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Summer Holiday Home-Work: Class 9
Mathematics
Summer Holiday Home-Work: Class 9
Mathematics
3
1. Check whether the polynomial p ( x ) = 4x + 4x 2 − x − 1 is a multiple of ( 2x + 1)
2. Evaluate: (i) 125
−2
3
3
+ 81 4 − 32
2
5
(ii) 8
−1
3
−1
− 81
2
+ 64
1
2
3. Express 0.36 as a fraction in simplest form.
4. Express 0.6 + 0.7 + 0.47 in the form
p
, where p and q are integers and q ≠ 0 .
q
5. Express 0.9999..... as a fraction in simplest form.
6. Find an irrational number between π and 10 .
7. Find the product of ( a − b − c ) and ( a 2 + b 2 + c 2 + ab + ac − bc )
(
)
8. Find the rationalizing factor of 1 − 3 3 .
9. Find the remainder when the polynomial f ( x ) = x 4 + 2x 3 + 3x 2 + x − 3 is divided by ( x + 2 ) .
10. Find the remainder when the polynomial q ( x ) = 4x 3 − 12x 2 + 14x − 3 is divided by ( 2x − 1)
11. Find the smallest rationalizing factor of
7
a 2 b 5 c 8 , where a, b, c are unequal prime numbers.
12. Find the value of a for which ( x + a ) is a factor of p ( x ) = x 3 + ax 2 − 2x + a + 6
1
13. If x = 3 + 8 , find the value of  x 2 + 2  .
x 

14. If a and b are rational numbers and
4+3 5
= a + b 5 , find the values of a and b.
4 −3 5
15. If a and b are rational numbers and
5− 6
= a − b 6 , find the values of a and b.
5+ 6
16. If
(
(
11 − 7
11 + 7
)(
)
2
11 − 7
)
= a + b 77 , find a and b.
17. If ( x 3 + ax 2 + bx + 6 ) has ( x − 2 ) as a factor and leaves a remainder 3 when divided by ( x − 3 ) , find the
values of a and b.
18. Without actual division, state whether
5
is terminating or non-terminating decimal. Justify your statement.
12
19. If x + 1 is factor of ( 2x 3 + ax 2 + 3x − 5 ) , find the value of a.
20. Represent 8.4 on the number line.
21. Express 0.245 as a fraction in simplest form.
Contd . . .
axisa
Ground Floor, E-17
Sector Market
Sector 5
BOKARO STEEL CITY
9905344655
Summer Holiday Home-Work: Class 9
Mathematics
Summer Holiday Home-Work: Class 9
Mathematics
1
1
22. If 49x 2 − b =  7 x + 
 7 x −  , find the value of b.
2 
2

23. If the polynomials ( 2x 3 + ax 2 + 3x − 5 ) and ( x 3 + x 2 − 2x + a ) leave the same remainder when divided by
( x − 2 ) , find the value of a.
24. Represent 7 on the number line.
25. Simplify:
 2 7 − 1 2 + 6 11  +  1 7 + 3 2 − 11 

 

2
2
3
 3

26. Simplify:
2
6 12 22   21 3 24
44 
+
+
−
 7−
+
 + 3 8 ⋅ 2 2 − 10 × 40
2 
2 3
8   27
3
3
27. Simplify:
1
1
1
1
1
−
+
−
+
3− 8
8− 7
7− 6
6− 5
5 −2
28. Simplify:
5
5
( )
2 ×3 − 6
8
8
1
2
5
4
.
29. The polynomial g ( x ) = x 3 + ax 2 − bx + 2 leaves the remainders 10 and 4 when divided by ( x − 2 ) and
( x + 1) respectively. Find the value of ( 3a − 2b ) .
30. The polynomial f ( x ) = x 4 − 2x 3 + 3x 2 − ax + b when divided by ( x − 1) and ( x + 1) leaves the remainders
5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f ( x ) is divided by ( x − 2 )
31. The polynomials ( ax 3 + 3x 2 − 3 ) and ( 2x 3 − 5x + a ) when divided by ( x − 4 ) leave the same remainder.
Find the value of a.
32. If x + 1 is a factor of the polynomial 2x 2 + kx , find the value of k .
33. Without actual division, prove that ( 2x 4 − 6 x 3 + 3x 2 + 3x − 2 ) is exactly divisible by ( x 2 − 3x + 2 )
34. Without actual division, state whether
48
is terminating or non-terminating decimal. Justify your statement.
375
Factorise the following:
35.
3x 3 − x 2 − 3x + 1
36.
9x 2 − 12x + 4
37.
ax 3 + x 2 − 2x + 4a − 9
38.
2x 2 − 7 x − 15
39.
2x 2 − 7 x − 15
Contd . . .
axisa
Ground Floor, E-17
Sector Market
Sector 5
BOKARO STEEL CITY
9905344655
Summer Holiday Home-Work: Class 9
Mathematics
Summer Holiday Home-Work: Class 9
Mathematics
Factorise the following:
40.
x 3 + x 2 − 4x − 4
41.
6 x2 +7 x − 3
42.
4x 2 + 20 x + 25
43.
9 y 2 − 66 yz + 121z 2
44.
9x 2 − 12x + 3
45.
2( x + y ) − 9( x + y ) − 5
46.
7 2x 2 − 10 x − 4 2
47.
2( x + y ) − 9( x + y ) − 5
48.
( 2x − 3 )2 − 8 x + 12
49.
a 2 + ab ( b + 1) + b 3
50.
108a 2 − 3 ( b − c )
51.
x − 64x 3
52.
1 2
x − 2x − 9
3
53.
6 x 2 + 17 x + 12
54.
6 − x − x2
55.
( 3a − 1)2 − 6a + 2
56.
x 2 − 21x + 108
57.
5 5 x 2 + 20 x + 3 5
58.
5 5 x 2 + 20 x + 3 5
59.
2x 2 + 3 3x + 3
60.
6 ( 2a + 3b ) − 8 ( 3b + 2a )
61.
6ab − b 2 + 12ac − 2bc
62.
x2 +
63.
a ( a − 1) − b ( b − 1)
64.
7 x 2 − 13 y 2
2
2
2
2
1
2
+ 2 − 2x −
2
x
x
Contd . . .
axisa
Ground Floor, E-17
Sector Market
Sector 5
BOKARO STEEL CITY
9905344655
Summer Holiday Home-Work: Class 9
Mathematics
Summer Holiday Home-Work: Class 9
Mathematics
Factorise the following:
65.
9x 2 − 22x + 8
66.
5
1
2x 2 − x +
6
12
67.
1 + 2ab − a 2 − b 2
68.
3x 2 + 11x + 6 3
69.
4 3x 2 + 5 x − 2 3
70.
5 ( 3x + y ) + 6 ( 3x + y ) − 8
71.
x 4 − 3x 2 + 2
72.
1 − 64a3
73.
16a 4 + 54a
74.
2a7 − 128a
75.
a3 − b3 − a + b
76.
(a
77.
8x 3 −
78.
216 x 3 +
79.
a3 − 8b3 + 64c 3 + 24abc
80.
( 5a − 7b )3 + ( 9c − 5a )3 + (7b − 9c )3
81.
4 x 2 + 9 y 2 + 16 z 2 + 12xy − 24 yz − 16 xz
82.
x6 + y6
83.
3a7 b − 81a 4 b 4
84.
8a3 + 125b3 − 64c 3 + 120abc
85.
86.
87.
88.
2
3
− 2 2b 3
)
1
27 y 3
1
125
8 − 27b3 − 343c 3 − 126bc
125 − 8 x 3 − 27 y 3 − 90 xy
2 2a 3 + 16 2b 3 + c 3 − 12abc
x 3 + y 3 − 12xy + 64
89.
x − 8 xy 3
90.
a3 + 0.008
axisa
Ground Floor, E-17
Sector Market
Sector 5
BOKARO STEEL CITY
9905344655