math formulas - the quicker way
DESCRIPTION
A Guide Book for those who want to Learn Maths in a easy and much Quicker way.TRANSCRIPT
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Mathematical Formulas
Easy, Precise, To the Point
Written By,
Anupam Gurung. www.facebook.com/anupamg7
For those who don’t hate Mathematics, but are forced to do so..!
Catch me On
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Contents
Basic Identities:
Factoring
Formulas:
Product Formulas:
Powers:
Roots:
Inequalities:
Compound Interest:
Probability
Formulas:
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1) Basic Identities:
i) Commutative of Addition.
a+b=b+a
ii) Associative of Addition.
(a+b)+c=a+(b+c)
iii) Multiplicative Inverse.
, a≠0
iv) Commutative of Multiplication.
v) Associative of Multiplication.
vi) Distributive Law.
vii) Definition of Division.
2) Factoring Formulas:
i) a2 - b
2 = (a+b) (a-b)
ii) a2+b
2 = (ab)
2 + 2ab
iii) a3 - b
3 = (a - b) (a
2+ab+b
2)
iv) a3+b
3 = (a+b) (a
2 - ab+b
2)
v) a4 - b
4 = (a
2 - b
2) (a
2+b
2) = (a - b) (a+b) (a
2+b
2)
vi) a5 - b
5 = (a - b) (a
4+a
3b+a
2b
2+ab
3+b
4)
vii) a5 + b
5 = (a+b) (a
4 - a
3b+a
2b
2 - ab
3+b
4)
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3) Product Formulas:
i) (a - b)2
= a2 – ab + b
2
ii) (a + b)2 = a
2 + ab + b
2
iii) (a - b)3 = a
3 – 3a
2b + 3ab
2 - b
3
iv) (a + b)3 = a
3+3a
2b + 3ab
2 + b
3
v) (a–b)4 = a
4 - 4a
3b
+ 6a
2b
2 - 4ab
3 + b
4
vi) (a + b)4 = a
4 + 4a
3b
+ 6a
2b
2 + 4ab
3 + b
4
vii) (a + b + c)2 = a
2 + b
2 + c
2 + 2ab + 2ac + 2bc
viii) (a+b)2 + (a - b)
2 = 2(a
2 + b
2)
4) Powers:
i) am*an = am+n
ii)
iii) (ab)m = ambm
iv)
v)
vi)
vii) a1 = 1
viii)
ix)
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5) Roots:
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x)
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6) Inequalities:
i) If a>b, then b<a.
ii) If a>b, then a – b>0 or b – a<0.
iii) If a>b, then a+c>b+c.
iv) If a>b, then a - c>b - c.
v) If a>b, and c>d, then a+c>b+d.
vi) If a>b, and c>d, then a - d>b – c.
vii) If a>b, and m>0, then ma>mb.
viii) If a>b, and m>0, then
ix) If a>b, and m<0, then ma<mb.
x) If a>b, and m<0, then
xi) If 0<a<b, and n<0, then an>b
n.
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7) Compound Interest:
Future Value: A.
Initial Deposit: C.
Annual Rate of Interest: r.
Number of Years Invested: t.
Number of times Compounded per Year: n.
i) General Compound Interest Formula.
ii) Simplified Compound Interest Formula.
iii) Continuous Compound Interest
If Interest is compounded continually
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8) Probability Formulas:
Events: A, B.
Probability: P.
Random Variables: X, Y, Z.
Value of Random Variables: x, y, z.
Expected Value of X: (Mu).
Any Positive Real Number: (Epsilon).
Standard Deviation: (Sigma).
Variance: (Sigma Square).
Density Functions: f(x), f(t).
i) Probability of an Event:
Where m is the number of possible positive outcomes, n is the
total number of possible outcomes.
ii) Range of Probability Values.
iii) Certain Event.
P(A) = 1.
iv) Impossible Event.
v) Complement.
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vi) Independent Events.
vii) Addition Rule for Independent Event.
viii) Multiplication Rule for Independent Event.
ix) General Addition Rule.
Where
is the union of events A and B,
is the intersection of events A and B.
x) Conditional Probability.
xi) Law of Total Probability.
Where Bi is a sequence of mutually exclusive events.
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