KENDRIYA VIDYALAYA, ORDNANCE FACTORY, DUMDUM
Class : IX
Subject: Mathematics
Sample questions on NUMBER SYSTEM (chapter-1)
Sample question on Number system
1. Find three rational numbers between
(i) -1 and -2 (ii) 0.1 and 0.11 (iii) 57 and 67 (iv) 14 and 15
2. Represent geometrically the following numbers on number line :
(i) 4.5 (ii) 5.6 (iii) 8.1
3. Write three numbers whose decimal expressions are non-terminating, non-recurring between 3 and 4
4. Express the following in the form pq where p, q are integers and 970.
(i) 0.12 (ii) 0.888 …. (iii) 12.34 (iv) 0.134
5. If a = 2 + 3 then find the value of ( a - 1a )
6. Simplify : (i) 38+12
(ii) 481 - 83216 + 15532 + 225
(iii) 33 + 2 27 + 73
(iv) 45 - 320 +45
7. Rationalize the denominator :
(i) 2+ 32-3 (ii) 43+5248+ 18 (iii) 35+ 35- 3 (iv) 3+23-2
8. Find the values of a and b
7+ 57-5 - 7- 57+5 = a + 7115b
5+2 37+43 = a - 63
9. Simplify : (i) 13 +23+33 12 (ii) 64-13 + 6413 - 6423
10. If a= 3+ 52 then find a2+ 1a2
11. If x = 3+23-2 and y = 3-23+2 then find the value of x2+y2.
12. Simplify : (256)-(4-32 )
13. Find the value of 4(216)-23 + 1(256)-34 + 2(243)-15
14. Find the value of 2+32-3
15. If x + 15 = 4 , then x+1x=?
16. 32 . 42 . 1232 = ?
17. if a=2 , & b=3 find the value of each of the following
(i) aa+bb (ii) ab+ba (iii) ab
18. Identify following as irrational number
(i) 4 (ii) 100 (iii) 0.10110111011110 ….. (iv) 22.3333333 …….
19. If x =3-23+2 and y = 3+23-2 find the value of x2+y2+ xy
20. Prove that :
13-8 - 18-7 + 17-6 - 16-5+ 15-2 =5
21. 16-1552 = ?
22. Between two rational numbers how many rational numbers lie?
23. Express 38 and 8732 in decimal form.
24. Show that 0.5555 …. Can be expressed in the form of pq
25. Find the value of x2+1x2, if x = 2+3
KENDRIYA VIDYALAYA, ORDNANCE FACTORY, DUMDUM
Class: IX
Subject: Mathematics
Sample questions on POLYNOMIALS (chapter-2)
1. Find the degree of polynomials2.
2. If p(x) = x2-22 x + 1, then p(22) = ?
3. If p(x) = x+3, then p(x) +p (-x) =?
4. Find zero of the polynomial p(x) =2x+5 .
5. If x51 + 51 is divided by (x+1) , Find the remainder.
6. Find the value of 2492 - 2482
7. If xy + yx = -1 ( x,y ≠ 0), Find the value of x3- y3 .
8. If (a+b+c) =0 then a3+ b3+ c3 =?
9. If 49x2 - b = (7x + 12) (7x - 12), then find the value of b?
10. Find the co-efficient of x in the expansion of (x+3)3
11. Factorize : x2 +y – xy –x
12. Expand : a2- b3+13
13. Find the degree of polynomials :
4x4+ 0.x3+ 0.x2+ 5x +7
14. Find the degree of the zero polynomials.
15. If (x+1) is a factor of p(x) = 2x2+Kx , then find the value of K .
16. If the polynomial az3 +4z2 +3z – 4 and z3 -4z +a leave the same remainder when divided by (z-3) . Find the value of a.
17. If a, b, c are all non zero and a+b+c =0 , prove that a2bc + b2ca+c2ab = 3
18. If both (x-2) and (x- ½ ) are factors of px2 +5x + r , show that p=r .
19. Without actual division, prove that
2x4 - 5x3+ 2x2 - x + 2 is divisible by (x2-3x+2)
20. P(x) = x4- 2x3 +3x2 -ax +3a -7 when p(x) divided by (x+1) leaves remainder 19. Find the values of a
21. Simplify (2x-5y)3 – (2x+5y)3
22. Factorize: (x6 – 64).
23. Using factor theorem , check wheather g(x) is factor of p(x)
P(x) = x3 – 4 x2 +x + 6
g(x) = x-3
24. 0.105 x 95=?
25. Find (x-z)3 +(x-b) 3 + (x-c)3 – 3(x-a) (x-b)(x-c) when a +b +c =3x