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#1 2022-03-03 16:57:56

ganesh
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Registered: 2005-06-28
Posts: 38,058

Quantitative Aptitude and Higher Mathematics

Quantitative Aptitude

Essential Quantitative Aptitude 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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#2 2022-03-03 17:24:21

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#3 2022-03-03 23:06:41

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#4 2022-03-04 20:34:59

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

v) Powers or Exponents

Exponents

Laws of Exponents

Illustrations:

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#5 2022-03-05 01:40:21

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#6 2022-03-09 01:04:30

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Before that, an Introduction to Trigonometry:

Trigonometry Basics

These will help in learning what are

Inverse Sin, Cos, Tan.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#7 2022-04-28 00:24:57

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

A very important topic to be dealt with:

Order of Operations : BODMAS.

Order of Operations : PEMDAS.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#8 2022-04-28 01:09:21

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

This is another fundamental subject in Mathematics:

Terminating Decimal

like

etc.

and

Recurring Decimal

like

etc.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#9 2022-06-19 22:12:48

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#10 2022-06-22 13:25:50

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Rational Numbers and Irrational Numbers



Rational Numbers

Irrational Numbers.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#11 2022-06-23 14:31:37

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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. 


Terminating Decimal

Recurring Decimal

Irrational Number

Algebraic Number

Transcendental Number.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#12 2022-06-24 13:38:13

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Operation on Rational Numbers

Operation on Rational Numbers


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#13 2022-06-26 13:31:34

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Binomial Theorem

Binomial Theorem.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#14 2022-06-28 22:26:16

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Arithmetic and Geometric Progressions, and Harmonic Mean

Arithmetic Progression

Geometric Progressions

Harmonic Mean.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#15 2022-07-02 02:01:44

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#16 2022-07-03 01:59:17

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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.

Linear Equations

Simultaneous Equations

Systems of Linear Equations.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#17 2022-07-04 03:20:44

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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.

Quadratic Equations

Graphing Quadratic Equations.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#18 2022-07-05 02:39:27

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Similarity and Congruence: Triangles

Similar Triangles

Congruent Triangles.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#19 2022-07-06 14:17:18

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Types of Triangles and Quadrilaterals

Triangles

Right Angled Triangles

Quadrilaterals.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#20 2022-07-07 03:25:58

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#21 2022-07-08 20:06:13

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#22 2022-07-09 23:02:53

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#23 2022-07-10 13:53:54

ganesh
Administrator
Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Parallel and Perpendicular

Parallel and Perpendicular

Parallel and Perpendicular Lines.

Equation of a Straight Line.

Equation of a Straight Line.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#24 2022-07-11 01:15:44

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

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.

Introduction

Sumple Interest

Compound Interest


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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#25 2022-07-12 00:03:39

ganesh
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Registered: 2005-06-28
Posts: 38,058

Re: Quantitative Aptitude and Higher Mathematics

Unit Price, Sale Price, Profit, and Percentage Change

Unit Price

Sale Price

Profit

Percentage Change


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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