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 consists of 31 question divided into four sections A, B, C and D. Section â€“ A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Section â€“ C comprises of 10 questions of 3 marks each and Section â€“ 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 â€“ A Question numbers 1 to 4 carry one mark each 1. What can you say about the sum of a rational number and an irrational number? 2. Find the coefficient of ( ) 3 2 2 2 x in x + 3. Write the measure of each exterior angle of an equilateral triangle. 4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the co-ordinates of P? Section â€“ B Question numbers 5 to 10 carry two marks each. 5. Rationalize the denominator of 2 3 3 2 2 3 3 - + + 6. If (x+1) is factor of 2 4 3 px px - + what is the value of p? 7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove that PQ=QR=PR. 8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find COD ? and reflex COD ? . 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 consists of 31 question divided into four sections A, B, C and D. Section â€“ A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Section â€“ C comprises of 10 questions of 3 marks each and Section â€“ 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 â€“ A Question numbers 1 to 4 carry one mark each 1. What can you say about the sum of a rational number and an irrational number? 2. Find the coefficient of ( ) 3 2 2 2 x in x + 3. Write the measure of each exterior angle of an equilateral triangle. 4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the co-ordinates of P? Section â€“ B Question numbers 5 to 10 carry two marks each. 5. Rationalize the denominator of 2 3 3 2 2 3 3 - + + 6. If (x+1) is factor of 2 4 3 px px - + what is the value of p? 7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove that PQ=QR=PR. 8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find COD ? and reflex COD ? . 9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the triangle. (use 15 3.87 = ) 10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals intersect each other at O. Find the area of the shaded region by using Heronâ€™s formula. Section â€“ C Question number 11 to 20 carry three marks each. 11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ? 12. If 5 2 3 3 7 4 2 a b + = + + , then find a and b. 13. When the polynomials 3 2 3 13 ax x + - and 3 2 5 x x a - + are divided by (x-2), then remainder is same. Find the value of a. 14. Factorise: 6 6 a b - 15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is double the smallest side. 16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that 1 ( ) 2 DAE C B ? = ? - ? . 17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the triangle ABC is an isosceles triangle. 18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD 19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of the diagonals. 20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest altitude. Section â€“ D Question numbers 21 to 31 carry four marks each. 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 consists of 31 question divided into four sections A, B, C and D. Section â€“ A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Section â€“ C comprises of 10 questions of 3 marks each and Section â€“ 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 â€“ A Question numbers 1 to 4 carry one mark each 1. What can you say about the sum of a rational number and an irrational number? 2. Find the coefficient of ( ) 3 2 2 2 x in x + 3. Write the measure of each exterior angle of an equilateral triangle. 4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the co-ordinates of P? Section â€“ B Question numbers 5 to 10 carry two marks each. 5. Rationalize the denominator of 2 3 3 2 2 3 3 - + + 6. If (x+1) is factor of 2 4 3 px px - + what is the value of p? 7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove that PQ=QR=PR. 8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find COD ? and reflex COD ? . 9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the triangle. (use 15 3.87 = ) 10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals intersect each other at O. Find the area of the shaded region by using Heronâ€™s formula. Section â€“ C Question number 11 to 20 carry three marks each. 11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ? 12. If 5 2 3 3 7 4 2 a b + = + + , then find a and b. 13. When the polynomials 3 2 3 13 ax x + - and 3 2 5 x x a - + are divided by (x-2), then remainder is same. Find the value of a. 14. Factorise: 6 6 a b - 15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is double the smallest side. 16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that 1 ( ) 2 DAE C B ? = ? - ? . 17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the triangle ABC is an isosceles triangle. 18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD 19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of the diagonals. 20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest altitude. Section â€“ D Question numbers 21 to 31 carry four marks each. 21. If 3 2 3 2 x - = + and 3 2 3 2 y + = - , then show that 2 2 99 x xy y + + = . 22. If (x+1)=3 find the value of 2 1 x x ? ? + ? ? ? ? 23. Factorise: 2 2 3 2 2 3 2 2 3 ( ) ( ) ( ) a b b c c a - + - + - 24. Simplify and factorise: 2 2 2 2 ( ) ( ) 4 4 a b c a b c b c + + - - - + - 25. Without actually calculating the cubes, find the value of 3 3 3 ( 12) (7) (5) - + + and 3 3 3 (28) ( 15) ( 13) + - + - . Also write the identify used. 26. Factorise: 3 2 13 32 20 x x x + + + 27. Builder has made a layout of a colony so that lane a is parallel to lane b? he also plans to leave green areas as shown in the figure. what value is the showing by doing so? If measure of 1 ? is 120° , find the measure of all other angles. 28. In a right angled triangle XYZ right angled at Z, M is the midpoint of XY. Z is joined to M and produced to a point P such that PM=ZM. Point P is joined to point Y. Show that a) XMZ YMP ? ? ? b) 90 PYZ ? = ° c) PYZ XZY ? ? ? d) 1 2 ZM XY = 29. Prove that sum of the angles of a triangle is 180° . If in ABC ? , 120 A B ? + ? = ° and 100 B C ? + ? = ° , then find B ? . 30. In figure, ABC is an isosceles triangle with AB=AC. D is a point in the interior of ABC ? such that CBD BCD ? = ? . Prove that AD bisects BAC ? of ABC ? . 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 consists of 31 question divided into four sections A, B, C and D. Section â€“ A comprises of 4 questions of 1 mark each; Section- B comprises of 6 questions of 2 marks each; Section â€“ C comprises of 10 questions of 3 marks each and Section â€“ 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 â€“ A Question numbers 1 to 4 carry one mark each 1. What can you say about the sum of a rational number and an irrational number? 2. Find the coefficient of ( ) 3 2 2 2 x in x + 3. Write the measure of each exterior angle of an equilateral triangle. 4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the co-ordinates of P? Section â€“ B Question numbers 5 to 10 carry two marks each. 5. Rationalize the denominator of 2 3 3 2 2 3 3 - + + 6. If (x+1) is factor of 2 4 3 px px - + what is the value of p? 7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove that PQ=QR=PR. 8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find COD ? and reflex COD ? . 9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the triangle. (use 15 3.87 = ) 10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals intersect each other at O. Find the area of the shaded region by using Heronâ€™s formula. Section â€“ C Question number 11 to 20 carry three marks each. 11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ? 12. If 5 2 3 3 7 4 2 a b + = + + , then find a and b. 13. When the polynomials 3 2 3 13 ax x + - and 3 2 5 x x a - + are divided by (x-2), then remainder is same. Find the value of a. 14. Factorise: 6 6 a b - 15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is double the smallest side. 16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that 1 ( ) 2 DAE C B ? = ? - ? . 17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the triangle ABC is an isosceles triangle. 18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD 19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of the diagonals. 20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest altitude. Section â€“ D Question numbers 21 to 31 carry four marks each. 21. If 3 2 3 2 x - = + and 3 2 3 2 y + = - , then show that 2 2 99 x xy y + + = . 22. If (x+1)=3 find the value of 2 1 x x ? ? + ? ? ? ? 23. Factorise: 2 2 3 2 2 3 2 2 3 ( ) ( ) ( ) a b b c c a - + - + - 24. Simplify and factorise: 2 2 2 2 ( ) ( ) 4 4 a b c a b c b c + + - - - + - 25. Without actually calculating the cubes, find the value of 3 3 3 ( 12) (7) (5) - + + and 3 3 3 (28) ( 15) ( 13) + - + - . Also write the identify used. 26. Factorise: 3 2 13 32 20 x x x + + + 27. Builder has made a layout of a colony so that lane a is parallel to lane b? he also plans to leave green areas as shown in the figure. what value is the showing by doing so? If measure of 1 ? is 120° , find the measure of all other angles. 28. In a right angled triangle XYZ right angled at Z, M is the midpoint of XY. Z is joined to M and produced to a point P such that PM=ZM. Point P is joined to point Y. Show that a) XMZ YMP ? ? ? b) 90 PYZ ? = ° c) PYZ XZY ? ? ? d) 1 2 ZM XY = 29. Prove that sum of the angles of a triangle is 180° . If in ABC ? , 120 A B ? + ? = ° and 100 B C ? + ? = ° , then find B ? . 30. In figure, ABC is an isosceles triangle with AB=AC. D is a point in the interior of ABC ? such that CBD BCD ? = ? . Prove that AD bisects BAC ? of ABC ? . 31. Sides BC, CA and BA of a triangle ABC are produced to D, Q, P, respectively as shown in the figure. If 100 ACD ? = °, 35 QAP ? = ° , find all the angles of the triangle.Read More