[Hourly Lessons] AP Calculus AB / BC｜1-on-1 Tutoring with Tim
About Course
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If you’re looking for clear, personalized help in math or physics, this is a live 1-on-1 lesson with me, Tim Chen. I work with students from a wide range of programs. Whether you’re preparing for big exams, tackling tough topics, or aiming for top scores and universities.
Lessons are always tailored to your pace, your goals, and your learning style. I’ll help you build a solid understanding, improve problem-solving, and feel more confident step by step.
Course Contents: AP Calculus AB / BC
1. Limits and Continuity
Introduces limits, continuity, and function behavior at boundaries.
- Defining limits, notation, and estimations from graphs/tables
- Algebraic manipulation & Squeeze Theorem
- Types of discontinuities & Continuity over intervals
- Infinite limits & Asymptotes (Vertical/Horizontal)
- Intermediate Value Theorem (IVT)
2. Differentiation: Fundamentals
Defines derivatives as rates of change and develops core rules.
- Average vs. Instantaneous rates of change
- Derivative definition and differentiability vs. continuity
- Power, Constant, Sum, Difference, and Multiple rules
- Product and Quotient rules
- Derivatives of Trig, Exponential (e^x), and Logarithmic (ln x) functions
3. Advanced Differentiation
Extends differentiation to more complex functions and higher-order derivatives.
- Chain Rule (Composite functions)
- Implicit differentiation
- Derivatives of Inverse and Inverse Trig functions
- Higher-order derivatives
4. Contextual & Analytical Applications
Applies derivatives to motion, modeling, and function analysis.
- Straight-line motion (Position, Velocity, Acceleration)
- Related Rates & Optimization problems
- Mean Value Theorem (MVT) & Extreme Value Theorem (EVT)
- First and Second Derivative Tests (Concavity/Inflection)
- L’Hospital’s Rule for indeterminate forms
5. Integration & Accumulation
Introduces integration and the Fundamental Theorem of Calculus.
- Riemann Sums and area approximations
- Fundamental Theorem of Calculus (FTC)
- Indefinite integrals & Substitution Method (U-Sub)
- BC ONLY: Integration by Parts, Partial Fractions, and Improper Integrals
6. Differential Equations & Applications
Explores slope fields and physical applications of integration.
- Modeling with Differential Equations & Separation of Variables
- Area between curves & Volumes (Discs, Washers, Cross-sections)
- BC ONLY: Euler’s Method & Logistic Growth Models
- BC ONLY: Arc length and distance traveled
7. BC ONLY: Advanced Topics
Parametric, Polar, and Infinite Series expansions.
- Parametric/Vector functions: Derivatives, Integrals, and Motion
- Polar Area and Derivatives
- Series Convergence Tests (Ratio, nth-term, Integral, Comparison, etc.)
- Taylor and Maclaurin Series & Error Bounds (Lagrange)
- Radius and Interval of Convergence
Subjects I Teach
- Standardized Tests: SAT math, ACT math
- AP Courses: Calculus AB/BC, Physics 1/2/C, Statistics, Precalculus
- IBDP: Math AA/AI, Physics, IA Guidance
- A-Level: Mathematics, Physics
- Other: Algebra, Geometry, Integrated Math (IM1-IM4)
About Me
I focus on clear explanations, strong fundamentals, and real progress. I’ve worked with students worldwide to help them navigate competitive exams and build confidence in math and physics.
Lesson Format
- Live 1-on-1 via Zoom (English or Mandarin)
- Flexible scheduling
- Optional recordings and handouts
Let’s work together. One concept, one session at a time.
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