**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 2 ^{2} .If we make the group by three we get common difference 3^{2} .Continue this process by 4,5,6… . We get c d 4^{2} , 5^{2}….**

**Question. EXPLAIN THIS PROPERTY? WHY DOES NUMBERS BEHAVE LIKE THIS?**

** (tenth standard students of H I B H S Varapuzha completes this as their mathematics project 2008)**

**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 n ^{2} 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**

** 1**

** 2 3**

** 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)**