SUMMATIVE ASSESSMENT - I (2012) MATHEMATICS CLASS IX Time allowed : 3 hours Maximum Marks :90 General Instructions: i. All questions are compulsory. ii. The question paper consists of 34 questions divided into four sections A,B,C and D. Section A comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks each, section C comprises of 10 questions of 3 marks each and section D comprises 10 questions of 4 marks each. iii. Questions numbers 1 to 10 in section A are multiple choice questions where you are to select one correct option out of the given four. iv. There is no overall choice. However, internal choice have been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. v. Use of calculation is not permitted. SECTION A Question numbers 1 to 8 carry one mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. If = 3.1622, the value of 1 is i) 31.622 ii) 3.1622 iii) 0.31622 iv) 316.22 2. If x 91 + 91 is divided by x +1, then the remainder is i) 0 ii) 1 iii) 90 iv) - 90 3. Degree of the zero polynomial is i) 1 ii) 0 iii) any natural number iv) not defined 4. If + = -1 ( a 0, b 0) then the value of a 3 - b 3 is i) 1 ii) -1 iii) 0 iv) ½ 5. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is i) An obtuse triangle ii) an isosceles triangle iii) an equilateral triangle iv) a right triangle 6. In ABC, AB=AC, if B = 50 o then A is equal to i) 50 o ii) 100 o iii) 80 o iv) 30 o 7. An isosceles right triangle has area 8 cm 2, the length of its hypotenuse is i) cm ii) cm iii) cm iv) cm Page 1 of 6
8. The area of a triangular board of sides 3m, 4m, and 5 m is i) 6m 2 ii) 12 m 2 iii) 15 m 2 iv) 10m 2 SECTION B (2 marks) 9. Rationalize the denominator of. 10. Without actually calculating the cubes, Find the value of the following ( 43) 3 + (-27) 3 + (-16) 3 11. Factorize 2x 3 + 3 + 7x. 12. In the given figure, AC = XD, C is the midpoint of AB and D is the midpoint of XY. Using a Euclid s axiom, show that AB= XY. 13. In the given figure : if AB CD, EF CD and GED = 126 o. Find GEF and FGE. In the given figure Q > R. If QS and RS are bisectors of Q and R respectively, then show that SR > SQ. Page 2 of 6
14. Name the quadrant or axis in which the points ( -4,2), (4,0), (0,-3),(3,3) lie. SECTION C (3 marks) 15. When the polynomials kx 3 + 9x 2 + 4x -8 is divided by x+3 then a remainder 7 is obtained. Find the value of k. 16. Find 3 rational numbers between -2 and 5. Express 0.00323232... in the form where p and q are integers and q 0. 17. Locate on the number line. 18. If x - y = 4 and xy = 21, Find the value of x 3 y 3. The polynomials ax 3 + 3x 2 3 and 2x 3 5x +a leave the same remainder in each case when divided by (x-4). Find the value of a. 19. In the given figure X = 62 o, XYZ = 54 o, if YO and ZO are the bisects of XYZ and XZY respectively of XYZ. Find OZY and YOZ. In the given figure AB CD. Determine x. Page 3 of 6
20. In the figure below AB CD and CD EF, also EA AB. If BEF = 55 o, Find the value of x, y, and z. 21. Two lines AB and CD intersects at a point O, prove that AOC = BOD. 22. Find the area of a triangle, two sides of which are 40m and 24 m and the perimeter is 96m.? 23. Prove that ABC is an isosceles triangle if the perpendicular AP from A to BC bisects the base BC. 24. In a triangle ABC AB=AC and D, E are points on BC such that BE = CD, show that AD=AE. SECTION D (4 marks) 25. If a and b are rational numbers and =, then find the value of a and b. Page 4 of 6
If x= then find the value of (x + ) 2. 26. Simplify (i) ( 3 + 3) ( 2 + 2) (ii) 27. Factorise x 3-3x 2-9x -5. x 3 23 x 2 +142 x -120 28. Prove that the sum of the angles of a triangle is 180 o. 29. Plot the following points A(2,0), B(5,0) and C(5,3) in the Cartesian plane, join these points. Find the co-ordinate of the point D such that ABCD is a square. 30. AB and CD are respectively the smallest and the longest sides of a quadrilateral ABCD. Show that i) A > C ii) B > D 31. ABC and DBC are two isosceles triangle on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at p, Show that i) ABD ACD ii) ABP ACP Page 5 of 6
32. AB is a line segment and p is its midpoint. D and E are points on the same side AB such that BAD = ABE and EPA = DPB. Show that i) DAP EBP ii) AD = BE 33. For what value of a is 2x 3 +ax 2 +11x+a+3 exactly divisible by 2x-1. 34. Without actual division, prove that 2x 4 6x 3 + 3x 2 +3x-2 is exactly divisible by x 2 3x +2. Page 6 of 6