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

 Page 1


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) 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. 
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted. 
SECTION-A 
Question number 1 to 4 carry one mark each. 
1. Area of parallelogram is 64 cm
2
. If base of the parallelogram is 16cm, find the height of the
corresponding attitude.
2. Find the side of a cube of its total surface area is 486 cm
2
.
3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?
4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.
SECTION-B 
Question number 5 to 10 carry two marks each. 
5. PQTS and PTRQ are two parallelograms. Show that ar (?PST) = ar (?QTR) = 
1
3
ar(PQRS).
Page 2


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) 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. 
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted. 
SECTION-A 
Question number 1 to 4 carry one mark each. 
1. Area of parallelogram is 64 cm
2
. If base of the parallelogram is 16cm, find the height of the
corresponding attitude.
2. Find the side of a cube of its total surface area is 486 cm
2
.
3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?
4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.
SECTION-B 
Question number 5 to 10 carry two marks each. 
5. PQTS and PTRQ are two parallelograms. Show that ar (?PST) = ar (?QTR) = 
1
3
ar(PQRS).
6. Draw a line segment of length 7.6 cm. Bisect Measure the length of each part.
7. In the figure, ABCD is a square. Find the measure of ?CDB.
8. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.
9. Teachers and students are selected at random to make teams of 20 members each on sports
day to participate in the event of “Tug of War’’. The number of volunteers are as follows:
TEACHERS STUDENTS 
Male Female Male Female 
12 18 20 10 
Find the probability that the person chosen at random 
(a) is a male 
(b) is a female student. 
10. An experiment is performed 400 times and three possible events A, B and C. Possible
occurrence of the three events are recorded. Out of the following which records are Possible
(give reason to support y our answer).
(a) A-176, B-54, C-170 
(b) A-200, B-100, C-75 
(c) A-180, B-170, C-50 
(d) A-175, B-125, C-200 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
11. Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 34, 43 are written in an ascending order. The
median of the data is 24.  Also, find their mean.
12. Draw Bar Diagram for the given expenditure of a family on different heads in the month:
Head Expenditure 
Page 3


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) 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. 
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted. 
SECTION-A 
Question number 1 to 4 carry one mark each. 
1. Area of parallelogram is 64 cm
2
. If base of the parallelogram is 16cm, find the height of the
corresponding attitude.
2. Find the side of a cube of its total surface area is 486 cm
2
.
3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?
4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.
SECTION-B 
Question number 5 to 10 carry two marks each. 
5. PQTS and PTRQ are two parallelograms. Show that ar (?PST) = ar (?QTR) = 
1
3
ar(PQRS).
6. Draw a line segment of length 7.6 cm. Bisect Measure the length of each part.
7. In the figure, ABCD is a square. Find the measure of ?CDB.
8. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.
9. Teachers and students are selected at random to make teams of 20 members each on sports
day to participate in the event of “Tug of War’’. The number of volunteers are as follows:
TEACHERS STUDENTS 
Male Female Male Female 
12 18 20 10 
Find the probability that the person chosen at random 
(a) is a male 
(b) is a female student. 
10. An experiment is performed 400 times and three possible events A, B and C. Possible
occurrence of the three events are recorded. Out of the following which records are Possible
(give reason to support y our answer).
(a) A-176, B-54, C-170 
(b) A-200, B-100, C-75 
(c) A-180, B-170, C-50 
(d) A-175, B-125, C-200 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
11. Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 34, 43 are written in an ascending order. The
median of the data is 24.  Also, find their mean.
12. Draw Bar Diagram for the given expenditure of a family on different heads in the month:
Head Expenditure 
Food 4000 
Education 2500 
Clothing 1000 
House rent 3500 
Others 2500 
 Savings 1500 
13. ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(?AOD)=4 cm
2
,
find area (ABCD).
14. Two concentric circle, shown in the given figure, have a common center O. A line l Intersects
the outer circle at A and B and the inner circle at C and D. If AB =x and CD=y, prove that
AC=BD=
1
2
(x-y).
15. Draw two lines AB and CD such that they intersect at point O and not perpendicular to each
other. Measure ? AOD and ? AOC. Bisect the greater angle.
16. A square ABCQ is inscribed in an isosceles right ?PQR such that A and C are mid-points of PQ
and QR respectively as shown in the figure. Find the measure of ? PBA.
17. (a) Is it possible to construct ?ABC if perimeter of the triangle is 11 cm, base angles are
60 A ? = ° and ? B=70
o
.
(b) Is it possible to construct ?EFG, if EF+FG+GE=11cm, ? E=105
o 
and ? F=90
o
.
(c) Is it possible to construct ?XYZ if perimeter is 12.5cm, ? X=75
o
 and ? Y=30
o
18. A boy has a spherical ladoo whose radius is 4 cm. A girl has 8 spherical ladoos each of radius
2 cm. Find the ratio of the volumes of ladoos girl has to the ladoo boy has.
SECTION-D 
Page 4


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) 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. 
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted. 
SECTION-A 
Question number 1 to 4 carry one mark each. 
1. Area of parallelogram is 64 cm
2
. If base of the parallelogram is 16cm, find the height of the
corresponding attitude.
2. Find the side of a cube of its total surface area is 486 cm
2
.
3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?
4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.
SECTION-B 
Question number 5 to 10 carry two marks each. 
5. PQTS and PTRQ are two parallelograms. Show that ar (?PST) = ar (?QTR) = 
1
3
ar(PQRS).
6. Draw a line segment of length 7.6 cm. Bisect Measure the length of each part.
7. In the figure, ABCD is a square. Find the measure of ?CDB.
8. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.
9. Teachers and students are selected at random to make teams of 20 members each on sports
day to participate in the event of “Tug of War’’. The number of volunteers are as follows:
TEACHERS STUDENTS 
Male Female Male Female 
12 18 20 10 
Find the probability that the person chosen at random 
(a) is a male 
(b) is a female student. 
10. An experiment is performed 400 times and three possible events A, B and C. Possible
occurrence of the three events are recorded. Out of the following which records are Possible
(give reason to support y our answer).
(a) A-176, B-54, C-170 
(b) A-200, B-100, C-75 
(c) A-180, B-170, C-50 
(d) A-175, B-125, C-200 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
11. Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 34, 43 are written in an ascending order. The
median of the data is 24.  Also, find their mean.
12. Draw Bar Diagram for the given expenditure of a family on different heads in the month:
Head Expenditure 
Food 4000 
Education 2500 
Clothing 1000 
House rent 3500 
Others 2500 
 Savings 1500 
13. ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(?AOD)=4 cm
2
,
find area (ABCD).
14. Two concentric circle, shown in the given figure, have a common center O. A line l Intersects
the outer circle at A and B and the inner circle at C and D. If AB =x and CD=y, prove that
AC=BD=
1
2
(x-y).
15. Draw two lines AB and CD such that they intersect at point O and not perpendicular to each
other. Measure ? AOD and ? AOC. Bisect the greater angle.
16. A square ABCQ is inscribed in an isosceles right ?PQR such that A and C are mid-points of PQ
and QR respectively as shown in the figure. Find the measure of ? PBA.
17. (a) Is it possible to construct ?ABC if perimeter of the triangle is 11 cm, base angles are
60 A ? = ° and ? B=70
o
.
(b) Is it possible to construct ?EFG, if EF+FG+GE=11cm, ? E=105
o 
and ? F=90
o
.
(c) Is it possible to construct ?XYZ if perimeter is 12.5cm, ? X=75
o
 and ? Y=30
o
18. A boy has a spherical ladoo whose radius is 4 cm. A girl has 8 spherical ladoos each of radius
2 cm. Find the ratio of the volumes of ladoos girl has to the ladoo boy has.
SECTION-D 
Question numbers 19 to 28 carry four marks each. 
19. The following data represents the population of girl child (per 1000 boy child) in a state.
Years Number of Girls 
2007-2008 
2008-2009 
2009-2010 
2010-2011 
2011-2012 
875 
900 
925 
945 
1000 
(a) Draw a bar graph to represent the above data. 
(b) What change in the value over the period of time is depicted by the state? 
20. In a question PQRS, diagonal PR and QS intersect each other at O such that ar(?POS) =
ar(?QOR). If distance between sides PQ and SR is 4 cm, PQ =3 cm and SR =7 cm, find
ar(?PQRS).
21. In the given figure, if y =36
o
and z =40
o
determine x. If y and z were complementary angle,
show that x would have been
1
2
right angle.
22. Construct ?XYZ in which XY =5 cm, ? X = 60
o
and sum of the other two sides is 7.6 cm.
23. In the parallelogram ABCD of the given figure, ? PAQ is an obtuse angle. Two equilateral
triangle ABP and ADQ are drawn outside the parallelogram. Prove that ?CPQ is also an
equilateral triangle.
Page 5


Mathematics 
Class -IX 
Summative Assessment – II 
Time: 3 Hours Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) 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. 
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted. 
SECTION-A 
Question number 1 to 4 carry one mark each. 
1. Area of parallelogram is 64 cm
2
. If base of the parallelogram is 16cm, find the height of the
corresponding attitude.
2. Find the side of a cube of its total surface area is 486 cm
2
.
3. The mean of the set of number 6, 3, x, 4 ,3, 5 and y is given as 5. What is the value of x+y?
4. Find the median of 37, 31, 42, 43, 46, 25, 39, 45, 32.
SECTION-B 
Question number 5 to 10 carry two marks each. 
5. PQTS and PTRQ are two parallelograms. Show that ar (?PST) = ar (?QTR) = 
1
3
ar(PQRS).
6. Draw a line segment of length 7.6 cm. Bisect Measure the length of each part.
7. In the figure, ABCD is a square. Find the measure of ?CDB.
8. The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.
9. Teachers and students are selected at random to make teams of 20 members each on sports
day to participate in the event of “Tug of War’’. The number of volunteers are as follows:
TEACHERS STUDENTS 
Male Female Male Female 
12 18 20 10 
Find the probability that the person chosen at random 
(a) is a male 
(b) is a female student. 
10. An experiment is performed 400 times and three possible events A, B and C. Possible
occurrence of the three events are recorded. Out of the following which records are Possible
(give reason to support y our answer).
(a) A-176, B-54, C-170 
(b) A-200, B-100, C-75 
(c) A-180, B-170, C-50 
(d) A-175, B-125, C-200 
SECTION-C 
Question numbers 11 to 18 carry three marks each. 
11. Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 34, 43 are written in an ascending order. The
median of the data is 24.  Also, find their mean.
12. Draw Bar Diagram for the given expenditure of a family on different heads in the month:
Head Expenditure 
Food 4000 
Education 2500 
Clothing 1000 
House rent 3500 
Others 2500 
 Savings 1500 
13. ABCD is a parallelogram and O is the point of intersection of its diagonals. If ar(?AOD)=4 cm
2
,
find area (ABCD).
14. Two concentric circle, shown in the given figure, have a common center O. A line l Intersects
the outer circle at A and B and the inner circle at C and D. If AB =x and CD=y, prove that
AC=BD=
1
2
(x-y).
15. Draw two lines AB and CD such that they intersect at point O and not perpendicular to each
other. Measure ? AOD and ? AOC. Bisect the greater angle.
16. A square ABCQ is inscribed in an isosceles right ?PQR such that A and C are mid-points of PQ
and QR respectively as shown in the figure. Find the measure of ? PBA.
17. (a) Is it possible to construct ?ABC if perimeter of the triangle is 11 cm, base angles are
60 A ? = ° and ? B=70
o
.
(b) Is it possible to construct ?EFG, if EF+FG+GE=11cm, ? E=105
o 
and ? F=90
o
.
(c) Is it possible to construct ?XYZ if perimeter is 12.5cm, ? X=75
o
 and ? Y=30
o
18. A boy has a spherical ladoo whose radius is 4 cm. A girl has 8 spherical ladoos each of radius
2 cm. Find the ratio of the volumes of ladoos girl has to the ladoo boy has.
SECTION-D 
Question numbers 19 to 28 carry four marks each. 
19. The following data represents the population of girl child (per 1000 boy child) in a state.
Years Number of Girls 
2007-2008 
2008-2009 
2009-2010 
2010-2011 
2011-2012 
875 
900 
925 
945 
1000 
(a) Draw a bar graph to represent the above data. 
(b) What change in the value over the period of time is depicted by the state? 
20. In a question PQRS, diagonal PR and QS intersect each other at O such that ar(?POS) =
ar(?QOR). If distance between sides PQ and SR is 4 cm, PQ =3 cm and SR =7 cm, find
ar(?PQRS).
21. In the given figure, if y =36
o
and z =40
o
determine x. If y and z were complementary angle,
show that x would have been
1
2
right angle.
22. Construct ?XYZ in which XY =5 cm, ? X = 60
o
and sum of the other two sides is 7.6 cm.
23. In the parallelogram ABCD of the given figure, ? PAQ is an obtuse angle. Two equilateral
triangle ABP and ADQ are drawn outside the parallelogram. Prove that ?CPQ is also an
equilateral triangle.
24. The patients in a hospital are given soup daily in a cylindrical bowl of diameter 7 cm. On a
particular day, the girl of NCC decided to cook the soup for the patients. If they fill the bowl
with soup to a height of 6 cm, then how much soup (in litres) is to be cooked for 200
patients? Which value is depicted by the girls?
25. A pit is 20 m long, 6m wide and 80 cm deep. Calculate the number of planks, each with
dimensions 5 m× 25 cm× 10cm that can be store in the pit.
26. Radha has a piece of canvas whose area is 550 m
2
. She uses it to make a conical tent with a
base diameter of 14 m, Find the volume of the tent that can be made with it.
27. The capacity of a closed cylindrical vessel of height 2 m is 30.8 litres. Haw many square
metres of metal sheet would be needed to make it?
28. The following table gives the distance (in km) that 40 students of a class have to travel from
their residence to their school.
Distance (In km) No. of students 
0-5 
5-10 
10-15 
15-20 
20-25 
25-30 
30-35 
5 
11 
11 
9 
1 
1 
2 
Find the probability that randomly choosen student lives at a distance of: 
(a)  more than 35 km. 
(b) 10-15 km. 
(c) atleast 25 km. 
In between 15-25 km. 
SECTION-E