Summative Assessment-I Topper Sample Paper - 3 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 1. π is: (A) a rational number (C) an irrational number (B) an integer (D) a whole number 2. If (x-1) is a factor of p (x) = x2+x+k, then value of k is: (A) 3 (B) 2 (C) -2 (D) 1 3. Zero of the polynomial p (x)= cx+d is: c (A) –d (B) −c (C) b 4. (D) − d c In figure 1, if OA= OB, OD= OC then ∆AOD ≅ ∆BOC by congruence rule: (A) SSS (B) ASA (C) SAS (D) RHS 5. If two supplementary angles are in the ratio 2:7, then the angles are: (A) 350, 1450 (B) 700, 1100 (C) 40O, 1400 (D) 500, 1300 6. The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is: (A) 1 7. (C) 4 (D) 3 A measure of the number of square units needed to cover the outside of a figure is called ______. (A) Volume 8. (B) 2 (B) Area (C) Surface area (D) Curved surface area The semi perimeter of a triangle with sides 32 cm, 30 cm and 30 cm is 46 cm. Its area is______. 2 2 (A) 106 6 cm (B) 204 7 cm 2 (C) 36 161 cm 2 (D) 32 161 cm SECTION- B 9. Simplify: (3+√3) (2+√2)2. 10. Evaluate (104)3 using suitable identity. 11. Expand: (2a – 3b + 5c) 2 . 12. In figure 3, X and Y are two points on equal sides AB and AC of an ∆ ABC such that AX= AY prove that XC= YB. OR In figure 4, ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that ∆ ABE ≅ ∆ ACF. 13. Name the quadrant in which the following point lie (-3, 2), (4, -3), (-5, -4) and (3, 2). 14. In figure 5, if ∠ POR and ∠ QOR from a linear pair and a-b = 800 then find the value of a and b. SECTION – C 15. 16. −3 −3 81 4 25 2 5 −3 Simplify ÷ . 16 2 9 Simplify the following by rationalizing the denominator. 3 2 −2 3 . 3 2 +2 3 OR 17. 2 −1 = a + b 2 , find the value of a and b. 2 +1 1 1 If x + . = 7 then find the value of x3 + x x3 If 18. OR 1 1 If x − = 3 then find the value of x3 − . x x3 If a2 + b2 + c2 = 250 and ab + bc + ca = 3 find a + b + c. 19. In figure 6, ∆ LMN is an isosceles triangle with LM = LN, and LP biscets ∠ NLQ, prove that LP MN . 20. In figure 7, find the value of x. 21. In figure 8, if AB CD then find the values of y. 22. How does Euclid’s fifth postulate imply the existence of parallel lines? Give a mathematical proof. 23. If AB || CD and CD || EF. If ∠BEF = 55°, find x, y and z. 24. A triangular park in a city has dimensions 30mx 26mx 28m. A gardnner has to plant grass inside the park at Rs. 1.50 per m2. Find the amount to be paid to the Gardner. OR Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area. SECTION – D 2 3 3 3 a − b2 + b2 − c2 + c2 − a2 . 25. Simplify 3 3 3 a − b + b − c + c − a ( ) ( ) ( ) 26. Find the value of: 1 3− 8 − 1 8− 7 + 1 7− 6 − 1 + 6− 5 1 5 −2 27. For what value of ‘a’ the polynomial 2x3 + ax2 + 11x + a + 3 is exactly divisible by 2x-1. 28. Factorise x3 − 23x2 + 142x − 120 . OR If (x-2) is a factor of the polynomial x3 + ax2 + b x + 6 and when divided by (x-3), it leaves remainder 3. Find the values of a and b. 29. Without actual division prove that x4 + 2x3 − 2x2 + 2x − 3 is exactly divisible by x2 + 2x − 3 . 30. Show that in a right angled triangle the hypotenuse is the longest side. 31. In figure 9, if AC= BC, ∠ DCA= ∠ ECB and ∠ DBC= ∠ EAC than prove that BD= AE. 32. In figure 10, if AD is the bisector of ∠ BAC then prove that: (i) AB>BD (ii) AC>CD 33. In figure 11, OP bisects ∠ AOC, OQ bisects ∠ BOC and OP ⊥ OQ . Show that points A, O and B are collinear. OR In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: (i) ∆AMC ≅ ∆BMD (ii) ∠DBC is a right angle. (iii) ∆DBC ≅ ∆ACB (iv) CM = 1 AB 2 34. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes. x 3 2 0 -1 y 2 -4 -5 5

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