Page 1 Summative Assessment1 Examination 20142015 Mathematics Class – X 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 and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) All questions in Section – A are very short answer questions. e) There are no overall choices in the question paper. f) Use of calculator is not permitted. g) If required Graph papers will be provided. Section A Question numbers 1 to 4 carry 1 mark each. 1. If a graph y=p(x) does not cut xaxis at any point, then how many zeroes does a polynomial have? 2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 3. If tan (30 ) Cot ? ? = + , then find the value of ? . 4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. Section B Question numbers 5 to 10 carry 2 marks each. 5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 6. Give the HCF (306,657)=9, find LCM (306,657). 7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 respectively. 8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation algebraically. 9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, find BC. 10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained 1 ( ) X Number of students 1 ( ) f Page 2 Summative Assessment1 Examination 20142015 Mathematics Class – X 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 and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) All questions in Section – A are very short answer questions. e) There are no overall choices in the question paper. f) Use of calculator is not permitted. g) If required Graph papers will be provided. Section A Question numbers 1 to 4 carry 1 mark each. 1. If a graph y=p(x) does not cut xaxis at any point, then how many zeroes does a polynomial have? 2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 3. If tan (30 ) Cot ? ? = + , then find the value of ? . 4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. Section B Question numbers 5 to 10 carry 2 marks each. 5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 6. Give the HCF (306,657)=9, find LCM (306,657). 7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 respectively. 8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation algebraically. 9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, find BC. 10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained 1 ( ) X Number of students 1 ( ) f 10 1 20 1 36 3 40 4 50 3 56 2 60 4 70 4 72 1 80 1 88 2 92 3 95 1 Section C Question number from 11 to 20 carry 3 marks each. 11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 12. Find the zeroes of the polynomial 2 2 8 x x   and verify the relationship between zeroes and the coefficient. 13. Solve 2x+3y=11 and 2x4y=24 and herice find the value of ‘m’ for which y=mx+3. 14. In the given figure if LM CB and , prove that AM AN AB AD = 15. If the areas of two similar Triangles are equal, prove that they are congruent. 16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine a) Sin A. Cos A b) Sin C. Cos C 17. If ( ) tan A B 3 + = and ( ) 1 tan AB 3 = , 0 90 A B ° < + = ° and A>B, find A and B. 18. If A, B and C are interior angles of a triangle ABC, then show that sin cos 2 2 B C A + ? ? ? ? = ? ? ? ? ? ? ? ? 19. The following data gives the information on the observed life times (in hours) of 225 electric components Lifetime (inhours) Frequency 020 10 2040 35 4060 52 Page 3 Summative Assessment1 Examination 20142015 Mathematics Class – X 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 and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) All questions in Section – A are very short answer questions. e) There are no overall choices in the question paper. f) Use of calculator is not permitted. g) If required Graph papers will be provided. Section A Question numbers 1 to 4 carry 1 mark each. 1. If a graph y=p(x) does not cut xaxis at any point, then how many zeroes does a polynomial have? 2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 3. If tan (30 ) Cot ? ? = + , then find the value of ? . 4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. Section B Question numbers 5 to 10 carry 2 marks each. 5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 6. Give the HCF (306,657)=9, find LCM (306,657). 7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 respectively. 8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation algebraically. 9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, find BC. 10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained 1 ( ) X Number of students 1 ( ) f 10 1 20 1 36 3 40 4 50 3 56 2 60 4 70 4 72 1 80 1 88 2 92 3 95 1 Section C Question number from 11 to 20 carry 3 marks each. 11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 12. Find the zeroes of the polynomial 2 2 8 x x   and verify the relationship between zeroes and the coefficient. 13. Solve 2x+3y=11 and 2x4y=24 and herice find the value of ‘m’ for which y=mx+3. 14. In the given figure if LM CB and , prove that AM AN AB AD = 15. If the areas of two similar Triangles are equal, prove that they are congruent. 16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine a) Sin A. Cos A b) Sin C. Cos C 17. If ( ) tan A B 3 + = and ( ) 1 tan AB 3 = , 0 90 A B ° < + = ° and A>B, find A and B. 18. If A, B and C are interior angles of a triangle ABC, then show that sin cos 2 2 B C A + ? ? ? ? = ? ? ? ? ? ? ? ? 19. The following data gives the information on the observed life times (in hours) of 225 electric components Lifetime (inhours) Frequency 020 10 2040 35 4060 52 6080 61 80100 38 100120 29 Determine the modal life time of the components. 20. The distribution below gives the weight of 30 students of a class. Find the median weight of students. Weight (in kg) Number of students 4045 2 4550 3 5055 8 5560 6 6065 6 6570 3 7075 2 Section D Questions 21 to 31 carry 4 marks each. 21. Prove that 3 2 5 + is irrational. 22. On dividing 3 2 3 2 x x x  + + by a polynomial g(x), the quotient and the remainder were (x2) and (2x+4) respectively. Find g(x). Or Find all the zeroes of 4 3 2 2 3 3 6 2 x x x x   +  if you know that two of its zeroes are 2 and 2  23. Form the pair of linear equations in the following problem and find their Solution graphically. 10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the number of boys. Find the number of boys and girls who took part in the Quiz. 24. Places A and B are 100 km apart on a highway. One can start from A and another from B at the same time if the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars. Or Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. 25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of the diagonals. 26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . Or Page 4 Summative Assessment1 Examination 20142015 Mathematics Class – X 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 and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) All questions in Section – A are very short answer questions. e) There are no overall choices in the question paper. f) Use of calculator is not permitted. g) If required Graph papers will be provided. Section A Question numbers 1 to 4 carry 1 mark each. 1. If a graph y=p(x) does not cut xaxis at any point, then how many zeroes does a polynomial have? 2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 3. If tan (30 ) Cot ? ? = + , then find the value of ? . 4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. Section B Question numbers 5 to 10 carry 2 marks each. 5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 6. Give the HCF (306,657)=9, find LCM (306,657). 7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 respectively. 8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation algebraically. 9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, find BC. 10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained 1 ( ) X Number of students 1 ( ) f 10 1 20 1 36 3 40 4 50 3 56 2 60 4 70 4 72 1 80 1 88 2 92 3 95 1 Section C Question number from 11 to 20 carry 3 marks each. 11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 12. Find the zeroes of the polynomial 2 2 8 x x   and verify the relationship between zeroes and the coefficient. 13. Solve 2x+3y=11 and 2x4y=24 and herice find the value of ‘m’ for which y=mx+3. 14. In the given figure if LM CB and , prove that AM AN AB AD = 15. If the areas of two similar Triangles are equal, prove that they are congruent. 16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine a) Sin A. Cos A b) Sin C. Cos C 17. If ( ) tan A B 3 + = and ( ) 1 tan AB 3 = , 0 90 A B ° < + = ° and A>B, find A and B. 18. If A, B and C are interior angles of a triangle ABC, then show that sin cos 2 2 B C A + ? ? ? ? = ? ? ? ? ? ? ? ? 19. The following data gives the information on the observed life times (in hours) of 225 electric components Lifetime (inhours) Frequency 020 10 2040 35 4060 52 6080 61 80100 38 100120 29 Determine the modal life time of the components. 20. The distribution below gives the weight of 30 students of a class. Find the median weight of students. Weight (in kg) Number of students 4045 2 4550 3 5055 8 5560 6 6065 6 6570 3 7075 2 Section D Questions 21 to 31 carry 4 marks each. 21. Prove that 3 2 5 + is irrational. 22. On dividing 3 2 3 2 x x x  + + by a polynomial g(x), the quotient and the remainder were (x2) and (2x+4) respectively. Find g(x). Or Find all the zeroes of 4 3 2 2 3 3 6 2 x x x x   +  if you know that two of its zeroes are 2 and 2  23. Form the pair of linear equations in the following problem and find their Solution graphically. 10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the number of boys. Find the number of boys and girls who took part in the Quiz. 24. Places A and B are 100 km apart on a highway. One can start from A and another from B at the same time if the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars. Or Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. 25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of the diagonals. 26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . Or The ratio of areas of two similar triangles is equal to the square of the ratios of their corresponding sides. 27. In PQR ? , right angled at Q, PR+QR=25 cm and PQ=5cm. determine the values of sin P, cos P and tan P. 28. Prove that sin cos 1 1 sin cos 1 sec tan A A A A A A  + = +   Using the identity 2 2 sec 1 tan A A = + 29. Show that 2 1 sec sin sec 1 cos A A A A + =  Or Prove that 1 sin sec tan 1 sin A A A A + = +  30. The following table gives production yield per hectare of wheat of 100 farms of a village Production yield Number of farms 5055 2 5560 8 6065 12 6570 24 7075 38 7580 16 Change the distribution to a more than type distribution and draw its ogive. What conclusion do you draw from this table. 31. If the median of the distribution given below is 28.5, find the values of x and y. Classinterval Frequency 010 5 1020 x 2030 20 3040 15 4050 y 5060 5 Total 60 Or The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Mr Sharma always saves electricity by switching off all electrical equipments immediately after their usage so his family belongs to the group 6585. Monthly consumption of electricity (in units) Number of consumers 6585 4 85105 5 105125 13 Page 5 Summative Assessment1 Examination 20142015 Mathematics Class – X 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 and D. c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. d) All questions in Section – A are very short answer questions. e) There are no overall choices in the question paper. f) Use of calculator is not permitted. g) If required Graph papers will be provided. Section A Question numbers 1 to 4 carry 1 mark each. 1. If a graph y=p(x) does not cut xaxis at any point, then how many zeroes does a polynomial have? 2. If the sides of two similar triangles are in ration 4:9, then find the ratio of their areas. 3. If tan (30 ) Cot ? ? = + , then find the value of ? . 4. The mean and mode of a frequency distribution are 28 and 16 respectively. Find the median. Section B Question numbers 5 to 10 carry 2 marks each. 5. Use Euclid’s division algorithm to find out the HCF of 135 and 225. 6. Give the HCF (306,657)=9, find LCM (306,657). 7. Find the quadratic Polynomial, the Sum and Product of whose zeroes are 4 and 1 respectively. 8. The cost of 2 kg of Apples and 1 kg of Grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of Apples and 2 kg of Grapes are Rs. 300. Represent the situation algebraically. 9. Let ABC DEF ? ? ~ and their areas be respectively 64 sq.cm and 121 sq.cm. If EF=15.4 cm, find BC. 10. The marks obtained by 30 students of class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students. Marks obtained 1 ( ) X Number of students 1 ( ) f 10 1 20 1 36 3 40 4 50 3 56 2 60 4 70 4 72 1 80 1 88 2 92 3 95 1 Section C Question number from 11 to 20 carry 3 marks each. 11. Show that every positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 12. Find the zeroes of the polynomial 2 2 8 x x   and verify the relationship between zeroes and the coefficient. 13. Solve 2x+3y=11 and 2x4y=24 and herice find the value of ‘m’ for which y=mx+3. 14. In the given figure if LM CB and , prove that AM AN AB AD = 15. If the areas of two similar Triangles are equal, prove that they are congruent. 16. In ABC ? , right angled at B, AB=24 cm, BC=7 cm. Determine a) Sin A. Cos A b) Sin C. Cos C 17. If ( ) tan A B 3 + = and ( ) 1 tan AB 3 = , 0 90 A B ° < + = ° and A>B, find A and B. 18. If A, B and C are interior angles of a triangle ABC, then show that sin cos 2 2 B C A + ? ? ? ? = ? ? ? ? ? ? ? ? 19. The following data gives the information on the observed life times (in hours) of 225 electric components Lifetime (inhours) Frequency 020 10 2040 35 4060 52 6080 61 80100 38 100120 29 Determine the modal life time of the components. 20. The distribution below gives the weight of 30 students of a class. Find the median weight of students. Weight (in kg) Number of students 4045 2 4550 3 5055 8 5560 6 6065 6 6570 3 7075 2 Section D Questions 21 to 31 carry 4 marks each. 21. Prove that 3 2 5 + is irrational. 22. On dividing 3 2 3 2 x x x  + + by a polynomial g(x), the quotient and the remainder were (x2) and (2x+4) respectively. Find g(x). Or Find all the zeroes of 4 3 2 2 3 3 6 2 x x x x   +  if you know that two of its zeroes are 2 and 2  23. Form the pair of linear equations in the following problem and find their Solution graphically. 10 students of class X took part in Mathematics Quiz. If the number of girls is 4 more than the number of boys. Find the number of boys and girls who took part in the Quiz. 24. Places A and B are 100 km apart on a highway. One can start from A and another from B at the same time if the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars. Or Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. 25. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of the diagonals. 26. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of another triangle PQR. Show that ABC PQR ? ? ~ . Or The ratio of areas of two similar triangles is equal to the square of the ratios of their corresponding sides. 27. In PQR ? , right angled at Q, PR+QR=25 cm and PQ=5cm. determine the values of sin P, cos P and tan P. 28. Prove that sin cos 1 1 sin cos 1 sec tan A A A A A A  + = +   Using the identity 2 2 sec 1 tan A A = + 29. Show that 2 1 sec sin sec 1 cos A A A A + =  Or Prove that 1 sin sec tan 1 sin A A A A + = +  30. The following table gives production yield per hectare of wheat of 100 farms of a village Production yield Number of farms 5055 2 5560 8 6065 12 6570 24 7075 38 7580 16 Change the distribution to a more than type distribution and draw its ogive. What conclusion do you draw from this table. 31. If the median of the distribution given below is 28.5, find the values of x and y. Classinterval Frequency 010 5 1020 x 2030 20 3040 15 4050 y 5060 5 Total 60 Or The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Mr Sharma always saves electricity by switching off all electrical equipments immediately after their usage so his family belongs to the group 6585. Monthly consumption of electricity (in units) Number of consumers 6585 4 85105 5 105125 13 125145 20 145165 14 165185 8 185205 4 Find the mean and mode of the data. What moral values of Mr. Sharma have been depicted in his situation?Read More
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