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DELHI PUBLIC SCHOOL
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2009-2010
Class: VIII
Assignment No. 1
Subject: Mathematics
Rational Numbers :
1.
2.
3.
4.
5.
6.
− 40
−8
. If one of the number is
, Find the other.?
27
3
−2
− 26
What number should be subtracted from
to get
3
21
3
Represent − 4 on the number line?
5
5
Represent − 2 on the number line.
6
The product of two numbers is
1
−2
and at equal intervals.
2
5
3
3
Find three numbers between and
at equal intervals.
4
5
Find three numbers between
2 3 −1 5 − 7
, , ,
,
in the ascending order?
3 4 5 − 6 12
7.
Arrange the numbers
8.
Name the property used in simplifying
9.
Express the number in standard form 0.000000000085.
10.
Find the largest member of the Pythagorean triplet whose smallest member is 13.
3  5 12 
× + .
7  6 13 
Exponents :
1.
Find the value of x if i) 2x + 2x + 2x =192
2.
Evaluate the following :
1
1 34
  1

3
3  
 
ii) 5 8 + 27 
 
 

i) 3x4 –(8x2 )2 + 6(x2 )2 + ( -3x2)2
x3 3 x5
iii)
5
30
x 77
iv)
x3
v) Simplify
ii) 2x-3 = 1
43 × 16 −1 / 4 × 1
1
×
26
2− 7
3 −5 × 10 −5 × 125
5 − 7 × 6 −5
3
8
−3
4
3 . So that the product may be equal to 9 .
3.
By what number should we multiply
4.
Simplify: i)
5.
3 2
If x =   ×  
2 3
6.
Simplify :
7.
Simplify : (x3 – 2x2 +3x – 4) (x – 1) – (2x – 3) (x2 – x + 1) (Ans. x4 – 5x3 + 10 x2 – 12x +7)
7 6 − 252 − 294 + 6 7
2
(6
−1
ii)
(2
)(
5 −3 6 2 5 +3 6
)
−4
− 8 −1
find the value of x-2.
)
−1
(
+ 2 −1 − 3 −1
)
−1
(Ans. 30)
8.
Simplify (x + y)(2x + y) + (x + 2y)(x – y).
9.
Evaluate :
10.
198 × 198 − 102 × 102
96
1
 12

2
Evaluate: (64 ) ×  64 + 1




Square and Square roots:
1.
By what smallest number should the number 16562 be divided to get a perfect square?
2.
The product of two numbers is 1575 and their quotient is
3.
Find the greatest no of 6 digits which is a perfect square.
4.
What is the fraction which when multiplied by itself gives 227.798649?
5.
Find the square root of
6.
Find the square root of a) 120409
394
c) 23
729
2
upto three decimal places.
3
b) 363609. Ans. a) 347
23
Ans. c) 4
27
d) 150.0625.
Evaluate
2.8 correct upto two places of decimal. (3M)
8.
Evaluate
0.8 correct upto two places of decimal. (3M)
9.
Find the value of
15625 . Also find the value of
583
Find the square root of 42
1369
b) 603
d) 12.25
7.
10.
9
. Find the numbers.
7
156.25 + 1.5625
Cube and Cube roots :
Evaluate :
i)
3
iv)
2.
− 456533
3
ii)
3
10648
12167
iii)
3
27 + 3 0.008 + 3 0.064
121 × 3 297
Find the smallest number by which 326592 be multiplied so that the product is a
perfect cube. Also find the cube root of the product.
1.
Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the number. ?
2.
Divide the number 29160 by the smallest number so that the quotient is a perfect cube. Also
find the cube root of the quotient.
3.
The volume of a cubical box is 24.389m3. Find the length of the box.
4.
Find the cube root of the following numbers
i) 74.088
ii)
31
15
− 19683
iii)
343
24389
7.
Find the cube root of : a) 17576 b) – 571787 Ans: a) 12 b) 83
5.
Wasim brought two cricket bats for Rs 560 and Rs 240 respectively. He sells the first bat at a
gain of 15 % and the second one at a loss of 5 %. Find his gain or loss percent in the whole
transaction.
6.
A shopkeeper sold two fans for Rs 990each. On one he gains 10% and on the other he loses
10%. Calculate his gain or loss percent in the whole transaction.
7.
A man covers a distance of 227 km in 4 hours, partly by bus and partly by car. If the
average speeds of bus and car be 54 kmph and 60 kmph respectively, find the distance
traveled by the man by car. Ans (110 km).
8.
A man row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes
to row to a place and back. How far is the place? Ans (3 km)
9.
10.
Find the value of (71)3 by the short-cut method.
Find the value of (68)3 by the short-cut method.
Playing with numbers
1.
If 2a25 is a multiple of 9, where a is a digit, what is the value of a? Ans: 0,9
2.
If 21a8 is a multiple of 6, where a is a digit, what is the value of a? Ans: 1,4,7
3.
If 65y1 is a multiple of 9, Find the value of the digit y?
4.
Check the divisibility of 15287 by 3
5.
Check the divisibility of 1771561 by 11.
6.
Construct a 3,3 square with even numbers greater than 6
7.
Construct a 3,3 square with numbers multiple of 3 and the centre
number is 24.
8.
If 31x5 is a multiple of 3, where x ia a digit, Find the value of x ?
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