Post on 19-Feb-2022
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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.
(a) What is the value of 2a + 2b? 14.
(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.
(a) What is the value of 5a + 5b? 40.
(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.
(a) Draw the figure based on the stem.
(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.
(a) Draw the figure based on the stem.
(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.
(a) Draw the figure based on the information of the stem.
(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.
(a) Draw the figure based on the information of the stem.
(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.
(a) Draw the figure based on the information of the stem.
(b) Prove that, AC > AB.
(c) Prove that, AB + AC> 2AD.
73. In the ABC, AB = AC and D is a point of AC.
(a) Draw the figure based on the information of the stem.
(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.
(a) Draw the figure based on the information of the stem.
(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.
(a) Draw the figure based on the information of the stem.
(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
?
2. Which one of the following is the square root
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.
Which one of the following is correct?
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.
6. Which one of the following is the square root
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.
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ii. ( ) ( ) . iii. ( )( )
Which one of the following is correct?
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
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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.
61. Observe the following information:
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.
Which one of the following is correct?
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.
75. Observe the following information:
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.
Which one of the following is correct?
76. Observe the following information:
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.
Which one of the following is correct?
i & ii.
77. Observe the following information:
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.
Which one of the following is correct?
i . ii & iii.
78. Observe the following information:
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..
Which one of the following is correct?
i , ii & iii.
79. Observe the following information:
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.
Which one of the following is correct?
i & ii.
80. Observe the following information:
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.
Which one of the following is correct?
81. Observe the following information:
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.
Which one of the following is correct?
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.
Which one of the following is correct?
i, ii & iii.
83. i. Square root of 361 is 19.
ii. Square root of 196 is 14.
iii. Square of 18 is 324.
Which one of the following is correct?
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.
86. Observe the following information:
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.
Which one of the following is correct?
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.
94. Observe the following information:
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.
Which one of the following is correct?
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____ .
100. Observe the following information:
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.
Which one of the following is correct?
i, ii & iii.
101. Observe the following information:
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.
Which one of the following is correct?
i, ii & iii.
102. Observe the following information:
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.
Which one of the following is correct?
i, ii & iii.
103. Observe the following information:
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.
Which one of the following is correct?
104. Observe the following information:
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.
Which one of the following is correct?
i, ii & iii.
105. Observe the following information:
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.
Which one of the following is correct?
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
109. Observe the following information:
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.
123. Observe the following information:
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.
Which one of the following is correct?
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.
Which one of the following is correct?
i & ii.
125. Observe the following information:
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.
Which one of the following is correct?
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.
Which one of the following is correct?
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.
147. Observe the following information:
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)
Which one of the following is correct?
148. Observe the following information:
i. The multiplicative inverse of 5 is
.
ii. 0 –1 = –1.
iii. 3* ( )+
Which one of the following is correct?
i & iii.
149. Observe the following information:
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.
Which one of the following is correct?
i & ii.
150. Observe the following information:
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.
Which one of the following is correct?
i & ii.
151. Observe the following information:
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.
Which one of the following is correct?
ii & iii.
152. Observe the following information:
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
Which one of the following is correct?
i , ii & iii.
153. What will be the sum if – 5 is added to 11? 6.
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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.
187. Observe the following information:
In an equilateral triangle ABC-
i. Three sides are equal.
ii. Three angles are equal .
iii. Measure of each angle is 60 degree
Which one of the following is correct?
i, ii & iii.
188. Observe the following information:
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.
Which one of the following is correct?
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.
Which one of the following is correct?
i & ii.
190. Observe the following information:
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.
Which one of the following is correct?
i, ii & iii.
191. Observe the following information:
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.
Which one of the following is correct?
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
.