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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of the ladder from the base of the wall. 2. If tan cot 2 ? ? + = , then find the value of 2 2 tan cot ? ? + 3. If 5 cos 4 ec? = , find the value of cot? . 4. In the following table, find x and y, where f and c.f. have their usual meanings: Class interval 08 816 1624 2432 f 2 10 y 5 c.f. x 12 30 35 Section B Question number 5 to 10 carry two marks each. 5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 6. What is the decimal expansion of the rational number 201 250 ? 7. Find the quadratic polynomial whose zeroes are 4 and 3 5  . 8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of the ladder from the base of the wall. 2. If tan cot 2 ? ? + = , then find the value of 2 2 tan cot ? ? + 3. If 5 cos 4 ec? = , find the value of cot? . 4. In the following table, find x and y, where f and c.f. have their usual meanings: Class interval 08 816 1624 2432 f 2 10 y 5 c.f. x 12 30 35 Section B Question number 5 to 10 carry two marks each. 5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 6. What is the decimal expansion of the rational number 201 250 ? 7. Find the quadratic polynomial whose zeroes are 4 and 3 5  . 8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 9. Show that: 1 sin sec tan 1 sin A A A A  =  + 10. In a section of class X, heights of 50 students are shown in the following table: Height (in cm) 148 154 160 150 152 149 155 Number of students 3 7 2 12 8 14 4 Find the median height of this section. Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is an irrational number. 12. Solve for x and y: 11 1 10 9 4 5 x y x y  =  = 13. If one zero of the polynomial 2 ( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value of a. 14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines represented by the pair are: a) Intersecting b) Coincident c) Parallel 15. In the figure of , ABC DE AC ? . If DC AP , where point P lies on BC produced, then shows that BE BC BC CP = 16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 17. When is an equation called ‘an identity’. Prove that trigonometric identity 2 2 1 tan sec A A + = . 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of the ladder from the base of the wall. 2. If tan cot 2 ? ? + = , then find the value of 2 2 tan cot ? ? + 3. If 5 cos 4 ec? = , find the value of cot? . 4. In the following table, find x and y, where f and c.f. have their usual meanings: Class interval 08 816 1624 2432 f 2 10 y 5 c.f. x 12 30 35 Section B Question number 5 to 10 carry two marks each. 5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 6. What is the decimal expansion of the rational number 201 250 ? 7. Find the quadratic polynomial whose zeroes are 4 and 3 5  . 8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 9. Show that: 1 sin sec tan 1 sin A A A A  =  + 10. In a section of class X, heights of 50 students are shown in the following table: Height (in cm) 148 154 160 150 152 149 155 Number of students 3 7 2 12 8 14 4 Find the median height of this section. Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is an irrational number. 12. Solve for x and y: 11 1 10 9 4 5 x y x y  =  = 13. If one zero of the polynomial 2 ( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value of a. 14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines represented by the pair are: a) Intersecting b) Coincident c) Parallel 15. In the figure of , ABC DE AC ? . If DC AP , where point P lies on BC produced, then shows that BE BC BC CP = 16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 17. When is an equation called ‘an identity’. Prove that trigonometric identity 2 2 1 tan sec A A + = . 18. If 12 cos 13 A = ,then verify that: 35 sin (1 tan ) 156 A A  = 19. Following frequency distribution gives the heights of students of class IX in a school: Height (in cm) 141145 146150 151155 156160 161165 Number of students 8 18 20 12 2 Find the median height. 20. The following frequency distribution gives the marks (out of 50) of students in a class test: Marks 010 1020 2030 3040 4050 Number of students 10 24 38 22 6 Using step deviation method to find the mean marks. Section D Question numbers 21 to 31 carry four marks each. 21. Dhudnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled. 22. The owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol /diesel. The taxi charges in city comprises of fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs. 89 and for journey of 20 km, the charge paid is Rs. 145. a) What will a person have to pay for travelling a distance of 30km? b) Why did he decide to use CNG for his taxi as a fuel? 23. If a polynomial 4 3 2 3 4 16 15 14 x x a x   + + is divided by another polynomial 2 4 x  , the remainder comes out to be px + q. Find the value of p and q. 24. Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditures are in the ratio 4:3. If each of them saves Rs 50 at the end of the month, find their pocket money. 25. Find the length of the diagonal of the rectangle BCDE if BCA DCF ? = ? . AC=6m and CF=13m. 26. If in the ABC ? , AD is median and AM BC ? , then prove that 2 2 2 2 2( ) AB AC AD BD + = + 27. Prove that: 2 2 sin tan cos cot 2sin cos tan cot ? ? ? ? ? ? ? ? · + · + · = + 28. If A, B, C are interior angles of a triangle ABC then prove that: 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of the ladder from the base of the wall. 2. If tan cot 2 ? ? + = , then find the value of 2 2 tan cot ? ? + 3. If 5 cos 4 ec? = , find the value of cot? . 4. In the following table, find x and y, where f and c.f. have their usual meanings: Class interval 08 816 1624 2432 f 2 10 y 5 c.f. x 12 30 35 Section B Question number 5 to 10 carry two marks each. 5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 6. What is the decimal expansion of the rational number 201 250 ? 7. Find the quadratic polynomial whose zeroes are 4 and 3 5  . 8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 9. Show that: 1 sin sec tan 1 sin A A A A  =  + 10. In a section of class X, heights of 50 students are shown in the following table: Height (in cm) 148 154 160 150 152 149 155 Number of students 3 7 2 12 8 14 4 Find the median height of this section. Section C Question numbers 11 to 20 carry three marks each. 11. Prove that 2 is an irrational number. 12. Solve for x and y: 11 1 10 9 4 5 x y x y  =  = 13. If one zero of the polynomial 2 ( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value of a. 14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines represented by the pair are: a) Intersecting b) Coincident c) Parallel 15. In the figure of , ABC DE AC ? . If DC AP , where point P lies on BC produced, then shows that BE BC BC CP = 16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 17. When is an equation called ‘an identity’. Prove that trigonometric identity 2 2 1 tan sec A A + = . 18. If 12 cos 13 A = ,then verify that: 35 sin (1 tan ) 156 A A  = 19. Following frequency distribution gives the heights of students of class IX in a school: Height (in cm) 141145 146150 151155 156160 161165 Number of students 8 18 20 12 2 Find the median height. 20. The following frequency distribution gives the marks (out of 50) of students in a class test: Marks 010 1020 2030 3040 4050 Number of students 10 24 38 22 6 Using step deviation method to find the mean marks. Section D Question numbers 21 to 31 carry four marks each. 21. Dhudnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled. 22. The owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol /diesel. The taxi charges in city comprises of fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs. 89 and for journey of 20 km, the charge paid is Rs. 145. a) What will a person have to pay for travelling a distance of 30km? b) Why did he decide to use CNG for his taxi as a fuel? 23. If a polynomial 4 3 2 3 4 16 15 14 x x a x   + + is divided by another polynomial 2 4 x  , the remainder comes out to be px + q. Find the value of p and q. 24. Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditures are in the ratio 4:3. If each of them saves Rs 50 at the end of the month, find their pocket money. 25. Find the length of the diagonal of the rectangle BCDE if BCA DCF ? = ? . AC=6m and CF=13m. 26. If in the ABC ? , AD is median and AM BC ? , then prove that 2 2 2 2 2( ) AB AC AD BD + = + 27. Prove that: 2 2 sin tan cos cot 2sin cos tan cot ? ? ? ? ? ? ? ? · + · + · = + 28. If A, B, C are interior angles of a triangle ABC then prove that: a) sin cos 2 2 B C A + = b) tan cot 2 2 C A B + = 29. If sec tan x ? ?  = , show that 1 sec tan x ? ? + = and hence find the values of cos? andsin? . 30. In a certain locality, monthly consumptions of electricity (in unit) of 122 families are given in the following table. Mode is given to be 139, find the missing frequencies x and y. Electricity consumed 7090 90110 110130 130 150 150 170 170 190 190 210 210 230 Number of families x 10 y 40 18 9 8 3 31. In a locality, weekly expenditure of 40 families on fruits and vegetable (n rupees) is given in the following frequency distribution: Expenditure (in Rs.) 500700 700900 9001100 11001300 13001500 Number of families 6 8 10 9 7 Find the mean weekly expenditure.Read More
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