Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Kendriya Vidyalaya (O.F),Dumdum Mathematics Worksheet Prepared by:- Mrs. S. Basu Class:-IX-C POLYNOMIALS 1. If x y z 0 , then find the value of x 3 y 3 z 3 . 2. Find the value of ( x a)3 ( x b)3 ( x c)3 3( x a)( x b)( x c) when a b c 3x 3. Factorise : x 2 3 2 x 4 4. Factorise : 27 x 3 y 3 z 3 9 xyz 5. Evaluate : 105 x 95 6. Using factor theorem check whether g (x ) is factor of P (x ) P( x ) x 3 4 x 2 x 6 2 3 g ( x) x 3 3 7. Expand x y 8. Factorise : x 6 64 9. The volume of a cuboid is given by the algebraic expression Kx 2 6kx 8k . Find the possible expression for the dimensions of the cuboid. 10. Factorise : x 2 y xy x 11. Show that 5 is a zero of Polynominal 2 x 3 7 x 2 16 x 5 1 1 12. Expand : a b 1 3 2 3 13. Factorise : (2 x 3 y)3 (3 y 4 z )3 (4 z 2 x)3 14. Find the remainder when the polynominal x 3 3x 2 3x 1 is divided by x 1 . 15. If P( x) x3 1, P(1) P(1) , then find the value of 16. Find the value of K, if x 1is a factor of P (x ) & P( x) 3x 2 Kx 2 17. Find the values of m & n so that the polynomial x 3 mx2 13x n has x 1& x 3 as factors. 18. Find the value of (102)3 . 19. Using identity (a b)3 a3 b3 3ab(a b) derive the formula a 3 b3 (a b)(a 2 ab b 2 ) . 20. Expand : ( x y z ) 2 21. Check whether 7 3x is a factor of 3 x 2 7 x . 22. Factorise : 27 m3 343n3 23. Without actually calculating the cubes. Find the value of (26) 3 (15) 3 (11) 3 24. Find the zeros of the polynomial : x 3 3x 2 x 3 25. Factorise the following : 16 x 2 4 y 2 9 z 2 16 xy 12 yz 24 xz . Number System 2 1 & 4 3 1. Find a rational number between 2. Express each of the following decimals in the form p : q (a) 0. 3 (b) 1.2 7 (c) 0.12 3 (d) 4.32 3. Find two irrational number between 0.12 & 0.13. 4. Write three numbers whose decimals expansions are nonterminating non recurring. 5. Give an example of each of two irrational numbers whose – (a) difference is a rational number. (b) difference is an irrational number. (c) Product is a rational number. (d) Quotient is a rational number. 6. Represent 6& 7 on the number line. 7. Represent 35 & 8. Simplify each of the following (a) (625) 1 / 4 (b) 5 (32) 3 9. 1 1 2 Simplify the following : (625) 2 10. Simplify : 11. Simplify : 3a 4b 3 . 18a 3b 5 12. Simplify : 13. Evaluate : 255 260 297 218 14. 2 2 3 Evaluate : 3 5 5 15. Prove that, 9 10.5 on the real number line. 5 2 3 3 3a 7 b 6 18a 6 b 8 2 3/ 2 3 2 1 3 5 81 0 1 / 2 15 2 16. Express each of the following with rational denominator : (a) 17. 1 (b) 3 2 1 3 2 1 (c) 6 5 2 5 3 Rationales the denominator & simplify : (a) (c) 4 3 5 2 3 2 (b) 48 18 3 2 2 3 5 2 2 3 3 2 1 3 5 3 3 2 5 2 18. Simplify : 19. Simplify : 20. In the following determine rational number a & b : 21. Determine rational numbers a & b : 22. If x 15 4 , then find x . 23. Find the rationalization factor of 2 3 . 24. Write the value of 2 3 2 3 25. If a 2 & b 3 find the value of each of the following : 73 5 73 5 3 5 3 5 43 5 ab 5 43 5 1 x (a) a a b b (b) a b b a (c) a b 3 1 a b 3 3 1