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.