Sample Paper - 2008
Class - X
Subject - Mathematics
1 .Let us think about the sequence of natural numbers. It starts from 1 and continue as 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ….
First we make these numbers as the groups of 2 as (1,2) (3,4) (5,6) (7,8) ( 9,10) (11,12)….The group sum is 3,7,11,15,19,23…. The group sum form an A P clearly. Its common difference is 22 .If we make the group by three we get common difference 32 .Continue this process by 4,5,6… . We get c d 42 , 52….
Question. EXPLAIN THIS PROPERTY? WHY DOES NUMBERS BEHAVE LIKE THIS?
(tenth standard students of H I B H
2.The interior angles of a polygon form an A P. The smallest angle is 120 degree. Common difference 5.
a) Find the number of sides of this polygon?
b) Write the interior angles as a sequence
c) While calculating the number of sides we get a quadratic equation.How can we decide solution?
d) Find the exterior angles
( assignment given to the students of H I B H S)
3 The sum of the first n terms of an A P and the sum of the next n terms of the same A P is differ by n2 d PROVE!
4 Prove that the sum of ( m + n) th term and (m─ n) th term is twice m th term
5 Can the base altitude and hypotenuse of a right triangle form an A P ? If possible find an example
( Group work given in H I B H S )
6. Appu put 1 rupee in the first day , 2 rupee in the second day 3 rupee in the third day, 4 rupee in the fourth day and so on in his money box.. After some days he decided to save 1 rupee less in the subsequent days. In the last day he put 1 rupee. The total amount in the box is in between 900 and 1000. Calculate total amount and days he continue this process
7 Look at the pattern given below
4 5 6
7 8 9 10
11 12 13 14 15
a) Count the numbers in each line and write it as sequence
b) Find the number in the end of 50 th line
c) Calculate the sum of all numbers in 50 lines
( chart made by H I B H S students)