Class 9 Maths: CBSE Past Year Paper (SA-2) - 4 | Past Year Papers For Class 9

 Page 1


SUMMATIVE ASSESSMENT –II
Subject: Mathematics 
Class: XI 
Time: 3 Hrs.  M.M. 90 
General Instructions: 
• All questions are compulsory.
• The question paper consists of 31 questions divided into five sections A, B, C, D and E.
Section – A comprises of 4 questions of 1 marks each, Section – B comprises of 6 questions
of 2 marks each, Section – C comprises of 8 questions of 3 marks each and Section – D
comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks
each and 1 question of 4 marks from Open Text Theme.
• There is no overall choice.
• Use of calculator is not permitted.
SECTION – A 
Question numbers 1 to 4 carry one mark each. 
1. If 2 10 x ky k + = , intersects x-axis at (2,0), find k.
2. Express 2 0 x + = in the form of 0 ax by c + + = .
3. A triangle and a parallelogram are on the same base and between the same parallels. If
altitude of triangle is 4 cm and its area is 
2
8cm , find the length of base of parallelogram.
4. Find the total surface area of a solid hemisphere with radius 7 cm.
SECTION – B 
Question numbers 5 to 10 carry two marks each. 
5. In the given figure, O is the centre of the circle. If 60 AOB ? = ° . Find the measures of AOC ?
and ABC ? .
6. Using protractor, draw 60 DEF ? = ° . Construct another angle equal to DEF ? using compass.
7. In the figure, ABCD is a rhombus whose diagonals meet at O. Find the values of x and y.
8. A solid right circular cylinder has radius 14 cm and height 8 cm. Find its curved surface area
and total surface area.
Page 2


SUMMATIVE ASSESSMENT –II
Subject: Mathematics 
Class: XI 
Time: 3 Hrs.  M.M. 90 
General Instructions: 
• All questions are compulsory.
• The question paper consists of 31 questions divided into five sections A, B, C, D and E.
Section – A comprises of 4 questions of 1 marks each, Section – B comprises of 6 questions
of 2 marks each, Section – C comprises of 8 questions of 3 marks each and Section – D
comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks
each and 1 question of 4 marks from Open Text Theme.
• There is no overall choice.
• Use of calculator is not permitted.
SECTION – A 
Question numbers 1 to 4 carry one mark each. 
1. If 2 10 x ky k + = , intersects x-axis at (2,0), find k.
2. Express 2 0 x + = in the form of 0 ax by c + + = .
3. A triangle and a parallelogram are on the same base and between the same parallels. If
altitude of triangle is 4 cm and its area is 
2
8cm , find the length of base of parallelogram.
4. Find the total surface area of a solid hemisphere with radius 7 cm.
SECTION – B 
Question numbers 5 to 10 carry two marks each. 
5. In the given figure, O is the centre of the circle. If 60 AOB ? = ° . Find the measures of AOC ?
and ABC ? .
6. Using protractor, draw 60 DEF ? = ° . Construct another angle equal to DEF ? using compass.
7. In the figure, ABCD is a rhombus whose diagonals meet at O. Find the values of x and y.
8. A solid right circular cylinder has radius 14 cm and height 8 cm. Find its curved surface area
and total surface area.
9. In a class probability that students are in uniform is
23
30
. Find the probability that students
are not in uniform. 
10. A coin is tossed 150 times and the outcomes are recorded as follows:
Outcomes H T 
Frequency 85 65 
Compute the probability of 
a) One head
b) One tail
SECTION –C 
Question numbers 11 to 18 carry three marks each. 
11. Write the equation of a line which is parallel to x-axis and is at a distance of 2 units below x-
axis. Represent this graphically also.
12. The auto fare in a city are as follow: for the first kilometer it is Rs. 10 and for subsequent
distance it is Rs. 8 per km. taking the distance as y km. and total fare as Rs. x, write a linear
equation for this draw and the draw the graph. Also, find the fare of 15 km.
13. PQR ? is right angled at Q. A and B are the mid-points of sides PQ and PR respectively. If
PQ=10 cm and PR=26 cm, then find the length of AB.
14. Construct KLM ? in which KL + LM + MK = 15 cm, 90 L ? = ° and 30 M ? = ° .
15. In a triangle ABC, E is mid-point of median AD. Prove that ( ) ( ) ar BED ar AEC ? = ?
16. In the given figure, O is the centre of the circle. Prove that a b c ? + ? = ? .
17. In the given figure, if O is the centre of the circle, BD=OD and CD AB ? , find CAB ? and
BCD ?
18. There is a solid cube which has been cut into two cuboids of equal volumes. Find the ration of
the total surface area of one of the cuboids to that of the given cube.
SECTION – D 
Question numbers 19 to 28 carry four marks each. 
Page 3


SUMMATIVE ASSESSMENT –II
Subject: Mathematics 
Class: XI 
Time: 3 Hrs.  M.M. 90 
General Instructions: 
• All questions are compulsory.
• The question paper consists of 31 questions divided into five sections A, B, C, D and E.
Section – A comprises of 4 questions of 1 marks each, Section – B comprises of 6 questions
of 2 marks each, Section – C comprises of 8 questions of 3 marks each and Section – D
comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks
each and 1 question of 4 marks from Open Text Theme.
• There is no overall choice.
• Use of calculator is not permitted.
SECTION – A 
Question numbers 1 to 4 carry one mark each. 
1. If 2 10 x ky k + = , intersects x-axis at (2,0), find k.
2. Express 2 0 x + = in the form of 0 ax by c + + = .
3. A triangle and a parallelogram are on the same base and between the same parallels. If
altitude of triangle is 4 cm and its area is 
2
8cm , find the length of base of parallelogram.
4. Find the total surface area of a solid hemisphere with radius 7 cm.
SECTION – B 
Question numbers 5 to 10 carry two marks each. 
5. In the given figure, O is the centre of the circle. If 60 AOB ? = ° . Find the measures of AOC ?
and ABC ? .
6. Using protractor, draw 60 DEF ? = ° . Construct another angle equal to DEF ? using compass.
7. In the figure, ABCD is a rhombus whose diagonals meet at O. Find the values of x and y.
8. A solid right circular cylinder has radius 14 cm and height 8 cm. Find its curved surface area
and total surface area.
9. In a class probability that students are in uniform is
23
30
. Find the probability that students
are not in uniform. 
10. A coin is tossed 150 times and the outcomes are recorded as follows:
Outcomes H T 
Frequency 85 65 
Compute the probability of 
a) One head
b) One tail
SECTION –C 
Question numbers 11 to 18 carry three marks each. 
11. Write the equation of a line which is parallel to x-axis and is at a distance of 2 units below x-
axis. Represent this graphically also.
12. The auto fare in a city are as follow: for the first kilometer it is Rs. 10 and for subsequent
distance it is Rs. 8 per km. taking the distance as y km. and total fare as Rs. x, write a linear
equation for this draw and the draw the graph. Also, find the fare of 15 km.
13. PQR ? is right angled at Q. A and B are the mid-points of sides PQ and PR respectively. If
PQ=10 cm and PR=26 cm, then find the length of AB.
14. Construct KLM ? in which KL + LM + MK = 15 cm, 90 L ? = ° and 30 M ? = ° .
15. In a triangle ABC, E is mid-point of median AD. Prove that ( ) ( ) ar BED ar AEC ? = ?
16. In the given figure, O is the centre of the circle. Prove that a b c ? + ? = ? .
17. In the given figure, if O is the centre of the circle, BD=OD and CD AB ? , find CAB ? and
BCD ?
18. There is a solid cube which has been cut into two cuboids of equal volumes. Find the ration of
the total surface area of one of the cuboids to that of the given cube.
SECTION – D 
Question numbers 19 to 28 carry four marks each. 
19. Draw the graphs of the following equations on the same sheet: 0, 0, 4 x y x y = = + = also, find
the area enclosed between these lines.
20. Angles of a triangle are x, 2x and y. write a linear equation which satisfies this data. Draw the
graph for the same.
21. In order to guide and help people in reaching school without any problem of finding the way
to school, students of the school decided to put up a sign board on main road. The sign board
ABCD in the shape of a parallelogram as shown in figure.
a) If x and y are the mid-point of sides AB and CD respectively, show that
( ) ( ) ar AXYD ar BXYC = .
b) What can you say about this gesture of the students?
22. Draw a line segment AB=12.4 cm. Find
1
4
AB using ruler and compass. Write steps of 
construction. 
23. Prove that a quadrilateral formed by bisectors of interior angles of a quadrilateral is a cyclic
quadrilateral.
24. In the figure, PQRS is a quadrilateral in which A, B, C and D are mid – points of the sides PQ,
QR, RS and PS respectively. Show that AC and BD bisect each other.
25. The frame of a lampshade is cylindrical in shape. It has base diameter 28 cm and height 17
cm. it is to be covered with a decorative clothe. A margin of 2 cm is to be given for folding it
over top and bottom of the frame. If
1
12
of cloth is wasted in cutting and pasting, find how
much cloth is required to be purchased for covering the frame. 
26. A fruit tin has a square base with side 14 cm and height 18.5 cm. another cylindrical tin has a
diameter of the base 14 cm and height 17.5 cm. Which tin has more capacity and by how
much?
27. The volume of a right circular cone is 
3
100 cm p and its height is 12 cm. Find its slant height
and hence its curved surface area.
28. A coin is tossed for a certain number of times. If the probability of getting a head is 0.4 and
the head appeared up for 24 times, find the number – of times the coin was tossed. Hence,
find the probability of getting a tail and verify that P(H) + P(T) = 1.
Page 4


SUMMATIVE ASSESSMENT –II
Subject: Mathematics 
Class: XI 
Time: 3 Hrs.  M.M. 90 
General Instructions: 
• All questions are compulsory.
• The question paper consists of 31 questions divided into five sections A, B, C, D and E.
Section – A comprises of 4 questions of 1 marks each, Section – B comprises of 6 questions
of 2 marks each, Section – C comprises of 8 questions of 3 marks each and Section – D
comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks
each and 1 question of 4 marks from Open Text Theme.
• There is no overall choice.
• Use of calculator is not permitted.
SECTION – A 
Question numbers 1 to 4 carry one mark each. 
1. If 2 10 x ky k + = , intersects x-axis at (2,0), find k.
2. Express 2 0 x + = in the form of 0 ax by c + + = .
3. A triangle and a parallelogram are on the same base and between the same parallels. If
altitude of triangle is 4 cm and its area is 
2
8cm , find the length of base of parallelogram.
4. Find the total surface area of a solid hemisphere with radius 7 cm.
SECTION – B 
Question numbers 5 to 10 carry two marks each. 
5. In the given figure, O is the centre of the circle. If 60 AOB ? = ° . Find the measures of AOC ?
and ABC ? .
6. Using protractor, draw 60 DEF ? = ° . Construct another angle equal to DEF ? using compass.
7. In the figure, ABCD is a rhombus whose diagonals meet at O. Find the values of x and y.
8. A solid right circular cylinder has radius 14 cm and height 8 cm. Find its curved surface area
and total surface area.
9. In a class probability that students are in uniform is
23
30
. Find the probability that students
are not in uniform. 
10. A coin is tossed 150 times and the outcomes are recorded as follows:
Outcomes H T 
Frequency 85 65 
Compute the probability of 
a) One head
b) One tail
SECTION –C 
Question numbers 11 to 18 carry three marks each. 
11. Write the equation of a line which is parallel to x-axis and is at a distance of 2 units below x-
axis. Represent this graphically also.
12. The auto fare in a city are as follow: for the first kilometer it is Rs. 10 and for subsequent
distance it is Rs. 8 per km. taking the distance as y km. and total fare as Rs. x, write a linear
equation for this draw and the draw the graph. Also, find the fare of 15 km.
13. PQR ? is right angled at Q. A and B are the mid-points of sides PQ and PR respectively. If
PQ=10 cm and PR=26 cm, then find the length of AB.
14. Construct KLM ? in which KL + LM + MK = 15 cm, 90 L ? = ° and 30 M ? = ° .
15. In a triangle ABC, E is mid-point of median AD. Prove that ( ) ( ) ar BED ar AEC ? = ?
16. In the given figure, O is the centre of the circle. Prove that a b c ? + ? = ? .
17. In the given figure, if O is the centre of the circle, BD=OD and CD AB ? , find CAB ? and
BCD ?
18. There is a solid cube which has been cut into two cuboids of equal volumes. Find the ration of
the total surface area of one of the cuboids to that of the given cube.
SECTION – D 
Question numbers 19 to 28 carry four marks each. 
19. Draw the graphs of the following equations on the same sheet: 0, 0, 4 x y x y = = + = also, find
the area enclosed between these lines.
20. Angles of a triangle are x, 2x and y. write a linear equation which satisfies this data. Draw the
graph for the same.
21. In order to guide and help people in reaching school without any problem of finding the way
to school, students of the school decided to put up a sign board on main road. The sign board
ABCD in the shape of a parallelogram as shown in figure.
a) If x and y are the mid-point of sides AB and CD respectively, show that
( ) ( ) ar AXYD ar BXYC = .
b) What can you say about this gesture of the students?
22. Draw a line segment AB=12.4 cm. Find
1
4
AB using ruler and compass. Write steps of 
construction. 
23. Prove that a quadrilateral formed by bisectors of interior angles of a quadrilateral is a cyclic
quadrilateral.
24. In the figure, PQRS is a quadrilateral in which A, B, C and D are mid – points of the sides PQ,
QR, RS and PS respectively. Show that AC and BD bisect each other.
25. The frame of a lampshade is cylindrical in shape. It has base diameter 28 cm and height 17
cm. it is to be covered with a decorative clothe. A margin of 2 cm is to be given for folding it
over top and bottom of the frame. If
1
12
of cloth is wasted in cutting and pasting, find how
much cloth is required to be purchased for covering the frame. 
26. A fruit tin has a square base with side 14 cm and height 18.5 cm. another cylindrical tin has a
diameter of the base 14 cm and height 17.5 cm. Which tin has more capacity and by how
much?
27. The volume of a right circular cone is 
3
100 cm p and its height is 12 cm. Find its slant height
and hence its curved surface area.
28. A coin is tossed for a certain number of times. If the probability of getting a head is 0.4 and
the head appeared up for 24 times, find the number – of times the coin was tossed. Hence,
find the probability of getting a tail and verify that P(H) + P(T) = 1.
SECTION E 
OPEN TEXT BASED ASSESSMENT (OTBA) 
(*Please ensure that open text of the given theme is supplied with this question paper.) 
Theme: Empower to learn 
29. 
a) For the site ‘superb’ prepare a bar chart showing percentage of campaigns conducted in
different subjects (refer figure 3)
b) In which subjects, students are benefitted least and most?
30. 
a) Name the site which has registered more than 80,00,000 students in two years.
b) For this site prepare a frequency distribution table and frequency polygon.
31. 
a) From which site students can directly ask questions from the academic experts?
b) If number of questions asked during different hours of the day are 150, 175, 400, 220,
150, 300, 160, 500, then find mean, mode and median.
OPEN TEXT MATERIAL 
1. Theme: Empower to Learn
Abstract: 
Harshit heard of the social networking sites and started exploring them on the internet. To his 
surprise he came across various educational as well as social networking sites that give 
innovative and improved ways of learning. He gradually got prone to the facilities these 
platforms offer which broadened his perspectives. He realized that this advancement in social 
networking platform is providing him with much better options to engage with his 
contemporaries, enhance his skills and access a wide variety of academic tools and resources 
which most definitely add up to his convenience. 
Harshit learn about LEARNOUT, a free social learning network of university and school students. 
It offers a platform for its users where they can engage in activities like sharing study related 
materials, counseling or simply connecting through a vast network of existing users from around 
the world. Within a small time span of two years, more than 80,00,000 students registered for 
the website and they use the website on daily basis. The distribution of the students in different 
age groups was graphically presented and he got inspired as he thought himself that maximum 
number of children of his age is gaining from this site. 
Figure 1: Histogram showing the number of students using learn-out in different age groups 
Page 5


SUMMATIVE ASSESSMENT –II
Subject: Mathematics 
Class: XI 
Time: 3 Hrs.  M.M. 90 
General Instructions: 
• All questions are compulsory.
• The question paper consists of 31 questions divided into five sections A, B, C, D and E.
Section – A comprises of 4 questions of 1 marks each, Section – B comprises of 6 questions
of 2 marks each, Section – C comprises of 8 questions of 3 marks each and Section – D
comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks
each and 1 question of 4 marks from Open Text Theme.
• There is no overall choice.
• Use of calculator is not permitted.
SECTION – A 
Question numbers 1 to 4 carry one mark each. 
1. If 2 10 x ky k + = , intersects x-axis at (2,0), find k.
2. Express 2 0 x + = in the form of 0 ax by c + + = .
3. A triangle and a parallelogram are on the same base and between the same parallels. If
altitude of triangle is 4 cm and its area is 
2
8cm , find the length of base of parallelogram.
4. Find the total surface area of a solid hemisphere with radius 7 cm.
SECTION – B 
Question numbers 5 to 10 carry two marks each. 
5. In the given figure, O is the centre of the circle. If 60 AOB ? = ° . Find the measures of AOC ?
and ABC ? .
6. Using protractor, draw 60 DEF ? = ° . Construct another angle equal to DEF ? using compass.
7. In the figure, ABCD is a rhombus whose diagonals meet at O. Find the values of x and y.
8. A solid right circular cylinder has radius 14 cm and height 8 cm. Find its curved surface area
and total surface area.
9. In a class probability that students are in uniform is
23
30
. Find the probability that students
are not in uniform. 
10. A coin is tossed 150 times and the outcomes are recorded as follows:
Outcomes H T 
Frequency 85 65 
Compute the probability of 
a) One head
b) One tail
SECTION –C 
Question numbers 11 to 18 carry three marks each. 
11. Write the equation of a line which is parallel to x-axis and is at a distance of 2 units below x-
axis. Represent this graphically also.
12. The auto fare in a city are as follow: for the first kilometer it is Rs. 10 and for subsequent
distance it is Rs. 8 per km. taking the distance as y km. and total fare as Rs. x, write a linear
equation for this draw and the draw the graph. Also, find the fare of 15 km.
13. PQR ? is right angled at Q. A and B are the mid-points of sides PQ and PR respectively. If
PQ=10 cm and PR=26 cm, then find the length of AB.
14. Construct KLM ? in which KL + LM + MK = 15 cm, 90 L ? = ° and 30 M ? = ° .
15. In a triangle ABC, E is mid-point of median AD. Prove that ( ) ( ) ar BED ar AEC ? = ?
16. In the given figure, O is the centre of the circle. Prove that a b c ? + ? = ? .
17. In the given figure, if O is the centre of the circle, BD=OD and CD AB ? , find CAB ? and
BCD ?
18. There is a solid cube which has been cut into two cuboids of equal volumes. Find the ration of
the total surface area of one of the cuboids to that of the given cube.
SECTION – D 
Question numbers 19 to 28 carry four marks each. 
19. Draw the graphs of the following equations on the same sheet: 0, 0, 4 x y x y = = + = also, find
the area enclosed between these lines.
20. Angles of a triangle are x, 2x and y. write a linear equation which satisfies this data. Draw the
graph for the same.
21. In order to guide and help people in reaching school without any problem of finding the way
to school, students of the school decided to put up a sign board on main road. The sign board
ABCD in the shape of a parallelogram as shown in figure.
a) If x and y are the mid-point of sides AB and CD respectively, show that
( ) ( ) ar AXYD ar BXYC = .
b) What can you say about this gesture of the students?
22. Draw a line segment AB=12.4 cm. Find
1
4
AB using ruler and compass. Write steps of 
construction. 
23. Prove that a quadrilateral formed by bisectors of interior angles of a quadrilateral is a cyclic
quadrilateral.
24. In the figure, PQRS is a quadrilateral in which A, B, C and D are mid – points of the sides PQ,
QR, RS and PS respectively. Show that AC and BD bisect each other.
25. The frame of a lampshade is cylindrical in shape. It has base diameter 28 cm and height 17
cm. it is to be covered with a decorative clothe. A margin of 2 cm is to be given for folding it
over top and bottom of the frame. If
1
12
of cloth is wasted in cutting and pasting, find how
much cloth is required to be purchased for covering the frame. 
26. A fruit tin has a square base with side 14 cm and height 18.5 cm. another cylindrical tin has a
diameter of the base 14 cm and height 17.5 cm. Which tin has more capacity and by how
much?
27. The volume of a right circular cone is 
3
100 cm p and its height is 12 cm. Find its slant height
and hence its curved surface area.
28. A coin is tossed for a certain number of times. If the probability of getting a head is 0.4 and
the head appeared up for 24 times, find the number – of times the coin was tossed. Hence,
find the probability of getting a tail and verify that P(H) + P(T) = 1.
SECTION E 
OPEN TEXT BASED ASSESSMENT (OTBA) 
(*Please ensure that open text of the given theme is supplied with this question paper.) 
Theme: Empower to learn 
29. 
a) For the site ‘superb’ prepare a bar chart showing percentage of campaigns conducted in
different subjects (refer figure 3)
b) In which subjects, students are benefitted least and most?
30. 
a) Name the site which has registered more than 80,00,000 students in two years.
b) For this site prepare a frequency distribution table and frequency polygon.
31. 
a) From which site students can directly ask questions from the academic experts?
b) If number of questions asked during different hours of the day are 150, 175, 400, 220,
150, 300, 160, 500, then find mean, mode and median.
OPEN TEXT MATERIAL 
1. Theme: Empower to Learn
Abstract: 
Harshit heard of the social networking sites and started exploring them on the internet. To his 
surprise he came across various educational as well as social networking sites that give 
innovative and improved ways of learning. He gradually got prone to the facilities these 
platforms offer which broadened his perspectives. He realized that this advancement in social 
networking platform is providing him with much better options to engage with his 
contemporaries, enhance his skills and access a wide variety of academic tools and resources 
which most definitely add up to his convenience. 
Harshit learn about LEARNOUT, a free social learning network of university and school students. 
It offers a platform for its users where they can engage in activities like sharing study related 
materials, counseling or simply connecting through a vast network of existing users from around 
the world. Within a small time span of two years, more than 80,00,000 students registered for 
the website and they use the website on daily basis. The distribution of the students in different 
age groups was graphically presented and he got inspired as he thought himself that maximum 
number of children of his age is gaining from this site. 
Figure 1: Histogram showing the number of students using learn-out in different age groups 
The website offers user generated contents in 7 different languages including Italian, English, 
Spanish, Polish, Russian, Serbian and Portuguese. The website is directly operated from its 
respective regional head offices thereby providing a direct approach to the users. Learn-out also 
has its free application available for all android devices. The website also has a dedicated 24/7 
support team to assist the students in their matters. He surveyed a number of people and 
recorded his finding on the percentage of users using this site in different languages: 
Table 1: The percentage of users in different languages of LEAROUT is given in the table below: 
Language Italian English Spanish Polish Russian Serbian Portuguese 
Percentage 
of users 
11 57 6 4 10 9 3 
He also discovered a site name TWOWAY which provides its students with a different approach 
towards studies. It offers an interactive way of studying where students get to create and 
animate flashcards. The website currently has about 1 million study content authored by the 
students. The website also conducts different quizzical campaigns for the students and tracks 
the progress of its users. The issues on which the campaigns were conducted are presented in 
the form of pie chart. 
Harshit also got a platform to spread awareness of the issues which he has to record in his 
project work given by his teacher. He could collect the data globally and interpret it from 
different perspectives. 
Figure 2: The pie chart shows the campaigns conducted on TWOWAY in different subjects. 
Mathematics was troubling him and he needed a special assistance in various concepts. He 
received many resource materials to gain more knowledge and achieved higher level of learning. 
The site name TROUBLE BUBBLE was the answer to his queries. TROUBLE BUBBLE offers a very 
interactive way to the students looking for answers to the distressing questions. They can ask 
questions directly from academic experts through their vast network. The following data shows 
the number of question asked by students between 2:00 pm to 9:00 pm. 
Table 2: The table below shows the average number of questions asked at different hours of the 
day on TROUBLE BUBBLE. 
Time 2 to 3 pm 3 to 4 pm 4 to 5 pm 5 to 6 pm 6 to 7 pm 7 to 8 pm 8 to 9 pm 
Number of 
questions 
180 270 360 440 520 300 190 
Harshit was pleased to know that he has the facility to get immediate answers to his queries 
though his site.