morning glory school & college study material class: vii

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Morning Glory School & College

Study Material

Class: VII

Subject: Mathematics

Manner: CQ and MCQ. Arithmetic

1. 0.000576 is a rational number .

(a) What is the least number by which the given number

will be multiplied so that the product will be a natural

number?

1000000.

(b) Find out the square root of the given number. 0.024.

(c) Find out the square root of the number obtained in

option (b) up to three decimal places.

0.155.

2. A troop can be arranged in 6, 7 and 8 rows, but not in a square from.

(a) Find out the factors of 8. a) 1, 2, 4 and 8.

(b) What is the least number by which the number in troop

is to be multiplied so that the troop can be arranged in

a square form?

b) 42.

(c) At least how many soldiers should have to join to

arrange troops so obtained in a square from?

c) 1.

3. 384 and 2187 are two numbers.

(a) Verify with factors whether the first number is a

perfect square or not.

a) Not a perfect

square .

(b) If the second number is not a perfect square number,

what is the least number is to be multiplied to get a

perfect square number? what is the perfect square

number?

b) 3, 6561.

(c) What is the least number is to be added to the second

number so that the total sum will be a perfect square

number?

c) 22.

4. 21952 and 565 are two numbers.

(a) Give reason whether the first number is perfect square

number or not.

a) Not a perfect

square

number for

being the

digit of unit

place 2.

(b) If the first number is not a perfect square number,

what is the least number by which it will be divided to

b) 7.

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get a perfect square number?

(c) What is the least number is to be added to the second

number so that the total sum will be a perfect square

number?

c) 20.

5. Suppose, your father told you to write a fixed fraction and

you wrote 3

.

(a) Turn the given fraction into improper fraction. a)

.

(b) Determine the square root of the given fraction. b) 1

.

(c) If the quotient of two numbers is the square root of the

given fraction and product of them is 364, determine

the numbers.

c) 26 and 14.

6. Suppose, you are told to write a number and you wrote 1.1025.

(a) Determine whether the number is rational or irrational. Rational.

(b) Determine the square root of the given number. 1.05.

(c) Determine the square root of the result obtained from

option (b) up to three decimal place.

1.025.

7. You are told to writhe a number and you wrote 0.00007225.

(a) What is the number by which the given number will be

multiplied to turn the number into an integer?

10,00,00,000.

(b) Determine the square root of the given number. 0.0085.

(c) Determine the square root of the number obtained

from option (b) up to three decimal place.

0.092.

8. Your mathematics teacher wrote a number 1328.6025 on the board.

(a) Determine whether the number 2.25 is perfect square

or not.

Perfect square

number.

(b) Determine the square root of the given number. 36.45,

(c) Determine the square root of the number obtained

from option (b) up to three decimal place.

6.037.

9. In a garden, there are 1024 nut trees.

(a) In each row, if there exits 8 nut trees, how many rows

are there in that garden?

a) 128.

(b) In each row along length and breadth of the garden, if

there are equal number of nut trees, how many nut

trees are there in each row?

b) 32.

(c) If the number of nut trees is 4210, at least, how many

nut trees will be added to the total number of nut trees

so that the number of nut trees in each row along

length and breadth will be equal?

c) 15.

10. A least perfect square number which is divisible by 9, 15 and 25?

(a) How many prime factors are there in 25? a) One .

(b) What is the least perfect square number? b) 225.

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(c) What is the largest number of three digits, which is

multiple of the least perfect square number obtained in

option (b)?

c) 900.

11. Product and quotient of two numbers are 288 and

respectively.

(a) Without dividing, how will you determine that the

number 288 is divisible by 3?

a) Sun of the

digits is

divisible by

3.

(b) What are the numbers? b) 16 and 18.

(c) If the digits of the product and numerator and

denominator of the quotient of the two numbers are

rearranged to their opposite order conversely

respectively, what will be the smaller number?

c) 28.

12. Each of the students of class VII of a Junior High School subscribes 5 times

the number of the students in Taka and total amount raised by Tk. 12500 .

(a) How many square numbers are there from 1 to 10? a) 3.

(b) Determine the number of students of class VII. b) 50.

(c) If 15 more students get themselves admitted to class

VII to that Junior High School and each student

subscribes Tk. 10, how much money will be raised?

c) Tk. 400.

13. Difference of squares of two consecutive numbers is 37.

(a) Determine the largest number of two digits, which is

multiple of 7?

a) 91.

(b) Determine the two numbers. b) 18 and 19.

(c) Without being the two numbers consecutive, if one

number is twice the other and difference of square of

them is 72, what will be the numbers?

c) 4 and 12.

14. A farmer buys 595 plants for making a garden. The price of each plant is

Tk.12.

(a) How much money did he spend to buy the plants? a) 7140.

(b) How many of the plants will be left if the number of

plants in each row of the garden is equal to the number

of rows?

b) 19.

(c) What is the least number which is to be added to the

difference of the number of spending of total taka and

the number of plants so that the sum will be a perfect

square number?

c) 16.

15. In a troop, there are 56728 soldiers.

(a) Without dividing directly, how will you conclude that

the number 56728 is divisible by 4?

(a) The number

formed by last

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two digit i.e. 28

is divisible by 4. (b) At least how many soldiers is to be removed so that

the soldiers can be arranged in the form of a square?

(b) 84.

(c) At least how many soldiers is to be added to the troop[

so that the soldiers can be arranged in the form of a

square?

c) 393.

16. Labours were employed to reap paddy from a paddy field. The daily wage of

each labour is 10 times of their numbers and the total daily wage is Tk.

6250.

(a) How many prime numbers are there from 1 to 10? (a) 4.

(b) Find the total number of labours. (b)25.

(c)What is the least number by which the number 6250

will be multiplied so the product will be a perfect square

number?

(c)10.

17. Each member of a cooperative society subscribes 20 times the number of the

members in Taka. The total amount raised being Tk.20480.

(a) How many prime numbers are there from 20 to 90? a) 16.

(b) Find the number of members of the society. b) 32.

(c) If Tk.20480 is the total number of people living in a

village, what is the least number of people should be

added to the total number of people so that the total

sum will be a perfect square number?

c) 256.

18. The monthly expenditure of each student is 10 times the total number

students living in a hostel and total monthly expenditure is Tk.6250.

(a) What is the square root of 81? a) 9.

(b) What is the number of students in that hostel? b) 25.

(c) If more 20 students join to that hostel and the monthly

expenditure of each of them becomes Tk. 350, what

will be the total monthly expenditure of that hostel?

c) Tk.13,250.

19. Your father wants to divide some taka among you, your younger sister and

your elder sister in such a way that the amount of your taka is

times as

amount of your younger sister and the amount of your younger sister is

times as the amount of your elder sister.

(a) Express

as the formation of ratio 1 : x. a) 1:

.

(b) Find the ratio of the amount of taka of you, your

younger sister and your elder sister.

b) 10: 15: 12.

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(c) If you get Tk. 50, how many Taka was your

father divided among you?

c) Tk. 1850.

20. The ratio of successful and unsuccessful students of a school of 1,800

students is 5: 4.

(a) Express the ratio 5 : 4 to be decimal fraction.

Answer: 1.25.

1.25.

(b) Find the number of successful and unsuccessful

students.

1000 and 800.

(c) How many students need to be more successful so

that the number of successful and unsuccessful

students will be 7 : 2?

400.

21. Three glasses of same size are full of mango juice. 1: 8 is the ratio of water

and mango in the first glass, 2: 7 is that in the second one and 4 : 5 is that in

the third one. The juice of three glasses was poured into another large

container.

(a) What is the compound ratio of the given ratios? 1 : 35.

(b) Find the ratio of water and syrup in the large

container.

7 :20.

(c) If the weight of water in the large container is 56

decagram, find the weight of water in gram.

1600 gram.

22. Product of the marginal quantities of a continued proportion is 36 and the

first marginal quantity is 9.

(a) What is the inverse ratio of the sub-duplicate

ratio of 9: 4?

2: 3.

(b) Find out the mid proportional and the second

marginal quantity.

6 and 4.

(c) Suppose, the sub-duplicate ratio of the first

marginal quantity and the second marginal

quantity of the continued proportion is the ratio

of the ages of father and his son. If the age of

son is 27 years, what will be the age of father?

54 years.

23. a: b: c = 2 : 3 : 5 and a = 12.

(a) What is the name of the ratio 2: 3: 5? Successive or

continuous

ratio.

(b) Find the value of b and c. b = 18 and c =

30.

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(c) If the value of b and c are the present age of 2

sons and

that of their father, find the ratio of the ages of

them after 10 years.

19 : 20.

24. Abul and Babul are two friends. They bought cow of Tk. 50,000 and sold

it by Tk. 76,900. Abul paid an amount of 1

times than that of Babul

during buying the cow.

(a) Express 1

as the formation of ratio 1 : x. 1 :

(b) How much money will Abul get from the profit? Tk. 11, 700.

(c) If the ratio of the capital of Abul and Babul for

buying the cow is the ratio of lengths of a square

and a rhombus having perimeter 80 cm, what is the

perimeter of the square?

180 cm.

25. a : b = 3 : 4

b : c = 4 : 5

(a) What is the duplicate ratio of 3 : 4? 9 : 16.

(b) If the mixed ratio of 3: 4 and 4 : 5 is the ratio of

the equal side and base of an isosceles triangle

of which perimeter is 33 metre, find the length

of equal side and length of the base of the

isosceles triangle.

9 m and 15m.

(c) If the ratio of a : c is the gold and silver of an

ornament having weight 40 gram, what is the

weight of gold that will be added to gold of the

ornament so that the ratio of gold and silver will

be c : a?

gram.

26. a : b = 1 : 2, b : c = 3 : 2, c : d = 2 : 5.

(a) What is the mixed ratio of 1: 2 and 3 : 2?

Answer: 3 : 4.

3 : 4.

(b) If the ratio of the lengths of four sides of a

quadrilateral is a: b: c : d and the perimeter of

the triangle is 69 cm, then find the lengths of the

four sides of the quadrilateral.

9 cm, 18 cm and

30 cm.

(c) If a: d is the ratio of present ages of daughter

and her mother and after 8 years the sum of the

ages of them is 68 years, find the present age of

mother.

40 years.

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27. Some labours come contact to finish a work in 18 days, but for being absent

of 9 labours among them, the work is finished in 36 days.

(a) Find a: b: c if a: b= 2: 3 and b: c = 2 : 3. 9 days.

(b) How many labours are come to contact to finish

the work in 18 days?

4 : 6 : 9.

(c) How many days will be required to finish work

by 36 labours?

18 labours.

28. Suppose, you have some takas. You want to divide that money among A, B,

C in such a way that, A gets 3 times more than the share of B and B gets 2

times more than the share of C.

(a) What is called ratio? The comparison

of two like

quantities is

called ratio.

(b) Find the ratio of the shares of A, B and C. 12: 3 : 1.

(c) If C gets Tk. 80, how many taka were there to

you?

Tk.1280.

29. Divide Tk. 2,040 among A, B, C and D in such a way that the portion of A

is

of the portion of B, the portion of B is

of the portion of C and the

portion of D is the sum of the portions of B and C.

(a) What is the mixed ratio of 4 : 5 and 8 : 9? 32: 45.

(b) Find the ratio of the portions of A, B, C and D. 4: 6: 9: 15.

(c) If the portions of B and A are interchanged and D

gives Tk. 60 to C, then find the ratio of the portion

of A, B, C and D.

3: 2: 5: 6.

30. Suppose, you have some taka. You want to divide your taka among A, B and

C in such a way that, 3 times of the share of A = 4 times the share of B = 2

times the share of C.

(a) What is the largest number of two digits multiple of 6

and 5?

90.

(b) Find the ratio of the shares of A, B and C. 4: 3: 6.

(c) If A gets Tk. 40 more than the share of B, then

determine the share of C.

Tk.240.

31. Suppose, you have some taka. You want to divide your taka among A, B and

C in such a way that, A gets 3 times the share of B and B gets 2 times the

share of C and A gets Tk. 270 more than the shares of B and C.

(a) What is the inverse ratio of the mixed ratio of 1: 2 and

2: 3?

3: 1

(b) Find the ratio of the shares of A, B and C. 6: 2 :1.

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(c) How many taka did you have? Tk. 810

32. Suppose, you have Tk. 800. You want to divide your taka among A, B and C

in such a way that, A gets 3 times the share of B and B and C together get

portion of the shares of A.

(a) Express the inverse ratio of 2: 3 into percentage.

20 : 15: 12

(b) Find the ratio of the shares of A, B and C.

3: 1 : 4.

(c) If C gives Tk. 100 to B and A gives Tk. 100 to B,

what will be the ratio of the shares of A, B and C?

2: 3: 3.

33. Suppose, you have Tk. 280. You want to divide your taka among A, B and C

in such a way that, A gets

portion of the sharesof B and C and A and C

gets

portion of the shares of A and B.

(a) What is the successive ratio of 3: 4 and 3: 5? 9 : 12 : 20.

(b) Find the share of A, B and C.. A = Tk. 120,

B = Tk. 80 and

C = Tk. 80

(c) If the ratio of the shares of A, B and C are the

ratio of the three sides of a triangle having

perimeter 28 meter, find the lengths of the three

sides of the triangle.

12 m, 8 m and 8

m.

34. Ratio of the shares of some taka of a business of three partners A, B and C is

and share of A is Tk. 2,500 more than that of B.

(a) Express

to be simple ratio. 20 : 15 : 12.

(b) Find the shares of A, B and C. A = Tk. 1,000,

B = Tk. 7,500

and C = Tk.

6000.

(c) How many taka will be given by B to A so that

the ratio of the share of A and B will be 3 : 2?

Tk. 2400.

35. A labour earns Tk. 540 in 24 days working 6 hours per day.

(a) How many prime numbers are there from 20 to 70? 11.

(b) How many takas can the labour earn in 30 days

working 8 hours per day? (Applying Multi

Expression or Rule of many)

Tk. 900.

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(c) If the taka obtained in option (b) is the sum of two

numbers having ratio of them 13: 5, find the two

numbers.

650 and 250.

36. 8 workers can finish a piece of work in 14 days working 7 hours per day.

(a) What is the smallest number of two digits multiple

of both 3 and 5?

90.

(b) In how many days 7 workers can finish that work

working 6 hours per day?(Applying Multi

Expression or Rule of many)

16 days.

(c) If the ratio of two numbers is equal to the ratio of

the least multiples of the required number days

obtained in option (b) and sum of the numbers is

27, find the two numbers.

9 and 18

37. In a hostel, 60 students have a stock of food for 25days. After 5 days,

20students moved to another place.

(a) How many prime factors are there in 60? 3

(b) How many days will run for the rest of the students

by the reaming food? [Use Rule of three]

30 days.

(c) If the ratio of the sum of the prime factors of 60

and number of prime numbers from 1 to 60 is the

ratio of number of female and male students of a

school and number of female students is 500, what

is the number of male students?

850.

38. Ratio of the weights of salt and sugar in 45 litre of saline of a vessel is 2 : 3.

(a) What is the value of x if 1: x = 1: 3? x = 3.

(b) Find the weights of guar salt and sugar. 18 gm and 27

gm.

(c) How much of salt should be mixed to saline of

the vessel to get the ratio 2: 3?

22.5 gm.

Algebra

39. A = , B = and C =

(a) Find the value of A – B. –2xy.

(b) Find the product of AB.

(c) Show that,

= 1.

40. A = , B = and C =

(a) Find the value of B – A. 2x.

(b) Prove that, AB = C.

(c) Putting x = –1, find the value of AB. 3.

41. P = 2a – 3b and Q = 3a + 2b.

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(a) Find the value of P + Q. 5a – b.

(b) Find the product of P and Q. 6 .

(c) Find the product of (Q–P) and (P–Q).

– 42. P = a + 1, Q = a – 1 and R = .

(a) Determine the value of P + Q. 2a.

(b) Prove that, PQ = R.

(c) Find the product of (P + Q) and (P–Q). 4a.

43. A = x + y, B = x–y and C = (a) Putting x = 1 and y = 1, find the value of A. 2.

(b) Prove that, AB = .

(c) Find the product of A, B and C. .

44. A = and B = x – y.

(a) If x = 1 and y = 1, prove that, the value of AB is zero.

(b) Prove that, AB = .

(c) Find the sum of A and Bx. 2 45. X = – and Y = a + b.

(a) If a = 1 and b = –1, find the value of Y. 0.

(b) Prove that, XY =

(c) Find the difference subtracting bY from X. 46. P = 3a + b, Q = 3a – b and R = 9

(a) What is the value of (P + Q)? 6a.

(b) Prove that PQ = R.

(c) What is the value of ( ) 4 47. 15 – and 5x –1 are two algebraic expressions.

(a) Subtract the second expression from the first

expression. 15 + 2x –1.

(b) Determine the product of the two expressions. 75 + 2.

(c) Putting x = 1, find the value of the product of the

given expressions.

80.

48. A = , B = and C = .

(a) A + B = what? 2 (b) Find the product of A and B.

.

(c) Determine AB–2C. .

49. P = and Q = 3 . (a) Which one of the above mentioned expression is

monomial?

Q.

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(b) Find the value of PQ in terms of a and b. 3 .

(c) Find the value of (P+ Q)(P–Q) in terms of a and x by

applying formula.

+ 81 .

50. and are two algebraic expressions.

(a) Find the difference subtracting the second expression

from the first one.

2x.

(b) Find the value of the square of the sum of the given

expressions if x = –1.

16.

(c) By applying formula, find the product of the given

expressions. +1

51. a + b = = 7 and ab = 9.

(a) What is the value of ( ) ? 49.

(b) Find the value of 31.

(c) Find the value of ( ) 13.

52. p –

= 8.

(a) What is the value of (

) ?

64.

(b) Prove that,

= 66.

(c) Find the value of (

)

60.

53. a + b = 4 and ab = 2.

(a) What is the value of 2a + 2b? 8.

(b) Find the value of ( ) . 8.

(c) Prove that, ( ) = 128.

54. a –

= 5.

(a) Find the value of 3a –

. 15.

(b) Prove that,

(c) Prove that,

55. A = 2x + 3y and B = 2x – 5y.

(a) What is the value of A + B? –2y.

(b) If x = 1 and y = –2, find the value of . 160.

(c) Simplify: . 64 .

56. a + b= 7 and ab = 3.


(b) Prove that, ( ) = 61.

(c) Prove that,

=

.

57. a + b = 5 and ab = 12.

(a) What is the value of 3a + 3b. 15.

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(b) Prove that,

(c) Prove that,

=

.

58. x +

= 5.

(a) What is the value of 2x +

? 10.

(b) Find the value of

. 23.

(c) Prove that, (

) = 525.

59. a + b = 8 and a – b = 4.


(b) What is the value of ab? 12.

(c) What is the value of 2( )? 40.

60. x + y = 7 and xy = 10.

(a) What is the value of 5xy? 50.

(b) What is the value of ( ) ? 29.

(c) What is the value of 79.

61. AB and CD are two parallel straight line and PQ is their transversal which

intersects the straight lines AB and CD at the points E and F.

(a) Draw the figure based on the stem.

(b) Prove that, AEF = alternate EFD.

(c) Prove that, BEF + EFD = 2 right angles.

62.

In the above mentioned figure, AB CD, BPE = and PQ = PR.

(a) Show that,

= .

(b) Determine the value of CQF. (c) Prove that, PQR is an equilateral triangle.

63. ABC is a triangle whose side BC is extended up to D and CE AB.

A B

E

F

C D

P

Q R

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(a) Draw the figure based on the above mentioned

information.

(b) Show that, ACD = A + B.

(c) Prove that, A + B + C = 2 right angles.

64. ABCD is a quadrilateral and AC is a diagonal of it.


(b) Prove that, A + B + C + D = 4 right angles.

(c) If CAB = ACB = 600, prove that, ABC = 120

0.

65. Two line segments PQ and RS intersect at O and L, M, E and F are four

points on them such that LM PQ.


(b) Prove that, MLO = FEO.

(c) Prove that, SEF = MLQ.

66. In ABC, AC BC; E is a point on AC produced.

ED AB is drawn to meet BC at O.

(a) draw the figure based on the stem.

(b) prove thatm, CEO = DBO.

(c) prove that, COD + CAD = 1800.

67. In ABC, AB>AC and the bisectors of the angle B and C intersect a the

point P.

(a) Draw the figure based on the information of the stem.

(b) Prove that, ACB > ABC.

(c) Prove that, PB> PC.

68. ABC is an isosceles triangle whose AB = AC. The side BC is extended up to

D.


(b) Prove that, AD > AB.

(c) If BA is extended to E and AF BC, prove that,

CAE = 1800 –A.

69. In the quadrilateral ABCD, AB = AD, BC = CD and CD >AD.


(b) Prove that, DAB>BCD.

(c) If B and D are joined, ABD = and CBD = , prove that, A +

C = . 70.

71.

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72. In ABC, ABC >ACB and D is the midpoint of BC.


(b) Prove that, AC > AB.

(c) Prove that, AB + AC> 2AD.

73. In the ABC, AB = AC and D is a point of AC.


(b) Prove that, AB> AD.

(c) If D is the midpoint of AC, Prove that, AB + BC >2BD.

74. In ABC, AB AC and D is a point on AC.


(b) Prove that, BC> BD.

(c) Prove that, BC is the largest side of the right angled ABC.

75. In ABC, AC is the largest side.


(b) Prove that, ABC is the largest angle.

(c) Prove that, AB + AC > BC.

76.

77.

In the above mentioned figure, QPM = RPM and

QPR = 900, PQ = 6 cm.

(a) Find the measure of the QPM. 450.

(b) What is the measure of the PQM and PRM? 450 and 45

0.

(c) Find the value of PR. 6 cm.

78. Two parallel straight lines AB and CE and he line PQ interests AB and CD

at E and F respectively.

(a) Draw the figure based on information.

(b) Show that, AEP = CFE.

(c) Prove that, AEF + CFE = 2 right angles.

Statistics

79. Following are the marks obtained on Mathematics by 60 students of a class

are: 50, 84, 73, 56, 97,90, 82, 83, 41, 92, 42, 55, 62, 63, 96, 41, 71, 77, 78,

22, 48, 46, 33, 44, 61, 66, 62, 63, 64, 53, 60, 50, 72, 67, 99, 83, 85, 68, 69,

45, 22, 22, 27, 31, 67, 65, 64, 64, 88, 63, 47, 58, 59, 60, 72, 71, 73, 49, 75,

64.

(a) Determine the range of the data.

(b) Develop a frequency distribution table taking 10 as

Q P

M

R

6cm

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class interval.

(c) Draw the histogram and find the mode from the table.

80.

1. Which one of the following is the square root

of

?


of 1.1025?

1.05

3. What is the square root of 121? 11.

4. What is the square of 1.2? 1.44.

5. What type of the number of the square root of

7?

Irrational.

6. What is the square of root of 784? 28.

7.

Length of each side of the larger square 5 cm

and length each side of smaller square half of

the larger square, what is the sum of the areas

of the squares of the shaded regions?

12.5 sq. cm.

8. Which sign is used to indicate the square root

of a number?

Answer the questions number () based on the following information:

Two numbers are 18 and 20.

9. What is the least number that will be

subtracted from the average of them so that

the difference will be a perfect square

number?

3.

10. What is the least number that will be added to

the sum of them so that the total sum will be a

perfect square number?

11.

11. What is the least number that would be added

to 20 so that the total sum will be a perfect

square number?

5.

16 | P a g e

12. What is the square root of

?

13. What is the square root of 1.21? 1.1.

14. A rational number is –

i. 0

ii. 5

iii.

Which one of the following is correct?

i, ii & iii

15. Observe the following information:

1. 81 is a perfect square number.

2. 71 is a perfect square number

3. The square root of 081 is 0.9.


i & iii

Answer the question no. 4 and 5 based on the following information:

The difference of square of two consecutive numbers is 19.

4. If the larger number is 10, what is the smaller

number?

9.

5. What is the sum total of squares of the two

numbers?

181.


of 0.01?

0.1.

7. What is the square of 0.01? 0.0001.

8. If the digit in unit place of a number is either 2

or 8, the digit in unit place of its square will be

4

9. By which number the multiplication or

division of 37573 will be a perfect

square number?

5.

Answer the questions number 12 -14 based on following stem:

Difference of square of two numbers is 13.

10. If larger number is 7, what will be the smaller

number?

6.

11. What is the sum of the square of them? 85.

12. What is the least number that will be

subtracted from the product of them so that the

difference will be a perfect square number?

6.

13. Which one of the irrational number? √

14. Which is the sub-duplicate ratio of 4: 9? 2 : 3.

15. If A: B = 4 : 7 and B : C = 10 : 7, what is the

value of C: B: A?

49: 70 : 40.

16. What is the value of second quantity is

successive ratio of 4 : 3 and 5: 6?

15.

Answer the questions number13 & 14 based on the following stem: 30 metre

17 | P a g e

cloth are divided among Maisa, Maria and Tania in the ratio of 5: 3: 2.

17. How many metre of cloth did Maisa get? 15metre.

18. How many metre of cloth did Maria get more

than Tania?

3 mrtre.

19. What is the successive ratio of 5: 3 and 2: 5? 10 : 6 : 15.

20. Which one is the fourth proportional of 3, 5

and 15?

25.

21. Which one of the following is the product of

3 and –4a ?

–12

22. If a = 3, b = 2, what is the value of (8a – 2b) +

(–7a + 4b)?

7.

23. If x = –1, which one of the following is the

value of –

0.

24. 4 is an algebraic

expression.

i. a is the variable of the polynomial

expression.

ii. degree of the polynomial is 4.

iii. 6 is the coefficient of Which one of the following is correct?

i & ii

25. If x = 3, y = 2, what is the value of ( ) ? .

26. If a 0, what is the value of ? 1

Answer the questions number 23 & 24 based on the information of the below

mentioned stem:

Two algebraic expressions are x + y and x –{x – (x–y)}.

27. Which one of the following is the value of the

second expression?

x – y.

28. Which one of the following is the product of

the two expressions? –

29. What is the value of ( ) ? – 30. What is the simple solution of [2 –{(1+1)–

2}]?

2.

31. What is the square of a – 5? –10a + 25.

32. Which one is the value of ( ) ( )( ) ( )

4 .

33. If a + b = 4 and a – b = 2, what is the value of

ab?

3.

34. A quantity is divisible without remainder by

another quantity, what is called dividend in

respect of divisor?

Multiple.

35. If a and b are real numbers,-

i. ( ) . i , ii & iii.

18 | P a g e

ii. ( ) ( ) . iii. ( )( )


36. If x –

= 0, --

i. x = 1

ii. x = –1

iii. x = 1

which one of the following is correct?

i, ii & iii.

37. What is the square of a + 5? + 10a + 25.

38. If a + b = 8 and a – b = 4, what is the value of

ab?

12.

39. Which one of the following pairs expresses

fractions

in equal denominators?

.

40. Which of the following is the equivalent to the

fraction

?

.

41. Which of the following is the lowest form of

?

.

Answer to questions in 38 & 39 the light of the following information:

is a fraction.

42. Numerator of the fraction is equivalent to

which one of the following monomial?

( ) .

43. What is the lowest form of the fraction?

.

44.

In the above mentioned figure, PQR = , LRN = and PQ MAR. which one of the

following is the value of MRN?

.

45.

In the above mentioned figure, PQ SR,

PQ = PR and PRQ = , what is the value

of the LRS?

. P

Q R

S

L

P

Q R

N M

L

19 | P a g e

Answer the questions number (42- 44) based on the following information of

the stem:

AB EF

46. Which one f the following is the value of the

x?

.

47. Which one of the following is the value of the

z?

.

48. Which one of the following is the value of

y – z? .

Answer the questions number 45 & 46 based on the following information of

the stem:

In the above mentioned figure, AB CD.

49. What is the measure of the PEA? . 50. What is the measure of the EFD? . 51. In ABC, B + C = , what is the

measure of the A?

.

Answer to the questions number 48 & 49 based on the following information of

the stem:

X

P

Q

E

A B

F

E

F

E

A

C

B

D

F

x

z

y

20 | P a g e

52. What is the value of X? . 53. What is the value of X + Y? . Answer to the questions number 50 & 52 based on the following information of

the stem:

In the above mentioned figure, CE is the bisector of the ACD, AB CE and

ECD = . 54. Which one of the following is the measure of

the BAC?

.

55. Which one of the following is the measure of

the ACD?

.

56. What type of triangle is ABC? Equilateral

57. The lengths of two sides of a triangle are 5cm

and 4 cm respectively. Which one of the

following is the possible measurement of the

other side of the triangle?

4 cm.

58. If one of the two acute angles of a right angled

triangle is , which of the following is the

measure of the other acute angle?

.

59. If the sum of two angles is equal to the third

angle of a triangle, what type of the triangle is

it?

Right angled triangle.

60. In which case is it possible to draw a triangle

when the lengths of the sides are respectively?

3cm, 4cm and 5 cm.


i. The triangle is constructed if its two sides

and the angle included between them

are given.

ii. The triangle is constructed if the sum of its

two sides is greater than its third side.

i & ii.

B

A

C D

E

Y

21 | P a g e

iii. There are more than one obtuse angles in

any triangle.


62. What is the sum of length of three sides of a

triangle called?

Perimeter.

63. How many internal angles are there in a

triangle?

3.

64. How much degree is each of the angles of a

equilateral triangle? .

65. If one angle of a right angled triangle is , how much degree in the other angle?

.

Answer the questions number 62 & 63 based on the following information of

the stem:

66. To draw a line segment parallel to BA through

the point C, equal to which angle is to be

constructed?

BAC.

67. Which one of the following is equal to

CAD?

ABC + ACB.

68. What is the class interval of 50 – 60? 11.

69. What is the midpoint of the class 60– 70? 65.

70. What is the average of odd numbers ranging

from 1 to 10?

5.

71. What is the median of the numbers 10, 12, 13,

15, 16, 19, 25?

15.

72. What is the numerical presentation of

information called?

Statistics.

Answer the questions number 69 & 70 based on the information of the

following stem:

The daily expenditures (in Taka) of 10 students of class 7 are as follows: 20, 22,

50, 40, 32, 28, 45, 30, 25, 48.

73. What is the range of the data? 31.

74. What is the average of the data? 29.


i. If the area of four squares equal of all

respect is 16 square unit, length of each

square will be 2 unit.

i & ii.

D

B

A

C

22 | P a g e

ii. If the perimeter of a square is 16 unit,

its area will be 16 square unit.

iii. If the length of a square is ‘3’ unit, its

area will be 12 square unit.



i. Square is actually geometric figure.

ii. Square root of the area of a square is the

length of that square.

iii. If the length of a square is ‘a’ unit, its

area will be 4a square unit.


i & ii.


i. If the digit of unit place of a number is 2

or, 3, or, 7 or 8, it will not be a perfect square

number.

ii. If odd number of zeros are in the right

of a number, it will not be a perfect

square number.

iii. Square of a perfect square number is

also a perfect square number.


i . ii & iii.


i. If the digit of unit place of a number is

either 1 or 9, the digit of unit place of its

perfect square will be 1.

ii. If the digit of unit place of a number is

either 4 or 6, the digit of unit place of its

perfect square will be 6.

iii. If the three times of a number is 48, the

square root the number will be 4..


i , ii & iii.


i. Square root of the number of prime

numbers from 1 to 100 is 5.

ii. Square of number of prime numbers

from 1 to 10 is 16.

iii. Square root of 8 is an integer.


i & ii.


i. What is the least number should be

added or subtracted can be determined

applying factor method.

ii &iii.

23 | P a g e

ii. What is the least number by which the

given number will be multiplied or

divided can be obtained applying factor

method.

iii. If the digit of unit place of a number is

either 3 or 7, the digit it unit place of the

square of that number will be 9.



i. If the digits of unit and ten place of a

number are zeros and the number

formed by the rest digits is a perfect

square number, digit of unit place of the

given number will single zero.

ii. A number may be a perfect square

number if the digit at its unit place is 1,

or, 4 or, 5 or, 6 or 9.

iii. Number of perfect square numbers from

1 to 10 is 3.


i, ii & iii

82. i. A factor is to take from the number of

pairs of factors of a perfect square

number.

ii. A square is the product of multiplication

of a number by itself and the number is

the square root of the product.

iii. The square root of 4th multiple of 4 is

also 4.


i, ii & iii.

83. i. Square root of 361 is 19.

ii. Square root of 196 is 14.

iii. Square of 18 is 324.


i, ii & iii

84. i. Square root of

is

.

ii. √ is a rational number.

iii. Square root of

is 4.

i & iii.

85. What type of the number

√

is?

Neither prime nor

composite.


i. Square root of the square root of a

perfect square number may be

rational or irrational.

i & ii

24 | P a g e

ii. Rational number can be shown on a

number line.

iii. Irrational number can never be

shown on a number line.


87. Two numbers are 9 and 10, what is the

difference of the square of them?

19.

88. The product of two numbers are 96 and their

quotient is

, what are the number?

8 and 12.

89. In a garden, there are 18 rows and each row

contains 8 coconut trees. What is the square

root of the total number of coconut trees?

12.

90. To arrange the some marbles in a square form,

it is seen that 7 ones are excess. How many

marbles are there in each row?

18.

91. What is ratio? A fraction.

92. What is the duplicate ratio of 4: 5? 16 : 25.

93. What is the sub-duplicate ratio of 36: 49? 6: 7.


i. Minor ratio is greater than 1.

ii. The quantities of successive ratio are

not like.

iii. 4 : 5 is read as 4 is to 5.


i & iii.

95. Minor ratio cannot be expressed as a ____

fraction.

Mixed fraction.s

96. If the antecedent and subsequent forming ratio

are equal, the ratio is called …..

Unique ratio.

97. In case of more than one ratios, if the product

of the antecedents of them is considered to be

antecedent and the product of the subsequent

is considered to be subsequent of a newly

formed dimple ratio, then such kind of simple

ratio is called ____ ratio with respect to the

given simple ratios.

Compound ratio.

98. The ratio formed by considering the

antecedent to be subsequent and the

subsequent to be antecedent of a given ratio is

called ____ ratio with respect to the given

ratio.

Inverse ratio.

99. The ratio formed by squaring the antecedent

and the subsequent of the given simple ratio is

Duplicate ratio.

25 | P a g e

called____ .


i. The ratio formed by performing

square root of the antecedent and the

subsequent of a given simple ratio is

called sub-duplicate ratio with

respect to the given simple ratio.

ii. The antecedent and the subsequent

of an algebraic ratio may be positive

or negative.

iii. The sub-duplicate ratio will be

significant only when if both the

antecedent and subsequent are

positive.


i, ii & iii.


i. Ratio can be expressed as a simple

fraction.

ii. Ratio can be expressed as a decimal

fraction.

iii. Ratio can be expressed as a

percentage.


i, ii & iii.


i. Between two Between two like

quantities, one is how many times

larger or smaller than another can be

compared by the ratio.

ii. Ratio is a comparative concept

expressed in proper or improper or

decimal fraction or percentage.

iii. First quantity of a ratio is called

antecedent and the second quantity is

called subsequent.


i, ii & iii.


i. First quantity ‘a’ of a ratio is called

antecedent and the second quantity ‘b’

is called subsequent.

ii. All rules of fractions are applicable in

case of ratio.

iii. If the antecedent and subsequent of a

ratio are multiplied or divided by the

i, ii & iii.

26 | P a g e

same digit or number (except zero, 0),

the value of ratio will not be changed.



i. The quantity obtained from ratio cannot

be told the value of the antecedent and

subsequent.

ii. Since, the quotient of two like quantities

does not depend on unit, the value of

ratio is a pure number and such pure

number obtained from ratio has no unit.

iii. To multiply the antecedent of a ratio

means to multiply the value of the ratio

by that number.


i, ii & iii.


i. In case of proportion, four quantities

are not required to be the same one.

ii. Both quantities of each ratio forming

proportion are required to be the like

ones.

iii. Each quantity forming proportion is

called proportional.


i, ii & iii.

106. If four quantities are such that the ratio of the

first two like quantities and the ratio of the

second like quantities are equal, then the

newly formed rule is called ____.

Proportion.

107. The first and fourth quantities of a proportion

are called_____.

Marginal quantities

108. The second and third quantities of a proportion

are called mid-ones.

Mid-quantity


i. the second quantity is called the

mean or mid-quantity of the first and

third ones.

ii. The third quantity is called the third

proportional of the first and the third

ones.

iii. All proportional in case of continual

or ordered or successive proportion

have to be like quantities.

i, ii & iii.

110. If three quantities of totally four such The rule of three.

27 | P a g e

quantities that two quantities are like and

another two quantities are also like are given,

then the process of finding out the fourth

quantity applying the concept of proportion is

called------.

111. The two inverse ratios of the ratios of

proportion -------.

Are also proportional.

112. What is the unit of raio? No ratio.

113. If two quantities exist to a ratio, such kind of

ratio is called ---- ratio.

Simple ratio.

114. Which one of the following is minor ratio? 3: 4.

115. Which one of the following is a unique ratio? 8: 8.

116. Which one of the following ratio is equivalent

to 3: 5?

15: 45.

117. What is the inverse ratio of 3: 7? 7b : 3.

118. What is the compound ratio of 4: 3, 7: 12 and

6: 5?

4.6.6 = 3: 12: 5

4 : 5.

119. which one of the following is the

multidimensional ratio?

3: 4: 5.

120. What is the sub-duplicate ratio of 64: 81? 8: 9.

121. Compound ratio of several ratios is a---- ratio. Simple.

122. What is the ratio of the quantities 7.5 and 2.5? 3 : 1.


i. To compare between two like

quantities, the word ratio is used.

ii. 2: 3 is read as two is to three.

iii. If the antecedent of a ratio is less than

the subsequent, the ratio is called minor

ratio.


i, ii & iii.

124. Observer the following information:

i. Ratio of two like quantities can be

expressed as a percentage.

ii. The express ratio the sign ‘t’ is used.

iii. 1: 3 can be written as 1 4.


i & ii.


i. If the subsequent is not 1, the ratio of

two like quantities is a integer.

i & ii.

28 | P a g e

ii. The ratio formed by two like

quantities is a simple ratio.

iii. The sub sequent of 4: 5 is 4.


126. Observe the following information :

i. Like the fraction, ratio of two like

quantities can be turned into reduction

form.

ii. Inverse of the ratio 3: 4 is 4; 3.

iii. 4: 5 is a unique ratio.


i & ii.

127. 8

: 4

= what? 9: 5.

Answer the questions number 128-130 based on the following stem:

The three ratios are 3: 5, 5: 7 and 14: 15.

128. What is the duplicate ratio of the first ratio? 9: 25.

129. What is the mixed ratio of the second and third

ratios?

2: 5.

130. What is the mixed ratio of the given ratios?

131. If 12: 16 = x : 20, what will be the value of x? 15.

132. If 4: x = 9: 18, what will the value of x? 8.

133. If 2.6: 1.3 = 1.1 : x, what will be the value of

x?

0.55

134. If

, what will be the value of x?

.

135. What is the value of (–2)(–1) (

)? 1.

136. What is the additive inverse of 5? –5.

137. What is the value of ( ) ? .

138. What is the product of 5 and 2 ? 10 .

139. What is the product of (– )

– a

140. What is the product of 2 and 4ab? 8 .

141. What is the product of 5ab and –4 ? –20a .

142. What is the product of 2b and 3 6 143. What is the product of –5a and –9 ? 45 144. What is the product of (– ) and

( )?

8 .

145. What is the product of (–21) and (–3–2) 10.

146. What is the product of (–3 + 2) and (2 –3)? 1.


i. Only positive number is used to

arithmetic.

i & iii.

29 | P a g e

ii. 1 – 1 + 1 – 1 + 1 = 5.

iii. (–a)b = a(–b)



i. The multiplicative inverse of 5 is

.

ii. 0 –1 = –1.

iii. 3* ( )+


i & iii.


i. The product of two quantities having

opposite signs contains negative (–)

sign.

ii. Associative law can be applied in

case of multiplication.

iii. 2(a – b) = 2a + 2b.


i & ii.


i. 2(a + b) = 2a + 2b is called the

distributive law of multiplication

over addition.

ii. The product of two like singed

expressions will be preceded by plus

(+) sign.

iii. The polynomial cannot be multiplied

by monomial.


i & ii.


i. If a monomial is multiplied by

another monomial, the product will

be a polynomial.

ii. x + 3y is a polynomial.

iii. 3xy is a monomial.


ii & iii.


i. Multiplicand is the multiple of

multiplier.

ii. The multipliers may be told the

factors of multiplicand.

iii. The brief rule of addition is called

multiplication


i , ii & iii.

153. What will be the sum if – 5 is added to 11? 6.

30 | P a g e

154. If a = 2 and b = –1, what will be the value of

a ?

2.

155. If a +

= 2, what will be the value of

(

) ?

0.

156. If x +

= 1, what will be the value of

(

)

5.

157. If a + b = 3 and a–b = 1, what will the value of

ab?

2.

158. What will be added to

to form

(

) ?

2.

Answer the questions number 159-161 based on the following stem:

159. What is the area of the quadrilateral AEKH? ab square unit.

160. What is the perimeter of quadrilateral DHKG? 4a unit.

161. What is the area of the quadrilateral ABCD? ( ) square unit.

162. What is the lowest form of the fraction

.

163. What is the lowest form of

( )

.

164. What will be formation of the fractions

if they are expressed with common

denominator?

165. is equivalent to which one of the following

fractions?

.

166. sign indicates -----. Therefore.

167. sign indicates ------. Since.

168. What is meant by the symbol ? Triangle.

169. What is meant by the symbol ` ’? is parallel to.

170. What is meant by the symbol ` ’? Is perpendicular to.

171. means -----. Is greater than.

a a

a

a b

b

b

b

A

B C

D

E

F

G

H

K

31 | P a g e

172. means ….. Is less than.

173. Without changing direction, how many

straight lines can be drawn through a point?

One and only one.

174. Which has no end point? Straight line.

175. Which has both end points? Line segment.

176. Which has only one end point? Ray.

177. How many common points of two rays are

required to form an angle?

One.

178. How many angles are there in a triangle ? Three.

179. How many triangles are there based on the

side?

Three

180. How many triangles are there based on the

angle?

Three

181. What is the sum of three angles of a triangle? 1800.

182. What is the name of the triangle whose three

sides are unequal?

Scalene triangle.

183. If the three sides are equal, what is the name

of that triangle?

Equilateral.

184. What is the measure of each angle of an

equilateral triangle?

600.

185. In ABC, if ABC = ACB, which one of

the following is true?

AC = AB.

186. In a right angled triangle. Which is the largest

side?

Hypotenuse.


In an equilateral triangle ABC-

i. Three sides are equal.

ii. Three angles are equal .

iii. Measure of each angle is 60 degree


i, ii & iii.


i. Each angle except the right angle in

a right angled triangle is an acute

angle.

ii. Except the right angle in a right

angled triangle, one angle is

supplementary to another.

iii. The perpendicular drawn upon

hypotenuse from the vertex

containing right angle forms an acute

angle with the adjacent sides.


i & iii.

32 | P a g e

189. Observe the following information:\

i. Sum of three angles of a triangle is

1800.

ii. Sum of two sides of a triangle is

greater than its third side.

iii. In a scalene triangle, there are two

obtuse angle.


i & ii.


ABC is an isosceles triangle whose AB = AC.

i. C = B.

ii. If B = 700, then A = 40

0.

iii. If C = 700 and BD AC, then

CBD = 200.


i, ii & iii.


i. Opposite angle of the hypotenuse of

a right angled triangle is a right

angle.

ii. Sum of the rest two angles except

right angle of a right angled triangle

is 900.

iii. If the measure of each angle except

the right angle of a right angled

triangle is 450, the triangle is called a

isosceles right angled triangle.


i, ii & iii.

Answer the questions number 192- 194 based

on the following stem:

In the above mentioned figure, AB = AC,

AB CE, BE is the bisector of the ABC and

ECD = 700.

192. What is the measure of the BEC? 350.

193. What is the measure of the ABE? 350.

A

B D C

E

33 | P a g e

194. What is the measure of the BAC? 700.

Answer the questions number 195- 197 based

on the following stem:

In the above mentioned figure, AB = AC,

AD BC, BD is the bisector of ABC and

DAC = 680.

195. What is the measure of the ACB?

196. What is the measure of the BAD? 1360.

197. What is the measure of the BDA? 340.

198. Which data is reliable? Primary data.

199. Which data depends of primary data? Secondary data.

200. Which data is less important than the primary

data?

Secondary data

201. Any numerical information or event is called -

---.

Statistics.

202. The numerals used to indicate information or

event are -----.

Data.

203. The data arranged in ascending or descending

order is called … data.

Organised.

204. Which data are required to form frequency

distributive table?

Organised data.

205. Number of classes of the data = ( )

Class interval.

206. (Highest number – lowest number) + 1 =

what?

Range.

207. To draw histogram, the class interval of

frequency distribution table is taken along ----

axis.

x.

208. The frequency at convenient scale is

considered along ---axis.

y.

209. What type of geometric figures are used to Rectangle

A

B

D

C

.

34 | P a g e

draw histogram?

210. What refers to the numerical width of any

class in a particular distribution

Class interval.

211. ----- of an event is the number of times of the

observation occurred or recorded in an

experiment or study.

Frequency.

morning glory school & college study material class: vii

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