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1. Which of the following rational numbers have terminating decimal representation?

[1] 3/5 [2] 3/13 [3] 40/27 [4] 23/7 2.

2.How many rational numbers can be found between two distinct rational numbers?

(i)Two (ii) Ten (iii) Zero (iv) Infinite

3. The value of (2+√3 )( 2-√3 ) is

(i)1 (ii)-1 (iii) 2 (iv) none of these

4. (27)^{-2/3} is equal to _____.

(i) 9 (ii) 1/9 (iii) 3 (iv) none of these

5. Simplify: ^{3}√2 x ^{4}√ 3 .

6. Find the two rational numbers between ½ and 1/3

7. Find two irrational numbers between 2 and 3.

8. Multiply √5 by 6 √2 .

9. Express 0.8888… in the form p/q

10. Simply by rationalizing denominator,( 7 + 3√5)** / **(7- 3√5).

11. Simplify { ( 625^{-1/2})^{-1/4}}^{2} .

12 Visualize 3.76 on the line using successive magnification

13. If x = 1 - √2 , find the value of ( x – 1/x)^{3 }.

14. Divide 12√15 by 4√3.

15. Represent in rational form 1. 23 .

16. Simplify by combining like terms, 2^{3}√40 + 3 ^{3}√625 - 4^{3}√320 .

17.If x = 1/ (2- √3) , find the value of x^{3} – 2 x^{2} – 7x + 5.

18. Prove that , 1/( 1+ √2) + 1/ (√2 + √3 ) + 1/ (√3 + √4) + ……… + 1/ (√8 +√9 ) = 2.

20. Find the value of x if ( 2/3 )^{x} (3/2)^{2x }= 81/16 .

21. If a = 2 and b= 3 , find the values of ( a^{b} + b^{a} ) ^{– 1} .

22. Simplify , ^{4}√ ^{3}√ x^{2} .

23. Simplify , [ (25)^{3/2} x (243)^{3/5}] **/** [ ( 16)^{5/4} x ( 8) ^{4/3} ] .

24 Which of the expressions are polynomials,
- x
^{3} – 5x + 2 . (b) y^{2} + √2 y -√5. (c) z + 5/z + 1 . (d) 2√x + 7 .

25. Give the coefficient of x in √3 - 2√2x + 4 x^{2} .

26. Verify that 4 is a zero of the polynomial p(x) = x – 4.

27. Find the remainder when f(x) = 12x^{3} – 13x^{2} – 5x + 7 is divided by ( 3x + 2 ).

28. If the polynomial ( 2x^{3} + ax^{2} + 3x – 5 ) and ( x^{3} ^{ }+ x^{2} – 2x + a ) leave the same reminder when divided by ( x-2 ), find the value of a . Also find the remainder in each case.

29. Show that ( x- 3 ) is a factor of the polynomial , f(x) = x^{3} ^{ }+x^{2} ^{ }-17x + 15.

30. find the value of k for which (x-4 ) is a factor of ( 2x^{3}-3x^{2} – 18 x + k).

31. Factorise , (a) x^{2} + 9x + 18 . (b) 6x^{2 }+ 7x + 3.

32. Factorise x^{3} – 6x^{2} + 3x + 10 .

33. Factorise 4√3 x^{2} + 5x - 2√3.

34. Factorise 5(3x +y)^{2} + 6( 4x +y) – 8 .

35. Expand , ( 3a – 5b – c )^{2} .

36. Evaluate (997 )^{2} .

37. Factorise 2x^{2} + y^{2} + 8z^{2} - 2√2 xy + 4√2 yz – 8 xz.

38. Factorise , 8a^{3} – 27 b^{3}.

39. Factorise ( 2x + 3y )^{3} – (2x – 3y)^{3}.

40. Factorise , a^{3} – 8b^{3} – 64c^{3} + 24 abc.

41. Factorize (p-q)^{3} + (q-r)^{3} + (r - p)^{3} .

42. If x^{2} + 1/x^{2} = 18 , find the value of x^{3} + 1/x^{3 }.

43. If x – y = 5 and xy = -6 , find the value of x^{3} – y^{3}.

44. Without actual calculating the cubes evaluate , 28^{3} + ( - 15 )^{3} + ( - 13 )^{3}.

45. What are the possible expression for the dimensions of a cuboid whose volume is

12ky^{2} + 8ky – 20 k ?

46. If 3x +y+z = 0 , show that 27 x^{3} + y^{3} + z^{3} = 9xyz .

47. Factorise , 2 x^{2} - x + 1/8 .

48. Factorise x^{6} – y^{6}.

49. The sum of 0. 3 and 0. 4 is (a) 7/11 (b) 7/10 (c) 7/9 (d) 11/ 15 .

50. Represent √9.3 on the real number line.

^{3}– 5x + 2 . (b) y^{2}+ √2 y -√5. (c) z + 5/z + 1 . (d) 2√x + 7 .