Download 9th - Maths - St. Claret School

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Question Bank
IX MATHS
CHAPTER – 1
Unit – 1 - Square Root
I. Choose the correct answer:
1. If a perfect square has n digits, then its square root has ____ digits. (if n is odd)
a) 2n
b) 4n
c)
d)
2. If a perfect square has n digits, then its square root has ___________ digits (if n is
even )
a) 2n,
b) n2
c)
d)
3. √
+√ = __________
a) 21
b) 19
c) √
√
4. Area of an equilateral triangle is ________________
a) (Side)2
b)
√
5. If a = b2, then b is the ___________ of a
a) Cube
b) cube root
6. √ - √ = ___________
a) 13
b) 2
7. √ × √ = _________________
a) 42
b) 40
8. √
c) √
d) √
d) r2
c) square
d) square – root
c) 15
d) 19
c) 13
d) 42
= ______________
a) √
b) ab
c)
√
√
d) a2b
II. Fill in the blanks:
9. A ________________ is the product of two equal numbers.
10. If a perfect square has 4 digits, its square root has __________ digits.
11. If a perfect square has 5 digits, its square root has ___________ digits.
12. √
-√
= _______________
13. √
= _____________
14. √
= ________________
√
15. The least number to be added to make 62 a perfect square is _______________
16. The least number to be subtracted to make 70 a perfect square is _____________
17. √
= ________________
√
18. √
+ √ = ________________
19. √
= ______________
20. √
= ____________
√
2
III. Do as directed: 2M
21. Find the square root of the following numbers by the factorization numbers:
82944
22. Find the square root of the following numbers by the factorization numbers:
155236
23. Find the square root of the following numbers by the factorization numbers:
19881
24. Find the square root of the following numbers:
19.5364
25. Find the square root of the following numbers:
184.96
26. Find the square root of the following numbers by division method:
5329
27. Find the square root of the following numbers by division method:
18769
28. Find the square root of the following numbers by division method:
28224
29. Find the square root of the following numbers by division method:
186624
30. Find the least number to be added to get a perfect square:
6200
31. Find the least number to be added to get a perfect square:
12675
32. Find the least number to be added to get a perfect square:
88417
33. Find the least number to be added to get a perfect square:
123456
34. Find the least number to be subtracted from the following numbers to get
square:
1234
35. Find the least number to be subtracted from the following numbers to get
square:
4321
36. Find the least number to be subtracted from the following numbers to get
square:
34567
37. Find the least number to be subtracted from the following numbers to get
square:
109876
38. Find the square root of the following numbers using division method:
651.7809
39. Find the square root of the following numbers using division method:
0.431649
40. Find the square root of the following numbers using division method:
95.4529
a perfect
a perfect
a perfect
a perfect
3
41. Find the square root of the following numbers using division method:
73.393489
42. Find the square root of the following numbers correct to 2 decimal places:
12
43. Find the square root of the following numbers correct to 2 decimal places:
1.8
44. Find the square root of the following numbers correct to 2 decimal places:
133
45. Find the square root of the following numbers correct to 2 decimal places:
12.34
46. Find the square root of the following numbers correct to 2 decimal places:
8.6666
47. Find the square root of the following numbers correct to 2 decimal places:
234.234
48. Find the square root of the following numbers correct to 2 decimal places
13
49. Find the square root of the following numbers correct to 2 decimal places
8.12
50. Find the square root of the following numbers correct to 2 decimal places
3333
51. Find √
by division method.
52. Find √
by division method.
53. Round off the following numbers to 3 decimal place (i) 12.341567
(ii) 1.73205
54. Find √
by division method.
55. Round off to 3 decimal places (i) 12.341567
(ii) 1.73205
56. Find √
by division method.
57. Find √
by division method.
58. Find the squares of 9, 10, 99, 100, 999, 1000. Tabulate these numbers.
59. Find the least number to be subtracted from 1234 to make it a perfect square.
IV. Solve the problems: 3m
60. A person has three rectangular plots of dimensions 112 m X 54 m, 84 m X 68 m and
140 m X 87 m at different places. He wants to sell all of them and buy a square plot of
integral length of maximum possible area approximately equal to the sum of these
plots. What would be the dimensions of such a square plot? How much area he may
have to lose?
61. A square garden has area 24686.6944 m2. A trench of one meter wide has to be dug
along the boundary inside the garden. After digging the trench, what will be the area
of the left out garden?
62. Find perfect consecutive perfect squares between which 4567 lie?
63. Find the least number to be added to make 88417 a perfect square?
64. Find √
by division method.
65. Find √
by division method.
66. Find √
by division method.
67. Find the square root of 12 and correct to 3 decimal places.
4
68. Find √
and correct to 3 decimal places.
69. Find the least number to be subtracted from 109876 to get a perfect square.
70. Find the square root of 19.5364.
71. Find the square root of 8 and correct to 2 decimal places.
V. Solve the problems: 4m
72. A square garden has area 900 m2. Additional land measuring equal area surrounding
it, has been added to it. If the resulting plot is in the form of square, what is its side?
(correct to 2 decimal places)
CHAPTER – 1
Unit – 2 – Real Numbers
I. Choose the correct answer: 1m
1. (-1) x (-1) = ________
a) -1
b) 1
2. √
3.
4.
5.
6.
7.
×
√
c) 0
d) 2
= ____________
a) 15
b) √
c) 1
d) 0
̅̅̅̅̅̅̅
0.11
= __________
a) 0.112233…
b) 0.1122332233… c) 0.1122333…
d) 0.123123…
In the decimal expansion 0. 33 …., length = ________
a) 0
b) 1
c) 3
d) 2
In the decimal expansion 0.00100…, __________ is the non repeating part
a) 4
b) 0
c) 004
d) nil
In the decimal expansion 0.153232…., ____________ is the repeating part
a) 32
b) 1532
c) 15
d) nil
In the decimal expansion 6.833….., _________ is the integer part
a) 8
b) 3
c) 6
d) 68
II. Fill in the blanks:
1. The set of rational and irrational numbers are called ___________
2. The repeating part of a rational number is called ____________
3. In a rational number the no of digits in the period is called ______________
4. The decimal expansion of ‘1’ is ___________
5. The square of a real number is always ___________
6. In a real number system _____________ is the additive identity.
7. In real number system __________ is the multiplicative identity.
8. Additive inverse of 1 + √ is _____________
9. Multiplicative inverse of √ is ___________
10. Every irrational number has an ______________ decimal expansion.
III. Solve the following: 2m
1. Write the additive inverse of the following nos.
a) √
b) 1 +
c)
√
d) 7 + √
5
2. What are the properties of R used in the following
a) a + ( + c) = (a + ) + c
b)
×1=
c) √ (1 + √ ) = 2 + √
d) 8 × 7 = 7 × 8
3. Write the multiplicative inverse of the following.
a) 3 + √
b)
-
c)
√
√
d) -10
4. Write down as the decimal expansion of
5. Write down the decimal expansion of
2.00̅̅̅̅
2013. ̅̅̅̅
0.11 ̅̅̅̅̅̅̅
5.8̅̅̅̅̅ (5.8̅̅̅̅̅)
0.00̅̅̅̅̅
6. Write the rational number for
7. Write the rational number for
8. Write the rational number for
9. Write the rational number for
10. Write the rational number for
IV. Solve the following: 3m
1. Find 3 irrational numbers between ⁄ and ⁄
2. Find 5 irrational numbers between 4 and 5.
3. Find 2 rational numbers between √ and √
4. Find 2 rational numbers between √ and √
V. Solve the following: 4m
1.
2.
3.
4.
Represent √ on number line.
Represent √ on number line.
Represent √ on number line.
Represent √ on number line.
CHAPTER – 1
Unit – 3 – Surds
I. Choose the correct answer:
1. In 5 √ , order is ______________
a) 5
b) 3
2. In 6 √ , radicand is __________
a) 6
b) 4
3.
c) 4
d) 2
c) 5
d) 2
c)
d)
c) 3
d) 24
c) an
d)
= _______________
a)
b)
⁄
4. ( ) = _______________
a) 2
b) 8
5.
= ________________
a) a-n
b) a
6
II. Fill in the blanks:
1. let a and b be positive real numbers, and let r1 and r2 be two rational number then
= _____________
2. the simplest form of √ is ______________
3. √ , 4 √ and 10 √ are ______________ surds.
4.
√ , 3 √ and 4 √ are ____________ surds.
5. √ √ and√ are ____________ surds.
6. The index form of √ is ______________.
III. Solve the following: 2m
1. Define surds? Give two examples.
2. Define mixed surds? Write two examples.
3. Define like and unlike surds?
⁄
4. Simplify:
⁄
5. Simplify: (
⁄
⁄
⁄
)
⁄
6. Write into simplest form
a) √
b) √
7. Write into simplest form
a) √
⁄
b) √
⁄
8. Reduce into same order
√ √
√
√
√
√
√
√
9. Reduce into same order
10. Reduce into same order
√
11. Find which is larges:
3 √ and 4 √
12. Find which is smaller
√ and√
13. Write in ascending order.
√
√
√
14. Write in descending order.
√ √ and√
IV. Solve the following: 3m
1. Simplify:
(16)-0.75 × (64)4/3
2. Simplify:
(0.25)0.5 × (0.01)-1
3. Simplify:
(6 . 25)0.5 × 102 × (100)-1/2 × (0.01)-1
4. Classify into like surds.
,√
,√ , √ ,√
√
5. Classify into like surds:
, √
, √
,√
√
6. Write the following into descending order √ √ , √ √
7. Arrange into ascending order:
√√ ,
√√
and √ √
,√
, √√
,√
.
7
V. Solve the following: 4m
1.
[
⁄
,
2. Simplify *,(
⁄
⁄
⁄
⁄
(
)
⁄
)⁄
-
,
] Find the value.
(
⁄
⁄
)-+
⁄
CHAPTER – 1
Unit – 4 – Sets
I. Choose the correct answer:
1. Founder of set theory ____________
a. George
b. George Cantor
c. Aryabatta
d. Pythogram
2. The objects in sets are called
a. Elements or members
b. Integers
c. Numbers
d. None of these
3. The visualize operations of sets using diagram are called ______________ diagram.
a. Graph
b. Venn diagram
c. Pictorial representation
d. Power point
4. Which of the following is a set?
a. All students of your school
b. Good teachers of your school
c. Honest students of your school
d. Disciplined students of the school
5. Here A∩ B is ________________
a. 1,3
b. 5,6
c. 2,4
d. 1,2,3,4,5,6
6. Let U={1,3,4,5,6,7,8} & B={1,3,4}. The compliment of B| is ______________
a. {1,3,5}
b. {5,6,7,8}
c. {1,2,4}
d. { }
7. Let A={3,6,15,9,12,18,21,24} B={4,8,12,16,20,24} A\B=_________________
a. {4,8,16,20}
8
b. {3,6,9,15,18,21}
c. {4,5,21,22}
d. {3,6,5,21,22}
8. If A={1,2,3} then 2A is ___________
a. 23
b. 21
c. 24
d. 2B
9. If is A subset of U, then U\A = ___________
a. A
b. A|
c. U
d. U|
II. Fill in the blanks:
10. Representing a set by writing all elements is called ______________ method
11. Set builder method is also called __________ method
12. Venn diagram are introduced by _________
13. Two sets A and B are said to be __________ if no element of B is in A and no
element of A is in B.
14. The sets containing only one element is called a ________
15. Two sets A&B are disjoint if only if A∩B = __________
16. In the adjacent diagram AUB is ___________________
17. A set of all vowels A = {a, e, I, o, u} represent the above in set builder method
18. In the adjacent Venn diagram find & write the elements of B/A is __
19. __________ is subset of every set.
20. In the adjacent diagram find A∩B
21. If A = {1,3,5,7} and B is {5,7,8} then A/B = ___________
22. If A = {p, q, r, s} and B = r, s, t} then B/A =_____________
23. If A = {1, 2, 3, 4, 5, 6} and B is {6, 7, 8} then AΔB = __________
24. If A = {a, b, c, d} U = {a, b, c, d, e, f} find A| in U
25. If A = {x/x is a even number less than 10} and B = {x/x is a square number less than
10} find A∩B
9
26. In the set A, B & C A∩B∩C is_____________
27. In the set A, B & C find AUBUC is ____________
28. State whether the set is finite or infinite set of points on a line is _______set
29. The colour of rainbow if we represent the set in roaster method the elements are
___________
30. If A = {P,Q, R, S} and B = {S, T, U, W} the intersection of A and B is ___________
31. A = {1, 4, 9, 16, 25, 36} if we represent the set in rule method the statement is written
as ________
III. Solve the following: 2m
32. If A ={ 1,2,3,4}, U= {1,2,3,4,5,6,7,8}, find A in U and draw Venn diagram.
33. If U={x|x  25, x  N}, A={ x | x  U , x  15 }and B = { x | x  U ,0  x  25 },list
elements of the following sets and draw Venn diagram: A in U
34. If U={x | x  25, x  N}, A={ x | x  U , x  15 }and B = { x | x  U ,0  x  25 },list
elements of the following sets and draw Venn diagram : B  in U
35. If U={x | x  25, x  N}, A={ x | x  U , x  15 }and B = { x | x  U ,0  x  25 },list
elements of the following sets and draw Venn diagram :A \ B
36. If U={x | x  25, x  N}, A={ x | x  U , x  15 }and B = { x | x  U ,0  x  25 },list
elements of the following sets and draw Venn diagram : A ∆ B
37. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and
{6,8,10,12,7}. Write down the following sets and draw Venn diagram : A
38. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and
{6,8,10,12,7}. Write down the following sets and draw Venn diagram : B 
39. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and
{6,8,10,12,7}. Write downthe following sets and draw Venn diagram : C 
40. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and
{6,8,10,12,7}. Write down the following sets and draw Venn diagram : ( A)
the
the
the
the
C=
C=
C=
C=
41. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C=
{6,8,10,12,7}. Write down the following sets and draw Venn diagram : ( B )
42. Suppose U= {3,4,5,6,7,8,9,10,11,12,13}, A= {3,4,5,6,9}, B = {3,7,9,5}and C=
{6,8,10,12,7}. Write down the following sets and draw Venn diagram : (C ).
43. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram: A
44. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram: B 
10
45. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram: A  B
46. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram: A  B
47. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram:  A  B 
48. Suppose U= {1,2,3,4,5,6,7,8,9}, A= {1,2,3,4}, B = {2,4,6,8}.write down the following
sets and draw Venn diagram:  A  B 
49. Find (A/B) and (B/A) for the following sets and draw Venn diagram:
A={a,b,c,d,e,f,g,h} and B = {a,e,i,o,u}
50. Find (A/B) and (B/A) for the following sets and draw Venn diagram:
A = {1,2,3,4,5,6} and B = {2,3,5,7,9}
51. Find (A/B) and (B/A) for the following sets and draw Venn diagram:
A = {1,4,9,16,25} and B = {1,2,3,4,5,6,7,8,9}
52. Find (A/B) and (B/A) for the following sets and draw Venn diagram:
A = {x | x is a prime number less than 5} and
B = {x | x is a square number less than 16}
53. Find A B and draw Venn diagram when:
A = {a, b, c, d} and B = {d, e, f}
54. Find A B and draw Venn diagram when:
A = {1, 2, 3, 4, 5} and B = {2, 4}
55. Find A B and draw Venn diagram when:
A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6}
56. Find A B and draw Venn diagram when:
A = {1, 4, 7, 8} and B = {4, 8, 6, 9}
57. Find A B and draw Venn diagram when:
A = {a, b, c, d, e} and B = {a, c, e, g}
58. Find A B and draw Venn diagram when:
A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7}
59. Find union of A and B, and represent it using Venn diagram:
A = {1, 2, 3, 4, 8, 9}, B = {1, 2, 3, 5}
60. Find union of A and B, and represent it using Venn diagram:
A = {1, 2, 3, 4, 5,}, B = {4, 5, 7, 9}
61. Find union of A and B, and represent it using Venn diagram:
A = {1, 2, 3}, B = {4, 5, 6)
62. Find union of A and B, and represent it using Venn diagram:
A = {1, 2, 3, 4, 5}, B = {1, 3, 5}
63. Find union of A and B, and represent it using Venn diagram:
A = {a, b, c, d} , B = {b, d, e, f}
64. Find the intersection of A and B, and represent it by Venn Diagram:
A = {a, b, d,e} , B = {b, d, e, f}
65. Find the intersection of A and B, and represent it by Venn Diagram:
A = {1, 2, 4, 5}, B = {2, 5, 7, 9}
66. Find the intersection of A and B, and represent it by Venn Diagram:
A = {1, 3, 5, 7}, B = {2, 5, 7, 10 12}
11
67. Find the intersection of A and B, and represent it by Venn Diagram:
A = {1, 2, 3}, B = {5, 4, 7}
68. Find the intersection of A and B, and represent it by Venn Diagram:
A = {a, b, c}, B = {1, 2, 9}
69. Find A  B and A  B when:
A is the set of all prime number and B is the set of all composite natural numbers.
70. Find A  B and A  B when:
A is the set of all positive real numbers and B is the set of all negative real numbers
71. Find A  B and A  B when:
A = N and B = Z
72. Find A  B and A  B when:
A = {x | x Z and x is divisible by 6} and
B = {x | x Z and x is divisible by 15}
73. Give examples to show that
A  A  A and A  A  A
IV. Do as directed: 3m
74. Find A Δ B and draw venn diagram if A = {1, 3, 5, 7} and B = {5, 7, 8}
75. If U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 5, 8} and B = {0, 1, 3, 5, 6}.
Find i) ( A  B) ii) ( A  B) . Draw venn diagram.
76. Find A Δ B if A = {a, b, c, d, e} and B = {a, c, e, g}. Draw venn diagram.
77. If U = { X : X N and X 9}, A = { X : X is a prime number less than 9}, B= { X :
X is perfect square less than 10} then find (A B) and draw venn diagram.
78. If A = { X/X is a prime number less than 5} and B= { X/X is a multiples of 2 than 10}
then find A\ B and B \ A and also find A Δ B, draw venn diagram for A Δ B.
79. If U = {a, b, c, d, e, f, g, h, i}, A = {a, d, f, h, i} and B = {a, b, d, h} show that
( A  B) = A  B
80. If U = {0, 1, 2, 3, 4, 5, 6, 7}, A={0, 2, 4,5} and B={0, 1, 2, 5,7} then show that
( A  B) = A  B
V. Solve the following: 4m
CHAPTER – 1
Unit – 5 – Statistics
I. Choose the correct answer:
1. The difference between the highest and lowest scores in a given distribution is called
___________
a) Mean
b) range
c) median
d) mode
2. The most repeated score in an ungrouped data is called ___________
a) Mean
b) median
c) mode
d) range
3. The average of the scores is called ____________
a) Mean
b) median
c) mode
d) deviation
4. Among the following, which is not a measure of dispersion?
a) Range
b) median
c) quartile deviation d) mean deviation
12
5. Mean of the following scores 3, 5, 7, 8, 10 is ____________
a) 5
b) 6
c) 6.6
6. The mode of the scores 18, 17, 20, 5, 22, 20, 23 is ___________
a) 18
b) 5
c) 17
7. Co – efficient of range is given by __________
a)
b)
(
c)
)
d)
(
d) 7.2
d) 20
)
8. The mean deviation is calculated by _____________
a) ∑| |
b)
∑| |
c) ∑ | |
d) ∑ | |
9. The event will not occur, if the probability is _______________
a) 1
b) 0.5
c) 0
d) 0.9
II. Fill in the blanks:
1. ________________ is a mathematical measure of uncertainly of events
2. Half of the inter quartile range is called ____________
3. Quartile divide the distribution into __________ parts.
4. Range = is calculated by using the formula _____________
5. The formula to calculate mean is ____________
6. Quartile deviation is calculated by using the formula _____________
7. The difference between the upper and lower quartile values is called ___________
8. In a histogram ____________ are marked on s-axis
9. The collection of numerical facts is called ____________
10. The graph obtained by plotting frequency against mid point of the class interval is
____________
III. Solve the following: 2m
1. What are the measuresof dispersion?
2. Calculate the range and coefficient of range for the following data.
122, 144, 154, 101, 168, 118, 155, 133, 160, 140.
3. Marks scored by 10 students in a test 31, 18, 27, 19, 25, 28, 49, 14, 41, 22, 33, 13.
Calculate range and coefficient of range.
4. Number of trees planted in 6 months 186, 234, 465, 861, 290, 142. Calculated range
and coefficient of range.
5. Calculate quartile deviation for the following data
3, 5, 8, 10, 12, 7, 5.
6. The runs scored by a batsman in five innings are 28, 60, 85, 58, 74, 20, 90. Find Q1,
Q2, Q3 and Quartile deviation.
7. Calculate mean deviation about mean for the following data
14, 21, 28, 21, 18
8. Find the mean deviation about mean for the following data
15, 18, 13, 16, 12, 24, 10, 20.
9. Find the mean deviation about medium for the following data
18, 23, 9, 11, 26, 4, 14, 21
10. A dice has the faces numbered 2, 4, 6, 8. 10 and 12. It is thrown once. What is the
probability that an even numbered face shown up?
13
11. In a pack of 52 playing cards, a card was selected at random. What is the probability
that the card selected was both red and black?
IV. Do as directed: 3m
1.
2.
3.
4.
5.
Calculate quartile deviation for the data: 30, 18, 23, 15, 11 29, 37, 42, 10, 21
Calculate quartile deviation for the data 3, 5, 8, 10, 12, 7, 5
Find the mean deviation about mean 14, 21, 28, 21, 18
Find the mean deviation about mean 15, 18, 13, 16, 12, 24, 10, 20
Construct histogram of variable width of the data
CI
25.29
30-35
36-40
41-50
51-56
57-60
f
10
24
15
20
12
16
6. Construct histogram
CI
0-10
10-15
15-20
20-30
30-40
40-60
60-70
f
20
15
10
25
5
30
50
7. Draw 0 gives (cumulative frequency curves) for the data
C-I
Frequency
1000-1100
52
1100-1200
35
1200-1300
25
1300-1400
14
1400-1500
41
1500-1600
33
8. Construct frequency polygon for the data
C-I
Frequency
5-10
2
10-15
5
15-20
7
20-25
6
25-30
1
30-35
9
35-40
14
40-45
8
9. Draw 0 gives (cumulative frequency curves)
C-I
Frequency
5-14
4
15-24
8
25-34
12
35-44
14
45-54
6
55-64
4
65-74
18
75-84
24
10. Runs scored by 22 batsmen in a test match are given here.
Runs
0-9
10-19 20-29 30-39 40-49 50 & along
No. of batsman
2
4
3
5
4
4
Find the probability that a batsman selected at random scored runs.
14
a) Between 0 and 9?
b) Between 20 and 39 and
c) Above 50
V. Solve the following: 4m
1. The heights of 100 students in 9th standard are given below.
Height (cm) 100 – 110 110 – 120
No. of
10
12
students (f)
Find quartile deviation.
120 – 130
16
130 – 140
30
140 – 150
12
150 – 160
20
2. Calculate mean deviation about mean for the given frequency distribution.
Class Interval
Frequency
1–5
2
6 – 10
3
11 – 15
4
16 - 20
1
3. The distribution of the ages (in years) of 20 persons in a locality are recorded as follows.
Age (in years)
30 - 34
35 – 39
No. of persons
2
5
Calculate mean deviation about mean.
40 - 44
6
45 - 49
5
50 - 54
2
4.The following frequency distribution shows the daily wages earned by 15 workers.
Wage (Rs)
30 – 40
40 – 50
No.of
2
3
workers
Calculate mean deviation about mean.
50 - 60
5
60 70
3
70 - 80
2
CHAPTER – 2
UNIT – 1 BANKING
II. Fill in the blanks:
1. ________________ is an institution that carries out the business of accepting the
deposit, lending money and investing money.
2. Single account and joint account are the types of ______________ account.
3. On opening SB account, a small book called saving bank ________ is issued by the
book.
4. A _____________ is an unconditioned order to the bank to pay the money on demand
in favour of a person/institution.
5. A ________________ is a form of cheque that is issued and guaranteed by the bank.
6. At present the interest is calculated on __________ product basis.
IV. Solve the following: 3m
7. The details of the entries of the passbook of Louis are given here. Calculate the
interest at rate of 4% per annum he gets the month on daily product basis.
15
Date
01.09.2011
02.09.2011
08.09.2011
17.09.2011
26.09.2011
Particulars
Balance
Forward
By Cheque
By cash
To Ravi
By draft
Cheque No.
Debit
Credit
Balance
4100.00
234156
314762
3000.00
500.00
1000.00
1700.00
4600.00
5600.00
2600.00
4300.00
8. Entre the following particulars into a saving Bank Pass book.
a) Balance brought forward Rs. 2250.
b) By Cash : Rs 3,500 on 6.06.2012
c) To self : Rs. 1,250 on 11.06.2012
d) By bank draft : Rs. 4,800 on 23.06.2012
e) By cheque no: 323263 Rs. 750 on 30.06.2012
9. The entries in an SB account pass book are given below. Calculate the interest at 4%
per annum for the month on daily product basis.
Date
Particulars
Cheque No. Debit
Credit
Balance
01.05.2010 Balance Forward
2842.00
4.05.2010 By cash
4600.00 7442.00
12.05.2010 To Geetha
843655
2500.00
4942.00
21.05.2010 To self
800.00
4142.00
30.05.2010 By Cheque
560090
7500.00 11642.00
10. The entries in an SB account pass book are given below. Calculate the interest at 4%
per annum for the month on daily product basis.
Date
Particulars
Cheque No. Debit
Credit
Balance
1.01.2009 Balance forward
6400.00
05.01.2009 By cash
2200.00 8600.00
10.01.2009 To cheque
945800
1250.00
7350.00
21.01.2009 By cash
7800.00 15150.00
27.01.2009 By Cheque
663119
750.00 15900.00
30.01.2009 By Cheque
124322
2100.00
13800.00
CHAPTER – 2
UNIT – 2 COMPOUND INTEREST
I. Choose the correct answer:
1. In compound interest principal _______________ for every period of time
a) Increases
b) decreases
c) remains
d) same
2. In fixed deposits, we get _______________ interest
a) Zero
b) simple
c) compound
d) unit
3. For appreciation, the growth factor is _______________
a) 1
b) greater than 1
c) less than 1
d) zero
4. For depreciation, the growth factor is __________________
a) 1
b) greater than 1
c) less than 1
d) zero
16
5. When the interest is compounded at different rates for successive years, amount is
____________
a)
(
)
(
b)
(
)
c)
(
)(
)
d)
)
II. Fill in the blanks:
1.
2.
3.
4.
The formula to find simple interest is ________________
The interest calculated on the principal and the accrued interest is called ___________
The formula to find amount when interest is compound annually is _____________
The formula to find amount when interest compounded half yearly (semi-annually) is
________________
5. The formula to find amount when interest compounded quarterly is
_______________
6. The population after n years is calculated using the formula __________________
7. Formula for depreciation or cost of vehicles after n years is _________________
III. Solve the following: 2m
1. Find the compound interest when principal is Rs. 7000, at 6% p.a and period is years
(compounded annually)
2. Calculate the compound interest that Shwetha gets by investing Rs. 5000 for 2 years
at 9% p.a (compounded annually)
3. Sanju deposited Rs. 700 in a bank for 2 years at 10% p.a Find compound interest
(compounded annually)
IV. Solve the following: 3m
1. Calculate amount & compound interest Rs. 12,000 for 2 years at 10% compounded
annually.
2. Calculate amount & compound interest Rs. 20,00 for 2 years at 8% compounded
annually.
3. Calculate amount & compound interest Rs. 5000 for 1 year at 4% compounded semi
– annually.
4. Rs. 10,000 for
years at 5% compounded half yearly.
5. Rs. 500 for 1 year at 2% compounded annually.
6. The present population of a village is 18,000. It is estimated that the population grows
by 3% per year. Find the population after 2 years.
CHAPTER – 2
UNIT – 3 Hire Purchase And Installment Buying
I. Solve the following: 2m
1. Mention the difference between hire purchase and installment.
II. Solve the following: 3m
17
1. The cost of a cell phone is Rs. 8,000 and the down payment is Rs. 1,000. The balance
amount is to be paid in 8 equal installment of Rs. 1,000. Find the rate of interest.
2. A washing machine costs Rs. 10,200 cash down payment of Rs. 2,000 and the
balance was agreed to be paid in 6 equal monthly installments of Rs. 1,500 each. Find
the rate of interest.
3. The cost of a motor bike is Rs. 48,000. The company offers it in 30 months of equal
installments at 10% rate of interest. Find the equated monthly installment.
4. The cost of a set of home appliances is Rs. 36,000. Siri wants to buy them under a
scheme of 0% interest and by paying 3 EMI in advance. The firm changes 3% as
processing charges. Find the EMI and the total installment for a period of 24 months.
5. Define:
a) down payment
b) installment
c) equated monthly installment (EMI)
I.
1.
2.
3.
CHAPTER – 2
UNIT – 4 RATIO AND PROPORTION
Choose the correct answer: 1m
The simplest form of 14:21 is ___________.
a) 2:3
b) 4:1
c) 1:2
d) 7:7
The simplest form of 20:100 is ________.
a) 2:10
b) 1:5
c) 5:20
d) 40:200
The third proportion of 16 and 8 is ________.
a) 2
b) 4
c)
d) 12
4. The fourth proportion of 5, 7, 15 is ________.
a) 21
b)
c) 17
5. In the proportion x:5 = 3:6, x = ____.
a) 10
b) 2.5
c) 5
d) 30
d) 3
II.
Fill in the blanks: 1m
1. In the ratio a : b, the first term ‘a’ is called ________ and the second term b is called
_________.
2. Ratio tells how many times the _________ is there in the second term.
3. A proportion is equality of two _________.
4. In the proportion a : b = c : d, we say a, d are ________.
5. In the proportion a : b = c : d, we say b, c are _______.
6. If three terms a, b, c are such that a : b = b: c we say ______ is the mean proportion.
7. If three terms a,b,c are such that a : b = b : c we say c is the ________.
8. In a proportion a : b = c : d, we say _______ is the fourth proportion of a, b, c.
9. If a : b = c : d and a b then (a – b) : (a – b) = __________.
10. If A can do a job in m units of time and B can do the same job in n units of time, then
A and B can do the job in t units of time where = __________.
18
11. In a school there are 850 pupils and 40 teachers. Then the ratio of teachers to pupils is
___________.
III.
Solve the following: 2m
1. On a map a distance of 5 cm represents an actual distance of 15 km. Write the ratio of
the scale of the map.
2. What number should be added to the terms of 49 : 68 to get the ratio 3: 4?
3. Find the mean proportion between 4 and 25.
4. Find the mean proportion between 0.3 and 2.7.
5. Find the mean proportion between 16 and 6.
6. Find the third proportion of 16 and 8.
7. Find the third proportion of 5 and 16 .
8. Find the fourth proportion of 5, 7, 15.
9. Find the fourth proportion of 3 , 1 , 2 .
10. In a map cm represents 25km. If two cities are 2
cm apart on the map, what is the
actual distance between them?
11. Suppose 30 out of 500 components of a computer were found defective at this rate
how many defective components would be found in 1600 components?
12. Suppose A alone can finish a piece of work in 15 days and B alone can do it in 20
days. If both of them work together, how much time will they take to finish it?
13. Tap A can fill a tank in 8 hours while tap B can fill it in 4 hours. In how much time
will the tank be filled if both A and B are opened together?
14. There are two pipes A and B connected to a tank. It is know that A can fill the tank in
4 hours while B can empty the tank in 6 hours. If both the pipes are opened together
how much time will it take to fill up the tank?
IV.
Solve the following: 3m
1. Find the value of x
a) x : 5 = 3 : 6
b) 13 : 2 = 6.5 : x
2. Find the value of y
a) 4 : y = 16 : 20
b) 2 : 3 = y : 9
3. Suppose A and B together can do a job in 12 days. While B alone can finish it in 30
days. In how many days A alone finish the work?
4. Suppose A is twice as good a work-men as B and together they can finish a job in 24
days. How many days A alone takes to finish the job.
5. Suppose B is 60% more efficient than A. If A can finish a job in 15 days, how many
days B needs to finish the same job.
V. Solve the following: 4m
CHAPTER – 3
Unit – 1 Multiplication of Polynomials
I. Choose the correct answer:
1. 2x – 3 is a _______________ polynomial
19
a) Linear
b) Constant
c) Quadratic
2
2. 8x + 10x + 3 is a _______________ polynomial.
a) Linear
b) Quadratic
c) Constant
3. (x + 5) (x -2) = _________
a) X2 – 7x + 10
b) x2 + 3x – 10
c) x2 + 3x + 10
4. (a + b+ 2c)2 = _______________
a) a2 + b2 + c2 + 2ab + 2bc + 2ac
b) a2 + b2+4c2 + 2ab + 4bc + 4ac
c) a2 + b2 + 4c2- 2ab - 4bc - 4ac
d) a2 + b2 + c2- 2ab - 2bc - 2ac
5. If a + b + c = 0, then
d) Zero
d) Zero
d) x2 – 3x – 10
= ______________
a) abc
b) 3
c) 3abc
d) 1
6. An identity is valid for all values of the _____________ in it.
a) Variables
b) constants
c) terms
3
2
7. x – 8 = ____________ (x + 2x + 4)
a) x + 2
b) x – 2
c) (x+2) (x – 2)
d) coefficients
d) (x2 – 2x + 4)
8. If a+b+c = 0 then
a) 3abc
b) -3
c) 3
9. (x-a) (x-b) (x-c) = ________________
a) x3 – (a+b+c) x2 + (ab + bc + ac) x – abc
b) x3 + (a+b+c) x2 + (ab + bc + ac) x + abc
c) x3 - (a+b+c)x2 + (ab + bc + ac) x + abc
d) x3 + (a+b+c) x2 + (ab + bc + ac) x – abc.
II. Fill in the blanks:
1. Degree of a constant polynomial is ________________
2. Degree of a linear polynomial is _____________
3. Degree of a quadratic polynomial is ______________
4. (x + a) (x + b) = ______________
5. 9x2 – 25y2 = _________________
6. (a + b)3 = _______________
7. (a – b)3 = _______________
8. a3– b3 = _______________
9. a3 + b3 = _______________
10. (x + b) (x + b) (x + c) = _______________
III. Solve the following: 2m
1.
2.
3.
4.
5.
6.
7.
Evaluate the following products:(x + 3)(x + 2)
Evaluate the following products:
(x + 5)(x – 2)
Evaluate the following products:
(y – 4)(y + 6)
Evaluate the following products:(a – 5)(a – 6)
Evaluate the following products:(2x + 1) (2x – 3)
Evaluate the following products:(a + b)(c + d)
Evaluate the following products:(2x – 3y)(x – y)
d) a+b+c
20
8. Evaluate the following products:(√ x + √ )(√ x + √ )
9. Evaluate the following products:
(2a + 3b)(2a – 3b)
2
10. Evaluate the following products: (x + y2)(x2 – y2)
11. Evaluate the following products:(6xy – 5)(6xy + 5)
12. Evaluate the following products:( + 3)( – 7)
13. Expand the following using appropriate identity:(a + 5)2
14. Expand the following using appropriate identity:(2a + 3)2
15. Expand the following using appropriate identity:(x + )2
16. Expand the following using appropriate identity:(√
a + √ b)2
)2
17. Expand the following using appropriate identity:( +
18. Expand the following using appropriate identity:(y – 3)2
19. Expand the following using appropriate identity: (3a – 2b)2
20. Expand the following using appropriate identity:(y - )2
21. Expand the following using appropriate identity: (√
22. Expand the following using appropriate identity: ( -
x - √ y)2
)2
23. Expand the following using appropriate identity:
(2x + 3)(2x +5)
24. Expand the following using appropriate identity:(3x – 3)(3x + 4)
25. Expand: (x + 3)(x – 3)
26. Expand: (3x – 5y)(3x + 5y)
27. Expand: ( + )( - )
28. Expand: (x2 + y2) (x2 - y2)
29. Expand: (a2 +4b2)(a + 2b)(a – 2b)
30. Expand: (x - 4)(x + 4)(x – 3)(x + 3)
31. Expand: (x – a)(x + a)( - )( + )
32. Find the product of : (x+4)(x+5)(x+2)
33. Find the product of : (a+2)(a-3)(a+4)
34. Find the product of : (x-5)(x-6)(x-1)
35. Find the cube of (2x+y)
36. Find the cube of (4a+3b)
37. Find the cube of (x+1/x)
38. By using the identity find the cube of 51.
39. Find the product of 101×105×102.
40. Find the product of 95×98×103.
41. Expand (a+b+2c) ² .
42. Expand (p+q-2r) ².
43. Expand (m-3- 1/m) ².
44. Find the cube of (x-1/x).
21
45. Find the cube of (2x-√5).
46. Find the cube of 108 by using the identity.
47. If x+1/x=3 prove that x³+1/x³=18.
48. If p + q=5 and pq=6 find p³+q³.
49. If a-b=3 and ab=10 find a³-b³.
50. If a+b+c=12 and a²+b²+c²=50 find ab+bc+ca.
51. If a, b, c are non-zero numbers such that a+b+c=0 prove that a+b/c + b+c/a +
c+a/b = -3
52. If a+b+c=abc prove that (1+a²)=(1-ab)(1-ac)
53. If a+b+c=0 prove that (b+c)(b-c)+a(a+2b)=0
54. If a+b+c=0 prove that (ab+bc+ca)²=a²b²+b²c²+c²a².
55. If a+b+c=0 prove that (a+b)(a-b)+ca-cb=0.
56. If a+b+c=0 prove that a²/bc + b²/ca + c²/ab = 3.
57. If a+b+c=0 prove that (b²-4ac) is a square.
58. If a+b+c=2s prove that s(s-a)+s(s-b)+s(s-c)=s².
59. If a+b+c=2s prove that s²+(s-a)²+(s-b)²+(s-c)²=a²+b²+c².
60.If x²-3x+1=0 prove that x²+ 1/x² =7.
IV. Solve the following: 3m
1. Simplify the following:
2. Simplify the following:
3. Simplify the following:
(2x – 3y)2 + 12xy
(3m + 5n)2 – (2n)2
(4a – 7b)2 – (3a)2
4. Simplify the following:
(x + )2 -(m - )2
5. Simplify the following:
6. Simplify the following:
(m2 + 2n2)2 – 4m2n2
(3a – 2)2 – (2a – 3)2
7. Find the volume of the cuboid with dimensions (x-1),(x-2) and (x-3).
8. The length ,breadth and height of a cuboid are (x+3),(x-2) and (x-1) respectively.
Find its volume.
9. The length ,breadth and height of a metal box are (x+5),(x-2) and (x-1)
respectively. Find its volume.
10. If a²+ 1/a²=20 and a³+ 1/a³=30 . Find a+ 1/a.
11. Simplify (3x+4y+5)²- (x+5y-4)².
22
12. Simplify (a-b+c)² – (a-b-c)².
13. (2m-n-3p)² + 4mn – 6np + 12pm.
14. If a+b+c=0 prove that a(b-c)²+b(c-a)²+c(c-b)²= -9abc.
15. If a+b+c=2s prove that (s-a)(s-b)+(s-b)(s-c)+(s-c)(s-a)+s²=ab+bc+ca.
CHAPTER – 3
Unit – 2 Factorisation
I. Choose the correct answer:
1. (5x2 – 20xy) = - (x – 4y)
a) 5x
b) x – y
c) 5x – 4y
d) x
2. 7xa – 70xb = 7x( _______ )
a) (a – b)
b) (a – 10b) c) (a – b)
d) (7a – 10b)
3
3
3. a – b = (a – b) ( _______ )
a) (a2 + ab + b2)
b) (a2 – b2)
c) (a2 – ab + b2)
d) (a2 + b2)
4. If a + b + c = 0 then a3 + b3 + c3 = ___________.
a) 3
b) 3abc
c) abc
d) 0
4
2 2
4
2
2
5. a + a b + b = (a +b + ab) ( _________ )
a) (a2 + b2) b) (a2 + b2 – ab)
c) (a + b + c) d) a2 – b2
II. Fill in the blanks:
1. The process of writing a given algebraic expressions as a product of two or more
expressions is called __________.
2. Factors of 9x2 + 12xy are ______ and (3x + 4y).
3. Factors of 25 – 50p – 100q are (1 – 2p – 4q) and ____________.
4. a3 + b3 = _______________.
5. a3 + b3 + c3 – 3abc = _______________.
6. (a + b + c)3 – a3 – b3 – c3 = __________.
III. Solve the following: 2m
1. Factorise:
2. Factorise:
3. Factorise:
4. Factorise:
5. Factorise:
6. Factorise:
7. Factorise:
8. Factorise:
9. Factorise:
10. Factorise:
11. Factorise:
12. Factorise:
a2 – ba + ac – bc
3x3 – 5x2 + 3x + 5
y4 – 2y3 + y – 2
25x2 – 64y2
12m4 – 75n4
(x + 4y)2 - 4z2
x2 + 11x +30
2x2 - 7x – 39
x2 + 9x +18
15x2 – x – 28
x3 + 27
27t3 – 343
23
13. Factorise:
⁄ +1
3
14. Factorise: 32x – 500
15. Factorise: x7 + xy6
IV. Solve the following: 3m
1. If x+y+4=0 find the value of x3+y3-12xy+64
2. If x=2y+6 find the value of x3-8y3-36xy-216.
3. Factorise
x3 – 8y3 – 27 – 18xy.
4. Factorise
a3+27b3 + 8c3 – 18abc.
5. Factorise
8a3 + 125b3 – 64c3 + 120abc
6. Find the prime factorization of
303 – 123 – 103 - 83
7. Find the prime factorization of
853 – 683 + 53 - 223
8. Without actually calculating the cubes find the value of (-12)3 + 73+53
9. Without actually calculating the cubes find the value of (-10)3 + 33 + 73
10. If a + b = 6 and ab = 8 find the value of a3+b3
11. Factorise:
3(x+y)3 + (xy)3
12. Factorise:
x6 – y6
13. Factorise:
a3 – b3 – a+b
14. Factorise:
x6 – 26 x3 – 27
15. Factorise:
64 a4 + 1
16. Factorise:
3 x4 + 12y4
17. Factorise:
2 (x + y)2 – 9(x+y) – 5
18. Factorise:
9 (2x – y)2 – 4 (2x – y) – 13
19. Factorise:
4x4 + 7x2 – 2
20. Factorise:
8x3 – 2x2y – 15xy2
21. The radices of a circle are 13cm in which a chord of 10cm is drawn. Find the distance
of the chord from the center of the circle.
22. Prove that (1+ ⁄ )(1 - ⁄ ) (1 +
⁄ ) (1 +
⁄ )+( )=1
23. Factorise by adding and subtracting appropriate quantity.
x2 + 10x + 8
24. Factorise by adding and subtracting appropriate quantity.
x2+ 2x - 1
V. Solve the following: 4m
CHAPTER – 3
Unit – 3 HCF and LCM
I. Choose the correct answer:
1. HCF of (a + b), (a + b)2 and (a +b)3 is ______________
a) (a + b)
b) (a + b)2
c) (a + b)3
2. LCM of 8x4 a2 and 48x2b4 is ______________
a) 8x2 b2
b) 8x4b4
c) 48x2a2b2
3. HCF of 9x2y2z3 and 15x3y2z4 is ______________
d) a3 + b3
d) 48 x4a2b4
24
4.
5.
6.
7.
8.
a) 3x2y2z3
b) 9x2y2z3
c) 15x3y2z4
HCF of 2x, 4y and 6z is ______________
a) 24xyz
b) 2xyz
c) 2
HCF of 2a, 3b, and 5c is __________
a) 1
b) 30
c) abc
3
3
LCM of (a – b) and (a – b ) is ____________
a) (a-b)
b) a3-b3
c) (a-b)(a3-b3)
LCM of a2bc, b3c3and ab2c2 is ____________
a) a2b2c2
b) a2b3c3
c) b3c3
LCM of 2a, 3b and 5c is ___________
a) 1
b) 30abc
c) abc
d) 45x3y2z4
d) 12xyz
d) 30 abc
d) (a+b)3
d) abc
d) 30
II. Fill in the blanks:
1. If there are two or more common factors then the product of the common factors will
be the ___________ of the given expressions.
2. If there are no common factors, then ______________ is the HCF of the given
expressions.
3. ___________ is a factor of LCM
4. If p(x) and q(x) are two polynomials with integer coefficients and if h(x) and m(x) are
respectively thus HCF and LCM. Then h(x) m(x) = _______________
III. Solve the following: 2m
1. Find the HCF of :
2. Find the HCF of :
3. Find the HCF of :
4. Find the HCF of :
5. Find the HCF of :
6. Find the HCF of :
7. Find the HCF of :
8. Find the LCM of:
9. Find the LCM of:
10. Find the LCM of:
11. Find the LCM of:
12. Find the LCM of:
13. Find the LCM of:
x3+27 and x2-9
x2-xy and x2-y2
2x2-x and 4x2-1
x3 + y3 and 3x2-3y2
a3 + 125 and a2 -25
4x2 – 1 and 4x2+4x+1
6x2 – 2x and 9x2- 3x
a2b + ab2 and a3 + a2b
x4 + x and x3-x
3x2 – 75 and 2x3+250
m2-n2 and 3m2-3mn
(xy)2, (xy)3, a2(xy)
(a+b) (b+c), (b+c)(c+a), (c+a) (a+b)
IV. Solve the following: 3m
1.
2.
3.
4.
5.
6.
7.
8.
Find the HCF of:
x2 + 2x – 15 and x2 – 7x + 12
Find the HCF of:
x2-xy-2y2 and x2+3xy + 2y2
Find the HCF of:
a4b – ab4, a4 b2- a2b4and a2b2(a4-b4)
Find the HCF of:
6(x2+10x+24), 4 (x2-x-20) and 8(x2+3x – 4)
Find the HCF of p(x) = (x3 – 27) (x2 – 3x +2) and q(x) = (x2 + 3x + 9) (x2- 5x + 6)
Find the HCF of f(x) = x3+x2-x-1 g(x) = x3+x2+x+1
Find the HCF of p(x) = x4-2x3-15x2 and q(x) = x3-9x
If the HCF of x2+x-12 and 2x2-kx – 9 is (x-k) find the value of k
25
9. Find the LCM of the following:
x2+4x + 4 and x2+ 5x + 6
10. Find the LCM of the following:
6m2 – 3m – 45 and 6m2+11m – 10
11. Find the LCM of the following:
a2-3a + 2, a3- 4a + 4 and a(a3-8)
12. Find the LCM of the following:
4x3 + 4x2 – x – 1, 8x3-1 and 8x2- x – 1
13. Find the LCM of the following:
6(x2 + 2xy – 3y2), 4(x2 – 3xy + 2y2)
14. Find the LCM of the following:
a2-1, a4-1 and a8 – 1
15. Find the LCM of the following:
21(x-1)2, 35(x4-x2), 14 (x4-x)
16. Verify p(x) q(x) = h(x) m(x) for HCF and LCM of two polynomials p(x) = 12(x 4-36)
and q(x) = 8 (x4+5x2-6)
17. Find the HCF h(x) and the LCM m(x) for the polynomials p(x) = x6-1, q(x) = x4+x2+1
and prove that p(x) q(x) = h(x) m(x).
18. Verify p(x) q(x) = h(x) m(x) for HCF and LCM of two polynomials p(x) = 2x 2 + 7x +
5 and q(x) = 8x3+ 125
19. Find h(x) of 3x2+5x – 2 and 3x2-7x + 2 by using h(x) find m(x)
20. Find h(x) of 16 – 4x2 and x2 + x – 6 by h(x) find m(x)
21. If (x-3) is the HCF of p(x) = x3+ax2+bx-6 and q(x) = x3-x(b-4) + a. find the value of a
and b
22. If p(x) = (x – 3) (2x2 – ax +2), q(x) = (x+4) (x2+bx -6) and h(x) = x2-5x + 6, find the
values of a and b.
CHAPTER – 3
Unit – 4 Division
I. Choose the correct answer:
1. Standard form of x2 + x5 – 2x3 – 2 + 3x is ______________.
a) x5 + 2x3- 2 + 3x + x2
c) x5 + 2x3 + x2 + 3x – 2
b) 2 + 3x + x2 + 2x3 + x5
d) x5 + 2x3 + x2 + 3x + 2
2. Standard form of x8 + x + x12 – 3x7 + x9 + 1 is ____________
a) x8 + x9 + x12 + x – 3x7 + 1
c) x + x8 + x9 + x12 – 3x7 + 1
b) x12 + x9 + x8 – 3x7 + x + 1
d) x – 3x7 + x8 + x9 + x12 + 1
3. The area of a triangle is 10x2 and its base is 2x, then its length of altitude is
__________
a) 10x
b) 2x
c) 5x
d) 20x
10
9
4. (-9 a
- 3a ) = ________
a) 3a
b) 3a2
c) 3
d) -3
5. ( ⁄
)
( ⁄
a)
) = _________
b) 2 x3
c) ⁄
d) 32 x3
6. If x4 – a4 is divisible by x + a, then the remainder = ________
a) 0
b) -2a2
c) x – a
II. Fill in the blanks:
7. Addition of two polynomials always give a _______________
8. Subtraction of two polynomials always give a _____________
9. Multiplication of two polynomials always give a ____________
10. Dividend = divisor * quotient + ______________
d) none of these.
26
11.
= ______________
12. (
x8) (5x5) = ______________
13. The area of a rectangle is 800 x2 and its length is 40x, then its breadth is
_______________
III. Solve the following: 2m
14. Divide:
3x2 + 4x – 4 by x + 2
15. Divide:
6x3 – 23x + x2 + 12 by 2x – 3
16. Divide:
2x2 – 7x + 6 by x – 2
17. Divide:
3x2 + x3 + 4 by x + 2
18. Divide:
x3 – 1 by x – 1
19. Find the remainder when x3 + px2 + qx + r is divided by x2+ px +q.
IV. Solve the following: 3m
20. Divide:
4x5 + 7x4 + 14x3 + 3x2-8x + 6 by x2 + 3x + 2
21. Divide:
x3 + 5x2 + 4x – 4 by x2 + 3x – 2
22. Divide:
x4 – 4x2 + 12x + 9 by x2 + 2x – 3
23. Divide:
2x5 – 7x4- 2x3 + 18x2 – 3x – 8 by x3 – 2x2 + 1
24. Divide:
x5 + a5 by x + a
25. Divide:
x7 – y7 by x – y
26. Divide:
x9 + y6 by x3 + y3
27. What should added to x5 – 1 to be completely divisible by x2 + 3x + 1?
28. What should be added to a6 – 64 to be completely divisible by a4 – 16?
V. Solve the following: 4m
CHAPTER – 3
UNIT – 5 Simultaneous linear equations
I .Choose the correct answer: 1m
1. If the two graph lines of the given equation intersect at a point, then it gives a
________ solution.
a) Unique
b) Infinite
c) Finite
d) Zero
2. An equation in which the variable occur to the first degree is called ________
equation.
a) Quadratic b) Linear
c)Pure
d) Adfected
3. If x – 15 = 0, the value of x is ___________.
a) 2 b) -15 c) 0 d) +15
4. If x + 9 = 20, then the value of x is ___________.
a) 11 b) 20 c) -9 d) -20
5. If 5x – 30 = 0, the value of x is _________.
a) 0 b) 30 c) -5 d) 6
6. If 7x = 49, the value of x is __________.
a) 3 b) 7 c) 8 d) -7
7. Which of the following is a linear equation having two variables?
a) 3x + 2y = 9
b) x + 3 = 5
c) x2 – 4 = 0
d) y2 + 2y – 1 = 0
27
II. Fill in the blanks: 1m
8. The general form of linear equation is ______________.
9. If the two graph lines of the given equation are parallel, then the equations have
___________ solution.
10. If two graphs coincide, we get _________ solutions.
11. If two graphs intersect at a point, then it has _________ solution.
12. x + 3 = 7 is a ________ equation.
III. Do as directed: 2m
13. Solve:
x + y = 10
x – y = 12
14. Solve:
x+y=3
3x – y = 5
15. Solve:
2x + y = 0
3x – y = -5
16. Solve:
3x + y = 7
x–y=5
17. Solve:
2x – y = 6
3x + y = 9
IV. Solve the following: 3m
18. Solve
3x – 7y =7
11x + 5y = 87
19. Solve:
3x – 4y = 10
4x + 3y = 5
20. Solve:
5x + 4y – 4 = 0
x – 20 = 12y
21. Solve:
2p + 3q = -5
3p – 2q = 12
22. Solve:
100 x + 200y = 700
200 x + 100 y = 800
23. Solve:
41x + 53y = 135
53x + 41y = 147
28
24. The sum of two numbers is 40. If the smaller number is doubled, it becomes 14 more
than the larger number. Find the numbers.
25. Two numbers are such that twice the smaller number added to 2 gives the larger
number. Also, double the larger number is 1 less than five times the smaller number.
Find the numbers.
26. Find the fraction which becomes when denominator is increased by 4 and when
the numerator is diminished(decreased) by 5.
27. There is a number which is equal to 4 times the sum of its digits. If 27 is added to the
number, the number’s digits get reversed. Find the number.
28. Solve the following:
i)
7x + 5y = 10
3x + y = 2
ii)
3a – 2b = 12
4a – 5b = 16
29. Solve:
i)
2x + y = 7
2x – 3y = 3
ii)
5x – 4y = -14
3x + 2y = -4
30. Solve:
i)
3x + 2y = 5
5x – 4y = 23
ii)
2x + 3y = 13
4x + y = 11
V. Solve the following: 4 Marks
31. Solve graphically
x+y=7
2x – 3y = 9
32. Solve graphically
2x + y = 6
x – 2y = -2
33. Solve graphically
x+y=3
2x + 5y = 12
34. Solve graphically
x – y = -2
x–y=1
35. Solve graphically
x–y=1
2x – 2y = 2
36. Solve graphically
3x – y – 2 = 0
2x + y – 8 = 0
29
CHAPTER – 3
UNIT – 6 VARIATION
I.
Choose the correct answer: 1m
1. If y varies directly as x and y=10 when x = 5, then the constant of proportionately is
a)
b) 50
c) 2
d) 0
2. If x varies as y and if x = 6 when y =3 then the value of x when y = 10 is
a) 20
b) 18
c) 60
d) 30
3. If p varies as q and if p = 5 when q =10 then the value of q when p = 20 is
a) 50
b) 40
c) 30
d) 80
4. If x varies directly as y and if x = 4 when y = 20. Then the value of y when x = 12 is
a) 40
b) 50
c) 60
d) 70
5. If y varies directly as √ and y = 24 when x = 3 then the value of y when x = 16 is
a)
√
b) 32 √
c) 192 √
d) 24 √
6. If Q inversely varies as square of P and if Q = 8 when p = 2, then the value of Q when
p=2√
a)
√
b)
c)
d) 32 √
II.
Fill in the blanks: 1m
7. A quantity which takes different values is called _____________.
8. Variation means ____________.
9. If the product of two variables is constant, then one variable varies _________ as the
other.
10. The symbol used to denote variation is ____________.
III.
Solve the following: 2m
11. The volume of sphere varies as the cube of its radius and its volume is 179.7 cm3
when radius is 3.5cm. Find the volume when radius is 1.75cm.
12. The distance through which a body falls from rest varies as square of time it takes to
fall that distance. It is known that the body falls 64cm in 2 seconds. How far does that
body fall in 6 seconds.
13. If 35 men can do a piece of work in 30 days, in how many days will 21 men can do it.
14. If 7 pipes can fill a tank in 1 hour 24 minutes, how long will it take to fill the tank if 6
pipes of the same type as used.
15. If 7 workers can build a trench in 25 hours. How many workers will be required to do
the same work in 35 hours.
16. A farmer has a stock of food enough to feed 28 animals for 9 days. He buys 8 more
animals which takes same quantity of food. How long would the food last now.
17. Suppose that y varies inversely with the square of x and y = 50 when x = 4. Find y
when x = 5.
IV.
Solve the following: 3m
18. If 195 men working 10 hours a day can finish a job in 20 days, how many men,
working 13 hours a day, should be employed to finish the job in 15 days.
19. If z varies jointly as x and the square not of y, and if z = 6. When x = 3 and y = 16.
Find z when x = 7 and y = 4.
20. If 36 men can build a wall of 140m long in 21 days, how many men are required to
build a similar wall of length 50m in 18 days.
30
21. If the total wages of 15 laborers for 6 days is Rs. 8100. Find the wages of 21 labourers
for 5 day.
22. Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it
take to fill the cistern if both of them are opened together?
V. Solve the following: 4m
CHAPTER – 4
UNIT – 1 Polygons
I. Choose the correct answers:
1. If the exterior angle of a polygon is 60o then the number of sides of a polygon is
____________.
(a) 5
(b) 6
(c) 8
(d) 10
2. If a polygon has 8 sides then the number of triangles are formed by fixing a vertex are
____________.
(a) 10
(b) 9
(c) 7
(d) 6
3. If a polygon has 10 sides, then the number of triangles are formed by fixing a vertex
are ____________.
(a) 8
(b) 9
(c) 10
(d) 12
o
4. If the exterior angle of a polygon is 120 , then the number of sides of a polygon is
___________.
(a) 5
(b) 4
(c) 3
(d) 6
5. If the exterior angle of a polygon is 72o then the polygon is named as
______________.
(a) Hexagon (b) Square
(c) Pentagon (d) Octagon
6. If the exterior angle of a polygon is 45o then the polygon is named as __________.
(a) Hexagon (b) Heptagon (c) Octagon (d) Nanogon
7. The sum of exterior angle and interior angle is equal to
(a) One right angle (b) 2 right angle
(c) 3 right angle
(d) 4 right angles
8. The sum of all exterior angles is equal to
(a) 4 right angles
(b) 6 right angles
(c) 2 right angles
(d) 8 right angles
9. In a regular n-gon all its interior angles are equal to
(a) (n-2)π
(b) (
)π
(c) (
)π
(d) (n+2)π
10. In a regular n-gon all its exterior angle are equal to
(a) 2πn
(b)
(c)
(d)
11. The sum of the interior angles of a n-gon is
(a) (n+2)π
(b) (n+2) right angles (c) (n-2)π
(d)
II. Fill in the blanks:
12. A rectilinear figure bounded by three or more sides is called __________.
13. In a polygon if one angle is a reflex angle then it is called ____________.
14. In a polygon if no angle is reflex angle then it is called ___________.
15. If a polygon has 10 sides then it is called _____________.
16. If a polygon has 4 sides then it is called ____________.
31
17. An example for regular quadrilateral ______________.
III. Solve the following: 2m
18. Find the number of sides of a regular polygon if each exterior angle is 30o.
19. Find the number of sides of a regular polygon if each exterior angle is 60 .
20. Find the number of sides of a regular polygon if each exterior angle is 72 .
21. Find the number of sides of a regular polygon if each exterior angle is 120 .
22. Find the sum of the interior angles of a octagon.
23. Find the sum of the interior angles of a pentagon.
24. If the sum of interior angles of a polygon is 1440 . Find the number of sides of the
polygon.
25. If the sum of interior angles of a polygon is 7 straight angles. Find the number of sides
of the polygon.
26. Find the number of sides of a polygon whose sum of interior angles is 900 .
27. Find the measure of each exterior angle of a regular polygon with the sides 20.
28. Find the number of sides of a regular polygon if its exterior angle is 45 .
29. Find the number of sides of a regular polygon if its exterior angle is 120 .
IV. Solve the following: 3m
30. Find the number of sides of a regular polygon if each exterior angle is equal to its
interior angle.
31. Find the number of sides of a regular polygon if each exterior angle is equal to half its
interior angle.
32. Find the number of sides of a regular polygon if each exterior angle is equal to twice
its interior angle.
33. Find the number of sides of a regular polygon of its interior angle is equal to four
times exterior angle.
34. Find the sum of interior angles of a hexagon.
35. The angles of a convex polygon are in the ratio 2:3:5:9:11. Find the measure of each
angle.
CHAPTER – 4
UNIT – 2 Quadrilaterals
I. Choose the correct answer:
1. The sum of 4 interior angles of a quadrilateral is equal to
a) 2 right angles
b) 3 right angles
c) 4 right angles
d) 8 right angles.
2. A quadrilateral in which all 4 sides are equal and all four angles are right angles is
a) Rectangle
b) Rhombus
c) square
d) trapezium
3. The minimum elements needed for the construction of a quadrilateral is
a) 4
b) 5
c) 6
d) 8
4. The line joining the mid points of a quadrilateral forms
a) Square
b) rectangle
c) kite
d) parallelogram
32
II. Fill in the blanks:
5. The line segment joins the opposite angular points of a quadrilateral is called
__________
6. If the non parallel sides of a trapezium are equal it is called an _________
7. Each diagonal divides the parallelogram in to two ____________ triangles.
8. Diagonals of a parallelogram are _____________ each other.
9. The angle between the angle bisector of the parallelogram on the same side is a
_________
10. The angles an the same side of the parallelogram is _______________
11. In a Rhombus diagonals bisect each others ______________
12. In a square _______________ bisect the opposite angles.
13. A _______________ of a quadrilateral which has two pairs of adjacent sides are
equal.
III. Solve the following: 2m
14. Write any properties of a parallelogram.
15. Is parallelogram a rectangle? Can you call a rectangle a parallelogram.
16. Write any 2 properties of a square.
17. Write any 2 properties of a Rhombus.
IV. Solve the following: 3m
18. Prove that the bisectors of two opposite angles of a parallelogram are parallel.
19. Prove that, it the diagonals of a parallelogram are perpendicular to each other, the
parallelogram is a Rhombus.
20. Prove that if the diagonals of a parallelogram are equal then it is a rectangle.
V. Solve the following: 4m
21. Construct a quadrilateral PQRS, given PQ = 5.1cm, 2R = 3.8cm, RS = 4.6cm, SP =
4.9 cm and the diagonal SQ = 4.7cm.
22. Construct a quadrilateral ABCD. Given AB = 7cm, CD = 4cm, AD = 4cm diagonal
AC = 6cm and
= 40 .
23. Construct quadrilateral ABCD, given AB = 4.8cm, BC = 4.4cm, CD = 7cm, DA =
3.4cm, BD = 6.2 cm
24. Construct quadrilateral ABCD, given AB = CD = 5.2cm, BC = AD = 3.2cm, BD =
7.2cm.
25. Construct quadrilateral ABCD. Given AC = 6cm, BD = 5.8cm, AB = 3.4cm, AD =
5.2cm and BC = 4.2cm.
CHAPTER – 4
UNIT – 3 Theorems and Problems on Parallelograms
I. Choose the correct answer: 1m
1. The area of parallelogram is given by formula
a) Length × breadth
b) breadth × height
c) base × height
d) side× side
33
2. The minimum number of elements needed to construct a parallelogram is
a) 5
b) 6
c) 2
d) 3
3. The minimum number of elements needed to construct rectangle is
a) 1
b) 2
c) 3
d) 5
4. The minimum number of elements needed to construct a Rhombus is
a) 2
b) 3
c) 4
d) 5
5. The minimum number of elements needed to construct of square is
a) 4
b) 3
c) 1
d) 2
6. Area of triangle is calculated by using the formula
a) ½ ×b×h b) b×h
c) l×b
d) side ×side
II. Fill in the blanks:
7. The diagonals of a parallelogram ____________ each other.
8. The line joining the mid points of any two sides of a triangle is __________ the third
side.
9. Each diagonal divides the parallelogram in to two ___________ triangles.
10. The area of parallelogram is the product of _____________ and ____________11. If one angle of a parallelogram is right angle then it is ____________
12. In a trapezium __________________ sides are equal
III. Theorem: 3m
13. Prove that each diagonal of a parallelogram divides the parallelogram in to two
congruent triangle.
14. Prove that the diagonals of a parallelogram bisect each other.
IV. Theorem: 4m
15. Prove that parallelograms standing on the same base and between same parallels are
equal in area.
16. State and prove mid-point theorem.
V. Do as directed: 2m
17. Suppose ABCD is a parallelogram and the diagonals intersect at E. Let PEQ be a line
segment with P on AB and Q on CD. Prove that PE – EQ.
18. Let ABCD be a parallelogram. Let BP and DQ be perpendiculars respectively from B
and D onto AC. Prove that BP = DQ
19. Prove that in a rhombus, the diagonals are perpendicular to each other.
20. Suppose in a quadrilateral the diagonals bisect each other perpendicularly. Prove that
the quadrilateral is a rhombus.
21. Let ABCD be a quadrilateral in which
. Prove that ABCD is a
parallelogram.
22. The area of parallelogram is 9.6cm2, and the base is 3.2 cm. find the height.
23. The area of a parallelogram is 153.6 cm2. The base measures 19.2 cm. what is the
measurement for the height of the parallelogram?
24. In a parallelogram ABCD, AD = 25 cm and AB = 50 cm. If the altitude from a vertex
D on to AB measures 22 cm. what is the altitude from a vertex B on to AD?
34
25. In a parallelogram ABCD, AB = 4x and AD = 2x + 1. If the perimeter is 38cm and
area is 60 cm2, find the length of the altitude from D on to AB.
26. Let ABCD be a parallelogram and consider its diagonal AC. Draw perpendiculars BK
and DL on to AC. Prove the BK = DL.
VI. Solve: 3m
27. Suppose E, F are the midpoints respectively of the oblique sides PS, QR of the
PQ  RS
trapezium PQRS. Prove that EF is parallel to SR and EF =
.
2
28. In a rectangle ABCD, P, Q, R and S are the midpoints of the sides AB, BC, CD and
DA respectively. Find the area of PQRS in terms of area of ABCD.
29. Suppose X, Y and Z are the midpoints of the sides PQ, QR and RP respectively of a
triangle PQR. Prove the XYRZ is a parallelogram.
30. Prove that if the mid-points of the opposite sides of a quadrilateral are joined, they
bisect each other.
VII. Solve the problem: 4m
31. Construct a parallelogram ABCD, where diagonal AC and BD are 6 cm and 4 cm
respectively, and side AB = 3.5cm.
32. Construct a parallelogram whose diagonals are 4.8 cm and 4.2 cm and interesct at an
angle of 60º.
33. Construct a parallelogram ABCD with AB = 3.5 cm, AD = 3.2 cm,
.
34. Construct a parallelogram ABCD given AB = 4 cm, BC = 4.4 cm and the diagonal
AC = 5.3 cm.
35. Construct a rectangle whose adjacent sides are 3.8 cm and 2.4 cm.
36. Construct a rectangle given that a diagonal is 3.4 cm and one side is 2.8 cm.
37. Construct a square having a diagonal of length 3 cm.
38. Construct a rhombus whose side is 2.8 cm and diagonal is 2 cm.
39. Construct a rhombus whose diagonals are 4 cm and 3 cm.
40. Construct parallelograms ABCD with the following measurements:
AD = 4.2 cm, DC = 5.8 cm,
41. Construct parallelograms ABCD with the following measurements:
AB = 4.3 cm, BC = 3.2 cm,
42. Construct parallelograms ABCD with the following measurements:
AD = 4.2 cm, DC = 5.8 cm, AC
43. Construct parallelograms ABCD with the following measurements:
AD = 4.3 cm, DC = 5.7 cm,
35
44. Construct parallelograms ABCD with the following measurements:
AC = 6.8 cm, DB = 7.6 cm, A
45. Construct rectangle ABCD with the following data:
AB = 4 cm, BC = 6 cm
46. Construct rectangle ABCD with the following data:
AB = 6 cm, AC = 7.2 cm
47. Construct square ABCD: Which has side- length 2 cm.
48. Construct square ABCD: Which has diagonal 6 cm.
49. Construct rhombus ABCD such that:
AB = 3.2 cm, AC = 4.8 cm.
50. Construct rhombus ABCD such that:
AB = 4.4 cm, BD = 5.4 cm.
51. Construct rhombus ABCD such that:
AC = 7 cm, BD = 4 cm.
52. Construct rhombus ABCD such that:
BD = 6.8 cm, AC = 5.4 cm.
CHAPTER – 4
UNIT – 4 CIRCLES
I. Choose the correct answer:
1. A part of a circle is called _________________
a) Chord
b) radius
c) arc
d) segment
2. The region bounded by a chord and an arc in a circle is called __________
a) Sector
b) arc
c) diameter
d) segment
3. The region bounded by two radii and an arc in a circle is called ____________
a) Sector
b) segment
c) chord
d) diameter
4. Angle in a semicircle is always _______________.
a) A cute angle
b) obtuse angle
c) right angle
d) straight angle
II. Fill in the blanks:
5. The line segment joining the centre and any point on the circle is called
_____________
6. The biggest chord of a circle is ____________
7. The longest arc of a circle which forms the circle is called ____________
8. The line which intersects a circle in the distinct point is called _________
9. Circles having same centre but different radii are called _____________
10. Circle having same radii but different centres are called ______________
11. Two circles cut each other at two distinct points are called __________
12. The perpendicular to the chord from the centre of the circle _____________ the
chord.
13. Angle in a minor segment is _____________
14. Angle in a major segment is ___________
15. Opposite angles of a cyclic quadrilateral are _____________
16. The line segment joining any two distinct points on the circle is called
_____________
III. Theorem: 3m
17. Prove that the line drawn through the centre of the circle bisecting a chord is
perpendicular to the chord.
36
IV. Theorem: 4m
18. Prove that the angle subtended by an arc of a circle at the centre is twice the angle
subtended by the same arc at any point in the circumference of the circle.
19. Prove that both pairs of opposite angles of a cyclic quadrilateral arc supplementary.
V. Do as directed: 2m
20. In a circle whose radius is 8 cm., a chord is drawn at a point 3 cm. from the centre of
the circle. The chord is divided into two segments by a point on it. If one segment of
the chord is 9 cm. What is the length of the other segment?
21. Suppose two chords of a circle are equidistant from the centre of the circle. Prove that
the chords have equal length.
22. Suppose two chords of a circle are unequal in length. Prove that the chord of larger
length is nearer to the centre than the chord of smaller length.
23. In the figure,
is a circle with centre O. if
= 82º, find x.
24. In the figure, A, B, C are points on a circle with centre O. if
25. In the figure, A, B, C are points on a circle with centre O and reflex angle
260º. Find x.
, find ̂.
=
37
26. In the adjoining figure, O is the centre of the circle. If
find
.
27. In the figure,
= 42º, find ̂.
28. In the figure, ABC is a circle with centre O and reflex
29. In the figure, AOB is a diameter. Find ̂ .
= 90º,
= 128º,
= 250º. Find ̂
38
VI. Solve the problem: 3m
30. Let AB and CD be parallel chords of a circle, with centre O; M is the midpoint of AB
and N is the Midpoint of CD. Prove that O, N, M are collinear. If MN = 3 cm., AB =
4 cm., CD = 10 cm., find the radius of the circle.
31. Suppose AB and CD are two parallel chords in a circle. Prove that the line joining
their mid-points pass through the centre of a the circle.
32. Prove that a parallelogram inscribed in a circle is a rectangle.
33. In the figure, ABCDE is a circle with centre O. if ̂ = 180º, find (i) ̂ (ii) ̂ (iii) ̂ (iv)
̂ (v) ̂ ̂ (vi) ̂
̂.
34. In the figure,
110º. Find
35. In the figure, AB is a diameter,
.
= 38º. Find
.
39
36. In the figure,
= 25º,
= 33º. Find
and
.
37. Inscribe a regular pentagon inside a circle of radius 4 cm.
38. Construct the circum circle of a triangle ABC in which AB = 3 cm,
= 78º and BC
= 4.6 cm.
39. Construct a triangle ABC with
= 55º,
= 48º and BC = 3.8 cm. construct its
circum – circle.
40. Construct a square of side length 5 cm and inscribe it in a circle.
41. Construct a square in a circle of radius 3 cm.
42. Construct a regular pentagon in a circle of radius 3. 6 cm.
43. Construct a regular hexagon in a circle of radius 5cm.
VII. Solve: 4m
44. Construct a cyclic quadrilateral ABCD in which AB = 4 cm, BC = 5 cm, CD = 2.8
cm, and
= 60º.
45. Construct a cyclic quadrilateral ABCD in which AB = 2.8 cm, BC = 4 cm, CD = 3
cm, and
= 105º.
CHAPTER – 4
UNIT – 5CONCURRENCY IN TRIANGLES
I. Choose the correct answer:
1. The medians of a triangle concur at its __________
a) Centroid b) incentre c) orthocentre d) circumcentre
2. Centroid divides each of the medians of a triangle in the ratio _________.
a) 3:2
b) 2:1
c) 3:1
d) 4:1
3. The three altitudes of a triangle concur at its ____________.
a) Centroid b) incentre c) orthocentre d) circumcentre
4. The orthocentre of triangle lies inside for an ______________ angled triangle.
a) Acute b) obtuse c) right angled d) linear
5. The three perpendicular bisectors of the sides of a triangle concur at its __________.
a) Centroid b) incentre c) orthocentre d) circumcentre
II. Fill in the blanks:
6. Diameters of a circle concur at _________________ of the circle.
7. The sides of the triangle are _______________ to the in-circle.
8. The line segment joining a vertex of a triangle to the midpoint of the opposite side is
called ________________ of that triangle.
40
9. Centroid always lies in the ________________ of triangle.
10. Circumcentre is equidistant from the ____________ of the given triangle.
11. The perpendicular drawn from a vertex of a triangle to its opposite side is called as
_____________ of a triangle.
12. The circumcentre of a right angled triangle is the midpoints of its ____________.
13. The point where the concurrent lines are meeting is called _____________.
14. Every triangle has only ___________ orthocenter.
15. Three or more straight lines pass through a same point are called ____________.
16. The angle bisectors of a triangle concur at a point called ____________.
17. Incircle touches all the three ___________ of the triangle.
18. The point of concurrency of medians of a triangle is called ____________.
19. The centroid divides the median in the ratio ___________.
20. The point of concurrency of the perpendicular bisectors of sides of a triangle is called
____________ of the triangle.
21. The circle passing through the vertices of a triangle is called __________________.
22. Circumcircle touches all the three __________ of the triangle.
23. In acute angled triangle, the circumcentrelies ___________ the triangle.
24. In obtuse angled triangle, the circumcentrelies ___________ the triangle.
25. In right angled triangle, the circumcentrelies ___________of the triangle.
26. The perpendicular drawn from a vertex of a triangle to its opposite side is called
___________ of a triangle.
27. The point of concurrency of three altitudes of a triangle is called ____________ of thr
triangle.
28. The orthocentre of a right angled triangle is that ____________ at which right angle is
formed.
III. Solve the following: 4m
29. Construct incentre of triangle DEF with DE = 3.5 cm, EF =5.3 cm and DF = 7.6 cm.
Measure the inradius.
30. Construct incentre of triangle ABC in which AB = BC = AC =5cm. measure the
inradius.
31. Construct incentre of triangle PQR with PQ= 7cm, PR= OR= 6cm. Measure the
inradius.
32. Construct ∆XYZ with XY = 6.5 cm, YZ = 6cm and XZ = 7.2 cm. Locate centroid.
33. Construct equilateral
with perimeter 18cm and locate centroid.
34. Construct
with AB = 6cm, BC = 5.2cm and
= 60 . Draw a circle passing
through A B and C.
35. Draw an equilateral triangle whose side is 4.5cm. Draw its circumcentre. Measure its
circum radius.
36. Construct
with XY = 7.5cm YZ = 6.2cm and XZ = 5.8cm and locate its
orthocentre.
37. Construct KLM with LM = 5.5cm
= 90 ,
= 45 and locate its
orthocenter.
38. Construct
with AB = BC = AC = 5.3cm and locate its orthocentre.
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CHAPTER – 4
UNIT – 6 MENSURATIONS
I. Choose the correct answer:
1. If the base of prism has n sides, then its has _______ faces.
a) n+2
b) n
c) n-1
d) n+1
2. If the base of a pyramid has ‘n’ sides, then it has _________ faces
a) n+2
b) n+1
c) n+1
d) n-1
3. Area of a equilateral triangle with side ‘a’ = _________
a)
⁄ ah
b) a2
c)
√
d) 3a
4. Lateral surface area of a square based prism with base edge 5cm and height 10cm is
_________
a) 50cm2
b) 100 cm2
c) 200 cm2
d) 20 cm2
5. The perimeter of a regular triangle based prism is 18m and height is 13m, then lateral
surface area is __________________
a) 234 m2
b) 31 m
c) 78 m2
d) 107 m2
6. The volume of a square pyramid with base area 150 cm2 and height 9cm is ________
a) 450 cm3
b) 1350 cm c) 675 m3
d) 159 m3
7. If ‘a’ is the side of the base of an equilateral triangle, pyramid with height ‘h’ then its
volume is _______
a)
b)
√
c)
√
d) a2h
8. In a right prism, the height of the prism is same as its ___________
a) Base edge
b) lateral height
c) area
d) perimeter.
II. Fill in the blanks:
9. In a regular prism, the base is a ________.
10. Shape of the base of a square based prism is _________
11. The base and top of a prism are __________ and parallel to each other.
12. In an irregular base prism the base is not a ____________
13. Total surface area of a square based prism = ____________
14. Lateral surface area of a equilateral triangle right prism = ___________
15. Base area a square based prism with base edge 7 cm = ____________
16. Volume of the pyramid = __________ × volume of the prism.
17. Base of a pyramid is a _______________
III. Solve the following: 2m
18. Differentiate between right prism and oblique prism.
19. Differentiate between height and slant height of a pyramid.
20. Differentiate between prism and pyramid.
21. Classify the following solids in to regular and irregular prism.
a) Rectangular based prism.
b) Equilateral triangle based prism.
c) Square based prism
d) Cubic
e) Right triangle
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22. The side of a square based prism is 2.5cm and its height is 6.5cm. Find its LSA and
TSA.
23. Find the perimeter of a triangular based pyramid with slant height 18m and lateral
surface area 360m3.
24. Find the lateral and total surface area of a square based pyramid with base 6cm and
slant height 14cm.
25. Find the volume of square based right prism whose base is 9cm and height is 12cm.
26. Calculate the height of a square based prism if the volume is 490cm3 and edge of the
base is 7cm.
27. If the volume of an equilateral triangle based prism is 72√ m3and height is 7m. Find
the base.
28. Find the volume of a equilateral triangle based prism if the perimeter of the base is
6cm and height is 18cm.
29. The height of a square based pyramid is 33cm. If the base is 27cm. Find the volume.
30. The height of a square based pyramid of volume 300cc is 10cm. Find the edge of the
base.
31. If the area of base of a rectangular based pyramid is 60m2 and its height is 7.5m. Find
the volume.
IV. Solve the following: 3m
32. The total surface area of a triangular based prism is 576 cm2 and its height is 22cm. If
the area of its base is 24cm2. Find the perimeter of its base.
33. The base of a prism is right angled triangle with legs 6cm, 8cm and hypotenuse 10cm.
If the total surface area of the prism is 156cm2. Find its height and lateral surface area.
34. The roof of a temple is in the shape of square based pyramid. The edge of the base is
7.5m and slant height is 7m. Find the area of metal sheet required to cover the top of
the roof.
35. The base and height of a square based pyramid is 10cm and 12cm respectively. Find
its total surface area.
36. A square based pyramid is placed on a square based prism with the same base 14cm.
If the height of the prism is 9cm and height of the pyramid is 7cm. Find the total
surface area of the solid obtained by joining them.
37. The base of a prism of height 8cm is trapezium. If the parallel side of 10cm and 16cm
area at a distance of 8cm. Find the volume.