Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22)
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Page 1
Sample Question Paper
Mathematics- Basic (241)
Class- X, Session: 2021-22
TERM II
Time Allowed: 2 hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C.
2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in
two questions.
3. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in
one question.
4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided
in one question. It contains two case study based questions.
SECTION A
Q.No. MARKS
1 Find the roots of the quadratic equation 3 ?? 2
- 7 ?? - 6 = 0 .
OR
Find the values of k for which the quadratic equation 3 ?? 2
+ ???? + 3 = 0 has real and
equal roots.
2
2 Three cubes each of volume 64cm
3
are joined end to end to form a cuboid. Find the
total surface area of the cuboid so formed?
2
3 An inter house cricket match was organized by a school. Distribution of runs made
by the students is given below. Find the median runs scored.
Runs
scored
0-20 20-40 40-60 60-80 80-100
Number of
students
4 6 5 3 4
2
4 Find the common difference of the AP 4,9,14,… If the first term changes to 6 and
the common difference remains the same then write the new AP.
2
5 The mode of the following frequency distribution is 38. Find the value of x.
Class
Interval
0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 7 9 12 16 x 6 11
2
6 XY and MN are the tangents drawn at the end points of the diameter DE of the circle
with centre O. Prove that XY ? ? MN.
2
X
M
Y
D
E
o
.
.
.
.
.
N
Page 2
Sample Question Paper
Mathematics- Basic (241)
Class- X, Session: 2021-22
TERM II
Time Allowed: 2 hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C.
2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in
two questions.
3. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in
one question.
4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided
in one question. It contains two case study based questions.
SECTION A
Q.No. MARKS
1 Find the roots of the quadratic equation 3 ?? 2
- 7 ?? - 6 = 0 .
OR
Find the values of k for which the quadratic equation 3 ?? 2
+ ???? + 3 = 0 has real and
equal roots.
2
2 Three cubes each of volume 64cm
3
are joined end to end to form a cuboid. Find the
total surface area of the cuboid so formed?
2
3 An inter house cricket match was organized by a school. Distribution of runs made
by the students is given below. Find the median runs scored.
Runs
scored
0-20 20-40 40-60 60-80 80-100
Number of
students
4 6 5 3 4
2
4 Find the common difference of the AP 4,9,14,… If the first term changes to 6 and
the common difference remains the same then write the new AP.
2
5 The mode of the following frequency distribution is 38. Find the value of x.
Class
Interval
0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 7 9 12 16 x 6 11
2
6 XY and MN are the tangents drawn at the end points of the diameter DE of the circle
with centre O. Prove that XY ? ? MN.
2
X
M
Y
D
E
o
.
.
.
.
.
N
OR
In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB=6cm,
BC=7cm and CD=4cm. Find AD.
Section-B
7 An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10
terms.
3
8 A tree is broken due to the storm in such a way that the top of the tree touches the
ground and makes an angle of 30
0
with the ground. Length of the broken upper part
of the tree is 8 meters. Find the height of the tree before it was broken.
OR
Two poles of equal height are standing opposite each other on either side of the
road 80m wide. From a point between them on the road the angles of elevation of
the top of the two poles are respectively 60
0
and 30
0
. Find the distance of the point
from the two poles.
3
9 PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and
? APB=60
0
, then find the length of the chord AB.
3
10 The sum of the squares of three positive numbers that are consecutive multiples of
5 is 725. Find the three numbers.
3
Section-C
11 Construct two concentric circles of radii 3cm and 7cm. Draw two tangents to the
smaller circle from a point P which lies on the bigger circle.
OR
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at
an angle of 60
0
. Also find the length of the tangent.
4
A
B
D C
A
B
P
6 cm
60°
O .
Page 3
Sample Question Paper
Mathematics- Basic (241)
Class- X, Session: 2021-22
TERM II
Time Allowed: 2 hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C.
2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in
two questions.
3. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in
one question.
4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided
in one question. It contains two case study based questions.
SECTION A
Q.No. MARKS
1 Find the roots of the quadratic equation 3 ?? 2
- 7 ?? - 6 = 0 .
OR
Find the values of k for which the quadratic equation 3 ?? 2
+ ???? + 3 = 0 has real and
equal roots.
2
2 Three cubes each of volume 64cm
3
are joined end to end to form a cuboid. Find the
total surface area of the cuboid so formed?
2
3 An inter house cricket match was organized by a school. Distribution of runs made
by the students is given below. Find the median runs scored.
Runs
scored
0-20 20-40 40-60 60-80 80-100
Number of
students
4 6 5 3 4
2
4 Find the common difference of the AP 4,9,14,… If the first term changes to 6 and
the common difference remains the same then write the new AP.
2
5 The mode of the following frequency distribution is 38. Find the value of x.
Class
Interval
0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 7 9 12 16 x 6 11
2
6 XY and MN are the tangents drawn at the end points of the diameter DE of the circle
with centre O. Prove that XY ? ? MN.
2
X
M
Y
D
E
o
.
.
.
.
.
N
OR
In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB=6cm,
BC=7cm and CD=4cm. Find AD.
Section-B
7 An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10
terms.
3
8 A tree is broken due to the storm in such a way that the top of the tree touches the
ground and makes an angle of 30
0
with the ground. Length of the broken upper part
of the tree is 8 meters. Find the height of the tree before it was broken.
OR
Two poles of equal height are standing opposite each other on either side of the
road 80m wide. From a point between them on the road the angles of elevation of
the top of the two poles are respectively 60
0
and 30
0
. Find the distance of the point
from the two poles.
3
9 PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and
? APB=60
0
, then find the length of the chord AB.
3
10 The sum of the squares of three positive numbers that are consecutive multiples of
5 is 725. Find the three numbers.
3
Section-C
11 Construct two concentric circles of radii 3cm and 7cm. Draw two tangents to the
smaller circle from a point P which lies on the bigger circle.
OR
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at
an angle of 60
0
. Also find the length of the tangent.
4
A
B
D C
A
B
P
6 cm
60°
O .
12 The following age wise chart of 300 passengers flying from Delhi to Pune is
prepared by the Airlines staff.
Age Less
than
10
Less
than
20
Less
than
30
Less
than
40
Less
than
50
Less
than
60
Less
than
70
Less
than
80
Number of
passengers
14 44 82 134 184 245 287 300
Find the mean age of the passengers.
4
13 A lighthouse is a tall tower with light near the top. These are often built on islands,
coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the
mariners and send warning to boats and ships for dangers. Initially wood, coal would
be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights.
Nowadays they are run by machines and remote monitoring.
Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately
40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and
a boat are coming towards the lighthouse from opposite directions. Angles of
depression of flash light from the lighthouse to the boat and the ship are 30
0
and 60
0
respectively.
i) Which of the two, boat or the ship is nearer to the light house. Find its
distance from the lighthouse?
ii) Find the time taken by the boat to reach the light house if it is moving at
the rate of 20 km per hour.
2
2
14 Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay
dolls are unique in their realism and quality of their finish. They are created by
modelling coils of clay over a metal frame. The figures are painted in natural colours
and their hair is made either by sheep’s wool or jute. Artisans make models starting
from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and
present comic characters. These creations are displayed in different national and
international museums.
30
0
60
0
A
B
C D
Page 4
Sample Question Paper
Mathematics- Basic (241)
Class- X, Session: 2021-22
TERM II
Time Allowed: 2 hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C.
2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in
two questions.
3. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in
one question.
4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided
in one question. It contains two case study based questions.
SECTION A
Q.No. MARKS
1 Find the roots of the quadratic equation 3 ?? 2
- 7 ?? - 6 = 0 .
OR
Find the values of k for which the quadratic equation 3 ?? 2
+ ???? + 3 = 0 has real and
equal roots.
2
2 Three cubes each of volume 64cm
3
are joined end to end to form a cuboid. Find the
total surface area of the cuboid so formed?
2
3 An inter house cricket match was organized by a school. Distribution of runs made
by the students is given below. Find the median runs scored.
Runs
scored
0-20 20-40 40-60 60-80 80-100
Number of
students
4 6 5 3 4
2
4 Find the common difference of the AP 4,9,14,… If the first term changes to 6 and
the common difference remains the same then write the new AP.
2
5 The mode of the following frequency distribution is 38. Find the value of x.
Class
Interval
0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 7 9 12 16 x 6 11
2
6 XY and MN are the tangents drawn at the end points of the diameter DE of the circle
with centre O. Prove that XY ? ? MN.
2
X
M
Y
D
E
o
.
.
.
.
.
N
OR
In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB=6cm,
BC=7cm and CD=4cm. Find AD.
Section-B
7 An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10
terms.
3
8 A tree is broken due to the storm in such a way that the top of the tree touches the
ground and makes an angle of 30
0
with the ground. Length of the broken upper part
of the tree is 8 meters. Find the height of the tree before it was broken.
OR
Two poles of equal height are standing opposite each other on either side of the
road 80m wide. From a point between them on the road the angles of elevation of
the top of the two poles are respectively 60
0
and 30
0
. Find the distance of the point
from the two poles.
3
9 PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and
? APB=60
0
, then find the length of the chord AB.
3
10 The sum of the squares of three positive numbers that are consecutive multiples of
5 is 725. Find the three numbers.
3
Section-C
11 Construct two concentric circles of radii 3cm and 7cm. Draw two tangents to the
smaller circle from a point P which lies on the bigger circle.
OR
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at
an angle of 60
0
. Also find the length of the tangent.
4
A
B
D C
A
B
P
6 cm
60°
O .
12 The following age wise chart of 300 passengers flying from Delhi to Pune is
prepared by the Airlines staff.
Age Less
than
10
Less
than
20
Less
than
30
Less
than
40
Less
than
50
Less
than
60
Less
than
70
Less
than
80
Number of
passengers
14 44 82 134 184 245 287 300
Find the mean age of the passengers.
4
13 A lighthouse is a tall tower with light near the top. These are often built on islands,
coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the
mariners and send warning to boats and ships for dangers. Initially wood, coal would
be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights.
Nowadays they are run by machines and remote monitoring.
Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately
40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and
a boat are coming towards the lighthouse from opposite directions. Angles of
depression of flash light from the lighthouse to the boat and the ship are 30
0
and 60
0
respectively.
i) Which of the two, boat or the ship is nearer to the light house. Find its
distance from the lighthouse?
ii) Find the time taken by the boat to reach the light house if it is moving at
the rate of 20 km per hour.
2
2
14 Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay
dolls are unique in their realism and quality of their finish. They are created by
modelling coils of clay over a metal frame. The figures are painted in natural colours
and their hair is made either by sheep’s wool or jute. Artisans make models starting
from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and
present comic characters. These creations are displayed in different national and
international museums.
30
0
60
0
A
B
C D
Here are a few images (not to scale) of some clay dolls of Krishnanagar.
The ratio of diameters of red spherical apples in Doll-1 to that of spherical
oranges in Doll-2 is 2:3. In Doll-3, male doll of blue colour has cylindrical body and
a spherical head. The spherical head touches the cylindrical body. The radius of
both the spherical head and the cylindrical body is 3cm and the height of the
cylindrical body is 8cm. Based on the above information answer the following
questions:
i) What is the ratio of the surface areas of red spherical apples in
Doll-1 to that of spherical oranges in Doll-2.?
ii) The blue doll of Doll-3 is melted and its clay is used to make the
cylindrical drum of Doll-4. If the radius of the drum is also 3cm,
find the height of the drum.
2
2
Page 5
Sample Question Paper
Mathematics- Basic (241)
Class- X, Session: 2021-22
TERM II
Time Allowed: 2 hours Maximum Marks: 40
General Instructions:
1. The question paper consists of 14 questions divided into 3 sections A, B, C.
2. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in
two questions.
3. Section B comprises of 4questions of 3 marks each. Internal choice has been provided in
one question.
4. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided
in one question. It contains two case study based questions.
SECTION A
Q.No. MARKS
1 Find the roots of the quadratic equation 3 ?? 2
- 7 ?? - 6 = 0 .
OR
Find the values of k for which the quadratic equation 3 ?? 2
+ ???? + 3 = 0 has real and
equal roots.
2
2 Three cubes each of volume 64cm
3
are joined end to end to form a cuboid. Find the
total surface area of the cuboid so formed?
2
3 An inter house cricket match was organized by a school. Distribution of runs made
by the students is given below. Find the median runs scored.
Runs
scored
0-20 20-40 40-60 60-80 80-100
Number of
students
4 6 5 3 4
2
4 Find the common difference of the AP 4,9,14,… If the first term changes to 6 and
the common difference remains the same then write the new AP.
2
5 The mode of the following frequency distribution is 38. Find the value of x.
Class
Interval
0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 7 9 12 16 x 6 11
2
6 XY and MN are the tangents drawn at the end points of the diameter DE of the circle
with centre O. Prove that XY ? ? MN.
2
X
M
Y
D
E
o
.
.
.
.
.
N
OR
In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB=6cm,
BC=7cm and CD=4cm. Find AD.
Section-B
7 An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10
terms.
3
8 A tree is broken due to the storm in such a way that the top of the tree touches the
ground and makes an angle of 30
0
with the ground. Length of the broken upper part
of the tree is 8 meters. Find the height of the tree before it was broken.
OR
Two poles of equal height are standing opposite each other on either side of the
road 80m wide. From a point between them on the road the angles of elevation of
the top of the two poles are respectively 60
0
and 30
0
. Find the distance of the point
from the two poles.
3
9 PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and
? APB=60
0
, then find the length of the chord AB.
3
10 The sum of the squares of three positive numbers that are consecutive multiples of
5 is 725. Find the three numbers.
3
Section-C
11 Construct two concentric circles of radii 3cm and 7cm. Draw two tangents to the
smaller circle from a point P which lies on the bigger circle.
OR
Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at
an angle of 60
0
. Also find the length of the tangent.
4
A
B
D C
A
B
P
6 cm
60°
O .
12 The following age wise chart of 300 passengers flying from Delhi to Pune is
prepared by the Airlines staff.
Age Less
than
10
Less
than
20
Less
than
30
Less
than
40
Less
than
50
Less
than
60
Less
than
70
Less
than
80
Number of
passengers
14 44 82 134 184 245 287 300
Find the mean age of the passengers.
4
13 A lighthouse is a tall tower with light near the top. These are often built on islands,
coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the
mariners and send warning to boats and ships for dangers. Initially wood, coal would
be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights.
Nowadays they are run by machines and remote monitoring.
Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately
40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and
a boat are coming towards the lighthouse from opposite directions. Angles of
depression of flash light from the lighthouse to the boat and the ship are 30
0
and 60
0
respectively.
i) Which of the two, boat or the ship is nearer to the light house. Find its
distance from the lighthouse?
ii) Find the time taken by the boat to reach the light house if it is moving at
the rate of 20 km per hour.
2
2
14 Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay
dolls are unique in their realism and quality of their finish. They are created by
modelling coils of clay over a metal frame. The figures are painted in natural colours
and their hair is made either by sheep’s wool or jute. Artisans make models starting
from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and
present comic characters. These creations are displayed in different national and
international museums.
30
0
60
0
A
B
C D
Here are a few images (not to scale) of some clay dolls of Krishnanagar.
The ratio of diameters of red spherical apples in Doll-1 to that of spherical
oranges in Doll-2 is 2:3. In Doll-3, male doll of blue colour has cylindrical body and
a spherical head. The spherical head touches the cylindrical body. The radius of
both the spherical head and the cylindrical body is 3cm and the height of the
cylindrical body is 8cm. Based on the above information answer the following
questions:
i) What is the ratio of the surface areas of red spherical apples in
Doll-1 to that of spherical oranges in Doll-2.?
ii) The blue doll of Doll-3 is melted and its clay is used to make the
cylindrical drum of Doll-4. If the radius of the drum is also 3cm,
find the height of the drum.
2
2
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FAQs on Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22) - Mathematics (Maths) Class 10
| 1. What topics are covered in the Class 10 Mathematics (Basic) Term II exam? |  |
Ans. The Class 10 Mathematics (Basic) Term II exam typically covers various topics including Algebra, Geometry, Statistics, and Probability. Specific chapters may include Quadratic Equations, Triangles, Areas related to circles, and some aspects of Data Handling. Students are advised to refer to their textbooks and syllabus for a comprehensive list.
| 2. How is the marking scheme structured for the Class 10 Mathematics (Basic) Term II exam? | |
Ans. The marking scheme for the Class 10 Mathematics (Basic) Term II exam usually consists of a total of 40 marks. The paper is generally divided into different sections, including very short answer questions, short answer questions, and long answer questions, with varying marks assigned to each section. It's important to manage time effectively during the exam to cover all sections.
| 3. What is the format of the question paper for the Class 10 Mathematics (Basic) Term II exam? | |
Ans. The format of the question paper for the Class 10 Mathematics (Basic) Term II exam usually includes a mix of objective type questions, short answer questions, and long answer questions. Students can expect a variety of question types, including multiple-choice questions, fill-in-the-blanks, and problem-solving questions that require detailed explanations.
| 4. How can students prepare effectively for the Class 10 Mathematics (Basic) Term II exam? | |
Ans. Students can prepare effectively for the Class 10 Mathematics (Basic) Term II exam by following a structured study plan. This includes reviewing the syllabus, practicing previous years' question papers, solving sample papers, and focusing on understanding concepts rather than rote memorization. Engaging in group study and seeking help from teachers for difficult topics can also be beneficial.
| 5. Are there any important tips for managing time during the Class 10 Mathematics (Basic) Term II exam? | |
Ans. Yes, managing time during the Class 10 Mathematics (Basic) Term II exam is crucial. Students should start by quickly scanning the entire paper to gauge the questions. It's advisable to allocate specific time limits for each section and stick to them. Prioritizing questions based on one's strengths and attempting easier questions first can help save time for more challenging ones later.
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Oct 24, 2025
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Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22) Notes
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Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22) Class 10 Questions
The "Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
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The content of Class 10 Mathematics (Basic) Term II: CBSE (Official) Sample Question Paper (2021-22) is prepared as per the latest Class 10 syllabus.
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