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
Test Strategy
Homework help
GCSE (UK)
Australian Curriculum (AU)
Exam Simulation
Practice Drills
Problem Solving
Math Tricks and Hacks
Practice Tests
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
Anxiety or Stress Disorders
Learning Disabilities
ASD
Elementary School students
ADHD
High School students
Middle School students
College students
Home schooled
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 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)
The Student and Tutor continued their mathematics lesson by reviewing sum of series problems, transitioning from arithmetic to geometric series. They practiced applying the general formula for the sum of a geometric series, focusing on correct application, handling different starting terms, and dealing with fractional common ratios. The Student was assigned to complete outstanding problems and will receive additional practice problems for homework.
General Formula for Sum of Geometric Series (GP)
Adjusting for Geometric Series Starting from x¹
Handling Constant Multipliers in GP Sums
Simplifying Expressions with Exponents
Distinguishing 'x' (Common Ratio) and 'n' (Upper Limit)
The Student and Tutor practiced solving problems related to identifying general terms of sequences and calculating the sum of arithmetic series. They focused on strategies for handling constants, coefficients, and varying summation ranges (including starting from zero or a number greater than one). The session involved step-by-step problem-solving to reinforce correct application of summation formulas.
Finding General Terms of Quadratic Sequences
Summation Formula for Natural Numbers (Σn)
Summation Formula for a Constant (Σc)
Linearity Property of Summation (Splitting Terms)
Adjusting Summation Bounds (Non-Standard Starting Point)
The student and Tutor practiced identifying patterns in complex number series, successfully determining the functions for both quadratic and cubic sequences. Subsequently, they moved on to understanding and applying the formulas for the sum of arithmetic series. The session concluded with the student planning to practice the summation problems for the next class.
Analyzing Number Series with Differences
Identifying Algebraic Rules for Number Series
Sum of First 'n' Natural Numbers
Sum of Arithmetic Series with a General Term
The Tutor initially introduced multivariable calculus concepts, including partial differentiation. However, the Student expressed a need for assistance with vector algebra, leading to a focused discussion on vectors in 2D and 3D, unit vectors, and methods for calculating dot and cross products. They concluded by planning to practice related problems in upcoming sessions to solidify understanding.
Cross Product (Vector Product)
Dot Product (Scalar Product)
Unit Vectors
Length (Magnitude) of a Vector
Partial Differentiation
Vectors in 2D and 3D Space
The Student and Tutor engaged in a session focused on sequences and series, specifically practicing the identification of arithmetic and geometric progressions from sigma notation. They worked through examples to understand how to interpret the lower and upper limits of summation and derive general terms for various sequences. The session concluded with exercises on matching given sequences to their correct sigma notation representations.
Sequences vs. Series
Identifying Arithmetic
Geometric
and Other Series
Understanding Sigma Notation (Σ)
Evaluating Series using Sigma Notation
Teaching tools used by tutor
Practice worksheets
Graphing Tools
Quizzes
Visualization & Exploration
Digital whiteboard
Interactive lessons
Pets are welcomed
Weekend lessons
Chat for quick help
Open Q&A
Note taking
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