math formulas - the quicker way

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1 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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A Guide Book for those who want to Learn Maths in a easy and much Quicker way.

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Page 1: Math Formulas - The Quicker Way

1

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

Page 2: Math Formulas - The Quicker Way

2

Contents

Basic Identities:

Factoring

Formulas:

Product Formulas:

Powers:

Roots:

Inequalities:

Compound Interest:

Probability

Formulas:

Page 3: Math Formulas - The Quicker Way

3

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)

Page 4: Math Formulas - The Quicker Way

4

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)

Page 5: Math Formulas - The Quicker Way

5

5) Roots:

i)

ii)

iii)

iv)

v)

vi)

vii)

viii)

ix)

x)

Page 6: Math Formulas - The Quicker Way

6

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.

Page 7: Math Formulas - The Quicker Way

7

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

Page 8: Math Formulas - The Quicker Way

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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.

Page 9: Math Formulas - The Quicker Way

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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.

END