Sir your explanation is very good.
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ALGEBRA FORMULA FOR BOARD EXAM REFERENCE

ALGEBRA FORMULAE FOR BOARD EXAM REFERENCE

1. t­n = Sn – Sn – 1

2.  tn = a + (n – 1) d

3. Sn = n/2 [2a + (n – 1) d]

4. Sn = n/2 [t1 – tn]

5. Three consecutive terms as a – d, a, a + d

6. Four consecutive terms as a – 3d, a – d, a + d, a + 3d

7. Five consecutive terms as a – 2d, a – d, a, a + d, a + 2d.

8. General form of quadratic equation is ax2 + bx + c = 0

9. Third term = (1/2 coeficient of x)2

10. Formula method

Formula method:

x

=

-b ± √ b2 – 4ac

2a

11. ∆ = b2 – 4ac

12. If ∆ > 0, then roots are real and unequal

13. If ∆ = 0, then roots are real and equal.

14. If ∆ < 0 , then roots are not real.

15. α + β = - b /a

16. α β = c/a

17. x2 + 1/x2 = (x + 1/x )2 – 2

18. x2 + 1/x2 = (x - 1/x )2 + 2

19. α 2  + β 2 = (α + β )2 – 2α β

20. α 2 + β 2 = (α - β )2 + 2α β

21. α 3 + β 3 = (α + β )3 – 3α β (α +β )

22. α 3 - β 3 = (α - β )3 + 3α β (α - β)

23. (α - β )2 = (α + β )2 – 4α β

24. By Cramer's Rule:    x = Dx / D                &         y = Dy / D

25. Simultaneous Equations

a1

b1

Unique solution

a2

b2

a1

=

b1

c1

No Solution

a2

b2

c2

a1

=

b1

=

c1

Infinitely Many Solutions.

a2

b2

c2

26. Sample Space: The set of all possible outcomes of a random experiment is called the sample space. It is denoted by 'S' .

27. Probability

P(A)

=

n(A)

n(S)

28. Statistics – I

Mean by Direct Method

=

Σ fx

Σ f

Mean by Assumed mean Method

or Shift of Origin Method

x̅

=

A + d̅

Mean by Step Deviation Method

or Shift or origin and scale method

=

A + hu̅

Median

L

+

(N/2– cf)h/f

Mode

L

+

fm – f1

h

2fm– f1– f2

Mean – Mode = 3(Mean – Median

29. Statistics – II

Central angle (θ )

=

Value of the component

×

360

Total Value of all the components

ECONOMICS PAPER ONE

ECONOMICS PAPER TWO

ECONOMICS PAPER THREE