CBSE Board Class 8 Math Sample Papers 2005

SAMPLE PAPER 2005
CLASS 8 MATHS

1.What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

2. What is the least number by which 12348must be divided to obtain a perfect square?

3. Find the cost of erecting a fence around a square field whose area is 9 hectares if fencing costs Rs 3.50 per metre

4. Find the least number of six digits which is a perfect square. Find the square root of this number.

5. Divide
(1) x3 - 1 by x - 1 (2) 7 +15x -13x2 +5x3 by 4 - 3x + x2

6. . x + y + z = 0, prove that x 3+ y3 + z3 = 3xyz. Or, Factorize : (a8 – b8)

7. If ( x2 + 1/X2) = 83 . Find X3- 1/X3

Or, , Factorize (i) 25a² – 4b² + 28bc – 49c² (ii) 5y² – 20y – 8z + 2yz


8. A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

9. Three prizes are to be distributed in a quiz contest. The value of the second prize is five sixths the value of the first prize and the value of the third prize is four – fifths that of the second prize. If the total value of three prizes is Rs. 150, find the value of each prize.

10. (a) Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the given triangle is 5 : 4, find the perimeter of the given triangle

(b) . The difference between two positive integers is 36. The quotient, when one integer is divided by the other is 4. Find the two integers.

11. Factorize

(1) x4 – (y + z)4 (2) y2 –7y +12 (3) 6xy – 4y + 6 – 9x  (4) a4 – 2a²b² + b4 (5) (x² – 2xy + y²) – z²

1. Factorization

(1) (a + b ) (1 – c ) – (b + c ) ( 1 – c ) (2) 1 6 a2 + 40 a b + 25 b2 (3) 4x2/9 - 2/3 x y + y2 /4

(4) 5x2yz - 5 x3y (5) 18 q2 + 338 p2 - 1 5 6 p q (6) -108 x2 - 363 y2 + 369 x y

2. Factorize

(1) 16- 4x2 (2) 20 x3 – 45 b4x (3) 4a2 – 9 b2 – c2 - 6bc

4) 25 ( x + 2y )2 - 36 (2x-5y)2 (5) a2 + 2 a b + b2 – c2 -2cd –d2

3. Factorize using a2+b2+c2 +2ab+2bc+2ca

(1) x2 + y2 + 25 z2 – 2 x y – 10 y z + 10 z x (2) 9x2 + 4y2 + 49z2 – 12 x y + 28 y z – 42 z x

(3) 4x6 + 9y6 + 16 x 6 + 12 x3 y3 + 16 x3 z3 + 24 y3z3 (4) a8 + 256 b8 + 96 a4b4-16a3b2 – 256a2b6 

12. The perimeter of a rectangular swimming pool is 154 metres. Its length is 2m more than twice its breadth. What are the length and breadth of the pool.

13. Sum of two numbers is 95. If one exceeds the other by 15 find the numbers.

14. Two numbers are in the ration 5:3. If they differ by 18, find these numbers

15. Three consecutive integers add up to 51. What are these integers?

16. The sum of three consecutive multiples of 8 is 888. Find the multiple.

17. Three consecutive integers are as such when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add up to 74. Find these numbers.

18. The number of boys and girls in a class is in 7:5 ratio. The number of boys is 8 more than that of girls. Fin their numbers.

19. The ages of Rahul and Haroon are in the ratio of 5:7. Four years from now sum of their ages will be 56 years. Find their present age.

9. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of their ages is 135. Find their ages.

20. Fifteen years from now Ravi’s age will be 4 times his current age. What is his current age.

21. Lakshmi is a cashier in a bank. She has notes of denominations of Rs. 100, 50 and 10 respectively. The ratio of number of these notes is 2:3:5 respectively. The total cash with Lakshmi is 4,00,000. How many notes of each denomination does she have?

22. I have total Rs 300 in coins of denominations of Rs.1, Rs.2, and Rs. 5.The number of Rs. 2 coins is 3 times the number of Rs. 5 coins. The total number of coins is 160. How many coins of each denomination are with me.

23. The organizers in an essay competition decide that winner will get a prize of Rs. 100 and a participation who doesn’t win gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find the number of winners if the total number of participants is 63.