Summative Assessment-I Topper Sample Paper - 5 MATHEMATICS CLASS IX Time: 3 to 3 1 hours 2 Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory. 2. The question paper is divided into four sections Section A: 8 questions (1 mark each) Section B: 6 questions (2 marks each) Section C: 10 questions (3 marks each) Section D: 10 questions (4 marks each) 3. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks and 2 questions of four marks each. 4. Use of calculators is not allowed. SECTION –A Q.1 Simplified value of (25) (A) 25 1 3 x (5) (B) 3 1 3 is: (C) 1 Q2. The area of an equilateral triangle of side 14 cm is (A) 18 cm2 (B) 49 3 cm2 (C) 56 3 cm2 (D) 58 3 cm2 Q.3 In figure 1, value of x is : (D) 5 (A) 50° (B) 40° (C) 60° (D) 70° Q.4 The bisectors of the base angles of an isosceles triangle ABC, with AB=AC, meet at O. If ∠B = ∠C = 50°. What is the measure of angle O? (A)120o (B) 130o (C) 150o (D) 80o The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is: Q.5 (A)4 (B) 2 (C) 3 (D) 1 Q.6 p(x)= 2x4 – 3x3 + 2x2 + 2x -1 is divided by (x-2) and q(x)= 3x3 – 2x2 + x -1 is divided by (x-1). So, twice the sum of the remainders is: (A)21 (B) 35 (C) 54 (D) 40 Q.7 The coefficient of x2 in (7x-5) (5x2 - 3x +1) is (A) - 46 (B) 46 (C) 16 (D) -16 Q8. The triangular side walls of a fly-over have been used for advertisements. The sides of the walls are 122m, 22m and 120m. The advertisements yield an earning of Rs. 5000 per m2 per year. A company hired one of its walls for 3 months. The rent paid by the company is (A) Rs. 165000 (B) Rs. 1550000 (C) Rs. 16500000 (D) Rs. 1650000 SECTION - B Q.9 In figure 3, find the value of ∠QRP when QP||RT. Q.10. In figure 4, find the value of ∠ CDE. 3 Q.11 If x = 2 - 1 3 , then find the value of x − . x OR Find the simplified value of Q.12 Factorise : (12x2 – 7x+1). 1 5−2 3 + 1 5+2 3 . Q.13 In figure 5, if ABC and ABD are equilateral triangles then find the co-ordinates of C and D. Q14. Rationalise: b2 a2 + b2 + a SECTION – C 2 −1 . Q.15 Given Q.16 Using suitable identity evaluate (-32)3+ (18)3+ (14)3. 2 = 1.4142, find the value of 2 +1 OR Simplify: (a+b+c)2 + (a-b+c)2 + (a+b-c)2. Q.17 Factorise : 4 (x2+1)2+13(x2+1) -12. Q.18` Find the area of a triangular park, two sides of which are 18cm and 10cm and the perimeter is 42cm. Q.19 ABCD is a quadrilateral, where, BP and DQ are perpendiculars on diagonal AC and BP =DQ. If AC, BD intersects at R, prove that, AC bisects BD. Q.20 ABC is a triangle right angled at A. AL is drawn perpendicular to BC. Show that ∠BAL = ∠ACB. OR In fig.5, ABC is an isosceles triangle with AB = AC. D and E are points on BC such that BE = CD. Show that AD = AE. Q.21 In ∆ABC, ∠B=35°, ∠C=65° and bisector of ∠A meets BC at point D. Find ∠ADB and ∠ADC. Q.22 In figure 6, prove that l || m. OR In figure7, prove that AB||EF. Q23. Find x3 + y3 when x = 1 3−2 2 and y= 1 3+2 2 Q24. . Prove that the sum of all the interior angles of a pentagon is 540° SECTION – D Q.25. If x2-3x+2 is a factor of x4-ax2+b then find a and b. OR Factorize: ax2+ (4a2-3b) x-12ab. Q26. Ram, Shyam and Anil are three friends standing at three different positions. Ram and Anil are in opposite direction but are at equal distance from Shyam. Shyam is at origin and position of Ram is (0,8). If the abscissa of position of Anil is 0, then what are the coordinates of Anil’s position? 3 Q27. Factorise: 3 1 5 3 3 2 3 (2x + 5y ) + − y + z − z + x 27 3 4 4 3 Q28. In ∆ABC, ∠A - ∠B = 15°, ∠B - ∠C = 30° find ∠A, ∠B and ∠C. Q29. Find the value of: 1 3− 8 − 1 8− 7 + 1 7− 6 − 1 6− 5 + 1 5 −2 1 (x+y+z) [(x-y)2+(y-z)2+(z-x)2]. 2 Q.30 Prove that: x3+y3+z3-3xyz= Q.31 Represent Q.32 In figure 8, if ∠AEO= ∠CDO and AB=CB, prove that ∆ABD ≅ ∆CBE. 9.3 on number line. Q.33 In figure 9, ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD=AB. Show that ∠BCD is a right triangle. Q.34 In quadrilateral PQRS the diagonals intersect at O than prove that PQ+QR+RS+PS > PR+QS. OR In figure 10, S is any point in its interior of ∆PQR. Show that SQ+SR<PQ+PR.
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