ICSE Board Practice

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ICSE Grade VIII - Real Numbers

Question 1

1.	Find the product of the rational numbers at the points labelled with letters D and E
	54 53 51 57 55

Question 2

2.	Rationalise the denominator of 1 ( − √ 6 − √ 3 )
	( − 1 3 √ 8 + 1 3 √ 3 ) ( − 1 3 √ 6 + 1 3 4 √ 3 ) ( − 1 3 √ 6 + 1 3 √ 3 ) ( − 1 3 √ 6 + 1 ) ( − 1 3 √ 4 + 1 3 √ 3 )

Question 3

3.	Rationalise the denominator of ( − 3 √ 3 + 5 √ 5 ) ( √ 2 + 2 √ 5 ) =
	( 1 6 √ 6 − 5 18 √ 10 − 1 3 4 √ 15 + 25 9 ) ( 1 6 √ 4 − 5 18 √ 10 − 1 3 √ 15 + 25 9 ) ( 1 6 √ 6 − 5 18 4 √ 10 − 1 3 √ 15 + 25 9 ) ( 1 6 √ 6 − 5 18 √ 10 − 1 3 √ 15 + 25 9 ) ( 1 6 √ 6 − 5 18 √ 10 − 1 3 √ 15 + 3 )

Question 4

4.	Which of the following are true?
	a) rational numbers are closed under subtraction b) rational numbers are closed under addition c) rational numbers are closed under division d) rational numbers are closed under multiplication
	{c,a} {c,d} {c,a,b} {a,b,d} {c,b}

Question 5

5.	Find the difference of the rational numbers at the points labelled with letters K and L
	-1 ( -1 5 ) ( -3 7 ) ( -3 5 )

Question 6

6.	Find the position of the rational number ( -50 9 ) on the number line
	E F Q I O

Question 7

7.	Find the rational number at the point labelled with letter F
	( -38 3 ) ( -38 7 ) ( -36 5 ) ( -38 5 ) -8

Question 8

8.	Find the sum of the rational numbers at the points labelled with letters F and G
	41 10 43 10 39 10 49 12 33 8

Question 9

9.	Rationalise the denominator of 1 ( − √ 2 − 9 √ 3 )
	( 1 241 √ 5 − 9 241 √ 3 ) ( 1 241 √ 2 − 9 241 4 √ 3 ) ( 1 241 √ 2 − 27 241 ) ( 1 241 √ 2 − 9 241 √ 3 ) ( 1 241 √ 1 2 − 9 241 √ 3 )

Question 10

10.	Find the rational number at the point labelled with letter S
	13 2 15 15 4 15 2 17 2

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