ALGEBRA FORMULA FOR BOARD EXAM REFERENCE

ALGEBRA FORMULAE FOR BOARD EXAM REFERENCE

1. t­_n = S_n – S_{n – 1}

2.  t_n = a + (n – 1) d

3. S_n = ⁿ/₂ [2a + (n – 1) d]

4. S_n = ⁿ/₂ [t₁ – t_n]

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 = D_x / D                &         y = D_y / 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	x̅	=	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	x̅	=	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