PODAR INTERNATIONAL SCHOOL (CBSE) Practice sheet Std: IX

Chapter: 1 Number Systems

Subject: Mathematics

Q. no. Q. I 1. 2. 3.

Q. II 1. 2.

Year Solve the following: (1 mark each) p , where p and q are integers and q ≠ 0 . q 5 Write the decimal expansion of . 16

Express 0.550 in the form

1

 9 2 Find the value of   . 4 Solve the following: (2 marks each) Rationalize the denominator: Simplify:

(

5−2

(

)

2

)

3.

Simplify:

4.

Simplify: 3 + 3 2 + 2

5.

3

(

[2010]

1 7− 6

15 − 60

)(

[2010]

)

[2010]

2

Show that 0.235 can be expressed in the form

p , where p and q are integers and q

[2010, 2011]

q ≠ 0. 6.

7. 8. 9.

Show that 2.218 can be expressed in the form

p , where p and q are integers and q

q ≠ 0. Find two rational numbers between 3.5 and 3.6. 1 2 and . 2 3 3 5 Find four rational numbers between and . 7 7

Find six rational numbers between

10. Find two irrational numbers between 4.56 and 5.1 .

[2011] [2010]

11.

4 and check whether the decimal expansion is 7 terminating or non-terminating recurring. 12. If 7 x = 1 , then find the decimal expansion of x . 13. Find two irrational numbers between 0.5 and 0.55. 14. 1 Taking 2 = 1.414 and π = 3.141 , evaluate + π upto three decimal places. 2 15. Simplify: 3 3 40 − 4 3 320 − 3 5

Write the decimal expansion of

(

) (

16. Simplify the product: 4 3 + 3 2 × 4 3 − 3 2

)

[2013]

17. Simplify: 4 16 − 6 3 343 + 18 5 243 − 196 18. p Express 0.6 in the form , where p and q are integers and q ≠ 0 . q Q. III Solve the following: (3 marks each)

(

)(

)

1.

Simplify 4 + 5 4 − 5 and identify whether the number is rational or irrational.

2.

Locate

3.

Represent 5 and 7 on the number line. 3 2 If + =+ a 5 b 3 , then find the values of a and b . 4 5− 3 4 5+ 3

4. 5.

3 on a real number line.

2 2 8 − + 5+2 10 − 2 2 2 1 Rationalize the denominator: 2 7 +3 3 Solve the following: (4 marks each)

[2010, 2012, 2013] [2010] [2013] [2013]

Simplify:

6. Q. IV 1. 2. 3.

Rationalize the denominator of

1 . 7 + 6 − 13

Represent 3.5 on the real number line. Find the values of a and b if

7+3 5 7−3 5 − = a+ 5b 3+ 5 3− 5 4. Find a and b , if

2 5+ 3 2 5− 3 + = a + 15 b . 2 5− 3 2 5+ 3

5. Find the values of a and b in

b 3− 5 = a 5− . 11 3+ 2 5

[2013]

[2012] [2012] [2010, 2011] [2013] [2012]

6.

[2013] 2 −1 is an irrational number”. Radha 2 +1 replied, “You are wrong.” And further claimed, “If there is a number ‘ x ’ such that x3 is an irrational number, then x5 is also irrational.” Geeta said, “No, Radha, you are wrong.” Radha took some time and after verification accepted her mistakes and thanked Geeta for pointing out these mistakes. (i) Justify both the statements. (ii) What value is depicted from this question? 7. Two classmates Salma and Anil simplified two different expressions during the [2013] revision hour and explained to each other their simplifications. Salma explains 2 simplification of and Anil explains simplification of 28 + 98 + 147 . 5+ 3 Write both the simplifications. What value does it depict? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Geeta told her classmates Radha that “