AP Calculus AB/BC: Complete Exam Preparation with Conceptual Mastery

From 24 C$ /h

This class is designed for high school students preparing for the AP Calculus AB or BC exams, as well as anyone seeking a rigorous foundation in single‐variable calculus. Whether you are aiming for a top score or simply want to understand calculus deeply, this course covers all required topics: limits, derivatives, integrals, the Fundamental Theorem of Calculus, and—for BC—additional topics such as sequences, series, parametric equations, polar coordinates, and vector‐valued functions.

My teaching approach emphasises conceptual understanding over rote memorisation. We will explore why calculus works, not just how to compute. You will learn to solve problems with confidence, interpret graphs, and connect ideas across the curriculum. Each session is tailored to your pace and goals, with plenty of practice problems and exam‐style questions.

With over 10 years of teaching experience across multiple curricula (AP, IB, A‐Level, CBSE, ICSE) and advanced mathematical training at IISc Bengaluru and the University of Surrey, I can help you master calculus and develop the analytical skills needed for success in higher mathematics.

We will cover:

Limits and continuity

Differentiation (rules, applications, related rates, optimisation)

Integration (techniques, applications, areas and volumes)

Differential equations

For BC: sequences and series, parametric, polar, and vector functions

Exam strategies and time management

Extra information

Previous materials from high school mathematics

Location

Online from Czech Republic

About Me

I specialize in teaching mathematics from advanced school level to university level, with a particular focus on bridging the gap between computational and proof‐based mathematics. My own background—advanced studies and research at the Indian Institute of Science (IISc), Bengaluru, research in theoretical physics at Charles University, Prague, and an MSc in Physics and Mathematics from the University of Surrey, London—allows me to help students not only solve problems but also understand the underlying mathematical ideas and develop rigorous analytical thinking.

My teaching approach emphasizes conceptual understanding, logical reasoning, and structured problem‐solving. Whether a student is preparing for school examinations, university coursework, competitive entrance examinations, or higher studies in mathematics, I adapt my teaching to their individual goals and learning style. I am particularly passionate about helping students transition from computational mathematics to proof‐based mathematics, where they learn how mathematicians think, construct arguments, and understand abstract concepts with confidence.

Education

Advanced Studies and Research in Mathematics
Indian Institute of Science (IISc), Bengaluru, India
Focus: Geometric Analysis, PDEs, Regularity Theory

Research in Theoretical Physics
Charles University (Univerzita Karlova), Prague, Czech Republic
Completed research in theoretical physics

MSc in Physics and Mathematics
University of Surrey, London, United Kingdom

Experience / Qualifications

10+ years of teaching experience globally, working with students from a variety of educational systems including A‐Level, IGCSE, IB, AP, CBSE, ICSE, and undergraduate mathematics programs.

Areas of expertise:

High‐School Mathematics

Pre‐college level Mathematics, all topics

Calculus (Single Variable and Multivariable, AP‐Calc‐AB/BC, Pre‐Calc)

Linear Algebra

Real Analysis

Differential Equations (ODE/PDE)

Mathematical Methods for Physics and Engineering

Differential Geometry (introductory and advanced topics / smooth manifolds / Riemannian Geometry)

Foundations of Partial Differential Equations

Proof Writing and Mathematical Reasoning

Skilled at adapting teaching to individual goals, whether for school examinations, university coursework, competitive entrance exams, or higher studies in mathematics.

Age

Teenagers (13-17 years old)

Adults (18-64 years old)

Seniors (65+ years old)

Student level

Beginner

Intermediate

Advanced

Duration

60 minutes

90 minutes

120 minutes

The class is taught in

English

Skills

Calculus

Availability of a typical week

(GMT -04:00)

New York

Online via webcam

Mon

Tue

Wed

Thu

Fri

Sat

Sun

00-04

04-08

08-12

12-16

16-20

20-24

Mathematics Tutor for All Levels: High School to University (Proof-Based & Applied)

29 C$ /h

My name is Sarbajit, and I have dedicated my academic and professional life to mathematics and its teaching. I have over a decade of experience teaching students from diverse educational systems—including IGCSE, CBSE, ICSE, State Board, AP, and undergraduate university programs—both in India and the UK.

I hold an MSc in Physics and Mathematics from the University of Surrey, UK, and I have pursued advanced mathematical studies and research at the Indian Institute of Science (IISc), Bengaluru. Currently, I am engaged in advanced mathematical research at IISc, focusing on geometric analysis, partial differential equations, and regularity theory. My own journey from computational to proof-based mathematics has given me a deep appreciation for the beauty of rigorous reasoning, and I love sharing that with my students.

I teach mathematics at all levels, from school to university, with a special emphasis on conceptual understanding and proof writing. My areas of expertise include:

High School Mathematics (all topics, including algebra, geometry, trigonometry, and pre‐calculus)

Calculus (Single Variable, Multivariable, AP Calculus AB/BC, Pre‐Calculus)

Linear Algebra

Real Analysis

Differential Equations (ODE and introductory PDE)

Mathematical Methods for Physics and Engineering

Differential Geometry (introductory to advanced, including smooth manifolds and Riemannian geometry)

Proof Writing and Mathematical Reasoning

I have been teaching online for several years with a full digital setup—including a pen tablet and webcam—to ensure a smooth, interactive experience. I believe every student can learn to think like a mathematician, and I adapt my teaching to your individual goals, whether you are preparing for exams, transitioning to university‐level mathematics, or simply seeking to understand the beauty of the subject.

Mathematics gives me immense joy, and I want to share that joy with you. Let’s explore the hidden structures and elegant logic of mathematics together.

Asdrúbal

4.89

(9)

Seven years of experience in the mission of providing academic support to students in ESO or Bachillerato (Science or Social Sciences), university students in the first year and students of the IGCSE, Alevel and IB programs (Ed Excel or Cambridge),
In addition to the classes themselves, I offer permanent online support for students' queries via WhatsApp (especially important during study periods prior to exams), guidance in the use of technological tools (programs, videos or web pages) that can contribute to improving the student's training in Mathematics. We educate to train the student in Mathematics.
University courses I have recently supported include Business Mathematics for students at IE Business School, Rey Juan Carlos University, European University of Madrid, CUNEF, and Carlos III University. I also provide support for programs in Probability and Statistics, Financial Mathematics, and Mathematical Programming (experience with students from the School of Economics at the Autonomous University of Madrid). My hourly rate decreases as the session length increases. The most cost-effective rate is for a two-hour session.

Emese

4.89

(9)

This course is for international students doing the IB Diploma Programme. Whether you are in the finishing line or you just started the course, I’m happy to help you reach your goals. All lessons are customised for your needs, we work together to get you the best results possible.

I’ve worked with IB students at different levels, so don’t worry if you’re just going for a 4, we can focus on the things that can get you there, but if you’re the person aiming for that 7, I’m happy to guide you and prepare you for your exam.

Beatrice

4.89

(9)

I have worked for 6 years now with kids from international schools who were "hating" maths because the methods used by their IB teachers were too complicated and hard to understand.

I believe that no one is "not mathematical", we just have to find the way to approach the subject together; I have indeed a few teaching methods that can be adapted to a kids' needs, I believe every kid needs a different method to fully understand the subject.

I provide 3 types of lessons that represent 3 phases:
1. THEORY - Understanding the theory behind the exercises, this phase is the shortest since I believe that to fully understand maths you need to exercise.
2. EXERCISES - Doing exercises divided by subject we. just went through in the theory part.
3. PAST PAPERS - Going through past papers to "simulate" a potential exam.

Dividing the process in 3 phases has proven really effective in succeeding not only during the year but also at the final exams.

Bibek

4.89

(9)

Hi! Welcome! I am a Ph.D. researcher in Physics at the University of Cologne, Germany. Recently, I graduated from the University of Groningen in the Netherlands with a Master's degree in Nanoscience (w/ cum Laude). I offer private tutoring (for high school and/or university-level students) so you can understand the fundamental concepts and excel in your studies. I have teaching experience of 5+ years in Physics and Mathematics to both high school and university-level students.

This class aims to provide an overview of calculus and linear algebra and focuses on the fundamental mathematical tools and concepts, such as limits, differentiation, and integration. Building on these basic concepts, we will review methods for solving problems related to optimization, linear differential equations, and matrix algebra.

Outline of the course:
1. Calculus:
1.1 Limits of functions
1.2 Continuity, types of discontinuities, intermediate value theorem
1.3 Differentiation (or derivative), slope, secant, tangent
1.4 Rules and theorems for differentiation, power rule, product rule, chain rule
1.5 Derivatives of exp, log, and trigonometric functions
1.6 Implicit differentiation and derivative of inverse functions
1.7 Rolle's theorem, mean value theorem, critical point, maximum/minimum of a function
1.8 First and second derivative tests, inflection points
1.9 Anti-derivative, indefinite integral, integration by substitution, integration by parts
1.10 Definite integral and its application (area between curves, application in physics)\
1.11 Optimization and linear differential equations

2. Linear Algebra:
2.1 Vectors and scalars in Euclidean space, vector arithmetic, scalar product, cross product
2.2 Equations for lines and planes, vector spaces, linear independence, span, basis, dimension
2.3 Linear transformations, coordinates, and representation of linear transformations by matrices
2.4 Matrix operations: matrix multiplication, transpose, determinant, inverse, and Hermitian conjugate
2.5 Systems of linear equations, Gaussian elimination
2.6 Eigenvalues and eigenvectors
2.7 Range, kernel, and rank-nullity theorem

and many more...

*Note that the sessions will be held online (via Discord/Zoom/Microsoft Teams).

Mohamed

4.89

(9)

Do you feel that your child is working hard in mathematics, but their results are not improving?

He understands the lesson, but doesn't know how to start an exercise?
He knows the formulas, but doesn't know when or how to use them?
Does he lack a solid foundation, accumulate difficulties from one chapter to the next, or lose confidence as soon as an exercise becomes more complex?
Does he have difficulty organizing his work, reasoning, or writing his solutions correctly?
Or perhaps he is preparing for an exam, the Brevet or the Baccalaureate, and doesn't know how to prepare effectively?

It is precisely in these difficulties that I can support him.

I am a mathematics teacher with 13 years of teaching experience, holding a Master's degree in mathematics and trained at ENSET Mohammedia. I tutor middle and high school students, particularly in the Moroccan and French curricula.

🎯 My goal: to understand the difficulty before trying to fix it

Not every student has the same problem.

Some have gaps in their basic knowledge.
Others understand the lesson but lack a method.
Some people know how to solve classic exercises but get stuck as soon as the problem statement changes.
Others primarily need to regain confidence and learn to work in a more organized way.

That's why I'm not simply suggesting we redo the course.

During the initial sessions, I identify the student's difficulties and the concepts that need reinforcement. We then create a learning plan tailored to their level, pace, and objective.

📚 How does my support work?

Depending on the student's needs, we can work on:

• understanding the course material and difficult concepts;
• the upgrading and the accumulated gaps;
• the method for solving the exercises;
• mathematical reasoning;
• drafting and presenting solutions;
• progressive exercises adapted to the student's level;
• homework and tests;
• preparation for the Brevet and the Baccalaureate;
• exam preparation;
• Work organization and priority management.

I adapt to the student's pace: the goal is not simply to give them the answer, but to allow them to understand, reason and gradually become autonomous.

💻 Truly interactive online courses

The classes are conducted remotely using Google Meet and an interactive whiteboard.

The student can follow the explanations, participate directly, solve the exercises with me and receive materials or screenshots of the work done during the session.

I favour a clear, progressive and interactive teaching method, with plenty of practice.

🏆 A concrete experience of academic support

During my years of teaching, I have worked with students of very different profiles and levels.

For my final year students who were tutored in mathematics, I achieved a 100% success rate in the Baccalaureate, with 75% obtaining a distinction of "Bien" or "Très Bien".

My goal, however, is not solely to obtain a better grade in the short term: I am primarily seeking to gradually eliminate the obstacles that prevent the student from progressing.

👨‍🎓 For which students?

• Middle school: 5th, 4th, 3rd grade
• High school: 10th, 11th, 12th grade
• Moroccan and French programs
• Mathematics specialization at the French high school
• Refresher course
• Regular support
• Preparation for tests and exams
• Preparation for the Brevet and Baccalaureate exams

The courses are designed for both students who are experiencing difficulties and those who wish to consolidate their level and aim for better results.

📩 You don't know exactly why your child is struggling with math?

You can describe his level, his current difficulties and his goal in your message.

I can tell you which points we should work on as a priority and suggest a suitable support method.

My goal is simple: to transform difficulties into skills and help the student gradually regain confidence in their mathematical abilities.

Baia

4.89

(9)

I work with two kinds of students: those preparing to meet university math admission requirements (OMPT, CCVX, VWO), and those already enrolled who need solid support in calculus, linear algebra, differential equations, probability & statistics, or discrete math including students at TUM, ETH Zurich, TU Delft, KTH, EPFL, and RWTH Aachen.
Lessons are in English; I can explain in German where it helps.

Vikash

4.89

(9)

I am a passionate educator dedicated to creating an engaging and inclusive learning environment for all my students. With a solid educational background and seven years of teaching experience, I am committed to helping students achieve their academic goals and develop a lifelong love for learning.

I really happy to teach people who will really want to part of my lesson.

My teaching style is the step by step oriented. We will start from basic and move towards advanced topics.

A very warm welcome my students on apprentus.com

Wish you all the best.

Vikas

4.89

(9)

I am an experienced mathematics tutor with 10+ years of experience teaching students and working professionals.

I love teaching students who are passionate about learning subjects or who want to understand any mathematics, Trigonometry, Algebra, Geometry , Calculus or statistics concept at the graduate or master’s level.

Reza

4.89

(9)

I hold a PhD in Mechanical Engineering and currently work as a post-doctoral researcher in the Aerospace Engineering Faculty at TU Delft (Delft University of Technology).
Key topics that I teach for this course include:
• Calculus: Differentiation & integration, Multivariable calculus
• Linear Algebra: Matrices, vectors, systems of equations, Eigenvalues and eigenvectors
• Differential Equations: First- and second-order ODEs, Laplace transforms
• Complex Numbers: Polar form, Euler’s formula
• Vector Calculus: Gradient, divergence, curl, Line and surface integrals
• Series & Transforms: Taylor series, Fourier series

I understand that not all teachers excel in teaching Engineering and Mathematics courses and explaining their importance to students. Courses with strong mathematical backgrounds may become boring for students who lack a solid mathematical basis. To address this, I take a student-centered approach, starting from the basics to actively engage all students, including those with weaker mathematical backgrounds. I also provide practical examples to demonstrate the real-world significance of what they are learning, inspiring and fostering their interest in the subject matter.

If you have any additional questions before starting a class, please feel free to ask me. I am here to assist! :)

Abubakar

4.89

(9)

Build a clear understanding of mathematics and physics, with lessons adapted to your course, current level and goals. I support upper-secondary students (videregående/VG), O-Level students and students taking introductory university mathematics or physics.

I completed my MSc in Mathematics and Physics, specialising in Physics, at the University of Stavanger in August 2026. My master's thesis received an A. My teaching experience includes six separate part-time student-assistant appointments at UiS and school teaching in O-Level physics and mathematics.

Topics we can work on include:
• Physics: motion, forces, energy, mechanics, electricity, waves and foundational concepts.
• Mathematics: algebra, functions, trigonometry, differentiation, integration and introductory calculus.
• Homework guidance, revision, practice questions and preparation for tests and exams.

We start by identifying what you understand and where you get stuck. I explain the ideas, work through examples with you and guide you towards solving problems independently. You will practise setting up problems, choosing useful methods and checking whether an answer makes sense.

Lessons are taught in English and can follow your own school or university materials. For lower-secondary science covering physics, chemistry and biology, please see my separate Naturfag class for grades 8–10.

Intasar

4.89

(9)

I have graduated with a degree in chemical engineering from the University of Edinburgh, UK. I am also an Erasmus Mundus scholar with a master's in Analytical Chemistry from Uppsala University. Currently, I am pursuing a PhD in physical chemistry.

I have been tutoring since 2012 to fund my education expenses. I formally began tutoring in 2014 as part of my vocational training as a teacher in Ghana, funded by the University of Edinburgh. The formal training has taught me a lot about curriculum development, time management, and fusing my teaching methodology to my students’ needs. I have been tutoring in Physics, Chemistry, and Math, in person and online; the hybrid model has allowed me to reach out and teach students in 8 different countries. I have successful students from these past nine years who have not only commended my work ethic but can also stand testament to my enthusiasm.

My excellent academic career has nurtured in me a natural talent for teaching. My experiences have taught me how to tackle one problem at a time, and I believe that using this approach—paired with my unconventional examples that force students to think outside the box—I can truly provide an excellent understanding and explanation. My teaching methodology is based on two main things: skill development and adaptation. Initially, I create a skeleton of the most suitable methodology tailored to the preferred curriculum, after which, I adapt that lecture to the specific needs of the student based on their knowledge and grasp of the concepts. Second, I like to develop analytical and scientific ability along with knowledge in my students, and for that, I use a combination of resources in the form of worksheets, class tasks, and past papers. Last, I believe in the strong ethic of providing feedback to the parents, so that they are aware of their child’s progress.

Frequently Asked Questions:
Which subject(s) do you teach?
I teach math, mechanics, statistics, chemistry and physics. I also teach biology up to GCSE level.

When are you available? My timetable is quite flexible. I am happy to work weekdays, week evening and weekends.

Which ages and levels do you teach? The majority of my students are between the ages of 10-18, but I also teach college Students. I am also helping foundation and first year university students.

Which qualifications do you prepare your students for? GCSE, IGCSE, A/S-level, A-level, IB, School entrance exams and SATs

Describe your arrangements for online tutoring? I use Zoom online sessions since it has many tools and features specially designed for interactive and visual learning. I am fully equipped with modern gadgets for e-learning. I use Google drive and docs to share files.

Nazir

4.89

(9)

Having coached 100+ students from more than 10 universities worldwide, I have developed a strong understanding of the homework expectations, assessment methods, and exam styles commonly used in university-level mathematics courses.

One of the biggest challenges students face in university calculus is the transition from high school mathematics. Differences in curriculum, notation, problem-solving approaches, and calculator usage can create significant knowledge gaps that make it difficult to keep up with the course material.

I help students identify and close these gaps by strengthening the underlying mathematical foundations and developing the skills required for success in higher education. Whether you are struggling with prerequisites, falling behind in lectures, or aiming for top grades, lessons are tailored to your specific needs and course requirements.

I provide comprehensive support in Calculus I, II, and III, including:

- Limits and continuity
- Differentiation and applications of derivatives
- Integration techniques and applications
- Sequences and series
- Multivariable calculus
- Partial derivatives and multiple integrals
- Vector calculus and related topics

I can help you understand assignments and prepare for exams, build the confidence and understanding needed to excel throughout your university studies.

Thelma

4.89

(9)

Struggling with Maths? Let's work towards better grades together!
Hi, I'm Thelma, and I offer supportive online mathematics lessons for students studying GCSE, IGCSE, AS and A-Level Pure Mathematics.
Whether you're struggling with the basics, finding algebra confusing or preparing for an important examination, my lessons are designed around your learning needs and goals.

•We will focus on;

📘 GCSE & IGCSE Mathematics
Topics include:
• Number, fractions, percentages and ratios
• Algebra, equations and inequalities
• Geometry and mensuration
• Graphs and functions
• Trigonometry
• Statistics and probability

📗 AS & A-Level Pure Mathematics
Topics include:
• Algebra, simultaneous equations and polynomials
• Sequences and series, including arithmetic and geometric progressions
• Coordinate geometry
• Trigonometry and trigonometric identities
• Differentiation and integration
• Functions and other relevant syllabus topics

🎯 Exam Preparation
We will practise exam-style questions, review challenging topics, identify areas for improvement and work through solutions step by step. Where appropriate, we will use past papers from your examination board, including Pearson Edexcel and AQA.

💻 What to expect in my lessons
• Clear, step-by-step explanations
• Interactive online teaching and worked examples
• Practice questions suited to your level
• Lessons tailored to your goals
• Support with revision and homework questions

Whether you need help understanding a topic or want structured exam preparation, we can focus on the areas where you need the most support.
Ready to improve your understanding of Maths? Book a lesson, tell me your exam board and the topics you find difficult, and let's get started!

Ammar

4.89

(9)

Mathematics, statistics, and data analysis become much easier when formulas, reasoning, computation, and real-world interpretation are connected clearly.

I am a PhD-qualified engineer, university professor, researcher, and multidisciplinary tutor with more than 30 years of experience in teaching, quantitative methods, mathematical problem solving, statistical analysis, research, engineering, data analysis, and professional decision support.

This class provides a structured and personalized learning pathway for school and university students, graduate researchers, engineers, professionals, and adult learners. Depending on your goals, we can focus on one specific area or connect several areas into a coherent program.

MATHEMATICS
• Arithmetic, fractions, ratios, percentages, and mathematical foundations
• Algebraic expressions, equations, inequalities, and systems
• Functions, graphs, and transformations
• Geometry and analytic geometry
• Trigonometry
• Precalculus
• Limits and continuity
• Differential calculus and applications
• Integral calculus and applications
• Sequences and series
• Multivariable calculus
• Linear algebra, matrices, vectors, and systems
• Differential equations
• Numerical methods
• Applied and engineering mathematics

STATISTICS, PROBABILITY & ECONOMETRICS
• Descriptive statistics
• Probability rules and probabilistic reasoning
• Conditional probability, independence, Bayes’ theorem, and counting methods
• Expected value, variance, covariance, and properties of common probability distributions
• Random variables and probability distributions
• Sampling and sampling distributions
• Confidence intervals
• Hypothesis testing
• Correlation and regression
• Multiple regression
• ANOVA, ANCOVA, and MANOVA
• Nonparametric methods
• Multivariate statistical analysis
• Econometrics and quantitative methods
• Time-series analysis and forecasting
• Mediation and moderation analysis
• Statistical modelling and predictive analysis
• Econometrics
• Multiple regression
• Time series
• Forecasting
• Mediation/moderation
• Predictive analysis

DATA ANALYSIS & VISUALIZATION
• Data organization and quality assessment
• Data cleaning and preparation
• Data transformation, filtering, grouping, merging, and reshaping
• Relationships between variables and graphical/statistical diagnostics
• Missing values, duplicates, inconsistencies, and outliers
• Exploratory data analysis
• Summary tables and analytical reporting
• PivotTables and aggregation
• Data visualization and appropriate chart selection
• Trend and pattern analysis
• KPI development and performance analysis
• Dashboard concepts and decision-support reporting
• Research and survey data preparation
• Interpretation and communication of analytical findings

Depending on your needs, practical work may involve Excel, SPSS, Stata, R, SAS, Power BI, SQL, Python, or other relevant analytical tools. Software is never treated as a substitute for understanding: I explain the reasoning behind the method, the assumptions involved, the meaning of the output, and how to verify whether the conclusion is sound.

My teaching approach follows a clear progression:
understand the problem → identify the appropriate concept or method → develop the reasoning → calculate or analyze → verify the result → interpret it → communicate the conclusion

We can work with your course syllabus, textbook, representative exercises, exam topics, dataset, statistical output, research question, spreadsheet, dashboard, engineering application, or professional analytical problem.

Whether you are rebuilding mathematical foundations, preparing for an examination, studying advanced calculus, learning statistics, conducting econometric analysis, interpreting research data, or developing practical analytical skills, I will adapt the sessions to your level, objectives, and pace.

My goal is not merely to help you obtain an answer, but to help you understand the reasoning, choose appropriate methods, verify results, interpret findings correctly, and solve new problems independently.

Abdenour

4.89

(9)

Struggling with mathematics or physics? Let's work through it together!

Hello! I offer online mathematics and physics tutoring for school students and university undergraduates. Whether you need help understanding difficult concepts, catching up with your coursework, solving exercises, or preparing for an exam, I will help you build your understanding step by step.

What can we work on?

- Mathematics: algebra, functions, equations, trigonometry, calculus, and other topics appropriate to your level.
- Physics:mechanics, electromagnetism, waves, thermodynamics, statistical physics, quantum mechanics, ...
- Academic support: understanding lessons, working through exercises, reviewing difficult topics, and preparing for tests and examinations.

My teaching approach

I believe that understanding is more important than memorizing formulas. I explain concepts clearly, work through examples step by step, and use exercises to help you apply what you have learned. I adapt each lesson to your current level, learning pace, and goals, so we can focus on the areas where you need the most support.

Whether you want to strengthen your fundamentals, improve your problem-solving skills, or explore more advanced topics, I will do my best to help you make steady progress.

Before our first lesson, tell me your current level, the topics you are studying, and what you would like to achieve. We can then plan our sessions around your needs.