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If you are a student of Mathematics, in Class 12, and if you find Mathematics a little overwhelming, then this page is for you.
Class 12 Mathematics is an adventure of its own with Relations and Functions which you may find a little abstract. Then there is Inverse Trigonometry which can totally overwhelm you if you do not know how to go about it properly.
Matrices and Determinants is easy but again finding the inverse of a matrix using elementary row and column operations can be challenging. Then you have Differential Calculus and Integral Calculus which may confuse you.
Vectors is relatively easy but 3 Dimensional Geometry can be challenging. Linear Programming again requires understanding on graphing the feasible solution.
Having taught Mathematics for close to 3 decades, I invite you to be mentored in Mathematics and overcome the barriers of study.Learn how to enjoy Mathematics. You will learn to take each problem as a challenge.
The secret is for you to start with basic formulas and then move over to more complex problems. Time management is also a valuable tool which you will learn along the journey.
As the days progress, you will begin to enjoy Mathematics and soon you will attain your goal of good scores plus a deeper understanding of the subject.
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VECTORS AND 3 DIMENSIONAL GEOMETRY
UNDERSTANDING LOGARITHMS
Do you know that logarithms are used extensively in Calculus, be it limits, derivatives or Integration? How then do you apply properties of logarithms while solving problems in Calculus? Learn this by watching this video. Here, we discuss the basic properties of logarithms such as the product rule, quotient rule, exponent rule. We also learn how to apply the change of base formula and a few formulae on exponential limits. Online tutoring is provided. You can choose between specific topics and the entire course.
Class 12 Math Marvels:Navigating Complexity with Confidence
Continuity and Differentiability Course-Part 1
This course is a your first step to understanding Differential Calculus. This would greatly benefit students preparing for ISC and CBSE Class 12 Mathematics.
The course starts with
An introductory video which also includes all the formulas learnt in this session.
The concept of Continuity at a point and continuity in an interval.
You will learn how to calculate the left hand and right hand limits for continuity .
The concept of derivative at point using limits is illustrated.
You will learn how to calculate the derivative using definition.
You will then learn how to differentiate using the formula.
The course concludes with how to calculate the derivative of composite functions and using the Chain Rule.
How to learn Probability for Class 12?
To start with, you'll learn the basic definition of Probability and how to apply it in problem solving. You need to keep in mind that probability=(number of favourable events)/total number of events. You'll learn about Conditional Probability, Mutually exclusive and independent events and properties regarding these.
Moving on, you learn about Total Probability and how it leads to Bayes' Theorem. There area a number of solved examples illustrated here for you to practice. This comes to the end of the first part of the course.
Next, you'll learn what are Random variables and how to calculate the mean and variance of discrete and continuous random variables. The course teaches you how to distinguish between a discrete and continuous variable. Moving on, you'll come to Binomial distributions and how to check if a variable is a random variable or follows Binomial distribution.
This is extremely important and the course teaches you how to distinguish between the two. Learn how to calculate the mean and variance of random variables and a Binomial distribution. You're also given all the formulas taught in the course as one module.
Bonus-Learn about the Poisson Distribution in Probability. You'll learn about the mean and variance of the Poisson distribution and its application in problems.
Enrol for the course and enhance your learning. Thank you!
Integral Calculus Made Easy-From Basic to Advanced Concepts
You know how important it is for you to know Integration if you are a student of Mathematics. But yet, somewhere, along the way, you get lost. Having taught Mathematics to teenagers and adolescents for the past three decades, I can help you understand the nuances of Integration.
Take up the Integration Challenge. Right from taking baby steps in Integration, you will move on to a Higher level of understanding This course starts with the very basics of Integration. You will start with the concept of Integral as antiderivative and a few basic formulas of Integration.
The course then introduces you to the substitution method. Take up the challenge to solve the problems given. You will learn how to compare methods and that any problem in Integration can be solved using this method.
You are getting an irresistible bargain in this course. Trigonometric Integrals and certain special integral formulas are taught here.. I would advise each one of you to hurry and join this course.
The next part of this course would show you how to integrate when the degree of the numerator is greater than the degree of the denominator. You will see the long division method. One can also learn about partial fractions here.
You'll learn how to integrate by parts and the right order to be followed when you do so. An interesting, yet important application is also illustrated here.
Watch step by step solutions to problems. Practice along with me and become adept in Integration. I hope this course will help you.
Learn about Definite Integrals and how to use it in problem solving.
Use the Objective Question Bank on Integrals.
Would you care to share this with your fellow students and friends who are finding Integration difficult? Spread the good word around. You are all worth it.
Advanced Differentiation Techniques-Calculus III
This is the third series of my course on Differentiation. The concepts and problems explained in this course will help you immensely while learning Integral Calculus.
I am Suman Mathews, mathematics educator and teacher. I have a double master's in Math and I have helped students achieve their goals in Maths for the past three decades. As you proceed with the course, take a pen and paper and practice the problems along with me .
You start with learning how to differentiate composite functions. This is an extremely important concept for you to master. Progressing through the course, you'll learn Implicit functions next.
So, what exactly is an Implicit function? How do you differentiate between an explicit and implicit function? Learn all this and how to differentiate Implicit Functions here.
Moving on, you learn about logarithmic differentiation.Given a function to the power of another function, a simple trick to follow will be to apply log to both sides. You then differentiate both sides, using the concept learnt in Implicit Differentiation.
You'll progress to learn how to differentiate Determinants. This can be done in two ways, either using row wise or column wise differentiation. Another extremely important concept you'll learn here is second order derivatives.
Learn what are second order derivatives and how to evaluate them. You'll also learn how to solve identities using second order derivatives. Formulas that you've learnt are also given to you as a special feature.
Bonus: Learn more about solving identities in Second order derivatives. Also , learn Lagrange's Mean Value theorem and it's applications in problem solving.
You'll also learn about Rolle's Theorem and how to apply it in problem solving. Check out the objective questions for mastering this topic.
A good self learning course for you here. You can encourage your friends to join this course. Join my road map for differentiation.
Taking your Derivative Skills to the next level
So, we start with going over the derivatives of Composite Functions.
You learn how to apply Chain Rule in a simple way. Moving on, you'll learn about how to incorporate differentiation of Inverse Trigonometric functions. The trick here, is to substitute and make the function simple.
A number of problems have been incorporated here and solved for your understanding. You'll learn what are Implicit Functions and how to differentiate them. The trick here is to just differentiate both sided of the equation.
Implicit Differentiation is explained quite in detail here. There is also an Assignment and a small test on multiple choice questions on what you've learnt so far. I hope this has served your purpose of learning Differentiation.
Bonus: Learn about L-Hospital's rule in Indeterminate form of limits. This lesson shows you how we use Differentiation in evaluating special limits.
Get inspired and enrol for this course. Remember, a journey of a thousand miles begins with one step! Thank you!
From Chance to Uncertainty-Understanding Probability
A good knowledge of Probability will also go a long way in helping you in SAT and GRE QUANT exams.
To start with, you'll learn the basic definition of Probability and how to apply it in problem solving. You need to keep in mind that probability=(number of favourable events)/total number of events. You'll learn about Conditional Probability, Mutually exclusive and independent events and properties regarding these.
Moving on, you learn about Total Probability and how it leads to Bayes' Theorem. There area a number of solved examples illustrated here for you to practice. This comes to the end of the first part of the course.
Next, you'll learn what are Random variables and how to calculate the mean and variance of discrete and continuous random variables. The course teaches you how to distinguish between a discrete and continuous variable. Moving on, you'll come to Binomial distributions and how to check if a variable is a random variable or follows Binomial distribution.
This is extremely important and the course teaches you how to distinguish between the two. Learn how to calculate the mean and variance of random variables and a Binomial distribution. You're also given all the formulas taught in the course as one module.
Bonus-Learn about the Poisson Distribution in Probability. You'll learn about the mean and variance of the Poisson distribution and its application in problems.
Enrol for the course and enhance your learning. Thank you!
Continuity and Differentiability-Part 1 Class 12 Mathematics
The course starts with
-
An introductory video which also includes all the formulas learnt in this session.
-
The concept of Continuity at a point and continuity in an interval.
-
You will learn how to calculate the left hand and right hand limits for continuity .
-
The concept of derivative at point using limits is illustrated.
-
You will learn how to calculate the derivative using definition.
-
You will then learn how to differentiate using the formula.
-
The course concludes with how to calculate the derivative of composite functions and using the Chain Rule.
Connecting the Dots: A Course on Relations and Functions
The course unfolds with the basic concept of Sets and a Relation as a subset of the cross product of two sets. You learn the different types of Relations and a very important concept, namely, what is an equivalence Relation.
Next, you'll be introduced to a function as a type of Relation. You'll understand what is meant by Domain and Range of a function. As you progress through the course, you'll learn about injective and surjective functions and consequently bijective functions.
You'll learn how to calculate the inverse of a bijective function. You'll glide to Binary Operations, a very important concept used in Group Theory in Higher Mathematics.
You'll receive all the formulas learnt in this course as a gift. There's also a set of Multiple choice questions at the end of the course. This will inspire you to think out of the box.
On a side note, the concepts taught here will also help you to answer SAT and GRE QUANT examinations.
I hope you'll find this course helpful. Encourage your friends and acquaintances to also enrol for the course and learn hassle free at your own pace.
Bonus-Learn how to find the domain and range of Inverse Trigonometric Functions. Also learn simple techniques to find the principal values of Inverse Trigonometric functions.