3 b) 510 cm3 c) 81 cm3 d) 345 cm3 e) 90 cm3 f) 756 cm3

10. a) 24 cm3 b) 48 m2 c) 12 m, 8m, 4 m d) 30 cm, 15 cm, 10 cm

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

21. Bearing and scale drawing

Exercise : 21.1

Creative Section

4. a) 045° b) 135° c) 180° d) 225° e) 270° f) 315°

5. a) 060° b) 090° c) 125° d) 160° e) 210° f) 230°

g) 270° h) 318° 6. A : 040° , B : 100°, C : 200° , D 230° , E: 325°

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 317 Vedanta Excel in Mathematics - Book 8

Answers

7. a) 220° b) 258° c) 295° d) 330° e) 020° f) 090°

g) 105° h) 150° 8. a) 235° b) 350° c) 275° d) 262° e) 235°

9. Please complete your project work and discuss in the class.

Exercise : 21.2

3. a) 100 m b) 300 m c) 4.2 km d) 110 km

4. a) 12 cm b) 65 cm c) 8 cm d) 8 cm

5. a) 22.5 m b) 32 km c) 470 km 6. Show to your teacher

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

22. Statistics

Exercise : 22.1

3. and 4. Show to your teacher
5. Please complete your project work and compare with your friends. Then show to your teacher.

Creative Section Exercise : 22.2 Miscellaneous
2. Show to your teacher
3. a) Items Food Rent Study Transportation

Rs 4,500 2,100 1,800 1,500 900

b) Items Wages Fuel Raw materials Rent
Rs 20,000
60,000 16,000 48,000

c) (i) 6720 (ii) B secured the least votes of 4,800.
d) Items
Cotton Nylon Polyster Other

(i) (%) 25 15 40 20

(ii) (Kg) 12.5 7.5 20 10

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

Exercise : 22.3

Creative Section

3. a) 13 years b) 9 c) 70 4. a) 10 b) 20 c) 20 5. a) 10 years b) 7 c) 7

6. a) 45 mm b) 43.2 kg c) 10 7. a) 5 b) 10 8. a) 34.25 b) 10.8 years c) 62.17 cm

9. a) 28.5 b) 70.75 c) 46.5 d) 38.6 e) Rs 400 f) 33.3 years 10. a) 28.6 b) 45

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

Exercise : 22.4

Creative Section

2. a) (i) 35 (ii) 30 (iii) 24 b) 52 kg c) 32 3. a) 2 b) 8

4. a) (i) 12 (ii) 10 (iii) 14 b) (i) 39 (ii) 34 (iii) 77.5

5. a) (i) 7 (ii) 21 b) 18 years c) Rs 1,500 to Rs 2,000 d) 7 e) Rs 150

6. a) 50 b) 20 c) Rs 65 7. a) 36 b) 80 c) 27, 37

8. a) (i) 120 cm (ii) 90 cm (iii) 30 cm b) 32 c) 10

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

Vedanta Excel in Mathematics - Book 8 318 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Lower Secondary Level Final Examination

Specification Grid - 2069

Subject: Mathematics

S. Areas Level of Knowledge Skills Problem

N. Objectives and Solving

Understanding

Types of Questions Very Short Short Long Long
Short
Total Marks
Topics No. of ques. Time Allocations
Marks Remarks
No. of ques.
Marks
No. of ques.
Marks
No. of ques.
Marks
No. of ques.
Marks

1. Line & Angles 1 1 12

2. Triangle, Parallel- 12 28 40 Minutes

1G ogram and Polygon 24 10 22
3. Similarity and
2 C-
G Congruency 11 12 2 3 5 Min-
4. Circle 11 12
3M 5. Solid Shapes 12
4T 6. Co-ordinates
5.
6. A 7. Perimeter, Area 12 14 26 utes
11
7S
8A and Volume Min-

- 8. Transformation 14 utes
9. Bearing and Scale 1 9 Min-
1 25 utes
Drawing 1 1 12 14 37
10. Sets 1 13 min
11. Whole Number

12. Integer 1 1 214 37
13. Rational Number
14. Real Number 12 38 Minutes
15. Ratio, Proportion

& Percentage 14 4 14
16. Profit and Loss
17. Unitary Method 14 3 7 13 min
18. Simple Interest 51
19. Statistics 14
20. Algebraic
1 1 1 2 14
1
11 2 3 12

Expression Min-
12 29 utes
21. Indices 11 24
2 4 14
22. Equation, In- 1 1

equality & Graphs

180

Total 10 10 3 6 1 4 28 10 40 4 16 41 100 Min-

utes

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 319 Vedanta Excel in Mathematics - Book 8

Class: VIII BLE Model Set
Compulsory Mathematics
Maximum Marks: 100
Time: 3 hrs.

Attempt all the questions: P X Q
M B
Group-A (5 × (1 + 1) = 10]
N
1. (a) In the given figure, write the corresponding angle of ‘PMN. A Y

(b) If the diameter of a circular pond is x meter, what is Q Y
the measure of its circumference? B

2. (a) From the given graph, find the solution of the x – y = –3 x+y=1
equations: x + y = 1, x – y = –3

(b) Sketch to show the bearing of 1000. X' A OP X

3. (a) Write down the set notation to represent the shaded region Y'
in the given Venn-diagram. U

P
Q

(b) Find the mode of the data given below. x – 3x – 10°
3cm, 4cm, 2cm, 3cm, 4cm, 5cm, 2cm, 3cm, 5cm, 3cm, 2cm 10°

4. (a) Factorize: 1 – 9x2
(b) If x ≠ 0, what is the value of (8x)°?

5. (a) If m = –3 and n = 2, what is the value of mn.
(b) If 4y – 1 = 19, find the value of y.

Group-B (17 × 2 = 34)

6. (a) Find the value of x from the given figure.

(b) Write two distinct properties of rectangle and parallelogram.

A

(c) In given figure, M is the mid-point of side BC and AM A BC,
by what axiom ∆ABM and ∆ACM are congruent. If AB = 5 cm,
what is the length of AC?
BMC

7. (a) In the given figure, AB // CD, show that ∆AOB a ∆COD. AB
O

CD

Vedanta Excel in Mathematics - Book 8 320 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Model Questions

(b) If the area of a circular meadow is 154 m2, what is its radius? (S = 22 )
7

(c) Draw the net of a cylinder.

8. (a) If the distance between the points (0, 6) and Q (x, 0) is 5 units, find the value
of x.

(b) If the length and breadth of rectangular meadow is 16m and 12m, what is the
length of its diagonal?

(c) If M = {natural numbers less than 6} and N = {first five even numbers}, find
M ª N and show it in a Venn-diagram.

9. (a) Change 1100112 into denary number system.

(b) There are 80 students in a class. If 4 of them are absent, find the percentage of
present students.

(c) Find the median of the data given below:

30, 10, 40, 20, 60, 50, 80, 70, 90

10. (a) Show a2 – b2 = (a + b) (a – b) in a diagram.

(b) Simplify: xa+b-c × xc-a-b × 1a+b+c
x0

(c) Prove that: 3p+1 – 3p = 1
2 × 3p

11. (a) Solve the inequality and show it in a number line: 2x – 3 ≤ 7.

(b) Solve: x2 – 1 = 5
3

Group-C (14 × 4 = 56)

12. Construct a rectangle PQRS, in which PQ = 4cm and diagonal PR = 6.2 cm.

13. Verify experimentally that the base angles of an isosceles triangle are equal. (Two
figures of different measurement are necessary)

14. The vertices of ∆PQR are P (3, 2), Q (2, 5), and R (-4, 2). Draw the ∆PQR on a graph
paper and reflect it about x – axis, find the coordinates of its image and draw it on
the same graph paper.

15. In an examination, 10% students secured A+ grade in Mathematics, 15% secured
A+ grade in Science, and 5% secured A+ grade in both the subjects.

(i) Sketch a Venn-diagram to show the above information.

(ii) What percent of students secured grades other than A+ in both the subjects?

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 321 Vedanta Excel in Mathematics - Book 8

Model Questions

16. The length of a hall is three times and width is two times of its height. If the room
contains 384 cubic metres of air, find the area of its floor.

17. The marked price of a mobile set is Rs 11,000. If it is sold at 20% discount and
levying 13% value added tax, find the selling price of the mobile set after value
added tax.

18. 20 men can complete a piece of work in 24 days, how many men should be left the
work so that it would complete in 32 days?

19. Mr. Suresh took a loan from an Agricultural Development Bank to start his fish
farming. If he paid Rs. 5454 and cleared his debt in 2 years 6 months at the rate of
8% per annum, how much loan was taken by him?

20. Simplify: 6 – 16 + 2 50 – 3 8
2 32

21. Find the arithmetic mean from the data given below.

Marks obtained 50 60 70 80 90

No. of students 7 4 14 11 4

22. If a + 1 = 5 , prove that: (i) a2 + 1 = 23 (ii) a3 + 1 = 110
a a2 a3

23. Find the highest common divisor of: x2 – 4, x3 + x2 – 6x and x4 – 8

24. Simplify: x 2 1 + 2x – x2 + 3
+ x–1 x2 – 1

25. Solve the equations 2x – y = 5 and x – 1 = y by graphical method.

Vedanta Excel in Mathematics - Book 8 322 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur