Mathematics Past Year Paper SA-1(Set-8)- 2014, Class 9, CBSE | Extra Documents & Tests for Class 9 PDF Download

 Page 1


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C, D and E. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 18 carry 3 marks each. Question No. 19 to 28 carry 4 marks each. Question No. 29 to 31 
carry 3 marks each and 1 question of 4 from open text theme. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Find one solution of the equation 0x+3y-7=0 
2. The linear equation 3x+2y=6 has how many solutions? 
3. In the figure, if ABCE and ABFC are parallelograms then show that CE=CF. 
4. If the circumference of the base of a right circular cone and the slant height are 120p and 10 
cm respectively, then find the curved surface area of the cone. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. PQR and QSR ? ? lie on same base QR. Also, PSQ RQS ? = ? . If ( )
2
12 ar PQR cm ? = , find 
( ) ar QSR ? 
6. Draw a 5.4 cm long line segment and construct its perpendicular bisector. 
7. In the figure, ABCD is a parallelogram and X and Y are mid-point of AB and CD respectively. 
Show that AD XY 
 , 
8. Calculate the height of a cone whose slant height is 25 cm and curved surface are is 
2
550cm , 
9. Three coins are tossed simultaneously 200 times with the following frequencies of different 
outcomes. 
Number of tails 0 1 2 3 
Frequency 35 45 12 78 
Compute the probability of getting the: 
a) At least 2 head 
b) All heads 
Page 2


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C, D and E. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 18 carry 3 marks each. Question No. 19 to 28 carry 4 marks each. Question No. 29 to 31 
carry 3 marks each and 1 question of 4 from open text theme. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Find one solution of the equation 0x+3y-7=0 
2. The linear equation 3x+2y=6 has how many solutions? 
3. In the figure, if ABCE and ABFC are parallelograms then show that CE=CF. 
4. If the circumference of the base of a right circular cone and the slant height are 120p and 10 
cm respectively, then find the curved surface area of the cone. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. PQR and QSR ? ? lie on same base QR. Also, PSQ RQS ? = ? . If ( )
2
12 ar PQR cm ? = , find 
( ) ar QSR ? 
6. Draw a 5.4 cm long line segment and construct its perpendicular bisector. 
7. In the figure, ABCD is a parallelogram and X and Y are mid-point of AB and CD respectively. 
Show that AD XY 
 , 
8. Calculate the height of a cone whose slant height is 25 cm and curved surface are is 
2
550cm , 
9. Three coins are tossed simultaneously 200 times with the following frequencies of different 
outcomes. 
Number of tails 0 1 2 3 
Frequency 35 45 12 78 
Compute the probability of getting the: 
a) At least 2 head 
b) All heads 
 
 
 
 
10. To know the opinion of the students about the subject statistics, a survey of 200 students was 
conducted. The data recorded is as given below: 
Opinion Number of students 
Like 135 
Dislike 65 
Find the probability that a student chosen at random 
a) Likes statistics 
b) Dislikes statistics 
 
Section C 
Question numbers 11 to 18 carry three marks each. 
11. Draw the graph of x=2 and y=5 in the same Cartesian plane and identify the figure formed by 
these graphs with x and y axis. 
12. Find the value of a, if the point (3,4) lies on the graph of ax-4y+10=0. Also the coordinates of 
the point on the graph for which y=1. 
13. In figure, D and F are points on side AE of ABE ? . Through point D a line DC is drawn which is 
parallel to AB and meets BE in C. Prove that ( ) ( ) ar ACF ar BCFD ? = . 
14. In the given figure, ABCD is a parallelogram. A circle through A, B and C intersects CD 
produced at E. prove that AD=AE. 
15. Draw a line segment AB of measure 6.4 cm. Construct its perpendicular bisector and verify it 
by actual measurement. 
16. The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle 
of the parallelogram is 70° . Find the angles of the parallelogram. 
17. In the given figure, ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD 
and BC at the points P and Q respectively. Prove that PQ is parallel to DC. 
18. The areas of three adjacent faces of cuboid are 
2 2 2
15 ,10 24 cm cm and cm . Find the volume of 
cuboid. 
 
Section D 
Question number 19 to 28 carry 4 marks each: 
19. Draw the graphs of the following equations on the same graph sheet: 
x=0, y=0, x+y=3. Also find the area enclosed between these lines. 
20. A student wrote the equations of the lines a and b drawn in the following graph as y=1 and 
2x+3y=6. Is he right? If yes, write coordinates of point of intersection lines a and b. Also, find 
the area enclosed between these lines and y-axis. 
21. In the given figure, ABCD is a parallelogram in which CB is produced to E such that BC=BE. 
The line segment DE intersects side AB at F. If 
2
( ) 4 ar ADF cm ? = , find the area of 
parallelogram ABCD. 
22. In the bisectors of the opposite angle P and R of a cyclic quadrilateral PQRS intersect the 
corresponding circle at A and B respectively, then prove that AB is a diameter of the circle. 
23. Construct BCD ? in which BC=7.8 cm, 70 B ? = ° and CD-BD=4 cm. 
Page 3


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C, D and E. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 18 carry 3 marks each. Question No. 19 to 28 carry 4 marks each. Question No. 29 to 31 
carry 3 marks each and 1 question of 4 from open text theme. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Find one solution of the equation 0x+3y-7=0 
2. The linear equation 3x+2y=6 has how many solutions? 
3. In the figure, if ABCE and ABFC are parallelograms then show that CE=CF. 
4. If the circumference of the base of a right circular cone and the slant height are 120p and 10 
cm respectively, then find the curved surface area of the cone. 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. PQR and QSR ? ? lie on same base QR. Also, PSQ RQS ? = ? . If ( )
2
12 ar PQR cm ? = , find 
( ) ar QSR ? 
6. Draw a 5.4 cm long line segment and construct its perpendicular bisector. 
7. In the figure, ABCD is a parallelogram and X and Y are mid-point of AB and CD respectively. 
Show that AD XY 
 , 
8. Calculate the height of a cone whose slant height is 25 cm and curved surface are is 
2
550cm , 
9. Three coins are tossed simultaneously 200 times with the following frequencies of different 
outcomes. 
Number of tails 0 1 2 3 
Frequency 35 45 12 78 
Compute the probability of getting the: 
a) At least 2 head 
b) All heads 
 
 
 
 
10. To know the opinion of the students about the subject statistics, a survey of 200 students was 
conducted. The data recorded is as given below: 
Opinion Number of students 
Like 135 
Dislike 65 
Find the probability that a student chosen at random 
a) Likes statistics 
b) Dislikes statistics 
 
Section C 
Question numbers 11 to 18 carry three marks each. 
11. Draw the graph of x=2 and y=5 in the same Cartesian plane and identify the figure formed by 
these graphs with x and y axis. 
12. Find the value of a, if the point (3,4) lies on the graph of ax-4y+10=0. Also the coordinates of 
the point on the graph for which y=1. 
13. In figure, D and F are points on side AE of ABE ? . Through point D a line DC is drawn which is 
parallel to AB and meets BE in C. Prove that ( ) ( ) ar ACF ar BCFD ? = . 
14. In the given figure, ABCD is a parallelogram. A circle through A, B and C intersects CD 
produced at E. prove that AD=AE. 
15. Draw a line segment AB of measure 6.4 cm. Construct its perpendicular bisector and verify it 
by actual measurement. 
16. The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle 
of the parallelogram is 70° . Find the angles of the parallelogram. 
17. In the given figure, ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD 
and BC at the points P and Q respectively. Prove that PQ is parallel to DC. 
18. The areas of three adjacent faces of cuboid are 
2 2 2
15 ,10 24 cm cm and cm . Find the volume of 
cuboid. 
 
Section D 
Question number 19 to 28 carry 4 marks each: 
19. Draw the graphs of the following equations on the same graph sheet: 
x=0, y=0, x+y=3. Also find the area enclosed between these lines. 
20. A student wrote the equations of the lines a and b drawn in the following graph as y=1 and 
2x+3y=6. Is he right? If yes, write coordinates of point of intersection lines a and b. Also, find 
the area enclosed between these lines and y-axis. 
21. In the given figure, ABCD is a parallelogram in which CB is produced to E such that BC=BE. 
The line segment DE intersects side AB at F. If 
2
( ) 4 ar ADF cm ? = , find the area of 
parallelogram ABCD. 
22. In the bisectors of the opposite angle P and R of a cyclic quadrilateral PQRS intersect the 
corresponding circle at A and B respectively, then prove that AB is a diameter of the circle. 
23. Construct BCD ? in which BC=7.8 cm, 70 B ? = ° and CD-BD=4 cm. 
 
 
 
 
24. In the figure, ABCD is a trapezium in which AB DC 
 . E and F are the mid-point of AD and BC 
respectively. DF and AB are produced to meet at G. Also, AC and EF intersect at the point O. 
Show that: 
a) EO AB 
 
b) AO=CO 
25. A conical heap is formed when a farmer pours food grains on a ground. The slant height of 
heap is 35 cm. The circumference of the base is 132 cm. What amount of tarpaulin is needed 
to cover the grains? Farmer goes to the orphanage and gives half of the food grains for the 
children living there. How much grains farmer donated? List values you learn from this act of 
the farmer. 
26. Manoj Sweets placed an order of making 30 20 6 cm cm cm × × cardboard boxes for packing 
their sweets. For all overlaps, 5% of total area is required extra. If cost of the cardboard is Rs. 
2 for 
2
1000cm , find the cost of the card board used for making 500 boxes. 
27. A hollow cylindrical iron pipe is 21 m long. Its outer and inner diameters are 10 cm and 6 cm 
respectively. Find the volume of the iron used in making the pipe. Also find the outer surface 
area of pipe. 
28. A survey of 2000 people of different age groups was conducted to find out their preference in 
watching different types of movies: 
Type I   – Family 
Type II – Comedy and Family 
Type III – Romantic, Comedy and Family 
Type IV – Action, Romantic, Comedy and Family 
Age Group Type I Type II Type III Type IV All 
18-29 440 160 110 61 35 
30-50 505 125 60 22 18 
Above 50 360 45 35 15 9 
Find the probability that a person chosen at random is: 
a) In 18-29 years of age and likes type II movies 
b) Above 50 years of age and likes all type of movies 
c) In 30-50 years and likes type I movies 
 
Section – E 
(Open Text) 
(*Please ensure that open text of the given theme is supplied with this question paper.) 
Theme: Atithidevo Bhavah 
29.