Maths Past Year Paper SA-2(Set -1) - 2016, Class 9, CBSE Class 9 Notes | EduRev

 Page 1


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-
A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks
each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10
question of 4 marks each. Section E comprises of two questions of 3 marks each and 1
question of 4 marks from Open Text theme.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION-A 
Question number 1 to 4 carry one mark each. 
(1) In ?XYZ, P is the mid-point of side YZ. Find the ratio ar(?XYZ):ar(?XYZ).
(2) If the total surface area of a cube is 96 cm
2
, then find its volume.    
(3) Find the mean of first 10 odd numbers. 
(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class 
is 8. Find the lower limit of the class - interval. 
SECTION-B 
Question number 5 to 10 carry two marks each. 
(5) ABCD is a trapezium with E being any point AB. IF AD?EC and DE?BC find the ratio 
ar(?DAE):ar(?BEC).
(6)  Using protractor, draw ?DEF=60
o
. Construct another angle equal to ?DEF, using compass. 
(7)  In the figure, ABCD is a parallelogram with ?B=110
o
. Find the value of x and y. 
Page 2


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-
A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks
each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10
question of 4 marks each. Section E comprises of two questions of 3 marks each and 1
question of 4 marks from Open Text theme.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION-A 
Question number 1 to 4 carry one mark each. 
(1) In ?XYZ, P is the mid-point of side YZ. Find the ratio ar(?XYZ):ar(?XYZ).
(2) If the total surface area of a cube is 96 cm
2
, then find its volume.    
(3) Find the mean of first 10 odd numbers. 
(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class 
is 8. Find the lower limit of the class - interval. 
SECTION-B 
Question number 5 to 10 carry two marks each. 
(5) ABCD is a trapezium with E being any point AB. IF AD?EC and DE?BC find the ratio 
ar(?DAE):ar(?BEC).
(6)  Using protractor, draw ?DEF=60
o
. Construct another angle equal to ?DEF, using compass. 
(7)  In the figure, ABCD is a parallelogram with ?B=110
o
. Find the value of x and y. 
(8) 20 circular plats each of radius 7 cm and thickness 1.5 cm are placed one above the other to 
form a solid right ciruclar cylinder. Find the total surface area of the cylinder so formed. 
(9) Three coins are tossed simultaneously 250 times with following frequencies of different 
outcomes: 
Number of tails 0 1 2 3 
Frequency 45 65 52 88 
Compute the probability of getting: 
i. At most 2 heads
ii. All heads
(10)  Following table shows the birth months of the 80 students of Class XII. 
Jan Feb Mar Apr May June 
5 6 7 4 10 3 
July Aug Sep Out Nov Dec 
5 10 6 8 8 8 
Find the probability that a student selected at random was born a month in which the 
Independence day or Republic day are celebrated. 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
(11)   The average monthly salary of 12 workers in a factory Rs. 12,850. IF the salary of the 
manager is included, the average becomes 13,550, what is the manager’s salary? 
(12) The median of the following observations arranged in ascending order, is 25. Find x. 11, 13, 
15, 19, x+2, x+4, 30, 35, 39, 46. Also find mean. 
(13)  In ?PQR, base QR is divided at X such that QX=
 1
2
XR. If ar(?PQR)= 81cm
2
, find ar(?PQX).
(14)  In the given figure, AB is a chord equal to the radius of the given circle with center O. 
Calculate the value of a and b. 
Page 3


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-
A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks
each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10
question of 4 marks each. Section E comprises of two questions of 3 marks each and 1
question of 4 marks from Open Text theme.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION-A 
Question number 1 to 4 carry one mark each. 
(1) In ?XYZ, P is the mid-point of side YZ. Find the ratio ar(?XYZ):ar(?XYZ).
(2) If the total surface area of a cube is 96 cm
2
, then find its volume.    
(3) Find the mean of first 10 odd numbers. 
(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class 
is 8. Find the lower limit of the class - interval. 
SECTION-B 
Question number 5 to 10 carry two marks each. 
(5) ABCD is a trapezium with E being any point AB. IF AD?EC and DE?BC find the ratio 
ar(?DAE):ar(?BEC).
(6)  Using protractor, draw ?DEF=60
o
. Construct another angle equal to ?DEF, using compass. 
(7)  In the figure, ABCD is a parallelogram with ?B=110
o
. Find the value of x and y. 
(8) 20 circular plats each of radius 7 cm and thickness 1.5 cm are placed one above the other to 
form a solid right ciruclar cylinder. Find the total surface area of the cylinder so formed. 
(9) Three coins are tossed simultaneously 250 times with following frequencies of different 
outcomes: 
Number of tails 0 1 2 3 
Frequency 45 65 52 88 
Compute the probability of getting: 
i. At most 2 heads
ii. All heads
(10)  Following table shows the birth months of the 80 students of Class XII. 
Jan Feb Mar Apr May June 
5 6 7 4 10 3 
July Aug Sep Out Nov Dec 
5 10 6 8 8 8 
Find the probability that a student selected at random was born a month in which the 
Independence day or Republic day are celebrated. 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
(11)   The average monthly salary of 12 workers in a factory Rs. 12,850. IF the salary of the 
manager is included, the average becomes 13,550, what is the manager’s salary? 
(12) The median of the following observations arranged in ascending order, is 25. Find x. 11, 13, 
15, 19, x+2, x+4, 30, 35, 39, 46. Also find mean. 
(13)  In ?PQR, base QR is divided at X such that QX=
 1
2
XR. If ar(?PQR)= 81cm
2
, find ar(?PQX).
(14)  In the given figure, AB is a chord equal to the radius of the given circle with center O. 
Calculate the value of a and b. 
(15) Construct a line segment of suitable length and using ruler and compasses divide it into four 
equal parts. Measure each equal part. Write steps of construction. 
(16)  In the figure, PQRS is a parallelogram whose diagonals intersect at O. Find the value of x and 
y. Also, find the angle of the parallelogram.
(17) Draw an angle of 70
o 
with the help of protractor. Now construct angle of (i) 35
o 
(ii) 140
o
, 
using compass. 
(18)  A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. 
Find the outer curved surface area of the bowl. 
SECTION-D 
Question numbers 19 to 28 carry four marks each. 
(19)  A batsman’s run in 80 one day matches are as follows: 
Runs 20-29 30-39 40-49 50-59 60-69 70-79 80-89 
No of 
Matches 
1 1 8 13 20 22 3 
What is the probability that in the next match the batsman will score: 
(a) atleast 70 runs, 
(b) atmost 59 runs. 
(20)  PQRS is a parallelogram in which QR is produced to E such QR=RE. PE intersects SR at F. If 
ar(?SFQ)=3 cm
2
, find ar(PQRS).
(21)  In the give figure, P is any point on the chord BC of a circle such that AB=AP. Prove that 
CP=CQ. If ?BAP=50
o
, find ?CQP and ?BRQ. 
Page 4


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-
A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks
each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10
question of 4 marks each. Section E comprises of two questions of 3 marks each and 1
question of 4 marks from Open Text theme.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION-A 
Question number 1 to 4 carry one mark each. 
(1) In ?XYZ, P is the mid-point of side YZ. Find the ratio ar(?XYZ):ar(?XYZ).
(2) If the total surface area of a cube is 96 cm
2
, then find its volume.    
(3) Find the mean of first 10 odd numbers. 
(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class 
is 8. Find the lower limit of the class - interval. 
SECTION-B 
Question number 5 to 10 carry two marks each. 
(5) ABCD is a trapezium with E being any point AB. IF AD?EC and DE?BC find the ratio 
ar(?DAE):ar(?BEC).
(6)  Using protractor, draw ?DEF=60
o
. Construct another angle equal to ?DEF, using compass. 
(7)  In the figure, ABCD is a parallelogram with ?B=110
o
. Find the value of x and y. 
(8) 20 circular plats each of radius 7 cm and thickness 1.5 cm are placed one above the other to 
form a solid right ciruclar cylinder. Find the total surface area of the cylinder so formed. 
(9) Three coins are tossed simultaneously 250 times with following frequencies of different 
outcomes: 
Number of tails 0 1 2 3 
Frequency 45 65 52 88 
Compute the probability of getting: 
i. At most 2 heads
ii. All heads
(10)  Following table shows the birth months of the 80 students of Class XII. 
Jan Feb Mar Apr May June 
5 6 7 4 10 3 
July Aug Sep Out Nov Dec 
5 10 6 8 8 8 
Find the probability that a student selected at random was born a month in which the 
Independence day or Republic day are celebrated. 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
(11)   The average monthly salary of 12 workers in a factory Rs. 12,850. IF the salary of the 
manager is included, the average becomes 13,550, what is the manager’s salary? 
(12) The median of the following observations arranged in ascending order, is 25. Find x. 11, 13, 
15, 19, x+2, x+4, 30, 35, 39, 46. Also find mean. 
(13)  In ?PQR, base QR is divided at X such that QX=
 1
2
XR. If ar(?PQR)= 81cm
2
, find ar(?PQX).
(14)  In the given figure, AB is a chord equal to the radius of the given circle with center O. 
Calculate the value of a and b. 
(15) Construct a line segment of suitable length and using ruler and compasses divide it into four 
equal parts. Measure each equal part. Write steps of construction. 
(16)  In the figure, PQRS is a parallelogram whose diagonals intersect at O. Find the value of x and 
y. Also, find the angle of the parallelogram.
(17) Draw an angle of 70
o 
with the help of protractor. Now construct angle of (i) 35
o 
(ii) 140
o
, 
using compass. 
(18)  A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. 
Find the outer curved surface area of the bowl. 
SECTION-D 
Question numbers 19 to 28 carry four marks each. 
(19)  A batsman’s run in 80 one day matches are as follows: 
Runs 20-29 30-39 40-49 50-59 60-69 70-79 80-89 
No of 
Matches 
1 1 8 13 20 22 3 
What is the probability that in the next match the batsman will score: 
(a) atleast 70 runs, 
(b) atmost 59 runs. 
(20)  PQRS is a parallelogram in which QR is produced to E such QR=RE. PE intersects SR at F. If 
ar(?SFQ)=3 cm
2
, find ar(PQRS).
(21)  In the give figure, P is any point on the chord BC of a circle such that AB=AP. Prove that 
CP=CQ. If ?BAP=50
o
, find ?CQP and ?BRQ. 
(22) Construct  ?MNO, when NO= 3.6cm, MN=MO=4.4cmand ?N=75
o
.
(23) In the figure, ABCD and ABPQ are two parallelograms. Prove that ?ADQ ? ?BCP.
(24) The “Caring old people organisation” needs money to build the old age home which requires 
164000 bricks. Bricks measure 10 cm ×8 cm× 4 cm and cost of brick depends on its volume 
at the rate of Rs.1 per 100cm
3
. It also requires 4 cylindrical cans of paint of radius 14 cm and 
height 30 cm. The cost of paint is Rs.1 per 20 cm
3
. How much money is required by 
organization? If “company A gives the money to the organization”, then what common value 
is depicted by company A and the organization? 
(25)  A closed cubical box of edge 20 cm is made up of wood of thickness 2 cm. Find the: 
(a) volume of the wood used to make it. 
(b) volume of air trapped in it. 
(26)  How many full bags of wheat can be emptied into a conical tent of radius 8.4 m and height 3.5 
cm, if space for the wheat in each bag is 1.96 m
3
? 
(27)  The curved surface area of cylindrical pillar is 264 m
2
and its volume is 924 m
3
. Find the 
diameter and height of the pillar. 
(28) The table shows the prefers snacks of 100 children: 
Prefered 
Snack 
Number of children 
Lays chips 
Crax 
Cheese Balls 
Uncle chips 
Fun flips 
22 
10 
15 
24 
29 
Find the probability that the child chosen at random likes: 
Page 5


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 question divided into five section A, B, C, D and E. Section-
A comprises of 4 question of 1 mark each, Section-B comprises of 6 question of 2 marks
each, Section-C comprises of 8 question of 3 marks each and Section-D comprises of 10
question of 4 marks each. Section E comprises of two questions of 3 marks each and 1
question of 4 marks from Open Text theme.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION-A 
Question number 1 to 4 carry one mark each. 
(1) In ?XYZ, P is the mid-point of side YZ. Find the ratio ar(?XYZ):ar(?XYZ).
(2) If the total surface area of a cube is 96 cm
2
, then find its volume.    
(3) Find the mean of first 10 odd numbers. 
(4) In a frequency distribution, the mid-point of a class – interval is 20 and the width of the class 
is 8. Find the lower limit of the class - interval. 
SECTION-B 
Question number 5 to 10 carry two marks each. 
(5) ABCD is a trapezium with E being any point AB. IF AD?EC and DE?BC find the ratio 
ar(?DAE):ar(?BEC).
(6)  Using protractor, draw ?DEF=60
o
. Construct another angle equal to ?DEF, using compass. 
(7)  In the figure, ABCD is a parallelogram with ?B=110
o
. Find the value of x and y. 
(8) 20 circular plats each of radius 7 cm and thickness 1.5 cm are placed one above the other to 
form a solid right ciruclar cylinder. Find the total surface area of the cylinder so formed. 
(9) Three coins are tossed simultaneously 250 times with following frequencies of different 
outcomes: 
Number of tails 0 1 2 3 
Frequency 45 65 52 88 
Compute the probability of getting: 
i. At most 2 heads
ii. All heads
(10)  Following table shows the birth months of the 80 students of Class XII. 
Jan Feb Mar Apr May June 
5 6 7 4 10 3 
July Aug Sep Out Nov Dec 
5 10 6 8 8 8 
Find the probability that a student selected at random was born a month in which the 
Independence day or Republic day are celebrated. 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
(11)   The average monthly salary of 12 workers in a factory Rs. 12,850. IF the salary of the 
manager is included, the average becomes 13,550, what is the manager’s salary? 
(12) The median of the following observations arranged in ascending order, is 25. Find x. 11, 13, 
15, 19, x+2, x+4, 30, 35, 39, 46. Also find mean. 
(13)  In ?PQR, base QR is divided at X such that QX=
 1
2
XR. If ar(?PQR)= 81cm
2
, find ar(?PQX).
(14)  In the given figure, AB is a chord equal to the radius of the given circle with center O. 
Calculate the value of a and b. 
(15) Construct a line segment of suitable length and using ruler and compasses divide it into four 
equal parts. Measure each equal part. Write steps of construction. 
(16)  In the figure, PQRS is a parallelogram whose diagonals intersect at O. Find the value of x and 
y. Also, find the angle of the parallelogram.
(17) Draw an angle of 70
o 
with the help of protractor. Now construct angle of (i) 35
o 
(ii) 140
o
, 
using compass. 
(18)  A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. 
Find the outer curved surface area of the bowl. 
SECTION-D 
Question numbers 19 to 28 carry four marks each. 
(19)  A batsman’s run in 80 one day matches are as follows: 
Runs 20-29 30-39 40-49 50-59 60-69 70-79 80-89 
No of 
Matches 
1 1 8 13 20 22 3 
What is the probability that in the next match the batsman will score: 
(a) atleast 70 runs, 
(b) atmost 59 runs. 
(20)  PQRS is a parallelogram in which QR is produced to E such QR=RE. PE intersects SR at F. If 
ar(?SFQ)=3 cm
2
, find ar(PQRS).
(21)  In the give figure, P is any point on the chord BC of a circle such that AB=AP. Prove that 
CP=CQ. If ?BAP=50
o
, find ?CQP and ?BRQ. 
(22) Construct  ?MNO, when NO= 3.6cm, MN=MO=4.4cmand ?N=75
o
.
(23) In the figure, ABCD and ABPQ are two parallelograms. Prove that ?ADQ ? ?BCP.
(24) The “Caring old people organisation” needs money to build the old age home which requires 
164000 bricks. Bricks measure 10 cm ×8 cm× 4 cm and cost of brick depends on its volume 
at the rate of Rs.1 per 100cm
3
. It also requires 4 cylindrical cans of paint of radius 14 cm and 
height 30 cm. The cost of paint is Rs.1 per 20 cm
3
. How much money is required by 
organization? If “company A gives the money to the organization”, then what common value 
is depicted by company A and the organization? 
(25)  A closed cubical box of edge 20 cm is made up of wood of thickness 2 cm. Find the: 
(a) volume of the wood used to make it. 
(b) volume of air trapped in it. 
(26)  How many full bags of wheat can be emptied into a conical tent of radius 8.4 m and height 3.5 
cm, if space for the wheat in each bag is 1.96 m
3
? 
(27)  The curved surface area of cylindrical pillar is 264 m
2
and its volume is 924 m
3
. Find the 
diameter and height of the pillar. 
(28) The table shows the prefers snacks of 100 children: 
Prefered 
Snack 
Number of children 
Lays chips 
Crax 
Cheese Balls 
Uncle chips 
Fun flips 
22 
10 
15 
24 
29 
Find the probability that the child chosen at random likes: 
(a)  crax and funflips 
(b) lays chips and cheese balls 
(c) only uncle chips. 
SECTION-E 
(Open Text) 
(*Please ensure that open text of the given theme is supplied with this question paper.) 
Theme: Childhood Obesity in India 
(29)  Two friend examined their BMI as 27 and 31, however both have equal height of 150 cm. 
Determine weight of both friends. Also state the health status of both friends. 
(30)  You want to burn 250 calories with the help of home activities for  x  min and running or y 
min. Then what will be the liner equation for this? Write it in standard from and write value 
of a, b and c. 
(31)  It is given that infants from age of one onward grow up to adolescence at a rate of 2 kg every 
year for weight. 
(a) Write a liner equation in 2 variable establishing a relation between age and weight 
assuming age to be x and weight as y, if weight at 1 year of age and is given as 3 kg. 
(b) Write two solution for the above equation.