Mathematics Class Viii

Maths Holidays Homework Class VIII 1. Perform the following activities in a separate cardboards: a. Take 3 different sized match bones, write their dimensions and find their surface area. b. Take 6 cubes of the same size. Measure its l, b, h i. Find the value of 1 cube. ii. Paste 2 cubes together and find the volume of cuboid so formed. iii. Paste 3 cubes together in two different ways and compare their volume. Present in the form of a model. c. Tale 3 cardboard circles. Name them as A and B. draw a chord on both the circles. i. On a circle A, make 2 angles in the major segment from the chord and write then degree measure. ii. On a circle B, make 2 angels in the minor segment from the chord and write their degree measure. Write your observations. 2. For Roll Nos – 13 Make a chart showing angles between parallel lines and transversal line. For Roll Nos 14 – 25 Make a chart showing relationship between sides and their opposite angles of different type of triangles like equilateral, isosceles and scalene. For Roll Nos 26 – 38 Make a chart showing the derivation of identity ( a + b)2 For Roll Nos 39 – 50 Make a chart showing the derivation of identity ( a - b)2

Chapter 1 : Square & Square Roots. 1. Fine the smallest number by which the number 1100 must be multiplied (or divided) so that the product (or quotient) becomes a perfect square. Also, in each case, find the square root of the perfect require so obtained 2. Find the least number of 5 digits which is a perfect square.

3. A general arranges his solids in rows to form a perfect square. He finds that in doing so, 50 soldiers are left out. If the total no. of soldiers be 4811, find the number of soldiers in each row. 4. Find the square root of 1.7 and 0.9 correct to three places of decimal. 5. Find the square root by long division method: i. 477.4225 ii. 0.00008281 iii. 9998.001 6. Find : 7. Find:

8. The area of a square field is

2

. Calculate the length of the side of the

square. 9. What must be added to 452664 to make it a perfect square? 10. Find the length of a side of a square playground whose area is equal to a rectangular field of dimensions 72m and 338m. 11. Find the least number which must be subtracted from 18265 to make it a perfect square. Also find the square root of resulting number. 12. Find the greatest number of six digits which is a perfect square. Find the square root of this number. 13. Find the least number which must be subtracted from 194491 to make it perfect square. Find the perfect square and its square root. 14. An officer wants to arrange 202500 cadets in the form of a square. How many cadets were there in each row? 15. Simplify:

Chapter 2 : Cube & Cube Roots 1. Is 1728 a perfect cube? What is that number whose cube is 1728. 2. Multiply 137592 by the smallest number so that the product is a perfect cube. Also, find the cube root of the product 3. Find the smallest number of which 6561 must be divided so that the quotient is a perfect cube. Find the cube root of the quotient. 4. Fine : + 5. Evaluate :

+

-

6. The volume of cube is 9261000 m3 side of the cube. Also find surface area of one face of cube. 7. The volume are in the ratio 2:3:4. The sum of their cubes is 33957. Find the numbers.

÷

8. Evaluate :

+

X

9. Find the cube root of

i. ii.

592704

Exponents & Radicals 1. a.

[[(240)-1/2] -1/4]2 1/3

X 576

7/2

- 369/2 365/2

b. 81 c. 36

1/3

d. + + 5/2 e. (0.00064) X (0.004)5/4 f. (0.00064)-3/4 X (0.09)-3/4 2. Express the following in exponential form: i. ii. iii. iv. 3. Express the following in radical form: i. ii. iii.

(100)-3/5 (129)1/8

iv. 4. Evaluate: a. 4 x 81-1/2 (811/2 + 813/2) b. 27-2/3 X 813/4 (1/3)-3

5. Find the Value of X: i. 2x + 2x + 2x = 192 ii.

(-7/8)3/2 [ (-7/8)2/3 ÷ (-7/8)-1/3] = (-7/8)2+x

iii. 9x+2 = 240+9x iv. 5x + 5x + 5x = 375 v. 7x * 3x = 1764 vi. 3x – 3x-1 = 18 vii. (23x-1 + 10) ÷ 7 = 6 viii. 27x = 9/3x ix. 51/3*51/6 = 5x x. 5 4/3 ÷ 53x+1 = 25 xi. 23 + 2x = 24 xii. )x-3 =1 xiii. [ { (2/5)2}4]x+2 = [ { ( 2/5)-2}x-1]-3 6. Simplify: a. (4-1 + 8-1) ÷ 1 (3/2)-2 b. c.

(5-1 x 5-19 )2 X (-5/2)40 3-5 x 10-5 x 125 5-7 x 6-5

b. (1/2)40 c. 55