Page 276 - ICSE Math 8

Self-Testing Exercise 1

NUMBER SYSTEM

1. Simplify.

− 5 7 13  − 15  − 2  − 1
(a) + (b) +   (c) −  
3 4 4  3  3  5 
1 2
2. Insert three rational numbers between 3 and 2 .
2 5
3. Find the square root of 1.275 up to two decimal places.
4. Find the least number to be subtracted from 1,889 so that the difference is a perfect square. Also, find
the square root of the difference.
5. Find the smallest number by which 3,528 should be multiplied to get a perfect cube.

 − −  2 − − 5  2  0 
  7  ×  5   7   
÷
6. Find the value of        .
 5   7    5       
  
7. 361 children participated in a sports competition. They were divided in groups in such a way that the
number of groups formed was equal to the number of children in each group. How many children were
there in each group?
8. If a number 31x3 is a multiple of 9, where x is a digit, then find the value of x.
9. Find X in the addition.

4 8 X
+ 2 X 5

7 1 8

10. Find the cardinal number of the following sets.
2
(a) P = {x : x ∈ N, 3 < x < 7} (b) Q = {a : a ∈ N, a < 38} (c) R = {x : x is a factor of 24}
11. Find the number of proper subsets of the following sets.
(a) {a, e} (b) {2, 3, 5} (c) {1, 9, 25, 49}
12. If A = {x : x is a letter of the word DICTIONARY} and B = {y : y is a letter of the word APPRECIATE},
find:
(a) A ∩ B (b) A – B (c) B – A (d) A ∪ B
13. If U = {x : x is an integer, –6 ≤ x ≤ 6}, A = {–6, –4, –2, 2, 4} and B = {–4, –3, –2, 4, 5}, then find the
following set.
(a) Aꞌ (b) (A ∩ B)ꞌ (c) Aꞌ ∩ Bꞌ (d) (A ∪ B)ꞌ
14. Find x when 6 x + 2 = (216) 2x – 1 .
15. Simplify the following.

(a) 35 2 7+ (b) 6 + ( 13 4 − )( 13 )
35 2 7−

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