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