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KENDRIYA VIDYALAYA, HVF AVADI (2014-15) Class IX Assignment 1: Number system Section A 1. The product of two irrational number is always (a) a rational number (b) an irrational number (c) an integer (d) a non-zero real number 2. Which of the following is irrational? (a) 4 9 3. Value of (a) 12 (b) 4 1 9 (c) 3 (b) 5. 13 10 1 81 (81) 2 is equal to 1 3 (c) 9 4. The value of 1.333…. in the form (a) (d) 7 (b) 1333 1000 is equal to 9 8 1 (a) (3 2 2 ) 2 (d) p , where p and q are integers and q q (c) (b) 1 81 4 3 (d) none of these 1 (d) 3 2 2 (c) 3-2 2 3 2 2 6. The decimal expansion of the number (a) A finite decimal (c) non-terminating recurring 0, is 2 is (b) 1.41421 (d) non-terminating non-recurring 1 7. The number obtained on rationalizing the denominator of is 7 2 (a) 7 2 45 (b) 7 2 3 (c) 7 2 5 (d) 7 2 3 Section B 8. Find seven different rational numbers between 9. Simplify: 10. Simplify: 1 1 and 2 3 3 6 5 6 3 ( 5 2 3 ) 2 17 15 3 11. Simplify: (343) 2 4 81 1 38 in recurring decimal form and hence write in recurring decimal form 7 7 1 69 13. Express the rational number in recurring decimal form and hence write in recurring 13 13 decimal form p 14. Express the rational number 0. 45 in the form of , where p and q are natural numbers q 12. Express 15. Express the rational number 0.1 6 in the form of p , where p and q are natural numbers q 5 9 and 7 11 1 1 17. Find three different irrational numbers between and 27 18 16. Find three different irrational numbers between 18. Visualize the representation of 1. 3 on the number line upto 4 decimal places, i.e., upto 1.3333. further locate 1.33333. 19. Express √ geometrically and represent it on number line. Assignment 2: Polynomials Section A 1. Find the value of the polynomial 7 – 2x + 3x2 at (a) x = 0 (b) x = 2 (c) x = -2 2. Find p(0), p(1), p(-1), p(3) and p(-3) for the following polynomials: (a) p(x) = x3 – x + 27 (b) p(y) = 3y2 + 4y – 5 (c) p(u) = (u + 2)(u + 3) (d) p(t) = 3t4 + 1 3. Find the value of each of the following polynomials at the indicated value of variables 3 1 1 ;x= ,(b) p(y) = 5y2 + 3; y = 0, 3. 2 2 2 2 2 (c) p(u) = 3u + 2 ; u = π, 2π (d) q(t) = t2 – 3at + 5a2; t = -a, a 1 2 (e) q(s) = 7s2 + 3; s = , 7 7 4. Verify whether the indicated values of variables are zeros of the polynomials corresponding to them: 1 1 (a) p(x) = 2x + 1; x = , (b) p(y) = 5y2 + 4y – 9; y = 1, 2 2 2 1 3 (c) q(t) = 3 at2 – 5a2t + 2a3; t = a, -a (d) q(s) = (3s-1)(2s-3); s = , 3 2 1 1 (e) r(u) = (u+1)(2u-1)(3u-1); u = 1, , 2 3 (a) p(x) = 5x - Section B 5. Find the reminder when 2x3 + 3x2 – 5x + 7 is divided by (a) x + 1 (b) x – 2 (c) 2x – 1 (d) 2x + 1 u 6. Find the reminder when 5u3 – 7u2 + 13 is divided by +1 2 3 2 2 3 7. Find the reminder when t + 3kt – k t + 2k is divided by (t-2k) 8. Examine whether 5 + 3x is a factor of the polynomial 3x2 + 11x + 10 9. Examine whether t-2 is a factor of polynomial 2t3 – t2 - 16t + 20 10. Find the value of k so that x-2 be a factor of polynomial 3x3 + 4x2 – 5x – 5k 11. Find the value of a so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + a Project 1. Prepare a mathematical model (working/PPT). or 2. Prepare an album on Golden Ratio and its usage. or 3. History of the number π. Investigations of various historical aspects of the number π : i. Knowledge about π in various ancient civilizations. ii. Write its approximate value up to 100 places. iii. Relation of circle with π.