Higher Mathematics

Jai Ganesh · 2022-03-03 16:57:56

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

Jai Ganesh · 2022-03-03 17:24:21

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

Jai Ganesh · 2022-03-03 23:06:41

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.

Jai Ganesh · 2022-03-04 20:34:59

v) Powers or Exponents

Exponents

Laws of Exponents

Illustrations:

.

Jai Ganesh · 2022-03-05 01:40:21

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.