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. SectionA comprises of 4 question of 1 mark each, SectionB comprises of 6 question of 2 marks each, SectionC comprises of 8 question of 3 marks each and SectionD 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. SECTIONA 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. SECTIONB 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. SectionA comprises of 4 question of 1 mark each, SectionB comprises of 6 question of 2 marks each, SectionC comprises of 8 question of 3 marks each and SectionD 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. SECTIONA 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. SECTIONB 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) A176, B54, C170 (b) A200, B100, C75 (c) A180, B170, C50 (d) A175, B125, C200 SECTIONC Question numbers 11 to 18 carry three marks each. 11. Ten observations 6, 14, 15, 17, x+1, 2x13, 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. SectionA comprises of 4 question of 1 mark each, SectionB comprises of 6 question of 2 marks each, SectionC comprises of 8 question of 3 marks each and SectionD 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. SECTIONA 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. SECTIONB 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) A176, B54, C170 (b) A200, B100, C75 (c) A180, B170, C50 (d) A175, B125, C200 SECTIONC Question numbers 11 to 18 carry three marks each. 11. Ten observations 6, 14, 15, 17, x+1, 2x13, 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 (xy). 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 midpoints 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. SECTIOND 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. SectionA comprises of 4 question of 1 mark each, SectionB comprises of 6 question of 2 marks each, SectionC comprises of 8 question of 3 marks each and SectionD 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. SECTIONA 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. SECTIONB 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) A176, B54, C170 (b) A200, B100, C75 (c) A180, B170, C50 (d) A175, B125, C200 SECTIONC Question numbers 11 to 18 carry three marks each. 11. Ten observations 6, 14, 15, 17, x+1, 2x13, 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 (xy). 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 midpoints 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. SECTIOND 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 20072008 20082009 20092010 20102011 20112012 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. SectionA comprises of 4 question of 1 mark each, SectionB comprises of 6 question of 2 marks each, SectionC comprises of 8 question of 3 marks each and SectionD 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. SECTIONA 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. SECTIONB 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) A176, B54, C170 (b) A200, B100, C75 (c) A180, B170, C50 (d) A175, B125, C200 SECTIONC Question numbers 11 to 18 carry three marks each. 11. Ten observations 6, 14, 15, 17, x+1, 2x13, 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 (xy). 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 midpoints 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. SECTIOND 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 20072008 20082009 20092010 20102011 20112012 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 05 510 1015 1520 2025 2530 3035 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) 1015 km. (c) atleast 25 km. In between 1525 km. SECTIONERead More
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