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} [t_{1} – 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 ax^{2} + bx + c = 0
9. Third term = (^{1}/_{2} coeficient of x)^{2}
10. Formula method
Formula method:

x

=

b ± √ b^{2} – 4ac

2a

11. ∆ = b^{2} – 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. x^{2} + ^{1}/_{x}^{2} = (x + ^{1}/_{x })^{2} – 2
18. x^{2} + ^{1}/_{x}^{2} = (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
a_{1}

≠

b_{1}

Unique solution
 
a_{2}

b_{2}
 
a_{1}

=

b_{1}

≠

c_{1}

No Solution
 
a_{2}

b_{2}

c_{2}
 
a_{1}

=

b_{1}

=

c_{1}

Infinitely Many Solutions.
 
a_{2}

b_{2}

c_{2}

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
29. Statistics – II
 
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