[Hourly Lessons] AP Calculus AB / BC｜1-on-1 Tutoring with Tim

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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.

  

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Course Contents

AP Calculus AB / BC

1. Limits and Continuity – Introduces limits, continuity, and the behavior of functions at boundaries.

1. • Introducing Calculus, instantaneous change

   • Defining limits and notation

   • Estimating limits from graphs and tables

   • Algebraic properties, manipulation, squeeze theorem

   • Multiple representations of limits

   • Types of discontinuities

   • Continuity at a point and over an interval

   • Removing discontinuities

   • Infinite limits, asymptotes (vertical & horizontal)

   • Intermediate Value Theorem

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2. Differentiation – Definition and Fundamental Properties – Defines derivatives as rates of change and develops core rules.

1. • Average vs instantaneous rates of change

   • Derivative definition and notation

   • Estimating derivatives at a point

   • Differentiability and continuity

   • Power rule

   • Constant, sum, difference, multiple rules

   • Derivatives of \(\cos x,\, e^x,\, \ln x\)

   • Product rule

   • Quotient rule

   • Trig derivatives: \(\tan,\, \cot,\, \sec,\, \csc\)

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3. Differentiation – Composite, Implicit, and Inverse Functions – Extends differentiation to more advanced functions and techniques.

1. • Chain rule

   • Implicit differentiation

   • Derivatives of inverse functions

   • Derivatives of inverse trig functions

   • Procedures for selecting derivative methods

   • Higher-order derivatives

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4. Contextual Applications of Differentiation – Applies derivatives to motion, modeling, and approximation problems.

1. • Derivatives in context (applied meaning)

   • Straight-line motion: position, velocity, acceleration

   • Rates of change in non-motion contexts

   • Related rates

   • Solving related rates problems

   • Approximations with local linearity

   • L’Hospital’s Rule for indeterminate forms

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5. Analytical Applications of Differentiation – Develops tools for analyzing function behavior using derivatives.

1. • Mean Value Theorem

   • Extreme Value Theorem (global vs local extrema)

   • Intervals of increase/decrease

   • First derivative test

   • Candidates test for extrema

   • Concavity and inflection points

   • Second derivative test

   • Graph sketching with derivatives

   • Linking function, derivative, and second derivative

   • Optimization introduction and solving problems

   • Implicit relation behavior

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6. Integration and Accumulation of Change – Introduces integration, accumulation, and the Fundamental Theorem of Calculus.

1. • Accumulations of change

   • Riemann sums and area approximations

   • Summation notation, definite integrals

   • Fundamental Theorem of Calculus

   • Accumulation functions and area interpretation

   • Properties of definite integrals

   • Antiderivatives and indefinite integrals

   • Substitution method

   • Integration with long division/completing the square

   • BC ONLY: Integration by Parts

   • BC ONLY: Partial Fractions

   • BC ONLY: Improper Integrals

   • Selecting techniques for antidifferentiation

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7. Differential Equations – Explores slope fields and solving differential equations.

1. • Modeling with differential equations

   • Verifying solutions

   • Slope fields

   • Reasoning with slope fields

   • BC ONLY: Euler’s Method

   • Separation of variables

   • Exponential models with initial conditions

   • BC ONLY: Logistic growth models

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8. Applications of Integration – Applies integration to physical and geometric contexts.

1. • Average value of a function

   • Motion: position, velocity, acceleration with integrals

   • Accumulation functions in context

   • Area between curves (x- and y-based)

   • Areas between intersecting curves

   • Volumes by cross-sections (squares, rectangles, triangles, semicircles)

   • Volumes by discs and washers (around x, y, or other axes)

   • BC ONLY: Arc length of curves and distance traveled

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9. BC ONLY: Parametric, Polar, and Vector-Valued Functions – Extends calculus to parametric, polar, and vector functions.

1. • Parametric derivatives and second derivatives

   • Arc length of parametric curves

   • Vector-valued functions: derivatives and integrals

   • Motion with parametric/vector functions

   • Polar derivatives

   • Area of polar regions (single or between two curves)

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10. BC ONLY: Infinite Sequences and Series – Develops series convergence tests and power series expansions.

• • Convergent vs divergent series

  • Geometric series

  • nth-term test

  • Integral test

  • Harmonic and $p$-series

  • Comparison tests

  • Alternating series test

  • Ratio test

  • Absolute vs conditional convergence

  • Alternating series error bound

  • Taylor polynomial approximations

  • Lagrange error bound

  • Radius/interval of convergence

  • Taylor and Maclaurin series

  • Representing functions as power series

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Subjects I Teach

• Standardized Tests
  • SAT math
  • ACT math

• AP Courses
  • AP Calculus AB / BC
  • AP Physics 1 / 2 / CM / CEM
  • AP Statistics
  • AP Precalculus

•  IBDP
  • IB Mathematics AA / AI
  • IB Physics
  • IB Internal Assessment (IA) Guidance

•  A-Level Subjects
  • A-Level Mathematics
  • A-Level Physics

• Other Subjects
  • Algebra 1 / 2
  • Geometry
  • Precalculus
  • Physics
  • Functions / Advanced Functions
  • Integrated Math (IM1 – IM4)

 

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About Me

I’ve worked with students from all over the world, helping them get through challenging material, prepare for competitive exams, and feel more confident in math and physics. I focus on clear explanations, strong fundamentals, and real progress.

 

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Lesson Format

• Live 1-on-1 via Zoom
• Flexible scheduling
• Lessons in English or Mandarin
• Optional whiteboard, handouts, or recordings based on your preference

If you’re serious about improving or want to feel more in control of your learning, let’s work together. Book a trial or message me with any questions.