Page 1 Summative Assessment-1 2014-2015 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. Write an irrational number between 2 and 3. 2. Find the value of 2 2 104 103 - . 3. In figure AB CD , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? Section B Question numbers 5 to 10 carry 2 marks each. 5. Express 2.3 in the form of p q , where p and q are integers and 0 q ? . 6. If a+b=10 and ab=16, then find 2 2 a b + . 7. Prove that “Two distinct lines cannot have more than one point in common”. 8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. Page 2 Summative Assessment-1 2014-2015 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. Write an irrational number between 2 and 3. 2. Find the value of 2 2 104 103 - . 3. In figure AB CD , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? Section B Question numbers 5 to 10 carry 2 marks each. 5. Express 2.3 in the form of p q , where p and q are integers and 0 q ? . 6. If a+b=10 and ab=16, then find 2 2 a b + . 7. Prove that “Two distinct lines cannot have more than one point in common”. 8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. 10. In which quadrant or on which axis do the points (-3, -1), (-3,4), (-1, 0) and (0,5) lie? Section C Question number from 11 to 20 carry 3 marks each. 11. Simplify: 8 4 16 4 81x y z . 12. Find the value of 2 3 1 3 4 64 1 25 125 64 256 625 - ? ? + + ? ? ? ? ? ? ? ? ? ? . 13. Find the value of k for which 2k+1 is a factor of the polynomial 3 2 2 2 ( 1) x x k x k + - + - 14. Check whether 2 4 4 x x + + is a factor of the polynomial 3 2 2 4 8 x x x - + + . 15. In given figure, GM and HL are bisector of AGH ? and GHD ? respectively, such that GM HL . Show that AB CD . 16. In the figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that ( ) 1 2 DAE C B ? = ? - ? . 17. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B. 18. In given figure, find a + b. 19. In the figure, ABCD is a square of side 6m. P, Q, R and S are mid-point of AB, BC, CD and DA respectively. Find the area of the shaded region. Page 3 Summative Assessment-1 2014-2015 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. Write an irrational number between 2 and 3. 2. Find the value of 2 2 104 103 - . 3. In figure AB CD , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? Section B Question numbers 5 to 10 carry 2 marks each. 5. Express 2.3 in the form of p q , where p and q are integers and 0 q ? . 6. If a+b=10 and ab=16, then find 2 2 a b + . 7. Prove that “Two distinct lines cannot have more than one point in common”. 8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. 10. In which quadrant or on which axis do the points (-3, -1), (-3,4), (-1, 0) and (0,5) lie? Section C Question number from 11 to 20 carry 3 marks each. 11. Simplify: 8 4 16 4 81x y z . 12. Find the value of 2 3 1 3 4 64 1 25 125 64 256 625 - ? ? + + ? ? ? ? ? ? ? ? ? ? . 13. Find the value of k for which 2k+1 is a factor of the polynomial 3 2 2 2 ( 1) x x k x k + - + - 14. Check whether 2 4 4 x x + + is a factor of the polynomial 3 2 2 4 8 x x x - + + . 15. In given figure, GM and HL are bisector of AGH ? and GHD ? respectively, such that GM HL . Show that AB CD . 16. In the figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that ( ) 1 2 DAE C B ? = ? - ? . 17. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B. 18. In given figure, find a + b. 19. In the figure, ABCD is a square of side 6m. P, Q, R and S are mid-point of AB, BC, CD and DA respectively. Find the area of the shaded region. 20. Find the percentage increase in the area of a triangle if its each side is doubled. Section D Questions 21 to 31 carry 4 marks each. 21. Given 2 1.4142 = and 2 1.4142 = . Find the value of 1 3 2 1 - - correct to three places of decimal. 22. Simply: ( )( ) ( )( ) 2 2 3 3 3 5 2 2 + - + - 23. Find the value of ‘a’ in the polynomial 3 2 ( ) 2 8 p x x ax x a = + - + , when it is given that it is completely divisible by x-3. Hence factorise the polynomial. 24. State factor theorem. Using factor theorem, factorise 3 2 3 3 x x x - - + . 25. Find the value of the polynomial 4 3 2 ( ) 4 3 1 p x x x x = - - - at x=1, 1 1 , 2 3 2 and - - . 26. If the polynomial 3 2 9 6 23 4 x x x p + - + is exactly divisible by x+1, then find value of p. Hence factorise the polynomial. 27. In a school, students were asked by their teacher to plant trees around the school to reduce air pollution. What value is being inculcated in them? 28. Diagonals PR and SQ of a quadrilateral PQRS meet at O. Prove that PQ + QR + RS + SP<2(PR + QS) 29. In figure, AO and DO are the bisectors of A ? and D ? respectively of the quadrilateral ABCD. Prove that ( ) 1 2 AOD B C ? = ? + ? 30. In the given figure, AB=AC and BE, CF are bisectors of B ? and C ? respectively. Prove that EBC FCB ? ? ? . 31. Show that in a right angled triangle the hypotenuse is the longest side.Read More

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