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
Practice Drills
Problem Solving
GCSE (UK)
Homework help
A-Levels (UK)
Math Tricks and Hacks
Practice Tests
Exam Simulation
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
ADHD
College students
Home schooled
ASD
Elementary School students
Learning Disabilities
High School students
Anxiety or Stress Disorders
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 practiced solving problems involving composite functions, including those with absolute values. They also defined and identified bijective functions, practiced finding inverse functions algebraically, and discussed the domain of functions in real-world contexts. The Student identified composite functions as an area needing more practice (rated 4/10), and the Tutor assigned problems for the Student to attempt and requested a list of topics with comfortability ratings for future planning.
Inverse Functions
Bijective Functions (One-to-One and Onto)
Composite Functions: f∘g and g∘f
Properties of Function Composition: (f + g) ∘ h
Graphing Quadratic Functions: Parabola Orientation
Domain Restrictions in Real-World Applications
The Student and Tutor reviewed the Student's comfort levels across several Algebra topics, including linear functions, inequalities, and absolute value functions, noting that complex numbers required more focus. They then worked extensively on understanding and solving problems related to composite functions, practicing the decomposition of functions and evaluation. The Tutor assigned additional problems on composite functions for follow-up.
Piecewise Functions
Rational and Irrational Numbers
Absolute Value Functions
Composition of Functions
Complex Numbers Introduction
Student and Tutor began by reviewing a recent math test, which included topics like graphing linear equations, solving quadratics, and exponential functions. The session then moved to practicing function composition and solving various types of inequalities. The class concluded with a detailed discussion on finding the domain of composite functions involving logarithms and square roots, with the Tutor assigning further practice problems on this topic for follow-up.
Function Composition
Solving Linear & Compound Inequalities
Solving Rational Inequalities
Domain of Functions (Square Root & Logarithm)
Domain of Composite Functions
The Tutor and Student focused on determining the domain and range of various functions, including rational, square root (with quadratic, cubic, and by-quadratic expressions), and linear functions. They practiced factoring polynomials, identifying roots, and performing sign analysis to understand graph behavior. The Tutor assigned a problem to be solved independently and stressed the importance of conceptual understanding over reliance on calculators for the Student's upcoming ACT practice exam.
Domain & Range: Rational Functions
Domain & Range: Radical Functions (Square Roots)
Polynomial Factoring & Root Identification
Sign Analysis for Polynomial Inequalities
Basic Graphing: Lines
Quadratics & Cubics
Solving Quadratic Inequalities
The Student and Tutor practiced identifying various functions (quadratic, logarithmic, exponential, and rational) by analyzing their given domains and ranges and interpreting their graphs. They discussed the algebraic representation of these functions and the inverse relationship between logarithmic and exponential functions. The Tutor also reviewed the importance of providing detailed step-by-step explanations for homework assignments to showcase a thorough understanding of the concepts.
Domain and Range Fundamentals
Identifying Functions from Domain & Range: Quadratic vs. Rational
Logarithmic and Exponential Functions as Inverses
Understanding Polynomial Function Orders
The Importance of Presenting Solutions Effectively
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.
Introduction to Sigma Notation (Σ)
Graphical Transformations: Adapting Range Constraints
Understanding One-to-One Functions
Domain and Range of Functions
Cultivating Mathematical Solving Ability
Visualizing Cubic Functions and Their Roots
Teaching tools used by tutor
Practice worksheets
Assessment
Visualization & Exploration
Quizzes
Graphing Tools
Interactive lessons
Weekend lessons
Open Q&A
Note taking
Parent feedback
Record lessons
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