Download Mathematics - KV Dum Dum

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 :
73 5 73 5

3 5
3 5
43 5
 ab 5
43 5
1
x

(a) a a  b b (b) a b  b a (c) a b


3 1
 a b 3
3 1