QUEST BOOK - ICSE 8 Maths Part 1.cdr

MATHEMATICSWORKSHEETS AND ASSIGNMENTS

8C.B.S.E.

QUESTION BANK: A CREATION OF QUEST CLASSES EXCLUSIVELY FOR QUEST STUDENTS

RATIONAL NUMBERS

EXERCISE 1: COMPARISON OF RATIONAL NUMBERS 1. Which of the two rational numbers in each of the following pairs of rational numbers is greater?

(I) 3/8 or 0

(ii) (-3)/8 or 0

(iii) (-2)/9 or 0

(iv) 2/5 or 0

(v) (-3)/4 or ¼

(vi) (-4)/11 or 3/11

(vii) (-5)/7 or (-4)/7

(viii) (-7)/12 or 5/(-8)

(ix) 2/3 or 3/4

(x) 4/(-9) or (-3)/(-7)

(xi) (-1)/2 or -1

(xii) (-5)/8 or 3/(-4)

(xiii) 5/9 or (-3)/(-8)

(xiv) 5/(-8) or (-7)/12

2. Arrange the following rational number ascending order:

(I) 2/3, 5/7, (-4)/(-9), 1/4

(ii) 4/(-9), (-5)/12, 7/(-18), (-2)/3

(iii) 3/5, (-17)/(-30), 8/(-15), (-7)/10

(iv) (-3)/4, 5/(-12), (-7)/16, 9/(-24)

(v) (-4)/9, 5/(-12), 7/(-18), 2/(-3)

(vi) 3/(-5), (-7)/10, (-11)/15, (-13)/20

(vii) 2/3, (-4)/7, (-8)/3, 6/(-9)

(viii) (-4)/7, (-9)/14, 13/(-28), (-23)/42


EXERCISE 2: ADDITION AND SUBTRACTION OF RATIONAL NUMBER

1. Add the following rational numbers:

(I) -5/7 and 3/7 (ii) -15/4 and 7/4

(iii) -8/11 and -4/11 (iv) 6/13 and -9/13

2. Add the following rational numbers:

(I) 3/4 and -3/5 (ii) -3 and 3/5

(iii) -7/27 and 11/18 (iv) 31/-4 and -5/8

3. Verify the following:

(I) (3/4 + -2/5) + -7/10 = 3/4 + (-2/5 + -7/10)

(ii) (-7/11 + 2/-5) + -13/22 = -7/11 + (2/-5 + -13/22)

(iii) -1 + (-2/3 + -3/4) = (-1 + -2/3) + -3/4

4. Subtract the following rational numbers:

(I) 3/4 from 1/3

(ii) -5/6 from 1/3

(iii) -8/9 from -3/5

(iv) -9/7 from -1

(v) -18/11 from 1

(vi) -13/9 from 0

(vii) -32/13 from -6/5

(viii) -7 from -4/7

5. The sum of two rational numbers is -2. If one of the numbers is -14/5, �ind the other.

6. The sum of two rational numbers is -1/2. If one of the numbers is 5/6 �ind the other.

7. What number should be added to -5/8 so as to get -3/2?

8. What number should be added to -1 so as to get 5/7?

9. What number should be subtracted from -2/3 to get -1/6?

10. Is the difference of two rational numbers a rational number?

11. What is the negative of a negative rational number?


EXERCISE 3: REPRESENTATION OF RATIONAL NUMBER ON A NUMBER LINE

1. Draw the number line and represent the following positive rational numbers on it:

(i) 1/3

(ii) 2/3

(iii) 2/7

(iv) 3/4

(v) 3/8

3(vi) 1 /4

2(vii) 2 /5

1(viii) 3 /2

5(ix) 5 /7

2(x) 4 /3

(xi) 8

(xii) 7/9

2. Represent each of the following negative rational numbers on the number line:

(i) (-5)/8

(ii) (-3)/16

(iii) (-1)/3

(iv) -3/4

(v) (-7)/3

(vi) 22/(-7)

(vii) (-31)/3

2(viii) -1 /3

1(ix) -3 /7

3(x) -4 /5

5(xi) -2 /6

(xii) -3

7(xiii) -2 /8

2(xiv) -5 /5


EXERCISE 4: WORD PROBLEMS ON RATIONAL NUMBERS

1. From a rope 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope?

2. A drum full of rice weighs 241/6 kg. If the empty drum weighs 55/4 kg, �ind the weight of rice in the drum.

3. A basket contains three types of fruits weighing 58/3 kg in all. If 73/9 kg of these be apples, 19/6 kg be oranges and the rest pears. What is the weight of the pears in the basket?

4. On one day a rickshaw puller earned $80. Out of his earnings he spent $68/5 on tea and snacks, $51/2 on food and $22/5 on repairs of the rickshaw. How much did he save on that day?

5. Find the cost of 17/5 meters of cloth at $147/4 per meter.

6. A car is moving at an average speed of 202/5 km/hr. How much distance will it cover in 15/2 hours?

7. Find the area of a rectangular park which is 183/5 m long and 50/3 m broad.

8. Find the area of a square plot of land whose each side measures 17/2 meters.

9. One liter of petrol costs $187/4. What is the cost of 35 liters of petrol?

10. An airplane covers 1020 km in an hour. How much distance will it cover in 25/6 hours?

11. The cost of 7/2 meters of cloth is $231/4. What is the cost of one meter of cloth?

12. A cord of length 143/2 m has been cut into 26 pieces of equal length. What is the length of each piece?

13. The area of a room is 261/4 m2. If its breadth is 87/16 meters, what is its length?

14. The product of two rational numbers is 48/5. If one of the rational number is 66/7, �ind the other rational number.

15. Rita had $300. She spent 1/3 of her money on notebooks and 1/4 of the remainder on stationery items. How much money is left with her?

16. Adrian earns $16000 per month. He spends 1/4 of his income on food; 3/10 of the remainder on house rent and 5/21 of the remainder on the education of children. How much money is still left with him?

1. Find out a rational numbers lying between 1/4 and 1/3.

2. Find out a rational number lying between 2 and 3.

3. Find out a rational number lying between -1/3 and 1/2.

4. Find out two rational numbers lying between -3 and -2.

5. Find out six rational numbers lying between -4/8 and 3/8.

6. Find out ten rational numbers lying between 7/13 and -4/13. 7. Find out three rational numbers lying between 4 and 5.

8. Find out three rational numbers lying between 2/3 and 3/4.

EXERCISE 5: FINDING RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS


EXERCISE 6: OPERATIONS ON RATIONAL EXPRESSIONS

1. Simplify the following rational numbers:

(I) (25/8 × 2/5) – (3/5 × -10/9)

(ii) (1/2 × ¼) + (1/2 × 6)

(iii) (-5 × 2/15) – (-6 × 2/9)

(iv) (-9/4 × 5/3) + (13/2 × 5/6)

2. Simplify the rational expressions:

(I) (3/2 × 1/6) + (5/3 × 7/2) – (13/8 × 4/3)

(ii) (1/4 × 2/7) – (5/14 × -2/3) + (3/7 × 9/2)

(iii) (13/9 × -15/2) + (7/3 × 8/5) + (3/5 × ½)

(iv) (3/11 × 5/6) – (9/12 × 4/3) + (5/13 × 6/15)

3. Find the value and express as a rational number in standard form:

(I) 2/5 ÷ 26/15

(ii) 10/3 ÷ (-35/12)

(iii) -6 ÷ (-8/17)

(iv) 40/98 ÷ (-20)

4. By what number should we multiply -15/28, so that the product may be -5/7?

5. By what number should we multiply -8/13, so that the product may be 24?

6. By what number should -3/4 be multiplied in order to produce 2/3?

7. Find (m + n) ÷ (m – n), if

(i) m = 2/3, n = 3/2

(ii) m = 2/5, n = 1/2

(iii) m = 5/4, y = -1/3

8. The cost of 7 2/3 meters of rope is $12 3/4. Find its cost per meter.

9. The cost of 2 1/3 meters of rope is $75 1/4. Find cost of cloth per meter.

10. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.

11. Divide the sum of 65/12 and 8/3 by their difference.

12. If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of the cloth is required for each trouser?

13. Divide the sum of 13/5 and -12/7 by the product of -31/7 and 1/-2.

14. Divide the sum of 65/12 and 8/3 by their difference.


ANSWERS

EXERCISE 1

1. (I) 3/8

(ii) 0

(iii) 0

(iv) 2/5

(v) 1/4

(vi) 3/11

(vii) (-4)/7

(viii) (-7)/12

(ix) 3/4

(x) (-3)/(-7)

(xi) (-1)/2

(xii) (-5)/8

(xiii) 5/9

(xiv) (-7)/12

2. (I) 1/4 < (-4)/9 < 2/3 < 5/7

(ii) (-2)/3 < 4/(-9) <(-5)/12 < 7/(-18)

(iii) (-7)/10 < 8/(-15) < (-17)/(-30) < 3/5

(iv) (-3)/4 < (-7)/16 < 5/(-12) < 9/(-24)

(v) 2/(-3) < (-4)/9 < 5/(-12) < 7/(-18)

(vi) (-11)/15 < (-7)/10 < (-13)/20 < 3/(-5)

(vii) (-8)/3, 6/(-9), (-4)/7, 2/3

(viii) (-9)/14 < (-4)/7 < (-23)/42 < 13/(-28)

EXERCISE 2

1. (I) -2/7

(ii) -2

(iii) -12/11

(iv) -3/13

2. (I) 3/20

(ii) -12/5

(iii) 9/54

(iv) -67/6

4. (I) -5/12

(ii) 7/6

(iii) 13/45

(iv) 2/7

(v) 29/11

(vi) 13/9

(vii) 82/65

(viii) 45/7

5. 4/5

6. -4/3

7. -7/8

8. 12/7

9. -1/2

10. Yes

11. The number itself.

EXERCISE 4

1. 51/10 m

2. 317/12 kg

3. 145/18 kg

4. $73/2

5. $2499/20

6. 303 km

7. 610 m2

8. 289/4 m2

9. $6545/4

10. 4250 km

11. $33/2

12. 11/4 m

13. 12 m

14. 56/55

15. $150

16. $6400QUESTION BANK: A CREATION OF QUEST CLASSES EXCLUSIVELY FOR QUEST STUDENTS

EXERCISE 5

1. 7/24

2. 5/2

3. 1/12

4. -5/2, -9/4

5. -3/8, -2/8, -1/8, 0/8, 1/8, 2/8

6. -3/13, -2/13, -1/13, 0/13, 1/13, 2/13, 3/13, 4/13, 5/13, 6/13

7. 17/4, 9/2, 19/4

8. 33/48, 17/24, 35/48

EXERCISE 6

1. (I) 23/12

(ii) 25/8

(iii) 2/3

(iv)5/3

2. (I) 47/12

(ii) 47/21

(iii) -34/5

(iv) -177/286

3. (I) 3/13

(ii) -8/7

(iii) 51/4

(iv) -1/49

4. 4/3

5. -39

6. -8/9

7. (I) -13/5

(ii) -9

(iii) 11/19

8. $1 61/92

9. $32 1/4

10. -2/5

11. 97/33

12. 9/4 meters

13. 2/5

14. 97/33

SQUARES AND SQUARE ROOTS

EXERCISE 1: PROPERTIES OF SQUARES

1. Using the prime factorization method, �ind which of the following numbers are perfect squares:

(I) 225

(ii) 189

(iii) 441

(iv) 729

(v) 1575

(iv) 900

2. Show that none of the following is a perfect square: Give reason in each case.

(I) 62

(ii)143

(iii) 217

(iv) 168

(v) 90

(vi) 4000

3. Which of the following are the squares of even numbers?

(I) 196

(ii) 441

(iii) 400

(iv) 324

(v) 625

(vi) 169

4. Which of the following are the squares of odd numbers?

(I) 121

(ii) 225

(iii) 196

(iv) 484

(v) 529

2


5. Evaluate:

(I) (38)² - (37)²

(ii) (75)² - (74)²

(iii) (92)² - (911)²

(iv) (105)² - (194)²

(v) (141)² - (140)²

(vi) (218)² - (217)²

6. Without adding, �ind the sum:

(i) (1 + 3 + 5 + 7 + 9 + 11)

(ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)

(iii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)

7. (i) Express 64 as the sum of eight odd numbers.

(ii) Express 121 as the sum of eleven odd numbers.

8. Write a Pythagorean triplet whose smallest member is

(I) 6

(ii) 14

(iii) 16

(iv) 20

9. Fill in the blanks:

(i) The square of an even number is …………………

(ii) The square of an odd number is …………………

(iii) The square of a proper fraction is ………………… than the given fraction.

(iv) n² = the sum of �irst n ………………… natural number.

10. Show that 1450 is not a perfect square.

11. Is 15625 a perfect square?

12. Write (T) for true and (F) for false for each of the statements given below:

(i) The number of digits in a perfect square is even.

(ii) The square of a prime number is prime.

(iii) The sum of two perfect squares is a perfect square.

(iv) The difference of two perfect squares is a perfect square.

(v) The product of two perfect squares is perfect square.


EXERCISE 2: SQUARE ROOT USING PRIME FACTORIZATION METHOD

Find the square root of each of the following numbers by using the method of prime factorization:

1. 225

2. 441

3. 729

4. 1296

5. 2025

6. 4096

7. 7056

8. 8100

9. 9216

10. 11025

11. 15876

12. 17424

13. Find the smallest number by which 1008 must be multiplied to get a perfect square. Also, �ind the square root of the perfect square so obtained.

14. 1225 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

15. The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1156, �ind the strength of the class.

16. Find the smallest number by which 768 must be multiplied to get the perfect square number.

Evaluate using long division method:

1. √56

2. √1444

3. √4489

4. √6241

5. √7056

6. √9O25

7. √11449

8. √14161

9. √10404

10. √7956

11. √19600

12. √92416

13. Find the least number which must be subtracted from 8105 to make it a perfect square.

14. Find the least number which must be subtracted from 7060 to obtain a perfect square.

15. Find the least number which must be added to 306455 to obtain a perfect square.

16. Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root.

17. Find the least number of four digits (4 digits) which is a perfect square. Also �ind the square root of the number so obtained.

18. Find the greatest number of �ive digits (5 digits) which is a perfect square. Also �ind the square root of the number so obtained.

EXERCISE 3: SQUARE ROOT USING LONG DIVISION METHOD


EXERCISE 4: SQUARE ROOT OF NUMBERS IN DECIMAL

Evaluate the square root of the following numbers in decimal form:

1. √1.69

2. √33.64

3. √156.25

4. √75.69

5. √9.8596

6. √10.0486

7. √1.0816

8. √0.2916

9. Evaluate √3 up to two places of decimal.

10. Evaluate √2.8 correct up to two places of decimal.

11. Evaluate √0.9 correct up to two places of decimal.


ANSWERS

EXERCISE 1

1. (I), (iii), (iv), (vi)

3. (I), (iii), (iv)

4. (I), (ii), (v)

5. (I) 75

(ii) 149

(iii) 183

(iv) 209

(v) 281

(vi) 435

6. (I) 36

(ii) 100

(iii) 14427. (i) 64 = 8 = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15)

2(ii) 121 = (11) = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21)

8. (i) (6, 8, 10)

(ii) (14, 48, 50)

(iii) (16, 63, 65)

(iv) (20, 99, 101)

9. (I) even

(ii) odd

(iii) smaller

(iv) odd

10. ending in one zero

11. Yes

12. (I) False

(ii) False

(iii) False

(iv) False

(v) True

EXERCISE 2

1. 15

2. 21

3. 27

4. 36

5. 45

6. 64

7. 84

8. 90

9. 96

10. 105

11. 126

12. 132

13. 7, 84

14. 35, 35

15. 34

16. 3

EXERCISE 3

1. 24

2. 38

3. 67

4. 79

5. 84

6. 95

7. 107

8. 119

9. 102

10. 134

11. 140

12. 304

13. 5

14. 4

15. 461

16. 64, 8464, 92

17. 1024, 32

18. 99856, 316

EXERCISE 4

1. 1.3

2. 5.8

3. 12.5

4. 8.7

5. 3.14

6. 3.17

7. 1.04

8. 0.54

9. 1.73

10. 1.67

11. 0.95QUESTION BANK: A CREATION OF QUEST CLASSES EXCLUSIVELY FOR QUEST STUDENTS

CUBES AND CUBE ROOTS

EXERCISE 1: CUBES AND CUBE ROOTS

A. Evaluate the cube root:

1. ∛64

2. ∛343

3. ∛729

4. ∛1728

5. ∛9261

6. ∛4096

7. ∛8000

8. ∛3375

9. ∛-216

10. ∛-512

11. ∛-1331

12. ∛(27/64)

13. ∛(125/216)

14. ∛(-27/125)

15. ∛(-64/343)

16. ∛1331

17. ∛(64 × 729)

18. ∛(729/1000 )

19. ∛(-512/343)

20. ∛6859

B. Find the cube roots of:

1. 1

2. 8

3. 343

4. 512

5. 64

3

6. 3375

7. 1728

C. Find the cube roots of:

1. -1

2. -125

3. -216

4. -512

5. -8000

6. -27000

7. -3375

D. Find the cube roots of:

1. 1/8

2. 3³/₈

3. 54/250

4. 15⁵/₈

5. 64/27

6. 4¹⁷/₂₄

7. -8/27


ALGEBRAIC EXPRESSIONS

EXERCISE 1: TYPES OF ALGEBRAIC EXPRESSIONS

1. State whether the following statements are true or false:

2(i) Expression 5a + a is a trinomial

2(ii) Expression ax + bx + c is a trinomial

(iii) 5 × mn is a binomial

(iv) 11 + xy is a binomial

3(v) a – 3ab + 7a + 9 is a polynomial

3(vi) 2x + 7xy + 3x + 2 is a multinomial

2 4 5(vii) 1 + 2x + 3x + x + x is a binomial

2 2 2(viii) p + q + r is a trinomial

2. Which of the following expressions are polynomials?

(i) 10 – 13x

2 5(ii) z + z + z - 7

2 3 4(iii) 1 + 1/a + 1/a + 1/a +1/a

2(iv) (m + m – 2)/(m – 3)

(v) 1/2 – 5/(4 + u)

(vi) 1 + 5m

2(vii) 1 + 5u + 4u

(viii) 1/√x + 5

3. For each expression, given below, state whether it is a monomial, binomial or trinomial:

(i) mn

(ii) mn + m

(iii) 2a ÷ b

(iv) 7abc

(v) 7 + u + v

2(vi) 2p – p

(vii) –k

2(viii) ax + bx – 7

4


(ix) -3mn + t

(x) 1 + a + z

(xi) 1 + a ÷ z

2(xii) a + ab – b

4. Identify the following expressions are monomials, binomials, trinomials, polynomials:

(i) 11pqr

(ii) m + 2n

(iii) a + b + c

2 5 7 9(iv) 1 – m + m + m – m + m

(v) 2ab + c

3(vi) 1 + 3a + 4a

1. Solve the following polynomials:

(i)Take –pq + qr – rp from qr – rp + pq

(ii) Take 5a + 6b – 3c from 3a + 5b – 4c

2. (i) How much is -3k less than 3k?

(ii) How much is 2a + b greater than a – 2b?

(iii) What should be added to 2p – q + r to make it p + q – 2r?

3. From the sum of 3x - 2y + 4z and 3y – 2z, subtract x - y - z.

4. Subtract a – 2b – c from the sum of 3a – b + c and a + b – 3c.

5. How much should a + 2b – 3c be increased to get 3a?

2 2 2 26. The sum of two expressions is 3x + 2xy – y . If one of them is 2x + 3y , �ind the other.

2 2 2 2 2 2 2 27. From the sum of 4b + 5bc, -2b – 2bc – 2z and 2bc + 4c , subtract the sum of 5b – c and -3b + 2bc + c .

8. What should be subtracted from 3x + 5y + 9 to get - 2x + 3y + 15?

2 2 2 29. What should be taken away from p – q + 2pq + 10 to obtain – 2p – 2q + 7pq + 10?

2 2 2 210. By how much must 5p – 3q be diminished to give 2p + q ?

2 311. Subtract 2m – 5q + 7 from 4p + 2q and add your result to m – 3m + m - 1.

2 2 2 2 212. Subtract 2a b – 3b from 3a – 5ab + 2b and subtract your result from the sum of the two expressions 2 2 2 2 2 2

3ab + 5b – 2a b and a b + 5a – 3ab .

EXERCISE 2: ADDITION AND SUBTRACTION OF POLYNOMIALS


EXERCISE 3: FACTORING ALGEBRAIC EXPRESSION

1. Write all the possible factors of:

a. 4x

b. 10xy

2c. 12xy

2d. 24x y

2 2e. 5xy z

2. Find the H.C.F. of the monomials:

2(a) 4x and 10xy

2 2(b) 21a b and 49ab

3 2 2(c) x y and – 5y

3 2(d) 4x , 6y and 8z

2 3 3 2(e) 2x y , 10x y and 14xy

3 2(f) 5x , -15x and 45x

3. Find the common factors of the given terms.

2(a) 3x , 15xy

2 2(b) 33x y, - 77xy

2 2 2(c) 9x y z, 54xyz

3 2 2(d) x y , - 5y

3 3 3(e) 4x , 10y , 6z

3 2 2(f) 2xyz , 3x y z, 5xyz

4. Find the H.C.F. of the terms of the expression:

2 3 4(a) – 2x - 8x - 20x

2 2 2 2(b) 3xy + 9x y – 6x y

2(c) 5x + 25x + 50

3 2 2(d) x y – 8y

5. Find the factors of the expression:

4 5 3(a) 3x – 9x – 15x

3 3 2 3(b) – 10ab + 30ba – 50a b

2 2 2(c) 15a – 20b + 25c

3 3 3(d) x yz + 5xy + 9x y

2 2 3(e) 3x – 9x y - 27x z

3 2 2(f) 7x + 7xy + 7xz


ANSWERS

EXERCISE 1

11. (I) false

(ii) true

(iii) false

(iv) true

(v) true

(vi) true

(vii) false

(viii) true

2. (I) polynomial

(ii) polynomial

(iii) not polynomial

(iv) not polynomial

(v) not polynomial

(vi) polynomial

(vii) polynomial

(viii) not polynomial

3. (I) monomial

(ii) binomial

(iii) monomial

(iv) monomial

(v) trinomial

(vi) binomial

(vii) monomial

(viii) trinomial

(ix) binomial

(x) trinomial

(xi) binomial

(xii) trinomial

4. (I) monomial

(ii) binomial

(iii) trinomial

(iv) polynomial

(v) binomial

(vi) trinomial

EXERCISE 2

1. (I) 2pq

(ii) -2a – b - c

2. (I) 6k

(ii) a + 3b

(iii) -p + 2q – 3r

3. 2x + 2y + 3z

4. 3a + 2b - c

5. 2a – 2b + 3c2 2

6. x + 2xy – 4y

27. 3bc + 2c

8. 5x + 2y - 6

2 29. 3p + q – 5pq

2 210. 3p – 4q

2 311. 4p + 7q – m + m – 3m - 8

2 2 212. 2a + a b + 5ab

EXERCISE 3

1. a. 1, 4, x, 4x

b. 1, 2, 5, 10, x, y, xy, 2x, 2y, 2xy, 5x, 5y, 5xy, 10x, 10y, 10xy

2 2c. 1, 2, 3, 4, 6, 12, x, y, y , xy , 2 2

xy, 2x, 2y, 2y , 2xy, 2xy , 3x, 2 2 23y, 3y , 3xy, 3xy , 4x, 4y, 4y ,

2 24xy, 4xy , 6x, 6y, 6y , 6xy,

2 26xy , 12x, 12y, 12y , 12xy 2

and 12xy

d. 1, 2, 3, 4, 6, 8, 12, 24, x, 2 2 2x , y, xy, xy , 2x, 2x , 2y, 2xy,

2 2 22xy , 3x, 3x , 3y, 3xy, 3xy ,

2 2 24x, 4x , 4y, 4xy, 4xy , 6x, 6x , 2 2

6y, 6xy, 6xy , 8x, 8x , 8y, 2 2

8xy, 8xy , 12x, 12x , 12y, 2 212xy, 12xy , 24x, 24x , 24y,

224xy and 24xy .

2 2 2e. 1, 5, x, y, y , z, z , xy, xy , yz,

2 2 2 2 2yz , xz, xz , y z , 5x, 5y, 5y , 2 2 2

5z, 5z , 5xy, 5xy , 5yz, 5yz , 2 2 25xz, 5xz , 5y z .

2.(a) 2x

(b) 7ab

2(c) y

(d) 2

(e) 2xy

(f) 5x

3. (a) 3x

(b) 11xy

(c) 9xyz

2(d) y

(e) 2

(f) xyz

24. (a) -2x

(b) 3xy

(c) 5

2(d) y

3 25.(a) 3x (x - 3x - 5)

2 2 2(b) -10ab(b - 3a + 5ab )

2 2 2(c) 5(3a - 4b + 5c )

2 3 2(d) x(x yz + 5y + 9x z)

2(e) 3x (1- 3y - 9xz)

2 2 2(f) 7x(x + y + z )


EXPONENTS

EXERCISE 1: EXPONENTS

1. Evaluate:

-3(i) 4

-5(ii) (1/2)

-3(iii) (4/3)

-4(iv) (-3)

-5(v) (-2/3)

2. Evaluate:

2 2(i) (5/3) × (5/3)

6 -4(ii) (5/6) × (5/6)

-3 -2(iii) (2/3) × (2/3)

-3 2(iv) (9/8) × (9/8)

3. Evaluate:

-2 -3 0(i) (5/9) × (3/5) × (3/5)

-4 2(ii) (-3/5) × ( -2/5)

-3 -2(iii) (-2/3) × (-2/3)

4. Evaluate:

2 -2(i) {(-2/3) }

2 -2 -1(ii) [{(-1/3) } ]

-2 2(iii) {(3/2) }

-3 -3 -35. Evaluate: {(1/3) - (1/2) } ÷ (1/4)

-1 -1 -16. Evaluate: {(4/3) – (1/4) }

-1 -1 -1 -17. Evaluate: [5 × 3 ] ÷ 6 ]

-4 -5 3x8. Find the value of x for which (5/3) × (5/3) = (5/3)

4 -7 2x - 19. Find the value of x for which (4/9) × (4/9) = (4/9)

-1 -110. By what number should (-6) be multiplied so that the product becomes 9 ?

-3 -211. By what number should (-2/3) be divided so that the quotient may be (4/27) ?

2x + 112. If 5 ÷ 25 = 125, �ind the value of x.

5


LINEAR EQUATIONS

EXERCISE 1: SOLVING LINEAR EQUATIONS

Solve the following equations and check the result:

6


EXERCISE 2: WORD PROBLEMS BASED ON LINEAR EQUATIONS

1. Convert the following statements into equations. (a) 5 added to a number is 9. (b) 3 subtracted from a number is equal to 12. (c) 5 times a number decreased by 2 is 4. (d) 2 times the sum of the number x and 7 is 13.

2. A number is 12 more than the other. Find the numbers if their sum is 48.

3. Twice the number decreased by 22 is 48. Find the number.

4. Seven times the number is 36 less than 10 times the number. Find the number.

5. 4/5 of a number is more than 3/4 of the number by 5 . Find the number.

6. The sum of two consecutive even numbers is 38. Find the numbers.

7. The sum of three consecutive odd numbers is 51. Find the numbers.

8. Rene is 6 years older than her younger sister. After 1 0 years, the sum of their ages will be 50 years. Find their present ages.

9. The length of a rectangle is 10 m more than its breadth. If the perimeter of rectangle is 80 m, �ind the dimensions of the rectangle.

10. A 300 m long wire is used to fence a rectangular plot whose length is twice its width. Find the length and breadth of the plot.

11. The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2, �ind the fraction.

12. A sum of $2700 is to be given in the form of 63 prizes. If the prize is of either $100 or $25, �ind the number of prizes of each type.

13. In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.

14. Among the two supplementary angles, the measure of the larger angle is 36° more than the measure of smaller. Find their measures.

15. My mother is 12 years more than twice my age. After 8 years, my mother’s age will be 20 years less than three times my age. Find my age and my mother’s age.

16. In an isosceles triangle, the base angles are equal and the vertex angle is 80°. Find the measure of the base angles.

17. Adman’s father is 49 years old. He is 5 years older than four times Adman’s age. What is Adman’s age?

18. The cost of a pencil is 25 cents more than the cost of a eraser. If the cost of 8 pencils and 10 erasers is $12.80, �ind the cost of each.

19. Divide 36 into two parts in such a way that 1/5 of one part is equal to 1/7 of the other.

20. The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. Find the length and breadth of the given rectangle.


ANSWERS

EXERCISE 1

I. 1. x = 3

2. x = 5/4

3. x = -3/2

4. x = -2/5

5. x = 1/2

6. x = 3/2

7. x = 17/36

8. x = 25/4

9. x = 1/4

10. x = 11/7

11. y = 14

12.m = 20/7

13. x = -3/13

14. t = -17

15. x = -7

16. x = 6

17. x = 0

18. y = 2

19. x = -1

20. x = 1

21. y = -1/4

22. x = 96/13

23. x = -2/7

24. x = 11/7

25. x = 113/6

26. x = 248/43

27. x = 72/7

28. x = 3.3

29. x = 2.1

30. x = 0.8

31. x = 18/5

32. x = -15/13

EXERCISE 2

1. (a) x + 5 = 9 (b) x - 3 = 12(c) 5x - 2 = 4 (d) 2(x + 7) = 13

2. 18, 30

3. 35

4. 12

5. 100

6. 18, 20

7. 15, 17, 19

8. 12, 18 years

9. 15 cm, 25 cm

10. 50 m, 100 m

11. 13/21

12. 15, 48

13. 30 girls, 12 boys

14. 72°, 108°

15. 16 years, 44 years

16. 50°

17. 11 years

18. eraser – 60 cents, pencil – 85 cents

19. 15, 21

20. length = 18 m, breadth = 15 m


PERCENT AND PERCENTAGES

EXERCISE 1: FINDING PERCENT OF A NUMBER

1. Find the following:

(i) 22 % of 140

(ii) 25 % of $ 750

(iii) 16.5 % of 5000 kg

(iv) 21/2 % of 80 l

(v) 0.4 % of 8 km

(vi) 120 % of 1000

(vii) 12 % of 360 m

(viii) 22/7 % of 7 l

(ix) 0.8 % of 250 g

(x) 3/4 % of $ 780

(xi) 12 % of 620

(xii) 1.25 % of 1250 mg

(xiii) 31/4 % of $ 5000(xiv) 3/5 % of 725 cm

(xv) 31/3 % of 90 km

2. What is 5 % of $ 1400?

3. What is 7 % of $ 7150?

4. What is 40 % of 400 kg?

5. How many liters is 20 % of 15.125 liters?

6. In a public show 75 % of seats were �illed. If there were 600 seats in the hall, how many seats were vacant?

7. A man earns $3580 per month and spends 65 % of it. How much money does he save every month?

8. To clear his stock a shopkeeper offers a discount of 15 %. Find the discount on goods worth $500?

9. An alloy of copper and zinc contains 45 % of copper and the rest is zinc. Find the weight of the zinc in 2 kg of the alloy?

10. In an exam, 85 % of the children pass. Find the number of children who passed, if there were 1700 children.

7


EXERCISE 2: FINDING PERCENT

1. What percent of 130 liters is 6.5 liters?

2. What percent of 5 kg is 200 g?

3. What percent is?

(i) $30 of $150

(ii) 160 m of 4 km

(iii) 8 litres of 24 litres

(iv) 62/3 g of 900 g

(v) 60 cm of 5 m

(vi) 3 hour of 24 hours

4. Express the following:

(i) 120 cm as percent of 5 m

(ii) 240 g as percent of 4 kg

(iii) 60 cents as percent of $3

(iv) 240 as percent of 800

(v) 12 hours as percent of 3 days

(vi) 33 cents as percent of $8.25

(vii) 2.7 mm as percent of 10.8 cm

(viii) 12 weeks as percent of 1 year

(ix) 50 cm as percent of 4 m


(i) 8 is _____ % of 24.

(ii) 3.5 kg is _____ % of 35 kg.

(iii) 60 litres is _____ % of 125 litres.

(iv) $10.28 is _____ % of $41.12.

6. An oil tanks contains 16 litres of oil. Due to leakage 2 litres of oil is lost. What percent of oil is lost?

7. Out of $20 pocket money, Ron spends $14. Express this as a percentage.

8. In a class of 48 students, 4 are absent. What percent is absent?

9. In a school there are 1000 boys and 800 girls. Calculate the percentage of boys and girls in that school.

10. Out of a group of 250 pupils, 10 pupils could not join the school’s excursion due to illness. What percent of the group went to the excursion?


EXERCISE 3: FINDING VALUE OF A PERCENTAGE

1. Find x if:

(i) 9 % of x is $36

(ii) 1/2 % of x is 250

(iii) 4.3 % of x is 86 kg

(iv) 62 % of x is 372

(v) 70 % of x is 14 minutes

(vi) 25 % of x is 30 days

2. Find the number whose 13 % is 780.

3. If 2.5 % of a number is 400, �ind the number.

4. Find the number if 12 % of it is 144.

5. Find the number if 2.3 % of it is 920.


(i) 25 is 10 % of ____.

(ii) 78 is 30 % of ____.

(iii) $102 is 24 % of ____.

(iv) 144 kg is 36 % of ____.

7. Find the number whose 12 1/2 % is 64.

8. What is the number, 6 1/4 % of which is 2?

9. If 6 is 50 % of a number, what is that number?

10. Find the following:

(i) 8 is 4 % of which number.

(ii) 6 is 60 % of which number.

(iii) 6 is 30 % of which number.

(iv) 12 is 25 % of which number.


EXERCISE 4: PERCENTAGE OF A GIVEN QUANTITY

1. If a man spends 70 % of his income, what % does he save?

2. A girl gets 65 marks out of 80. What percent marks did she get?

3. An alloy contains 64 % of zinc. How many kg of alloy is required to get 372 kg of zinc?

4. A classroom contains 25 children, out of which 6 are girls. What percentage of the class are boys?

5. Steve deposits $ 1800 per month in his savings bank account. If this is 20 % of the monthly income, �ind his monthly income. 6. A tin contains 20 litres of petrol. Due to leakage, 3 litres of petrol is lost. What percent is still present in the tin?

7. In an election, a candidate got 82 % votes. He won the election beating his rival candidate by 576 votes. How many votes were polled?

8. A boy got 60 out of 80 in French, 70 out of 90 in English and 35 out of 40 in Mathematics. In which subject his percentage of marks is best?

9. Arthur did not go to school for 36 days in a year. If his absence from school is 15 %, �ind the number of days the school opened.

10. In a camp, there were 500 solders. 60 more solders joined them. What percent of the earlier (original) number have joined?

11. Gunpowder contains 65 % nitre, 15 % sulphur and the rest of it is charcoal. Find the amount of nitre, sulphur and charcoal in 8 kg of gun powder.

12. In a plot of ground of area 6000 sq. m, only 4500 sq. m. is allowed for construction. What percent is to be left without construction?

13. In a school there are 1800 boys and 1200 girls. In an exam only 32 % of the boys passed and 50 % of the girls passed. Find the percentage of the total who did not pass.

14. Mr. Baker has a monthly salary of $ 7,500. If he spends $ 6,250 every month; �ind:

(i) his expenditure as percent.

(ii) his savings as percent.

(iii) his total savings in one year.

15. Thomas scored 90 % marks in maths, 85 % in science, 80 % marks in social sciences and 75 % in languages. If the maximum mark in maths is 200, in science 150, in social sciences 150 and languages 100, �ind his aggregate percentage.


EXERCISE 5: INCREASE AND DECREASE PERCENTAGE

1. Find the resulting new increased or decreased quantity due to:

(i) 8 % decrease in $ 400

(ii) 5 % increase in 25 km

(iii) 121/2 % increase in a speed of 600 km/h

(iv) 30 % decrease in a temperature of 40° Celsius

(v) 2.5 % increase in a salary of $ 1250

(vi) 2.5 % decrease in 800 gram

2. Find the percentage change from the �irst quantity to the second quantity:

(i) $75; $90

(ii) 40 cm; 60 cm

(iii) 20 gm; 5 gm

(iv) 60 km/h; 45 km/h

(v) 5 dozen eggs; 100 eggs

(vi) 13.5; 18

3. Increase 150 by 10 % and decrease the same by 15 %. Find the new number in each case.

4. The population of a place in a particular year increased by 15 %. Next year it decreased by 15%. Find the net increase or decrease per cent in the initial population.

5. While measuring a line segment of length 5 cm, it was measured 5.2 cm by mistake. Find the percentage error in measuring the line segment.

6. A number is increased by 40 % and then decreased by 40 %. Find the net increase or decrease per cent.

7. The price of wheat increased by 10 %. By how much per cent should mother reduce her consumption in the house so that her expenditure on wheat does not increase?

8. The salary of a doctor is increased by 40 %. By what per cent should the new salary be reduced in order to restore the original salary?

9. A number 75 is misread as 57. Find the reading error per cent.


ANSWERS

EXERCISE 11. (I) 30.8

(ii) $ 187.50

(iii) 825 kg

(iv) 2 l

(v) 32 m

(vi) 1200

(vii) 43.2 m

(viii) 4/25 l

(ix) 2 g

(x) $ 5.85

(xi) 74.4

(xii) 15.625 mg

(xiii) $ 162.50

(xiv) 4 .35 cm

(xv) 3 km

2. $ 70

3. $ 500.50

4. 160 kg

5. 3.025 liters

6. 150 seats

7. $ 1253

8. $ 75

9. 1.1 kg

10. 1445

EXERCISE 21. 5 %

2. 4 %

3. (I) 20 %

(ii) 4 %

(iii) 33.33 %

(iv) 20/27 %

(v) 12 %

(vi) 12.5 %

4. (I) 24 %

(ii) 6 %

(iii) 20 %

(iv) 30 %

(v) 162/3 %

(vi) 4 %

(vii) 21/2 %

(viii) 231/73 %

(ix) 121/2 %

5. (I) 33.33

(ii) 10

(iii) 48

(iv) 25

6. 12.5 %

7. 70 %

8. 8.33 %5 49. boys: 55 / %, girls: 44 / %9 9

10. 96 %

EXERCISE 31. (I) $400

(ii) 50000

(iii) 2000 kg

(iv) 600

(v) 20 minutes

(vi) 120 days

2. 6000

3. 16000

4. 1200

5. 40000

6. (I) 250

(ii) 260

(iii) $425

(iv) 400 kg

7. 512

8. 32

9. 12

10. (I) 200

(ii) 10

(iii) 20

(iv) 48

EXERCISE 41. 30 %

2. 81.25 %

3. 581.25 kg

4. 76 %

5. $9000

6. 85 %

7. 900 votes

8. Mathematics (87.5 %)

9. 240 days

10. 12 %

11. Nitre 5 kg 200 grams, sulphur 1 kg 200 grams and charcoal 1 kg 600 grams.

12. 25 %

13. 60.8 %

14. (I) 83.33 %

(ii) 162/3 %

(iii) $ 15,000

15. 83.75 %

EXERCISE 51. (i) $368

(ii) 26.25 km

(iii) 675 km/h

(iv) 28° Celsius

(v) $1281.25

(vi) 780 gram

2. (i) 20 % increase

(ii) 50 % increase

(iii) 75 % decrease

(iv) 25 % decrease2(v) 66 / % increase 3

1(vi) 33 / % increase3

3. 165, 127.5

4. 2.25 % decreased

5. 4 %

6. 16 %1

7. 9 / % 1148. 28 / %7

9. 24 %


PROFIT, LOSS AND DISCOUNT

EXERCISE 1: PROFIT AND LOSS PERCENTAGE

1. Find gain or Loss per cent when:

(a) Cost Price = $ 350 and Selling Price = $ 400

(b) Cost Price = $ 250 and Selling Price = $ 235

(c) Cost Price = $ 300 and Pro�it = $ 75

(b) Cost Price = $ 720 and Loss = $ 63

(e) Selling Price =$ 1518 and Loss = $ 132

(f) Selling price = $ 540 and Gain = $ 60

2. Find cost price when:

(a) Selling Price = $ 795 and Gain % = 6%

(b) Selling Price = $ 980 and Loss % = 12%

(c) Selling Price = $ 66.95 and Gain % = 15.25%

(d) Selling Price = $ 2640 and Loss = $ 196

(e) Selling Price = $ 216 and Loss % = 4%

(f) Selling Price = $ 504 and Gain % = 12%

3. Find selling price when

(a) Cost Price = $ 875 and Gain % = 5%

(b) Cost Price = $ 750 and Loss % = 15%

(c) Cost Price = $ 480 and Gain % = 12 ¹/₂%

(e) Cost Price = $ 675 and Loss % = 92%

(f) Cost Price = $ 1020 and Loss = $ 109

4. Andy purchased 120 pencils at the rate of $2 per pencil. He sold 72 of them at the rate of $2.5 per pencil and the remaining at the rate of $2 per pencil. Find his pro�it or loss per cent.

5. Mike sold two horses for $18000 each. On one he gained 20% and on the other he lost 20%. Find his total gain or loss.

6. A television set was bought for $3900. $200 was spent on transportation and $900 on repair. It was sold at a loss of 10%. Find the S.P. of television.

7. A bed sheet was sold for $483 thereby gaining 15%. Find the C.P. of the bed sheet.

8. Aaron bought an almirah for $1520 and sold it at a pro�it of 12 ¹/₂ %. Find the selling price of the almirah.

9. By selling a camera for $2400, Ron loses 4%. At what price must he sell it to gain 12 %.

10. By selling a stool for $240 a carpenter loses 20%. How much per cent would he gain or lose by selling it for $360?

11. The selling price of 12 eggs is equal to the cost price of 15 eggs. Find the gain per cent.

12. The cost price of 10 bananas is equal to the S.P. of 12 bananas. Find the loss per cent.

8


EXERCISE 2: DISCOUNT AND DISCOUNT PERCENTAGE

1. The marked price of a water cooler is $ 4650. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.

2. The price of a sweater was slashed from $ 960 to $ 816 by a shopkeeper in the winter season. Find the rate of discount given by him.

3. Find the rate of discount being given on a shirt whose selling price is $ 546 after deducting a discount of $ 104 on its marked price.

Hint. MP = (SP) + (discount).

4. After allowing a discount of 8% on a toy, it is sold for $ 216.20. Find the marked price of the toy.

5. A tea set was bought for $ 528 after getting a discount of 12% on its marked price. Find the marked price of the tea set.

6. A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the marked price. Find his gain or loss per cent.

7. A cell phone was marked at 40% above the cost price and a discount of 30% was given on its marked price. Find the gain or loss percent made by the shopkeeper.

8. A dealer purchased a fan for $ 1080. After allowing a discount of 25% on its marked price, he gains 25%. Find the marked price of the fan.

9. A dealer bought a refrigerator for $ 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of the refrigerator.

10. A carpenter allows a discount of 16% to his customers and still gains 20%. Find the marked price of a dining table which costs the carpenter $ 1190.

11. After allowing a discount of 10% on the marked price, a trader still makes a gain of 17%. By what percent is the marked price above the cost price?

12. How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he gains 8%?

13. The marked price of a television is $ 18500. A dealer allows two successive discounts of 20% and 5%. For how much is the television available?

14. Find the single discount which is equivalent to two successive discounts of 20% and 5%.


ANSWERS

EXERCISE 1

1. (a) gain 14 ¹/₂ %

(b) loss 6 %

(c) pro�it 25 %

(d) loss 8 ³/₄ %

(e) loss 8 %

(f) gain 12 ¹/₂ %

2. (a) $750

(b) $1113.63

(c) $51.70

(d) $2835

(e) $225

(f) $450

3. (a) $918.75

(b) $637.37

(c) $540

(d) $815

(e) $767

(f) $911

4. Pro�it 15 %

5. Loss 4¹/₆ %

6. $4500

7. $420

8. $1766.25

9. $2800

10. Pro�it 10 %

11. Pro�it 25 %

12. Loss 16²/₃ %

EXERCISE 2

1. $ 3813

2. 15%

3. 16%

4. $ 235

5. $ 600

6. Gain = 8%

7. Loss = 2%

8. $ 1800

9. $ 16450

10. $ 1700

11. 30%

12. 20%

13. $ 14060

14. 24%


TIME AND WORK

EXERCISE 1: TIME AND WORK

1. A can do a piece of work in 24 days while B can do it in 30 days. In how many days can they complete it, if they work together?

2. A can do a piece of work in 15 hours while B can do it in 12 hours. How long will both take to do it, working together?

3. A and B, working together can �inish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to �inish it?

4. Two motor mechanics, Ron and Sam, working together can overhaul a scooter in 6 hours. Ron alone can do the job in 15 hours. In how many hours, can Sam alone do it? 5. A, B and C can do a piece of work in 8 days, 12 days and 15 days respectively. How long will they take to �inish it if they work together?

6. A can do a piece of work in 6 hours while B alone can do it in 16 hours. If A, B and C working together can �inish it in 8 hours, in how many hours can C alone �inish the work?

7. A, B and C working together can �inish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

8. A and B can �inish a piece of work in 6 days and 4 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to �inish the work.

9. A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 7 days. Then, A was not well and B had to complete the work. In how many days was the work completed?

10. A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by A and B?

11. A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can �inish it in 36 days. In how many days can A, B, C �inish it, if they all work together?

12. A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to �inish the job?

13. Pipes A and B can �ill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to �ill it completely?

14. Pipe A can �ill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to �ill it up completely?

15. Three taps A, B and C can �ill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to �ill the empty tank, if all of them are opened together?

16. A cistern has two inlets A and B which can �ill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty tank, how much time will they take to �ill the tank completely?

17. A pipe can �ill a cistern in 9 hours. Due to a leak in its bottom, the cistern �ills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?

Hint. Work done by the leak in 1 hour = (¹/₉ – ¹/₁₀) = ¹/₉₀

18. Pipe A can �ill a cistern in 6 hours and pipe B can �ill it in 8 hours. Both the pipes are opened and after two hours, pipe A is cl?sed. How much time will B take to �ill the remaining part of the tank?

9


ANSWERS

EXERCISE 1

1. 13¹/₃ days.

2. 6 hours 40 minutes.

3. 18 days.

4. 10 hours

5. 3⁷/₁₁ days.

6. 48 hours.

7. 30 hours.

8. 3³/₅ days.

9. 10¹/₂ days.

10. 4 days.

11. 16 days.

12. 30 days.

13. 6 hours.

14. 30 hours.

15. 2 hours 40 minutes.

16. 20 minutes.

17. 90 hours.

18. 3¹/₃ hours.


UNITARY METHOD

EXERCISE 1: 1. Shelly bought a dozen pens for $ 144. Find the cost of 15 such pens. How many pens can be bought for $ 84?

2. The cost of 2 kg of onions is $24. What will the cost of 12 kg of onions be?

3. 12 tailors can stitch 15 shirts in a day. How many shirts will be stitched by 28 tailors in a day?

4. A train is moving at a uniform speed of 68 km per hour. How far will it go in 15 minutes?

5. A man is paid $770 for 7 days. If he works for 21 days, how much will he get?

6. In 8 hours, workers �ill 960 bottles of cold drinks. How many bottles will be �illed in 6 hours.

7. The weight of 56 books is 7 kg.

(a) What is the weight of 90 such books?

(b) How many such books weigh 7.5 Kg?

1. 12 farmers harvest the crops in the �ield in 20 hours. How many workers will be required to do the same work in 15 hours?

2. 2 men or 3 women can earn $192 in a day. Find how much 5 men and 7 women will earn in a day?

3. The weight of 56 books is 8 kg. What is the weight of 152 such books? How many such books weigh 5 kg?

4. John types 450 words in half an hour. How words would he type in 7 minutes?

5. A worker is paid Rs.750 for 6 days’ work. If he works for 23 days, how much will he get? 6. A water tank can be �illed in 7 hours by 5 equal sized pumps working together. How much time will 7 pumps take to �ill it up?

7. 15 masons can build the wall in 20 days. How many masons will build the wall in 12 days?

8. 76 persons can complete the job in 42 days. In how many days will 56 persons do the same job?

9. In a camp, there are provisions for 400 persons for 23 days. If 60 more persons join the camp, �ind the number of days the provision will last?

10. If 10 workers, working for 4 hours complete the work in 12 days, in how many days will 8 workers working for 6 hours complete the same work?

11. The freight for 75 quintals of goods is Rs. 375. Find the freight for 42 quintals.

12. A car travels 228 km in 3 hours.

(a) How long will it take to travel 912 km?

(b) How far will it travel in 7 hours?

10

EXERCISE 2:


EXERCISE 3: 1. If 32 men can reap a �ield in 15 days, in how many days can 20 men reap the same �ield?

2. 12 men can dig a pond in 8 days. How many men can dig it in 6 days?

3. A hostel has enough food for 125 students for 16 days. How long will the food last if75 more students join them?

4. A fort had enough food for 80 soldiers for 60 days. How long would the food last if 20 more soldiers join after 15 days?

5. 500 soldiers in a fort had enough food for 30 days. After 6 days, some soldiers were sent to another fort and thus the food lasted for 32 more days. How many soldiers left the fort?

Hint: On the day of transfer of some soldiers from this fort, 500 soldiers had enough food for (30 - 60) = 24 days. But, the food lasted for 32 days.

6. 8 taps having the same rate of �low, �ill a tank in 27 minutes. If two taps go out of order, how long will the remaining taps take to �ill the tank?

7. If 12 men or 15 women can �inish a piece of work in 66 days, how long will 24 men and 3 women take to �inish the work?

8. 70 patients in a hospital consume 1350 litres of milk in 30 days. At the same rate, how many patients will consume 1710 litres in 28 days?

9. If 30 labourers working 7 hours a day can �inish a piece of work in 18 days, how many labourers working 6 hours a day can �inish it in 30 days?

10. If 5 men working 6 hours a day can reap a �ield in 20 days, in how many days will 15 men reap the �ield if they work for 8 hours a day?

11. If 18 binders can bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days?

12. If 20 men can build a 112-m-long wall in 6 days, what will be the length of a similar wall that can be built by 25 men in 3 days?

13. 6 men, working 8 hours a day, earn $ 8400 per week. What will be the earning per week of 9 men who work for 6 hours a day?

14. If 270 kg of corn would feed 42 horses for 21 days, for how many days would 360 kg of it feed 21 horses?

15. Five machines, when operated for 9 hours each day, can harvest a farm in 16 days. How many days would 8 machines take to harvest the same farm, if each machine is now operated for 10 hours each day?


ANSWERS

EXERCISE 1

1. $180, 7 pens

2. $144

3. 35 shirts

4. 17 km

5. $2310

6. 720 bottles

7. (a) 11.25 kg

(b) 60 books

EXERCISE 2

1. 16 farmers

2. $928

3. 21 5/7 kg, 35 books

4. 105 words

5. $2875

6. 5 hours

7. 25

8. 57 days

9. 20 days

10. 10 days

11. $210

12. 12 hours, 570 km

EXERCISE 3

1. 24 days

2. 16 men

3. 10 days

4. 51 days

5. 125 soldiers

6. 36 minutes

7. 30 days

8. 95 patients

9. 21 labourers

10. 5 days

11. 11 binders

12. 70 m

13. $ 9450

14. 56 days

15. 9 days

RATIO AND PROPORTIONS

EXERCISE 1: CONCEPT BASED QUESTIONS

1. Express each of the following ratios in the simplest form. (a) 5.6 m to 28 cm(b) dozen to a score (c) score to a gross (d) 6 hours to a day (e) 20 litres to 0.75 litres (f) 1728 : 2400

2. Simplify the following ratios. (a) 1/4 : 1/6 : 1/8 (b) 3.6 : 4.5 (c) 3²/₃ : 4¹/₂ (d) 3 : 2.4 : 2¹/₄

3. Compare the following ratios. (a) 5 : 7 and 4 : 3 (b) 1/3 : 1/4 and 1/5 ∶ 1/4 (c) 2¹/₂ : 3¹/₃ and 0.3 : 1 (d) 2³/₄ : 1²/₃ and 1.2 : 1.5

4. Arrange the following in ascending order.

5. In the ratio 3 : 5, the consequent is 15. Find the antecedent.

6. Divide 3000 among P, Q, R in the ratio 2 : 3 : 5

7. Which of the following statements are true? (a) 25 : 35 = 45 : 55 (b) 105 : 30 = 49 : 14(c) 45 : 48 = 60 : 64 (d) 2/3 : 7/9 = 3/4 : 5/6 (e) 4.2 : 12.6 = 1.5 : 4.5 (f) 12 : 18 = 28 : 12

8. Determine if the following ratios form a proportion. (a) 25 cm : 1 m = $40 : $160 (b) 200 ml : 2.5 l = $4 : $50 (c) 32 m : 64 m = 7 seconds : 14 seconds (d) 6.5 litres : 13 litres = 50 kg : 10 kg

9. Find the value of x in each of the following. (a) 4, 5, x, 480(b) 9, 21, 33, x (c) x, 28, 20, 4 (d) 15, x, 27, 63 (e) x, 30, 60 (f) 6, x, 24

10. Find the fourth proportional to (a) 5.6, 2.1, 1.6, x (b) 3/4, 15/16, 2/4, x(c) 5³/₅, 3¹/₂, 2, x (d) 8, 6, 4, x

11. Find the third proportional to (a) 9, 6, x (b) 0.2, 0.4, x

11


EXERCISE 2: WORD PROBLEMS 1. The ratio of monthly income to the savings in a family is 5 : 4 If the savings be $9000, �ind the income and the expenses.

2. What should be added to the ratio 5 : 11, so that the ratio becomes 3 : 4?

3. Two numbers are in the ratio 7 : 5. If 2 is subtracted from each of them, the ratio becomes 3 : 2. Find the numbers.

4. Two numbers are in the ratio 3 : 7. If their sum is 710, �ind the numbers.

5. Find the ratio of A : B: C when

(a) A : B = 3 : 5 A : C = 6 : 7

(b) B : C = 1/2: 1/6 A : B = 1/3 ∶ 1/5

6. A sum of money is divided among Ron and Andy in the ratio 4 : 7. If Andy’s share is $616, �ind the total money.

7. Two numbers are in the ratio 5 : 7. On adding 1 to the �irst and 3 to the second, their ratio becomes 6/9 . Find the numbers.

8. The difference between two numbers is 33 and the ratio between them is 5 : 2. Find the numbers.

9. The ages of A and B are in the ratio 3 : 5. Four years later, the sum of their ages is 48. Find their present ages.

10. Ramon has notes of $100, $50 and $10 respectively. The ratio of these notes is 2 : 3 : 5 and the total amount is $2,00,000. Find the numbers of notes of each kind.

11. If 4A = 5B = 6C, �ind the ratio of A : B : C.

12. Divide $430 into 3 parts such that A gets 5/4 of B and the ratio between B and C is 3 : 4.

13. A certain sum of money is divided among A, B, C in the ratio 2 : 3 : 4. If A's share is $200, �ind the share of B and C.

14. Divide $940 among A, B, C in the ratio 1/3: 1/4 ∶ 1/5

15. The ratio of number of male and female teachers in a school is 3 : 4. If there are 16 female teachers, �ind the number of male teachers.

16. In a library the ratio of English books to Math books, is the same as the ratio of Math books to Science book. If there are 1200 books on English and 1800 books on Math, �ind the number of Science books.

17. Set up all the possible proportions from the numbers 12, 15, 8, 10.

8. Find the �irst term, if second, third and fourth terms are 21, 80, 120.

19. Find the second term, if �irst, third and fourth terms are 15, 27, 63.

20. Find the mean term, if the other two terms of a continued proportion are 15 and 60.


ANSWERS

EXERCISE 1

1. (a) 20 : 1

(b) 3 : 5

(c) 5 : 36

(d) 1 : 4

(e) 80 : 3

(f) 18 : 25

2. (a) 6 : 4 : 3

(b) 4 : 5

(c) 22 : 27

(d) 20 : 16 : 15

3. (a) 5 : 7 < 4 : 3

(b) 1/3 ∶ 1/4 > 1/5 : 1/4

(c) 2¹/₂ : 3¹/₃ > 0.3 : 1

(d) 2³/₄ : 1²/₃ > 1. 2 : 1.5

4. (a) 1 : 3, 3 : 8, 5 : 6

(b) 7 : 10, 4 : 5, 17 : 20

(c) 1 : 5, 5 : 14, 3 : 7, 7 : 10 5. 9

6. $600, $900, $1500

7. (b) true

(c) true

(e) true

8. (a) (b) (c) in proportion

9. (a) 384

(b) 77

© 140

(d) 35

(e) 15

(f) 12

10. (a) 0.6

(b) 5/8

EXERCISE 2

1. $11250, $2250

2. 13

3. 14, 10

4. 213, 497

5. (a) 6 : 10 : 7

(b) 5 : 3 : 1

6. $968

7. 15, 21

8. 55, 22

9. 15 years, 25 years

10. 1000, 1500, 2500

11. 15 : 12 : 10

12. $150, $120, $160

13. $300, $400

14. $400, $300, $240

15. 12

16. 2700

17. (i) 12 : 15 = 8 : 10

(ii) 15 : 12 = 10 : 8

(iii) 12 : 8 = 15 : 10

(iv) 8 : 12 = 10 : 15

18. 14

19. 35

20. 30


PRACTICAL GEOMETRY

EXERCISE 1: 1. Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.

2. Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.

3. Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ∠PQR = 60°.

4. Construct a parallelogram ABCD in which BC = 5 cm, ∠BCD = 120° and CD = 4.8 cm.

5. Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.

6. Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.

7. Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

8. Construct a rectangle ABCD whose adjacent sides are 11 cm and. 8.5 cm. 9. Construct a square, each of whose sides measures 6.4 cm.

10. Construct a square, each of whose diagonals measures 5.8 cm.

11. Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.

12. Construct a rhombus when the length measures of the diagonals are 8 cm and 6 cm.

13. Construct a rhombus ABCD in which AB = 4 cm and diagonal AC is 6.5 cm.

14. Draw a rhombus whose side is 7.2 cm and one angle is 60°.

15. Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC ∥ AB.

16. Draw a trapezium ABCD in which AB ∥ DC, AB = 7 cm, BC = 5 cm, AD = 6.5 cm and ∠B = 60°.

1. Construct a quadrilateral LMNO in which LM = 4.2 cm, MN = 6 cm, NO = 5.2 cm, OL = 5 cm And LN = 8 cm.

2. Construct a quadrilateral PQRS in which PQ = 5.4 cm, BC = 6 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal BD = 5.6 cm 3. Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.

4. Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

5. Construct a quadrilateral LMNO in which LN = LO = 6 cm, MN = 7.5 cm , MO = 10 cm and NO = 5 cm. Measure the remaining side.

6. Construct a quadrilateral ABCD in which AB = 3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.

7. Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120°.

8. Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ∠A = 70°.

9. Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ∠B = 125° and ∠C = 60°.

10. Construct a quadrilateral LMNO in which LM = 6 cm, MN = 5.6 cm, NO = 2.7 cm, ∠M = 45° and ∠N = 90°.

11. Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°.

12

EXERCISE 2:


FACTORISATION

EXERCISE 1: FACTORING BY GROUPING 1. Factor the following:

(i) 12x + 15

(ii) 14m - 21

2(iii) 9n - 12n

2. Factor by grouping the expressions:

2(i) 16a - 24ab

2 2(ii) 15ab - 20a b

2 3 3 2(iii) 12x y - 21x y

3. Factorize the expressions:3 2

(i) 24x - 36x y

3 2(ii) 10x - 15x

3 2 3(iii) 36x y - 60x y z

4. Factorize:

3 2(i) 9x - 6x + 12x

2(ii) 8x - 72xy + 12x

3 3 2 3 3 2(iii) 18a b - 27a b + 36a b

5. How to factor by grouping?

3 4 2 2(i) 14x + 21x y - 28x y

2(ii) -5 - 10t + 20t

6. Factoring:

(i) x (x + 3) + 5(x + 3)

(ii) 5x (x - 4) - 7 (x - 4)

(iii) 2m (1 - n) + 3(1 - n)

7. Factoring the expressions:

(i) 6a (a - 2b) + 5b (a - 2b)

3 2(ii) x (2a - b) + x (2a - b)

8. How to factor by grouping polynomials?

2(i) 9a (3a - 5b) - 12a (3a - 5b)

2(ii) (x + 5) - 4 (x + 5)

2(iii) 3(a - 2b) - 5(a - 2b)

9. How to factor by grouping polynomials?

(i) ar + br + at + bt

(ii) x² - ax - bx + ab

13


1. Factorize each of the following by regrouping:2

(i) x + xy + 9x + 9y

(ii) 6xy - 4y + 6 – 9x

(iii) 10ab + 6a + 5b +3

3 2(iv) x + x + x + 1

2(v) a – y + ay – a

3 2(vi) x – x y + 5x - 5y

(vii) a(a + 3) – a – 3

(viii) 3ax + 3ay – 2bx – 2by

(ix) x(x + y – z ) – yz

3 2 2 2 2(x) a – a + ab – a b

2. Factor grouping the algebraic expressions:

(i) 4xy – 7y + 12x – 21

(ii) 7ab – 5a – 28b + 20

2(iii) 5xy – 2x – 5y + 2y

2(iv) 6x – 15xz - 8yx + 20yz

(v) 4ax + 5bx – 12ay – 15by

3. Factorize by regrouping the terms:

(i) 7ab – 21bc – 7ax + 21xc

2 3(ii) x + xy(y + 1) + y

2(iii) ba – 2a(1 - b) - 4

2(iv) x – x(a + 4b) + 4ab

2(v) x – 9 - (x – 9) + xy – 9y

4. Factorize by grouping the following expressions:

2(i) (p - 4) – (p – 4) + 12 – 3p

2(ii) q (r – s ) – p (s - r) + 3r – 3s

2 2 2 2(iii) (x + 2x) – 7 (x + 2x) – y (x + 2x) +7y

4 3(iv) a x + a (2x – y ) – a(2ay + z) - 2z

3 2 2 3(v) a – 2a b + 3ab – 6b

2(vi) a + b – ab – a

2(vii) 5xy – y + 15zx - 3yz

2 2 2(viii) ab – bc - ab + c

EXERCISE 2: FACTORING BY REGROUPING

EXERCISE 3: FACTORING DIFFERENCE OF SQUARES

1. Factorize the following by taking the difference of squares:2

(i) x – 9 2(ii) a – 1

2(iii) 49 – x

2(iv) 4x – 252 2

(v) a b – 164 4(vi) a – b

2. Factoring by the Difference of Two Perfect Squares:2 2(i) 144a – 169b

2(ii) 1 – 0.09a

2(iii) 16x – 1212 2(iv) – 64a + (9/25) b

4(v) x – 256

4 4(vi) (x + y) – z

3. Factorize using the formula of differences of two squares:2(i) 36a – b2

2 2(ii) x y – 16

4 4 4 4(iii) 9a b – 25p q4

(iv) x – 2562 2(v) 81x – 49y

2 2(vi) x – (y – z)

4. Factor the difference of two perfect squares:2 2

(i) 16m – (3n + 2y) 2 2(ii) (3a + 4b) - (4b + 5b)

2 2(iii) (x + y) - (x – y)

2 2(iv) 50p – 72q4 4

(v) a - (b + c)2(vi) m - 1/169

5. Factor each expression: 2 2

(i) 9 (x + y) - 4 (x – y)2(ii) 16/49 - 25p

2 3(iii) 9xy – x

2 2(iv) 4 (3x + 1) - 9 (x – 2)

2(v) 1 - 121a2

(vi) 169p - 1

6. Factor using the identity:2

(i) 1 - (a + b)2 2 2(ii) x y - 25/z

12 4 4 12(iii) x y - x y

2 2(iv) 100 (x – y) – 121 (a + b)3

(v) 2x – 50x2 2(vi) 25/x - (4x )/9

4 4(vii) x - 1/(y )


EXERCISE 4: FACTORING USING IDENTITIES

1. Factor the given expressions using identity:

2(i) m + 8m + 16

2(ii) 4x – 4x + 1

4 4 2 2(iii) x + 9y + 6x y

4 2 2 4(iv) (a - 8a b + 16b ) - 18

2 2(v) 256 – x – 2xy – y

2. Factorize the expressions:

2 2(i) 4x – 12xy + 9y

2 2(ii) 36x – 84xy + 49y

2 2(iii) 9a + 42ab + 49b

2 2(iv) (3a – 5b) + 2 (3a – 5b ) (2b – a) + (2b - a)

2(v) 36x + 36x + 8

4 4(vi) 4a + b

3. Factor the identities:

2 2(i) 4x + 12xy + 9y

2(ii) x + 22x + 121

2 2(iii) 9x - 24xy + 16y

2(iv) 36x - 36x + 9

4 2 2 4(v) 16x - 72x y + 81y

2 2 2(vi) (a + c + 2ac) - b

4. Factor completely using the formula:

2 2(i) 100 – [121p – 88pq + 16q ]

2(ii) 36 - a - b2 - 2ab

2 2(iii) 25a + 49b -70ab – 15a + 21b

2(iv) 4x - 4x – 3

2 2(v) 64 - a – b - 2ab

2 2(vi) 25x – (3y + 4z)

ANSWERS

EXERCISE 1

1. (i) 3 (4x + 5)

(ii) 7 (2m - 3)

(iii) 3n (3 - 4n)

2. (i) 8a (2a - 3b)

(ii) 5ab (3b - 4a) 2 2

(iii) 3x y (4y - 7x) 23. (i) 12x (2x - 3y)

2(ii) 5x (2x - 3) 2 2(iii) 12x y (3x - 5y z)

24. (i) 3x (3x - 2x + 4)

(ii) 4x (2x - 18y + 3) 2 2(iii) 9a b (2ab - 3b + 4a)

2 25. (i) 7x (2x + 3xy - 4y )

2(ii) -5 (1 + 2t - 4t )

6. (i) (x + 3)(x + 5)

(ii) (x - 4)(5x - 7)

(iii) (1 - n)(2m + 3)

7. (i) (a - 2b)(6a + 5b) 2(ii) x (2a - b)(x + 1)

8. (i) 3a (3a - 5b)(3 - 4a)

(ii) (x + 5)(x + 1)

(iii) (a - 2b)(3a - 6b - 5)

9. (i) (r + t)(a + b)

(ii) (x - a)(x - b)

EXERCISE 2

1. (i) (x + y) (x + 9)

(ii) (2y - 3) (3x - 2)

(iii) (2a + 1) (5b + 3)

2(iv) (x + 1) (x + 1)

(v) (a - 1) (a + y)

2(vi) (x - y) (x + 5)

(vii) (a + 3) (a - 1)

(viii) (x + y) (3a - 2b)

(ix) (x + y) (x – z)

2(x) a(a - 1) (a – b )

2. (i) (y + 3) (4x - 7)

(ii) (a - 4) (7b - 5)

(iii) (x - y) (5y - 2)

(iv) (3x - 4y) (2x - 5z)

(v) (x – 3y) (4a + 5b)

3. (i) 7(b - x) (a – 3c)

2(ii) (x + y ) (x + y)

(iii) (a + 2) (ab – 2)

(iv) (x – 4b) (x - a)

(v) (x - 9) (10 – x + y)

4. (i) (p – 4) (2 – p)

(ii) (r – s) (qr – qs + p + 3)

2 2(iii) (x + 2x - 7) (x + 2x - y)

3 2(iv) (a + 2) (a x – a y - z)

2 2(v) (a - 2) (a + 3b )

(vi) (a - 1) (a - b)

(vii) (y + 3z) (5x - y)

2(viii) (ab – c ) (b – 1)

EXERCISE 3

1. (i) (x + 3) (x - 3)

(ii) (a + 1) (a - 1)

(iii) (7 + x) (7 - x)

(iv) (2x + 5) (2x - 5)

(v) (ab + 4) (ab - 4)

2 2(vi) (a + b ) (a + b) (a - b)

2. (i) (12a + 13b) (12a - 13b)

(ii) (1 + 0.3a) (1 - 0.3a)

(iii) (4x + 11) (4x - 11)

(iv) [(3/5)b + 8a] [(3/5)b - 8a]

2(v) (x + 16) (x + 4) (x – 4)

2 2(vi) [(x+y) +z ](x+y+z)(x+y-z)

3. (i) (6a + b) (6a - b)

(ii) (xy + 4) (xy - 4)

2 2 2 2 2 2 2 2(iii) (3a b + 5p q ) (3a b - 5p q )

2(iv) (x + 16) (x + 4) (x - 4)

(v) (9x + 7y) (9x - 7y)

(vi) (x + y - z) (x – y + z)


4. (i) (4m + 3n + 2y) (4m - 3n - 2y)

(ii) (3a + 8b + 5d) (3a – 5d)

(iii) 4xy

(iv) 2(5p + 6q) (5p - 6q)

2 2 2(v) (a + b + c + 2bc) (a + b + c) (a – b - c)

(vi) (m + 1/13) (m - 1/13)

5. (i) (5x + y) (x + 5y)

(ii) (4/7 + 5p) (4/7 - 5p)

(iii) x(3y + x) (3y - x)

(iv) (9x – 4) (3x + 8)

(v) (1 + 11a) (1 - 11a)

(vi) (13p + 1) (13p - 1)

6. (i) (1 + a + b) (1 – a - b)

(ii) (xy + 5/z) (xy - 5/z)

4 4 4 4 2 2(iii) x y (x + y ) (x + y ) (x + y) (x – y)

(iv) (10x - 10y + 11a + 11b) (10x - 10y - 11a - 11b)

(v) 2x (1 + 5x) (1 - 5x)

2 2(vii) (x + 1/y ) (x + 1/y) (x - 1/y)

EXERCISE 41. (i) (m + 4) (m + 4)

(ii) (2x – 1) (2x – 1) 2 2 2 2(iii) (x + 3y ) (x + 3y ) 2 2 2 2

(iv) (a - 4b + 9) (a - 4b - 9)

(v) (16 + x + y) (16 - x - y)

2. (i) (2x – 3y) (2x – 3y)

(ii) (6x – 7y) (6x – 7y)

(iii) (3a + 7b) (3a + 7b)

(iv) (2a - 3b) (2a - 3b)

(v) 4(3x + 2) (3x + 1)2 2 2 2

(vi) (2a + b + 2ab) (2a + b - 2ab)

3. (i) (2x + 3y) (2x + 3y)

(ii) (x + 11) (x + 11)

(iii) (3x - 4y) (3x - 4y)

(iv) 9(2x - 1) (2x - 1)

(v) (2x + 3y) (2x - 3y) (2x + 3y) (2x - 3y)

(vi) (a + c + b) (a + c – b)

4. (i) (10 + 11p - 4q) (10 - 11p + 4q)

(ii) (6 + a + b) (6 - a - b)

(iii) (5a - 7b) (5a - 7b - 3)

(iv) (2x + 1) (2x - 3)

(v) (8 + a + b) (8 – a - b)

(vi) (5x + 3y + 4z) (5x - 3y - 4z)

SIMPLE AND COMPOUNDINTEREST

EXERCISE 1: SIMPLE INTEREST

1. Find the simple interest and amount in each of the following:

(a) P = $1800 R = 5% T = 1 year

(b) P = $2600 R = 12% T = 3 years

2. What sum would yield an interest of $36 in 3 years at 3% p.a.?

3. At what rate per cent per annum will $250 amount to $330 in 4 years?

4. At what rate per cent per annum will $400 yield an interest of $78 in 1¹/₂ years ?

5. In what time will $400 amount to $512 if the simple interest is the calculated at 14% p.a.?

6. A sum amount to $2400 at 15% simple interest per annum after 4 years. Find the sum.

7. Ken borrowed $2000 from Sam at 8% per annum. After 6 year he cleared the amount by giving $2600 cash and a watch. Find the cost of the watch.

8. In how many years will $400 yield an interest of $112 at 14% simple interest?

9. In how many years will $12000 yield an interest of $13230 at 10% simple interest?

10. In how many years will $600 double itself at 10% simple interest?

11. At what rate of simple interest will $5000 amount to $6050 in 3 years, 4 months?

12. At what rate of simple interest will the sum of money double itself in 6 years?

13. Find the simple interest at the rate of 5% p.a. for 3 years on that principal which in 4 years, 8 months at the rate of 5% p.a. gives $1200 as simple interest.

14. At what rate per cent per annum will $4000 yield an interest of $410 in 2 years?

1. Find the amount and the compound interest on $ 2500 for 2 years at 10% per annum, compounded annually.

2. Find the amount and the compound interest on $ 16000 for 3 years at 5% per annum, compounded annually.

3. Find the difference between the simple interest and the compound interest on $ 5000 for 2 years at 6% per annum.

4. Roby obtained a loan of $ 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to discharge her debt?

5. Henna borrowed $ 20000 from her friend Nancy at 12% per annum simple Interest. She lent it to Andy at the same rate but compounded annually. Find her gain after 2 years.

6. Mike deposited a sum of $ 64000 in a post of�ice for 3 years, compounded annually at 7¹/₂ % per annum. What amount will he get on maturity?

7. David deposited a sum of $ 6250 in the ICICI Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.

8. Mike borrowed $ 16000 from a �inance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1¹/₂ years?

14


EXERCISE 2: COMPOUND INTEREST

ANSWERS

EXERCISE 1

1. (a) $90, $1890

(b) $936, $3536

2. $400

3. 8%

4.13%

5. 2 years

6. $1500

7. $360

8. 2 years

9. 10¹/₄ years

10. 8¹/₃ years

11. 6.3%

12. 16²/₃%

13. $771.42

14. 5¹/₈%


EXERCISE 2

1. Amount = Rs 3025, CI = Rs 525

2. Amount = Rs 18522, CI = Rs 2522

3. Rs 18

4. Rs 29160

5. Rs 288

6. Ps 79507

7. Rs 510

8.Rs 18522

,etc

DATA HANDLING15



POLYGONS

EXERCISE 1: SUM OF INTERIOR AND EXTERIOR ANGLES OF POLYGONS

1. Mention whether the polygons below are convex or concave.

2. Find the sum of all the interior angle of a polygon having 29 sides.

3. If the sum of the measure of the interior angle of polygon is 3240, �ind the number of sides of the polygon.

4. Find the sum of interior angles of a decagon.

5. What is the sum of exterior angles of a decagon.

6. Sum of all interior angles of a polygon is 3060°. How many sides does the polygon have?

7. Find the number of sides in a regular polygon when the measure of each exterior angle is 45°.

8. The exteriors angles of a pentagon are (m + 5)°, (2m + 3)°, (3m + 2)°, (4m + 1)° and (5m + 4)° respectively. Find the measure of each angle.

9. The measures of the exterior angles of a hexagon are (3x – 4)°, (x + 4)°, (7x – 3)°, (8x – 1)°, (2x + 3)°, (9x + 1)°. Find the measure of each angle.

10. Is it possible to have a regular polygon each of whose exterior angle is 50°? Give reason.

11. Each interior angle of a regular polygon is 135 degree then �ind the number of sides.

12. Find the sum of the measure of interior angle of a polygon having 19 sides.

13. Find the number of sides of a regular polygon if each of its exterior angle is:

(a) 45°

(b) 60°

(c) 120°

(d) 40°

16


ANSWERS

EXERCISE 1

1. Convex - 1, 2, 3

2. 4860

3. 20

4. 1440

5. 360

6. 19

7. 8

8. 35

9. 24

10. No. Number of sides cant be decimal

11. 8

12. 3060

13. (a) 8

(b) 6

(c) 3

(d) 9

QUADRILATERALS

EXERCISE 1: PROPERTIES OF QUADRILATERALS


(i) A quadrilateral has …………… sides.

(ii) A quadrilateral has …………… angles.

(iii) A quadrilateral has …………… vertices, no three of which are……………… .

(iv) A quadrilateral has …………… diagonals.

(v) A diagonal of a quadrilateral is a line segment that joins two ……………… vertices of the quadrilateral.

(vi) The sum of the angles of a quadrilateral is ……………… .

2. In the adjoining �igure, ABCD is a quadrilateral.

(i) How many pairs of adjacent sides are there? Name them.

(ii) How many pairs of opposite sides are there? Name them.

(iii) How many pairs of adjacent angles are there? Name them.

(iv) How many pairs of opposite angles are there? Name them.

(v) How many diagonals are there? Name them.

3. Prove that the sum of the angles of a quadrilateral is 360°.

4. The three angles of a quadrilateral are 76°, 54° and 108°. Find the measure fourth angle.

5. The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

6. A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

7. Three angles of a quadrilateral are equal and the measure of the fourth angle is 120°. Find the measure of each

of the equal angles.

8. Two angles of a quadrilateral measure 85° and 75° respectively. The other two angles equal. Find the measure

of each of these equal angles.

9. In the adjacent �igure, the bisectors of ∠A and ∠B meet in a point P. If ∠C = 1000 and ∠D = 60°, �ind the

measure of ∠APB.

17


QUEST BOOK - ICSE 8 Maths Part 1.cdr

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