All Important Basic Math formulas List
Mathematics is the most important for all the students, those who are studying in the classes of any schools board like CBSE, ICSE, Other STATE BOARDS(BSE ODISHA)Basic mathematics is common for all. Mathematics subjects at the school levels seem to be easy, in primary to class 5th.because the design of math course where the kids or student use the play and learn methods like adding two numbers, Multiplication, simplification, division, remembering the tables, etc. The actual journey of maths starts from (Class 6,7,8,9,10).
Most of the students or children keep interested in Mathematics and some students or kids facing problems in remembering the Math formulas. here we try to avoid the fear of maths and keep focus to create an interest in a simple way to remembering the Maths formulas with simple examples. the Content present here is from Basic Maths to Advance mathematics. also, discuss here some Important competitive exams maths for the different exams.
List of All Maths formulas topics (Basic to advance )
We All use simple maths, in our day today life to calculate common things like Counting the numbers, stars in the sky, buying and sell essential goods, adding and substracting any items.
For all this purpose we all use the General Mathematics and its rule.
- Addition
- Subtraction
- Division
- Multiplication
Most important topics which always use to derive the Basic concepts of Maths uses to in the industry, Banking systems, Computers, Building, and infrastructure. Measurement of the length of matter, calculating the area, radius of any shape of an object, etc.
- Number system
- Algebra
- Set theory
Definition
Basic Set theory :
A set is a well-defined collection of objects. The individual objects of the set are called elements.
We have 2 types of methods to describing the sets.
1. Tabular or Roaster method (ତାଲିକା ପଦ୍ଧତି)
2.Set builder method (ସୂତ୍ର ପଦ୍ଧତି)
Tabular or Roaster method:-
In this tabular method, a set is represented by listing all its elements in a row with in this {} curly bracket. Example:- set of all-natural numbers. N={1,2,3....}
Set builder method:- (ସୂତ୍ର ପଦ୍ଧତି)
In this method, a set can be described by stating some characteristics which is satisfied by all its elements within this {}curly bracket. Example:- N={x|x is a natural number.}
Symbols of sets(ସେଟ୍ ର ସଂକେତ):-
N=ଗଣନ ସଂଖ୍ୟା ମାନଙ୍କର ସେଟ୍ । set of all-natural numbers N={1,2,3...} or N ={n|n is a natural number}
Z=ପୂର୍ଣ୍ଣମାନଙ୍କର ସେଟ୍ ।set of all integers. Z={....-2,-1,0,1,2...} or Z={P:P is an integers}
Q=ପରିମେୟ ସଂଖ୍ୟା ମାନଙ୍କର ସେଟ୍ ।set of all rational numbers. {P/q, p,q ∈Z,q not equal to 0}
Q'= ଅପରିମେୟ ସଂଖ୍ୟାମାନଙ୍କର ସେଟ୍ ।set of Irrational numbers.
R=ବାସ୍ତବ ସଂଖ୍ୟା ମାନଙ୍କର ସେଟ୍ ।set of real numbers. R= {x|x is a real numbers}
C=set of Complex numbers. (Z= x+iy),where i is the imaginary part.
Subset(ଉପସେଟ୍):-
If A &B two sets then A is a subset of set B if every element of A is also an element of B. In symbolically we write A⊂B. Example:- A={1,2,3}B={0,1,2,3,4} then A⊂B because every element of A is in set B.
ଯଦି AଓB ଦୁଇଟି ସେଟ୍ ।ସେଟ୍ ଦ୍ୱୟ ମଧ୍ୟରେ ଯଦି Aର ପ୍ରତ୍ୟେକ ଉପାଦାନ ସେଟ୍ Bରେ ଥାଏ ।ତେବେ A ସେଟ୍ କୁ Bର ଏକ ଉପସେଟ୍ କୁହାଯାଏ ।ଏବଂ ଏହାକୁ ସଂକେତ ରେ A⊂B ଲେଖାଯାଏ ।
Super set (ଅଧିସେଟ୍):-
If A is subset of B then B is said to be the superset of A. In symbolically we write B⊃A. Example:- {0,1,2,3,4}⊃{1,2}
Proper subset:-
If A& B two sets then A is said to be proper subset if A is subset of B &A≠ B
Empty set( ଶୂନ୍ୟ ସେଟ୍):-
If there is no element in a set it is called an empty set or symbolically it is denoted by {}orØ it is also called null set.
ଯଦି ସେଟ୍ ରେ କୌଣସି ଉପାଦାନ ନ ଥାଏ ତାହାକୁ ଶୂନ୍ୟ ସେଟ୍ କୁହାଯାଏ ।ଏହାକୁ ସଂକେତ ରେ {}କିମ୍ବା Ø ସୂଚିତ କରାଯାଏ ।
Order of a set :-
If A is any set containing some elements then the number of elements is called the order of a set. Symbolically we write |A| example:-A={1,2,3}, |A|=3
ଯଦିA ଗୋଟିଏ ସେଟ୍ ତେବେ Aସେଟ୍ ରେ ଥିବା ସମସ୍ତ ଉପାଦାନର ସମାହାରକୁ order of a set କୁହାଯାଏ ।
Power set:-
It is the set of all possible subsets of the given set A.It is denoted by P(A). Example:- consider A={a,b} ,P(A)={Ø,{a},{b},{a,b}}. If A is a set having n elements then P(A)has 2ⁿ elements or If |A|=n, P(A)=2ⁿ.
Operation on sets:-
(a) Union set
(b) Intersection
(c) Difference
(d) Complement of a set
(e) Symmetric difference
- Union (ସଂଯୋଗ ପ୍ରକ୍ରିୟା):-
If A&B two sets, then the union of A&B consists of all elements which belong to A or B or both. Symbolically we write A∪B ={x|x∈A or x∈B}.Example:- A={1,2,3}& B={3,4,5}, A∪B={1,2,3,4,5}.ଯଦି AଓB ଦୁଇଟି ସେଟ୍, ତେବେ AଓB ର ସମସ୍ତ ଉପାଦାନ ଗୁଡିକ A∪B ରେ ରହିଥାଏ । ଏହାକୁ ସଂଯୋଗ ପ୍ରକ୍ରିୟା କୁହାଯାଏ(union of Set) ।
Law:
1. A∪A= A (idempotent laws)
2. A∪B= B∪A (Commutative law)
3. (A∪B)∪C=A∪(B∪C) (associative law)
4. A∪Ø=A(Identity law)
5. A∪U= U( Universal law)
Intersection (ଛେଦ ପ୍ରକ୍ରିୟା):-
If A&B any two sets then the intersection of A&B is the set of common elements of both A&B. Symbolically we write A∩B={x|x∈A and x∈B} Example:- A={a,b,c,d}, B={c,d,e,f}, A∩B={c,d}, ଯଦି A ଓ Bଦୁଇଟି ସେଟ୍, ତେବେ ସେଟ୍ A ଓ B ମଧ୍ୟରେ ଥିବା ସାଧାରଣ ଉପାଦାନ ଗୁଡିକୁ A∩B ରେ ଲେଖା ଯାଇଥାଏ ।ଏହାକୁ ଛେଦ ପ୍ରକ୍ରିୟା କୁହାଯାଏ ।
If A&B do not have any common elements then A∩B=Ø or it is also called Disjoint set.
1. A∩A=A (idempotent law)
2.A∩B=B∩A(Commutative law)
3.(A∩B)∩C=A∩(B∩C) (associative law)
4. A∩Ø=Ø(identity law)
5.A∩U=A (universal law)
Difference(ଅନ୍ତର ପ୍ରକ୍ରିୟା):-
If A&B are two sets then the difference of A&B is a set containing all the elements of A & does not consisting the elements of B. Symbolically we write A-B .Example:- A={1,2,3,4},B={3,4,5,6}, A-B={1,2}
Similarly, the difference of B&A is a set consisting all the elements of B &doesn't belong to set A. Symbolically we write B-A={x|x∉B and x∈A}, Examples:- A={1,2,3,4}, B={3,4,5,6},B-A={5,6}
1. A-A=Ø
2.A-Ø=A
3.A-B≠B-A
4.(A-B)-C ≠A-(B-C)
Symmetric Differences (ସମଞ୍ଜସ ଅନ୍ତର ପ୍ରକ୍ରିୟା):-
If A&B two sets then the symmetric differences of A&B is the set of all elements that belongs to A or B but not to both A&B. Symbolically we write A∆B={x|x∈A∪B and x∉A∩B}.
Some important laws:
1.(A')'=A (involution law)
2.A∪A'=U (complement law)
3.A∪A'=Ø
4.U'=Ø
5.Ø'=U
6. Demorgan's law (A∪B)'=A'∩B',(A∩B)'=A'∪B'
7. Distributive law
A∪(B∩C)=(A∪B)∩(A∪C)
A∩(B∪C)=(A∩B)∪(A∩C)
trigonometry basics :
Trigonometric Ratios (ତ୍ରିକୋଣମିତିକ ଅନୁପାତ):-
Consider a Right angled triangle ∆MNO, where ∠MNO= 90⁰ in which Base/adjacent = NO =b, Perpendicular =MN= p, Hypotaneous = MO= h .
There are six trigonometric ratios among three sides of a triangle, i. e.
Sine, cosine, tangent, cotangent, secant, cosecant are called the trigonometric functions.
- It represents the ratio of the length of the sides of a right-angled triangle.
- sinθ= p/h = perpendicular/hypotaneous = MN/MO
- cosθ=b/h= base or adjacent/hypotaneous =NO/MO
- tan θ= p/b= perpendicular/base= MN/NO
- cot θ=b/p= base/perpendicular =NO/MN
- Secθ= h/b= hypotaneous/base= MO/NO
- cosecθ=h/p =hypotaneous/perpendicular =MO/MN
Reciprocal of trigonometric ratios:-
- sinθ=1/cosecθ , cosecθ= 1/sinθ,
- tanθ=1/cotθ, cotθ=1/tanθ,
- tanθ= sin(θ)/cos(θ),
Trigonometrical identities:-
a.sin²θ+cos²θ= 1
b.1+tan²θ=sec²θ
c.1+cot²θ=cosec²θ
Pythagoras theorem (ପିଥାଗୋରାସ୍ ଉପପାଦ୍ୟ) :-
In a right-angled triangle ∆MNO,∠MNO=90⁰ & the sum of squares of the perpendicular and bases is equal to the squares of the hypotaneous sides.
This is known as the Pythagoras theorem. The formula, h²=P²+b², also we can write sin²θ+cos²θ=1
Using Pythagoras theorem we can find the sides of a right-angled triangle & also trigonometric ratios.
Example:- In ∆PQR,∠Q=90⁰ ,PQ=3,QR=4,then PR=? & Sin R=? ANSWER:- according to pythagoras theorem ,
h²=p²+b²
In ∆PQR, h=PR, p=PQ, b=QR now,PR²= PQ²+QR² =>PR²=3²+4²=5² =>PR=5 Sin R=PQ/PR=3/5
ଏକ ସମକୋଣୀ ତ୍ରିଭୁଜର ସମକୋଣ ସଂଲଗ୍ନ ବାହୁଦ୍ୱୟର ଦୈର୍ଘ୍ଯ ର ବର୍ଗର ସମଷ୍ଟି ତାହାର କର୍ଣ୍ଣ ର ଦୈର୍ଘ୍ଯ ର ବର୍ଗ ସହ ସମାନ ହୋଇଥାଏ ।
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