Page 1 Summative Assessment-1 2014-2015 Mathematics Class â€“ 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 of Section â€“ A are very short type questions, carrying 1 mark each. Question No. 5 to 10 of Section â€“ B are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 of Section â€“ C carry 3 marks each. Question No. 21 to 31 of Section â€“ D 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. In PQR ? , E and F points on the sides PQ and PR respectively such that EF QR . If PE=6 cm, QE=2 cm and FR=3cm, then find PF. 2. Find the value of 1 cos36 3 sec16 . . 3 sin 54 2 cos 74 ec ° ° - ° ° 3. If 1 tan 3 ? = , find the value of sin(90 ) ? ° - 4. Write the empirical relationship between the three measures of central tendency. Section B Question numbers 5 to 10 carry 2 marks each. 5. Find the value of: 2 2 1 4 2 ( 1) ( 1) ( 1) ( 1) n n n n + + - + - + - + - , where n is any positive odd integer. 6. Determine the values of m and n so that the prime factorization of 10500 is expressible as 2 3 5 7 m n × × × 7. Find the zeroes of the quadratic polynomial 2 7 12 x x - + and verify the relationship between the zeroes and the coefficients. 8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm. 9. Simplify: tan 28 1 [tan 20 .tan 60 .tan 70 ] cot 62 3 ° ÷ ° ° ° ° 10. Given below is a cumulative frequency distribution table showing daily income of 50 workers of a factory: Page 2 Summative Assessment-1 2014-2015 Mathematics Class â€“ 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 of Section â€“ A are very short type questions, carrying 1 mark each. Question No. 5 to 10 of Section â€“ B are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 of Section â€“ C carry 3 marks each. Question No. 21 to 31 of Section â€“ D 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. In PQR ? , E and F points on the sides PQ and PR respectively such that EF QR . If PE=6 cm, QE=2 cm and FR=3cm, then find PF. 2. Find the value of 1 cos36 3 sec16 . . 3 sin 54 2 cos 74 ec ° ° - ° ° 3. If 1 tan 3 ? = , find the value of sin(90 ) ? ° - 4. Write the empirical relationship between the three measures of central tendency. Section B Question numbers 5 to 10 carry 2 marks each. 5. Find the value of: 2 2 1 4 2 ( 1) ( 1) ( 1) ( 1) n n n n + + - + - + - + - , where n is any positive odd integer. 6. Determine the values of m and n so that the prime factorization of 10500 is expressible as 2 3 5 7 m n × × × 7. Find the zeroes of the quadratic polynomial 2 7 12 x x - + and verify the relationship between the zeroes and the coefficients. 8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm. 9. Simplify: tan 28 1 [tan 20 .tan 60 .tan 70 ] cot 62 3 ° ÷ ° ° ° ° 10. Given below is a cumulative frequency distribution table showing daily income of 50 workers of a factory: Daily income (in Rs.) More than or equal to 200 More than or equal to 300 More than or equal to 400 More than or equal to 500 More than or equal to 600 Number of workers 50 42 30 18 05 Draw cumulative frequency curve (ogive) â€˜of more thanâ€™ type for this data. Section C Question number from 11 to 20 carry 3 marks each. 11. Prove that 8 is an irrational number. 12. Solve the following pair of equations for x and y: 4 5 7 y x + = 3 4 5 y x + = 13. Solve the following pair of linear equations by the elimination method: 2x+3y=7 3x-2y=3 14. What should be added in the polynomial 4 3 2 3 4 6 4 x x x - - + so that it is completely divisible by 2 2 x - 15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that 2 2 2 2 2 AB AC BC = - 16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA and PR BD , then prove that QR AD 17. Prove that: (1 + tan A + cot A).(sin A â€“ cos A)=sin A. tan A â€“ cot A. cos A 18. Evaluate: 2 2 sec .cos (90 ) tan .cot(90 ) sin 55 sin 35 tan10 .tan 20 .tan 60 .tan 70 .tan80 ec ? ? ? ? ° - - ° - + ° + ° ° ° ° ° ° 19. Heights of students of class X are given in the following frequency distribution: Height (in cm) 150-155 155-160 160-165 165-170 170-175 Number of students 15 8 20 12 5 Find the modal height. 20. A school conducted a test (of 100 marks) in English for students of class X. The marks obtained by students are shown in the following table: Page 3 Summative Assessment-1 2014-2015 Mathematics Class â€“ 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 of Section â€“ A are very short type questions, carrying 1 mark each. Question No. 5 to 10 of Section â€“ B are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 of Section â€“ C carry 3 marks each. Question No. 21 to 31 of Section â€“ D 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. In PQR ? , E and F points on the sides PQ and PR respectively such that EF QR . If PE=6 cm, QE=2 cm and FR=3cm, then find PF. 2. Find the value of 1 cos36 3 sec16 . . 3 sin 54 2 cos 74 ec ° ° - ° ° 3. If 1 tan 3 ? = , find the value of sin(90 ) ? ° - 4. Write the empirical relationship between the three measures of central tendency. Section B Question numbers 5 to 10 carry 2 marks each. 5. Find the value of: 2 2 1 4 2 ( 1) ( 1) ( 1) ( 1) n n n n + + - + - + - + - , where n is any positive odd integer. 6. Determine the values of m and n so that the prime factorization of 10500 is expressible as 2 3 5 7 m n × × × 7. Find the zeroes of the quadratic polynomial 2 7 12 x x - + and verify the relationship between the zeroes and the coefficients. 8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm. 9. Simplify: tan 28 1 [tan 20 .tan 60 .tan 70 ] cot 62 3 ° ÷ ° ° ° ° 10. Given below is a cumulative frequency distribution table showing daily income of 50 workers of a factory: Daily income (in Rs.) More than or equal to 200 More than or equal to 300 More than or equal to 400 More than or equal to 500 More than or equal to 600 Number of workers 50 42 30 18 05 Draw cumulative frequency curve (ogive) â€˜of more thanâ€™ type for this data. Section C Question number from 11 to 20 carry 3 marks each. 11. Prove that 8 is an irrational number. 12. Solve the following pair of equations for x and y: 4 5 7 y x + = 3 4 5 y x + = 13. Solve the following pair of linear equations by the elimination method: 2x+3y=7 3x-2y=3 14. What should be added in the polynomial 4 3 2 3 4 6 4 x x x - - + so that it is completely divisible by 2 2 x - 15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that 2 2 2 2 2 AB AC BC = - 16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA and PR BD , then prove that QR AD 17. Prove that: (1 + tan A + cot A).(sin A â€“ cos A)=sin A. tan A â€“ cot A. cos A 18. Evaluate: 2 2 sec .cos (90 ) tan .cot(90 ) sin 55 sin 35 tan10 .tan 20 .tan 60 .tan 70 .tan80 ec ? ? ? ? ° - - ° - + ° + ° ° ° ° ° ° 19. Heights of students of class X are given in the following frequency distribution: Height (in cm) 150-155 155-160 160-165 165-170 170-175 Number of students 15 8 20 12 5 Find the modal height. 20. A school conducted a test (of 100 marks) in English for students of class X. The marks obtained by students are shown in the following table: Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90- 100 Number of students 1 2 4 15 15 25 15 10 2 1 Find the modal marks. Section D Questions 21 to 31 carry 4 marks each. 21. State Euclid division Lemma. Using it show that square of any positive integer is either of the form 5cm or 5 1 m ± , where m is an integer. 22. On the independence day celebration in the school, number of students participated in the celebration. School management has decided to distribute some sweets amongst the participants and athe audience. If total number of sweets were represented by 4 3 2 8 14 2 7 8 x x x x + - + - , each one received 2 2 2 1 x x + - sweets and 14x â€“ 10 remained undistributed, find the number of students to whom sweets were distributed. 23. If a polynomial 4 3 2 2 3 6 3 2 x x x x - - + + - is divided by another polynomial 2 2 3 4 x x - - + , then remainder is px+q. Find the value of p and q. 24. Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks for each wrong answer. Had 4 marks been awarded for each correct answer and 1 mark been deducted for each incorrect answer, then she would have scored 250 marks. How many questions were there in the test, if she attempted all the questions. 25. In the given figure, AB and CD are two pillars P is a point on BD such that BP=16 m and PD=12 m. If CD=16 m and AC=52 m, then find AB and AP when it is given that 90 APC ? = ° 26. If ABC DEF ? ? ~ and AX, DY are respectively the medians of ABC ? and DEF ? . Then prove that a) ABX DEY ? ? ~ b) ACX DFY ? ? ~ c) AX BC DY EF = 27. Given that ( ) tan tan tan A â€“ B 1 tan .tan A B A B - = + ; evaluate tan15° in two ways. a) Taking 60 , 45 A B = ° = ° b) Taking 45 , 30 A B = ° = ° 28. If 4 tan 5 tan ? ? + = , find sin? and cos? . 29. If x=cot A + cos A = cot A â€“ cos A; prove that: Page 4 Summative Assessment-1 2014-2015 Mathematics Class â€“ 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 of Section â€“ A are very short type questions, carrying 1 mark each. Question No. 5 to 10 of Section â€“ B are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 of Section â€“ C carry 3 marks each. Question No. 21 to 31 of Section â€“ D 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. In PQR ? , E and F points on the sides PQ and PR respectively such that EF QR . If PE=6 cm, QE=2 cm and FR=3cm, then find PF. 2. Find the value of 1 cos36 3 sec16 . . 3 sin 54 2 cos 74 ec ° ° - ° ° 3. If 1 tan 3 ? = , find the value of sin(90 ) ? ° - 4. Write the empirical relationship between the three measures of central tendency. Section B Question numbers 5 to 10 carry 2 marks each. 5. Find the value of: 2 2 1 4 2 ( 1) ( 1) ( 1) ( 1) n n n n + + - + - + - + - , where n is any positive odd integer. 6. Determine the values of m and n so that the prime factorization of 10500 is expressible as 2 3 5 7 m n × × × 7. Find the zeroes of the quadratic polynomial 2 7 12 x x - + and verify the relationship between the zeroes and the coefficients. 8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm. 9. Simplify: tan 28 1 [tan 20 .tan 60 .tan 70 ] cot 62 3 ° ÷ ° ° ° ° 10. Given below is a cumulative frequency distribution table showing daily income of 50 workers of a factory: Daily income (in Rs.) More than or equal to 200 More than or equal to 300 More than or equal to 400 More than or equal to 500 More than or equal to 600 Number of workers 50 42 30 18 05 Draw cumulative frequency curve (ogive) â€˜of more thanâ€™ type for this data. Section C Question number from 11 to 20 carry 3 marks each. 11. Prove that 8 is an irrational number. 12. Solve the following pair of equations for x and y: 4 5 7 y x + = 3 4 5 y x + = 13. Solve the following pair of linear equations by the elimination method: 2x+3y=7 3x-2y=3 14. What should be added in the polynomial 4 3 2 3 4 6 4 x x x - - + so that it is completely divisible by 2 2 x - 15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that 2 2 2 2 2 AB AC BC = - 16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA and PR BD , then prove that QR AD 17. Prove that: (1 + tan A + cot A).(sin A â€“ cos A)=sin A. tan A â€“ cot A. cos A 18. Evaluate: 2 2 sec .cos (90 ) tan .cot(90 ) sin 55 sin 35 tan10 .tan 20 .tan 60 .tan 70 .tan80 ec ? ? ? ? ° - - ° - + ° + ° ° ° ° ° ° 19. Heights of students of class X are given in the following frequency distribution: Height (in cm) 150-155 155-160 160-165 165-170 170-175 Number of students 15 8 20 12 5 Find the modal height. 20. A school conducted a test (of 100 marks) in English for students of class X. The marks obtained by students are shown in the following table: Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90- 100 Number of students 1 2 4 15 15 25 15 10 2 1 Find the modal marks. Section D Questions 21 to 31 carry 4 marks each. 21. State Euclid division Lemma. Using it show that square of any positive integer is either of the form 5cm or 5 1 m ± , where m is an integer. 22. On the independence day celebration in the school, number of students participated in the celebration. School management has decided to distribute some sweets amongst the participants and athe audience. If total number of sweets were represented by 4 3 2 8 14 2 7 8 x x x x + - + - , each one received 2 2 2 1 x x + - sweets and 14x â€“ 10 remained undistributed, find the number of students to whom sweets were distributed. 23. If a polynomial 4 3 2 2 3 6 3 2 x x x x - - + + - is divided by another polynomial 2 2 3 4 x x - - + , then remainder is px+q. Find the value of p and q. 24. Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks for each wrong answer. Had 4 marks been awarded for each correct answer and 1 mark been deducted for each incorrect answer, then she would have scored 250 marks. How many questions were there in the test, if she attempted all the questions. 25. In the given figure, AB and CD are two pillars P is a point on BD such that BP=16 m and PD=12 m. If CD=16 m and AC=52 m, then find AB and AP when it is given that 90 APC ? = ° 26. If ABC DEF ? ? ~ and AX, DY are respectively the medians of ABC ? and DEF ? . Then prove that a) ABX DEY ? ? ~ b) ACX DFY ? ? ~ c) AX BC DY EF = 27. Given that ( ) tan tan tan A â€“ B 1 tan .tan A B A B - = + ; evaluate tan15° in two ways. a) Taking 60 , 45 A B = ° = ° b) Taking 45 , 30 A B = ° = ° 28. If 4 tan 5 tan ? ? + = , find sin? and cos? . 29. If x=cot A + cos A = cot A â€“ cos A; prove that: 2 2 1 2 x y x y x y ? ? - - ? ? + = ? ? ? ? + ? ? ? ? 30. The annual profits earned by shops of a particular shopping mall are given in the following distribution: Profit (in lakh) 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 Number of shops 4 8 15 20 25 18 12 7 3 Draw a â€˜less than typeâ€™ ogive and a â€˜more than typeâ€™ ogive for this data. 31. In a check-up of heart beat rate of 50 females, it was found that median heart beat is 78. Find the missing frequencies 1 f and 2 f in the following frequency distribution: Number of heart beats per minute 64-68 68-72 72-76 76-80 80-84 84-88 88-92 Number of females 4 5 1 f 2 f 9 7 1Read More

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