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**ganesh****Administrator**- Registered: 2005-06-28
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**Higher Mathematics**

**Mathematics for Competitive Examinations**

1. Fundamentals

2. Number System

3. Average

4. Mixture & Alligation

5. Percentage

6. Profit, Loss and Discount

7. Interest

8. Ratio, Proportion, Variation and Partnership

9. Time and Work

10. Time, Speed, and Distance

11. Progressions

12. Linear Equations

13. Functions

14. Quadratic and Cubic Equations

15. Inequalities

16. Logarithms

17. Set Theory.

18. Geometry

19. Mensuration

20. Coordinate Geometry

21. Permutations and Combinations

22. Probability

23. Trigonometry and Its Applications

24. Data Interpretation

25. Data Sufficiency

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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1. Fundamentals

i) BODMAS Rule

The acronym BODMAS means

B : Brackets

O : Orders

D : Division

M : Multiplication

A : Addition

S : Subtraction

ii) Brackets

Brackets are used for grouping of things or entities. The various types of Brackets are

a) '_' is known as line (or bar) bracket or vinculum

b) () is known as Parenthesis, common bracket or small bracket

c) {} is known as curly bracket, brace or middle bracket

d) [] or big bracket (i.e., rectangular bracket)

The order of eliminating is

i) line bracket

ii) small bracket (i.e., common bracket)

iii) middle bracket (i.e., curly bracket)

iv) big bracket (i.e., rectangular bracket)

Illustration : Calculate

See: Order of Operations

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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iii) Factorial

The product of n consecutive natural numbers (or positive integers) from 1 to n is called the factorial n. Factorial n is denoted by n!.

n! = 1 x 2 x 3 x .... x (n - 2) x (n - 1) x n

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

5! = 5 x 4 x 3 x 2 x 1 = 120

4! = 4 x 3 x 2 x 1 = 24

3! = 3 x 2 x 1 = 6

2! = 2 x 1 = 2

1! = 1

0! = 1

iv) Roman Numbers

In this system, there are basically seven symbols used to represent the whole Roman Number system. The sysbols and their respected values are given below:

I - 1,

V - 5,

X - 10,

L - 50,

C - 100,

D - 500,

M - 1000.

In general, the symbols in the numeral system read from left to right, starting with the symbol representing the largest value; the same number cannot occur continuously more that three times; the largest value of the numeral is the sum of the values of the symbols.

For example, LXVII = 50 + 10 + 5 + 1 + 1 = 67.

MCDLXIV = 1000 + (500 - 100) + 50 + 10 + (5 - 1) = 1000 + 400 + 60 + 4 = 1464.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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iv) Algebraic Identities

From fundamentals to higher levels

From the above, you can see you can from the basics to the next levels, in these topics:

* The Basics

* Exponents

* Simplifying

* Factoring

* Logarithms

* Polynomials

* Linear Equations

* Quadratic Equations

* Solving Word Questions

* Functions

* Sequences and Series

Examples will follow.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Before that, an Introduction to Trigonometry:

These will help in learning what are

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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This is another fundamental subject in Mathematics:

like

etc.and

like

etc.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Laws of Exponents**

**The Important Laws of Exponents are**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Termination decimals, recurring decimals, and Irrational numbers**

A terminating decimal is like 0.25, 0.65, 0.775 etc,

A recurring decimal is like 0.16666....., 0.3333....., 0.66666.... etc.

An irrational number is neither terminating nor recurring. For example square root of 2, square root of 3 etc.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Operation on Rational Numbers**

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**ganesh****Administrator**- Registered: 2005-06-28
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**Binomial Theorem**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Arithmetic and Geometric Progressions, and Harmonic Mean**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Logarithms**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Simultaneous Equations**

Look at the two linear equations:

x + 2y = 7

2x + 3y = 12.

This can be be easily solved by trial and success, x = 3 and y = 2.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Quadratic Equations**

The solution of a Quadratic Equation is given by

where the quadratic equation is given by

Sum of the roots is -b/a and product of the roots is c/a.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 41,268

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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**Polygons**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 41,268

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 41,268

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 41,268

**Simple and Compound Interest**

Simple Interest = Prt where

P is Principal,

r is rate of interest,

and t is time (month/quarter/half year, or year).

Compound Interest is calculated thus:

where A is Amount,

P is Principal,

r is rate of interest,

and t is time.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**ganesh****Administrator**- Registered: 2005-06-28
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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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