Page 1 Summative Assessment-1 2014-2015 Mathematics Class â€“ IX Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper contains of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C compromises of 10 questions of 3 marks and Section-D comprises of 11 questions of 4 marks each. c) There is no overall choice in this question paper. d) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry one mark each. 1. Express 0.3 in the form p q , where p and q are integers and 0. q ? 2. If 3 2 4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 3. If fig, AB XY , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 4. Write the distance of point A(3,5) from x-axis. Section B Question numbers 5 to 10 carry two marks each. 5. Find the value of x if 5 5 2 2 x + = 6. Factorise: ( ) 3 3 8 2 x x y - - 7. State any two Euclidâ€™s axioms. 8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that ABD ACD ? = ? . Page 2 Summative Assessment-1 2014-2015 Mathematics Class â€“ IX Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper contains of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C compromises of 10 questions of 3 marks and Section-D comprises of 11 questions of 4 marks each. c) There is no overall choice in this question paper. d) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry one mark each. 1. Express 0.3 in the form p q , where p and q are integers and 0. q ? 2. If 3 2 4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 3. If fig, AB XY , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 4. Write the distance of point A(3,5) from x-axis. Section B Question numbers 5 to 10 carry two marks each. 5. Find the value of x if 5 5 2 2 x + = 6. Factorise: ( ) 3 3 8 2 x x y - - 7. State any two Euclidâ€™s axioms. 8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that ABD ACD ? = ? . 9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 cm. find its area. 10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is formed on joining the points in order? Also, identify the shape of figure. Section C Question numbers 11 to 20 carry three marks each. 11. Simplify: 72 5 72 3 288 2 648 + - 12. If 5 2 6, p = - find 2 2 1 p p - 13. Factorise: 3 3 3 ( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 14. Prove that 4 3 2 2 3 38 32 x x x x + + - + is exactly divisible by 2 3 2 x x - + 15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90 2 A BOC ? ? = ° + 16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 17. In figure; if l m and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 1 2 ? = ? . Page 3 Summative Assessment-1 2014-2015 Mathematics Class â€“ IX Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper contains of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C compromises of 10 questions of 3 marks and Section-D comprises of 11 questions of 4 marks each. c) There is no overall choice in this question paper. d) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry one mark each. 1. Express 0.3 in the form p q , where p and q are integers and 0. q ? 2. If 3 2 4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 3. If fig, AB XY , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 4. Write the distance of point A(3,5) from x-axis. Section B Question numbers 5 to 10 carry two marks each. 5. Find the value of x if 5 5 2 2 x + = 6. Factorise: ( ) 3 3 8 2 x x y - - 7. State any two Euclidâ€™s axioms. 8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that ABD ACD ? = ? . 9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 cm. find its area. 10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is formed on joining the points in order? Also, identify the shape of figure. Section C Question numbers 11 to 20 carry three marks each. 11. Simplify: 72 5 72 3 288 2 648 + - 12. If 5 2 6, p = - find 2 2 1 p p - 13. Factorise: 3 3 3 ( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 14. Prove that 4 3 2 2 3 38 32 x x x x + + - + is exactly divisible by 2 3 2 x x - + 15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90 2 A BOC ? ? = ° + 16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 17. In figure; if l m and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 1 2 ? = ? . 19. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral triangle of side 8 cm. find the area of the figure so formed. 20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area ( ) 2 108 FBE cm ? = , find the length of AB. Section D Question numbers 21 to 31 carry four marks each. 21. Find the values of a and b if 7 1 7 1 7 7 1 7 1 a b - + - = + + - 22. Simplify: 1 1 1 1 2 5 5 6 6 7 7 8 + + + + + + + 23. If x-5 and 1 5 x - are the factors of the polynomial 2 3 px x r + + , show that p=r. 24. Show that 2x-1 is a factor of the polynomial 3 2 2 2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise the polynomial. 25. Divide polynomial 4 3 2 ( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in p(x) so that it is divisible by q(x). 26. Factorise: 6 3 5 8 x x + + 27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting by doing so In the figure below, AB CD . What is the value of x? Also find angle A and B. 28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE Page 4 Summative Assessment-1 2014-2015 Mathematics Class â€“ IX Time allowed: 3:00 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper contains of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C compromises of 10 questions of 3 marks and Section-D comprises of 11 questions of 4 marks each. c) There is no overall choice in this question paper. d) Use of calculator is not permitted. Section A Question numbers 1 to 4 carry one mark each. 1. Express 0.3 in the form p q , where p and q are integers and 0. q ? 2. If 3 2 4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 3. If fig, AB XY , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 4. Write the distance of point A(3,5) from x-axis. Section B Question numbers 5 to 10 carry two marks each. 5. Find the value of x if 5 5 2 2 x + = 6. Factorise: ( ) 3 3 8 2 x x y - - 7. State any two Euclidâ€™s axioms. 8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that ABD ACD ? = ? . 9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 cm. find its area. 10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is formed on joining the points in order? Also, identify the shape of figure. Section C Question numbers 11 to 20 carry three marks each. 11. Simplify: 72 5 72 3 288 2 648 + - 12. If 5 2 6, p = - find 2 2 1 p p - 13. Factorise: 3 3 3 ( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 14. Prove that 4 3 2 2 3 38 32 x x x x + + - + is exactly divisible by 2 3 2 x x - + 15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90 2 A BOC ? ? = ° + 16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 17. In figure; if l m and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 1 2 ? = ? . 19. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral triangle of side 8 cm. find the area of the figure so formed. 20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area ( ) 2 108 FBE cm ? = , find the length of AB. Section D Question numbers 21 to 31 carry four marks each. 21. Find the values of a and b if 7 1 7 1 7 7 1 7 1 a b - + - = + + - 22. Simplify: 1 1 1 1 2 5 5 6 6 7 7 8 + + + + + + + 23. If x-5 and 1 5 x - are the factors of the polynomial 2 3 px x r + + , show that p=r. 24. Show that 2x-1 is a factor of the polynomial 3 2 2 2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise the polynomial. 25. Divide polynomial 4 3 2 ( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in p(x) so that it is divisible by q(x). 26. Factorise: 6 3 5 8 x x + + 27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting by doing so In the figure below, AB CD . What is the value of x? Also find angle A and B. 28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE 29. Sides BC, CA and BA of a triangle ABC are produced to D, Q, P, respectively as shown in the figure. If 100 , 35 ACD QAP ? = ° ? = ° , find all the angles of the triangle. 30. In figure, AB=BC and AD=EC, then show that ABE CBD ? ? ? 31. Prove that the angles opposite to equal sides of a triangle are equal.Read More