Page 1 Summative Assessment1 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) 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. If LCM(12,28)=84, find HCF(12,28). 2. Write the polynomial whose zeroes are 5 and 4. 3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 4. If sec A + tan A = 7, then find sec A – tan A. Section B Question numbers 5 to 10 carry two marks each. 5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 6. After how many decimal places, the decimal expansion of 3 4 37 2 5 will terminate? 7. For what value of k, the pair of equations 4x3y=9, 2x+ky=11 has no solution? 8. If 3 sin 2 A = , find the value of 2 2cot 1 A  . 9. If A, B and C are interior angles of a ABC ? , prove that: tan cot 2 2 B C A + ? ? = ? ? ? ? 10. Find x and y from the following cumulative frequency distribution: Classes 08 816 1624 2432 3240 Frequency 15 x 15 18 9 Cumulativ e frequency 15 28 43 y 70 Section C Page 2 Summative Assessment1 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) 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. If LCM(12,28)=84, find HCF(12,28). 2. Write the polynomial whose zeroes are 5 and 4. 3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 4. If sec A + tan A = 7, then find sec A – tan A. Section B Question numbers 5 to 10 carry two marks each. 5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 6. After how many decimal places, the decimal expansion of 3 4 37 2 5 will terminate? 7. For what value of k, the pair of equations 4x3y=9, 2x+ky=11 has no solution? 8. If 3 sin 2 A = , find the value of 2 2cot 1 A  . 9. If A, B and C are interior angles of a ABC ? , prove that: tan cot 2 2 B C A + ? ? = ? ? ? ? 10. Find x and y from the following cumulative frequency distribution: Classes 08 816 1624 2432 3240 Frequency 15 x 15 18 9 Cumulativ e frequency 15 28 43 y 70 Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is rational. 12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits of the number. Find the number. 14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide his entire land among his four children as shown in the figure. D, E, F are midpoints of sides AB, BC and AC respectively. Find ratio of area of EFD ? to area of ABC ? . Is length of 1 2 DF BC = ? Why? Which values of Krishna can one imbibe in his life? 15. ABCD is a trapezium in which AB DC and its diagonal intersect each other at the point O. Show that AO CO BO DO = . 16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, Prove that a) ABC AMP ? ? ~ b) CA BC PA MP = 17. Find the value of sin 60° geometrically 18. State whether the following are true or false. Justify your answer. sin(A+B)=sin A + sin B The value of tan A is always less than 1. 12 sec 5 A = for some value of A ? 19. Prove that: cos(90 ) 1 sin(90 ) 2cos 1 sin(90 ) cos(90 ) ec ? ? ? ? ? °  + °  + = + °  °  20. Find the mode of the following frequency distribution: Page 3 Summative Assessment1 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) 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. If LCM(12,28)=84, find HCF(12,28). 2. Write the polynomial whose zeroes are 5 and 4. 3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 4. If sec A + tan A = 7, then find sec A – tan A. Section B Question numbers 5 to 10 carry two marks each. 5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 6. After how many decimal places, the decimal expansion of 3 4 37 2 5 will terminate? 7. For what value of k, the pair of equations 4x3y=9, 2x+ky=11 has no solution? 8. If 3 sin 2 A = , find the value of 2 2cot 1 A  . 9. If A, B and C are interior angles of a ABC ? , prove that: tan cot 2 2 B C A + ? ? = ? ? ? ? 10. Find x and y from the following cumulative frequency distribution: Classes 08 816 1624 2432 3240 Frequency 15 x 15 18 9 Cumulativ e frequency 15 28 43 y 70 Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is rational. 12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits of the number. Find the number. 14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide his entire land among his four children as shown in the figure. D, E, F are midpoints of sides AB, BC and AC respectively. Find ratio of area of EFD ? to area of ABC ? . Is length of 1 2 DF BC = ? Why? Which values of Krishna can one imbibe in his life? 15. ABCD is a trapezium in which AB DC and its diagonal intersect each other at the point O. Show that AO CO BO DO = . 16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, Prove that a) ABC AMP ? ? ~ b) CA BC PA MP = 17. Find the value of sin 60° geometrically 18. State whether the following are true or false. Justify your answer. sin(A+B)=sin A + sin B The value of tan A is always less than 1. 12 sec 5 A = for some value of A ? 19. Prove that: cos(90 ) 1 sin(90 ) 2cos 1 sin(90 ) cos(90 ) ec ? ? ? ? ? °  + °  + = + °  °  20. Find the mode of the following frequency distribution: Classes 06 612 1218 1824 2430 Frequency 7 5 10 12 6 Section D Question numbers 21 to 31 carry four marks each. 21. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two side are divided in the same ratio. 22. BL and CM are median of a triangle ABC right angled at A. Prove that 2 2 2 4[ ] 5 BL CM BC + = 23. Divide 4 3 2 3 5 7 2 5 x x x x +  + + by 2 3 1 x x + + and verify the division algorithm. 24. Find the other zeroes of the polynomial 4 3 2 9 3 18 x x x x +   + , if it is given that two of its zeroes are 3 or 3  25. Radha wants to construct a rectangular garden for children and other to play. The area of this rectangle remains the same if the length is increased by 7m and breadth is decreased by 3m. the area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. Find dimensions of the rectangular garden. 26. Represent the following pair of equations graphically and write the coordinates of point where the lines intersect the yaxis: x+3yy=6; 2x3y=12 27. Calculate the average daily income (in Rs) of the following data about workers working in a company: Average daily income (in Rs.) Number of workers Less than 100 12 Less than 200 28 Less than 300 34 Less than 400 41 Less than 500 50 28. Prove that: 1 cos sin 1 sin cos sin 1 cos ? ? ? ? ? ?  + + = +  29. Prove that: sec 1 sec 1 2cos sec 1 sec 1 ec ? ? ? ? ?  + + = +  30. The following distribution shows the daily pocket allowance given to the children of a multistoried building. The average daily pocket allowance is Rs 18. Meera is one of the children, residing in the same building, who instead of spending his daily pocket money prefers to save it. Page 4 Summative Assessment1 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) 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. If LCM(12,28)=84, find HCF(12,28). 2. Write the polynomial whose zeroes are 5 and 4. 3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 4. If sec A + tan A = 7, then find sec A – tan A. Section B Question numbers 5 to 10 carry two marks each. 5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 6. After how many decimal places, the decimal expansion of 3 4 37 2 5 will terminate? 7. For what value of k, the pair of equations 4x3y=9, 2x+ky=11 has no solution? 8. If 3 sin 2 A = , find the value of 2 2cot 1 A  . 9. If A, B and C are interior angles of a ABC ? , prove that: tan cot 2 2 B C A + ? ? = ? ? ? ? 10. Find x and y from the following cumulative frequency distribution: Classes 08 816 1624 2432 3240 Frequency 15 x 15 18 9 Cumulativ e frequency 15 28 43 y 70 Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is rational. 12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits of the number. Find the number. 14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide his entire land among his four children as shown in the figure. D, E, F are midpoints of sides AB, BC and AC respectively. Find ratio of area of EFD ? to area of ABC ? . Is length of 1 2 DF BC = ? Why? Which values of Krishna can one imbibe in his life? 15. ABCD is a trapezium in which AB DC and its diagonal intersect each other at the point O. Show that AO CO BO DO = . 16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, Prove that a) ABC AMP ? ? ~ b) CA BC PA MP = 17. Find the value of sin 60° geometrically 18. State whether the following are true or false. Justify your answer. sin(A+B)=sin A + sin B The value of tan A is always less than 1. 12 sec 5 A = for some value of A ? 19. Prove that: cos(90 ) 1 sin(90 ) 2cos 1 sin(90 ) cos(90 ) ec ? ? ? ? ? °  + °  + = + °  °  20. Find the mode of the following frequency distribution: Classes 06 612 1218 1824 2430 Frequency 7 5 10 12 6 Section D Question numbers 21 to 31 carry four marks each. 21. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two side are divided in the same ratio. 22. BL and CM are median of a triangle ABC right angled at A. Prove that 2 2 2 4[ ] 5 BL CM BC + = 23. Divide 4 3 2 3 5 7 2 5 x x x x +  + + by 2 3 1 x x + + and verify the division algorithm. 24. Find the other zeroes of the polynomial 4 3 2 9 3 18 x x x x +   + , if it is given that two of its zeroes are 3 or 3  25. Radha wants to construct a rectangular garden for children and other to play. The area of this rectangle remains the same if the length is increased by 7m and breadth is decreased by 3m. the area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. Find dimensions of the rectangular garden. 26. Represent the following pair of equations graphically and write the coordinates of point where the lines intersect the yaxis: x+3yy=6; 2x3y=12 27. Calculate the average daily income (in Rs) of the following data about workers working in a company: Average daily income (in Rs.) Number of workers Less than 100 12 Less than 200 28 Less than 300 34 Less than 400 41 Less than 500 50 28. Prove that: 1 cos sin 1 sin cos sin 1 cos ? ? ? ? ? ?  + + = +  29. Prove that: sec 1 sec 1 2cos sec 1 sec 1 ec ? ? ? ? ?  + + = +  30. The following distribution shows the daily pocket allowance given to the children of a multistoried building. The average daily pocket allowance is Rs 18. Meera is one of the children, residing in the same building, who instead of spending his daily pocket money prefers to save it. Daily pocket allowance 1113 1315 1517 1719 1921 2123 2325 Number of children 7 6 9 13 x 5 4 Find the missing frequency x. Which moral values of Meera can one imbibein his life? 31. The following gives the daily wages (in Rs.) of 58 workers of a factory. Daily wages 2040 4060 6080 80100 100120 120140 140160 Number of workers 4 6 10 16 12 7 3 Convert the above distribution into a less than cumulative frequency distribution. Draw its ogive and find the median.Read More
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