ICSE 9 Math Test ( Real Numbers )

Benjamin Academia ICSE9/19042011/T 1 ICSE 9 Maths Assessment ( Rational and Irrational Numbers ) MM 50 Time 1h Attempt all questions. Q 1. Following are few real numbers : 3 3 7 5 5,3, 1,1.5, ,0, 3, 9, 8, 5, 6 2 + − − ( a ) Select a set A of all integers from among the above real numbers. ( b ) Select a set B of whole numbers. ( c ) Select all natural numbers and represent them as a set C. ( d ) Select all irrational numbers and represent them as a set D [ 4 ] Q 2. Give definition of rational numbers. [ 2 ] Q 3. Identify the real numbers that have non-terminating non-repeating decimal expansions from among the following real numbers : [ 2 ] Q 4. What is the period of the following decimal expansion of a rational number ? 0.857142857142857……. [ 2 ] Q 5. Convert each of the following recurring decimal expansions into rational numbers , of the form pq : ( a ) 6.3 ( b ) 0.54 ( c ) 0.227272727….. [ 6 ] 3 3 5 11 237 5, 1.5, 3, , , 5, , 7 4 12 800 −Benjamin Academia ICSE9/19042011/T 2 Q 6. Prove that 3 is an irrational number. [ 3 ] Q 7 State whether true or false : ( a ) Sum of two irrational numbers is always rational. ( True /False ) ( b ) The difference of two irrationals is always irrational number. ( True /False ) ( c ) The product of two irrational numbers is a rational number. ( True /False ) ( d ) Sum of a rational and an irrational number is always rational number.(T/F) ( e ) Difference of a rational and irrational number is always irrational. (T/F ) [ 5 ] Q 8. Insert two rational and two irrational numbers between 5 and 8 . [ 4 ] Q 9. Compare following irrational numbers : ( a ) 3 7 and 6 . ( b ) 6 11 and 4 10 . [ 4 ] Q 10. State with reason which of the following ar surds and which are not : ( a ) 4 16 , ( b ) 4 125 , ( c ) 243 3 × [ 6 ] Q 11. Simplify each of the following by rationalising the denominator : ( a ) 2 5 2 + , ( a ) 3 5 3 5 +− [ 6 ] Q 12. Find the value of p and q if : 3 2 2 3 2 p q + = + − [ 4 ] Q 13. Write the least rationalising factor of : ( a ) 2 27 ( b ) 23 [ 2 ]