Fundamental Mathematics for IIT JEE | Olcademy
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Fundamental Mathematics for IIT JEE

Basic Mathematics for IIT JEE(Main & Advanced)

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Description

Math class was always so frustrating.

I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half.

I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep others out of that aggravating, time-sucking cycle.

Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all.

Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even effective communication skills

HOW TO BECOME EXPERT IN BASIC MATH IS SET UP TO MAKE COMPLICATED MATH EASY:

This course contains 50+ online live classes and text explanations of everything from the Fundamentals, and it includes 48 quizzes (with solutions!) and an additional 20+ workbooks with extra practice problems (containing almost 1000+ questions), to help you test your understanding along the way. Master the Fundamentals of Math is organized into the following sections:

  • Number System

  • Scientific notation

  • Set theory

  • Interval

  • Inequality

  • Modulus

  • Rational Inequation

  • Greatest Integer Function

  • Irrational Inequation

     

 

AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Online Live Classes: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Assessments: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the assessments. If you pass, great! If not, you can review the notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.

What will you learn?
  • The student will learn all the basic concepts of mathematics, which help them to understand higher mathematics.
  • Master the Fundamentals of Math is organized into the following sections: Numbers and negative numbers Factors and multiples Decimals Fractions Mixed numbers Ratio and proportion Exponents Radicals Scientific notation
  • Students of Foundation course or 2 year program.
What knowledge and tools are required?
  • Students should be familiar with only the basic operation of mathematics. Like: Addition, Subtraction, Multiplication, Division, faction, etc
  • For live classes, students should have good internet connections
Who should take this course?
  • IIT-JEE Aspirants and Students taking Mathematics for higher secondary Education.
  • Current middle school/junior high students, or students about to start middle school who are looking to get ahead Homeschool parents looking for extra support with the fundamentals Anyone who wants to study math for fun after being away from school for a while
  • High School Students up to 12th class, Who want to understand Mathematics easily.
Lecture 1 :- Introduction of this course

Basic Mathematics 1. Introduction 2. Natural Number · Natural Number, Whole Number, Integers · Even number, Odd Number, Properties of Divisibility. · Prime Numbers and Composite Numbers and their properties. · Rational Numbers, their properties and representation. · H.C.F or G.C.D. and L.C.M, Co-Prime and Twin Prime numbers and Their properties. · Method to Convert decimal to Rational and Vise-versa, Irrational Number. · Real Numbers, their representation and properties. · Tree form of Different types of Real Numbers. · Important Symbols (Part 1) such as "infinity, number line, implies, iff" · Important Symbols (Part 2) such as "min, max, <, >, <=, >=, " · Important Symbol (Part 3) Such as "Modulo, Factorial, congruent, for all" · Sigma, Pie, Summation, Permutation, Vers(x), Covers(x) · Combination (nCr), exp(x), symbol(e) · fast calculation in Mathematics · Double factorial and their representation 3. Set Theory · Definition of set, form of representation (Roster and set builder form) · Types of sets, conversion of forms · pair set, subset, equal set and their properties · super set, Proper subset, Finite and infinite set, equivalent set. · Venn diagram, power set, Universal set, some operations on sets. · Union, intersection, compliment of sets, difference of 2 set. · Problems based on set theory. 4. Interval · Definition of interval, types (open interval, closed, open-closed, closed-open) · Graphical and set builder notation of different intervals. · Intersection and Union of interval, Problems based on intervals. 5. Inequality · Definition of inequality and examples, operation on inequality · Properties of inequality, reciprocal of number, Some definition (solution set) · Solution of single and double inequality · System of inequality, inequality of the form a.b and a/b is positive or negative · Properties of inequality, solution of inequality of the form (x-a) *(x-b)> or >=0 · Properties of inequality, solution of inequality of the form (x-a) *(x-b) < or <=0 · double inequality of the form f(x) <g(x)< h(x), operation of inequality · squaring of inequality, and some important results using inequality. 6. Modulus · Definition of modulus, their representation and geometrical meaning of modulus · Properties of Modulus with suitable examples · Properties of Modulus with suitable examples (|x| < or > a when a>0) · Properties of Modulus with suitable examples (|x| < or > a when a<0 and a=0) · max, min in term of modulus, steps to solve inequality involved modulus · problems based on equality involving modulus. · problems based on Multiple modulus with equality · problems based on inequality involving modulus. · Square root, Multiple modulus involving inequality · Relation between Square root and Modulus with suitable examples. · Quadratic express (definition and their standard and their sign scheme) · Sign scheme of quadratic expressions when D=0. · problems based on sign scheme of quadratic expressions. · Problem Based on Quadratic Expression 7. Monomial, Polynomial and Rational Function · Definition and Examples of Monomial, Polynomial and rational function

  • Topics

  1. 1. over view of syllabus of this course
Lecture 2 :- Number System

This section contains all about Numbers like : Real Number, Natural Numbers, Whole Numbers, Integer, Rational Number, Irrational Number, Even Number, Odd number and many more classification of Number.

  • Topics

  1. 1. Natural Number, Whole Number, Integers
  2. 2. Even number, Odd Number, Properties of Divisibility.
  3. 3. · Prime Numbers and Composite Numbers and their properties.
  4. 4. Rational Numbers, their properties and representation.
  5. 5. H.C.F or G.C.D. and L.C.M, Co-Prime and Twin Prime numbers and Their properties.
  6. 6. Method to Convert decimal to Rational and Vise-versa, Irrational Number.
  7. 7. Real Numbers, their representation and properties.
  8. 8. Tree form of Different types of Real Numbers.
  9. 9. Important Symbols (Part 1) such as "infinity, number line, implies, iff"
  10. 10. Important Symbols (Part 2) such as "min, max, <, >, <=, >=, "
  11. 11. Important Symbol (Part 3) Such as "Modulo, Factorial, congruent, for all"
  12. 12. Sigma, Pie, Summation, Permutation, Vers(x), Covers(x)
  13. 13. Combination (nCr), exp(x), symbol(e)
  14. 14. fast calculation in Mathematics
  15. 15. Double factorial and their representation
Lecture 3 :- Set theory

Definition of set and related terms. Representation of set and their element. Symbol used in set theory (belongs to or not belongs to). Method of representation of set Discussed Set builder form and roaster form of a set. Related examples have discussed.

  • Topics

  1. 1. Definition of set, form of representation (Roster and set builder form)
  2. 2. Types of sets, conversion of forms
  3. 3. pair set, subset, equal set and their properties
  4. 4. super set, Proper subset, Finite and infinite set, equivalent set.
  5. 5. Venn diagram, power set, Universal set, some operations on sets.
  6. 6. Union, intersection, compliment of sets, difference of 2 set.
  7. 7. Problems based on set theory.
Lecture 4 :- Interval

at the end of this section, you will able to solve and understand concepts of interval, their representation, types and their application in mathematics.

  • Topics

  1. 1. Definition of interval, types (open interval, closed, open-closed, closed-open)
  2. 2. Graphical and set builder notation of different intervals.
  3. 3. Intersection and Union of interval, Problems based on intervals.
Lecture 5 :- Inequality

Properties of inequality reciprocal of any number some definitions the solution of an inequality solution set

  • Topics

  1. 1. Definition of inequality and examples, operation on inequality
  2. 2. Properties of inequality, reciprocal of number, Some definition (solution set)
  3. 3. Solution of single and double inequality
  4. 4. System of inequality, inequality of the form a.b and a/b is positive or negative
  5. 5. Properties of inequality, solution of inequality of the form (x-a) *(x-b)> or >=
  6. 6. Properties of inequality, solution of inequality of the form (x-a) *(x-b) < or <
  7. 7. double inequality of the form f(x) <g(x)< h(x), operation of inequality
  8. 8. squaring of inequality, and some important results using inequality.
Lecture 6 :- Modulus

  • Topics

  1. 1. Definition of modulus, their representation and geometrical meaning of modulus
  2. 2. Properties of Modulus with suitable examples
  3. 3. Properties of Modulus with suitable examples (|x| < or > a when a>0)
  4. 4. Properties of Modulus with suitable examples (|x| < or > a when a<0 and a=0)
  5. 5. max, min in term of modulus, steps to solve inequality involved modulus
  6. 6. problems based on equality involving modulus.
  7. 7. problems based on Multiple modulus with equality
  8. 8. problems based on inequality involving modulus.
  9. 9. Square root, Multiple modulus involving inequality
  10. 10. Relation between Square root and Modulus with suitable examples.
Lecture 7 :- Quadratic Expressions

  • Topics

  1. 1. Quadratic express (definition and their standard and their sign scheme)
  2. 2. Sign scheme of quadratic expressions when D=0.
  3. 3. problems based on sign scheme of quadratic expressions.
  4. 4. Problem Based on Quadratic Expression
Lecture 8 :- Monomial, Polynomial and Rational Function

  • Topics

  1. 1. Definition and Examples of Monomial, Polynomial and rational function
  2. 2. Definition and Examples of Monomial, Polynomial and rational function
  3. 3. Wavy curve method to find sign scheme of rational function
  4. 4. Solving inequality using wavy curve method
  5. 5. Solution of Inequality involving Modulus using Wavy curve method
  6. 6. Min and Max Value of Quadratic Expression and factorization of Quadratic express
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Instructor Profile

Ankit Kumar

Professional Online Teacher

Skills: MathematicsSwimming

Persuing Batchelor of Technology from Indian Institute of Technology Dhanbad, Jharkhand India. Math class was always so frustrating. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!” So I started tutoring to keep others out of that aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. I love to teach mathematics through my unique method of explanation.


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