CBSE Important Questions

Q. 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 S  Varapuzha  completes this as their mathematics project 2008)

Q. 2. The interior angles  of a polygon form an A P. The smallest angle is 120  degree. Common   difference 5.

1. Find the number of sides of this polygon?
2. Write the interior angles as a sequence
3. While calculating the number of sides  we get a quadratic equation.How  can we decide solution? 
4. Find the exterior angles.

Q. 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 n²d PROVE!

Q. 4. Prove that  the sum  of  ( m + n) ^th term  and (m─ n) ^th term is twice  m th  term

Q. 5. Can the base altitude  and hypotenuse of a right triangle form an A P  ? If possible find an example

Q. 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.

Q. 7. Look at the pattern given below
  1
  2  3
  4  5  6
  7   8  9  10
  11   12   13    14   15
  …………………………
  ………………………………..
  …………………………………….

1. Count the numbers in each line and write it as sequence
2. Find the number in the end of 50^th line
3. Calculate the sum of all numbers in 50 lines

Q. 8. Look at the pattern
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16

1. Make five more steps in this pattern
2. Count the number of numbers in each line and write it as a sequence
3. How many numbers are there in the 50 th line of this pattern?
4. Which number is in the end of the 50 th line of this pattern?
5. Which is the first number of the 50 th line?
6. Calculate the sum of all numbers up to the end of 50 lines

Q. 9. Appu put 1 rupee in the first day,2 rupee in the second day, 3 rupee in the third day and so on . After some days he decided to put one rupee less in the subsequent days. At last he put 1 rupee . He opened the box and found the amount which was in between 900 and 1000.

1. How many days he continue the saving?
2. calculate the exact amount in the box

Q. 10. Prove that the sum of the first n terms and the sum of the next n terms of an A P is differ by n² d where d is the common difference

Q. 11. x,y,z are in A P. Also x ─ y = k( z ─ x) find the value of k