Kapil Arora
Semiconductors Hardware Engineer providing tutoring classes in Mathematics focused on fundamentals and basics [first principles].
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Kapil Arora
Bachelors degree
/ 55 min
Kapil - Know your tutor
Myself Kapil Arora, I am a BITS Pilani graduate in Electronics and Electrical Engineering and currently working as an Analog Engineer in the Semiconductor industry. I offer personalized learning experiences in a wide range of subjects including Probability, Geometry, Calculus, Algebra and almost all mathematics topics for middle school, high school, elementary school and college students. My teaching style includes innovative methods focusing on the depth of approach (first principles). I like to teach mathematics and have tutored numerous students who have aced almost all competitive examinations. My students confidence gets boosted after my classes and there mathematics performance and scores improve a lot. I focus also on problem solving and practicing as practice makes a man perfect. Let's get started and conquer mathematics together!
Meet Kapil
Kapil graduated from BITS Pilani
Specialities of your tutor
Mental Math
International Baccalaureate (IB)
Math Tricks and Hacks
Exam Simulation
A-Levels (UK)
GCSE (UK)
Test prep strategies
Australian Curriculum (AU)
Homework help
CoTutorAI modules
Summary
Podcast
Quiz
Learnings
Flashcard
Spotlight
Zero Risk Guaranteed
15-days refund
Free tutor swap
No cancel fee
1-yr validity
24/7 support
Student types for classes
High School students
ASD
ADHD
Anxiety or Stress Disorders
Learning Disabilities
Home schooled
College students
Elementary School students
Middle School students
Class overview
My approach is focused on fundamentals and basics [first principles] as I believe these are foundational to a person's overall understanding and knowledge about a topic. I know fundamentals and basics are foundational to a person's knowledge and hold over any particular topic/subject and my focus is to develop fundamentals of students. My approach is very simple and focusing on the basics - the understanding about a topic has to be so deep that student does not have to remember any formulas/words/topics. It needs to be ingrained in the mind with a level of deep understanding such that there is no need for remembering. I integrate practice drills and question solving to build concepts within the live class to make the concepts engrained into the mind of the student. My live class includes Google meet and interactive whiteboards to make the most of the live lessons and explain students doubts and questions on the fly. And also clearly follow the students' approach to problem solving observing the minute details and correcting the students' approach for the best results and performance. Let's get started and boost your Mathematics scores.
Kapil also teaches
Algebra
Arithmetic
Calculus
Discrete Math
Elementary School Math
Geometry
Mathematics concepts taught by Kapil
The Student and Tutor discussed the optimal approach to mathematics practice, weighing the use of calculators against traditional pen-and-paper methods. They collaboratively analyzed problems involving cubic functions, domain and range, and the application of sigma notation in a design context, exploring how graphical properties are influenced by given constraints. The Student committed to submitting their current homework solutions for the Tutor's review by the next day.
Cultivating Mathematical Solving Ability
Domain and Range of Functions
Visualizing Cubic Functions and Their Roots
Understanding One-to-One Functions
Graphical Transformations: Adapting Range Constraints
Introduction to Sigma Notation (Σ)
The Student and Tutor worked on various problems related to proportional relationships in mathematics, including calculating the constant of proportionality from numerical data and graphs. They practiced writing equations for proportional relationships and interpreting unit rates from graphical representations. The Student will have another trial lesson with a different tutor at a later date.
Identifying Constant from an Equation
Unit Rate as the Constant of Proportionality
Writing Equations for Proportional Relationships
Identifying Proportional Relationships Graphically
Constant of Proportionality (k)
The Student and Tutor focused on foundational concepts of exponential and logarithmic functions, including their definitions, graphing, and key properties. They practiced solving limit problems involving these functions, particularly those requiring factoring to resolve indeterminate forms. The plan for the next session includes reviewing asymptotes and addressing specific problems from a past exam the Student found challenging.
Exponential Functions & Their Graphs
Logarithmic Functions: The Inverse of Exponentials
Logarithm Properties: The Division Rule
Logarithm Properties: The Multiplication Rule
Evaluating Limits with Logarithms and Rational Expressions
The Student and Tutor reviewed matrix multiplication rules, focusing on the conditions for multipliability and determining the dimensions of the resulting matrix. The Student practiced matrix multiplication and was introduced to the concept of multiplication inverses and the identity matrix. They then learned and successfully practiced the algebraic method for finding the inverse of a 2x2 matrix by solving a system of linear equations.
Matrix Multiplication: Compatibility & Dimensions
Identity Matrix
Multiplicative Inverse of Matrices: Definition
Finding the Inverse of a 2x2 Matrix (Algebraic Method)
The Student and Tutor reviewed summation formulas for Arithmetic and Geometric Progressions, including how to apply them for specific ranges. The session then introduced the fundamentals of matrices, covering dimensions, identity matrices, addition, subtraction, and multiplication, with the Student actively practicing matrix multiplication problems. The Student was encouraged to complete homework related to matrices.
Matrix Dimensions & Identity
Matrix Addition & Subtraction
Matrix Multiplication Rules
Performing Matrix Multiplication
The session focused on reviewing and practicing the summation of Arithmetic Progressions (AP) and Geometric Progressions (GP). Student and Tutor revisited the formulas for both types of series, particularly addressing how to apply them when the series does not start from the first term (n=0 or n=1). The Student was assigned two practice problems as homework, requiring the application of the learned formulas.
Sum of Arithmetic Progression (AP) Review
Sum of Geometric Progression (GP) Formula & Starting Point
Advanced Techniques for Summing Complex Series (Mixed AP & GP)
Teaching tools used by tutor
Digital whiteboard
Graphing Tools
Practice worksheets
Assessment
Visualization & Exploration
Interactive lessons
Open Q&A
Pets are welcomed
Parent feedback
Note taking
Chat for quick help
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