AP Calculus BC: Advanced Concepts in Calculus

AP Calculus BC is an advanced college-level course that extends the foundational principles of AP Calculus AB.

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AP Calculus BC is an advanced college-level course that extends the foundational principles of AP Calculus AB. Covering topics such as sequences, series, parametric equations, and polar functions, this course is ideal for students looking to deepen their understanding of calculus and prepare for higher-level mathematics and science studies.

What You’ll Learn:

  1. Limits and Continuity:
    • Exploring advanced limit concepts, including L'Hôpital's Rule for indeterminate forms.
    • Understanding continuity in piecewise and complex functions.
  2. Differentiation:
    • Mastering derivative rules: power, product, quotient, and chain rules.
    • Differentiating parametric, polar, and vector-valued functions.
    • Applying derivatives to solve problems in physics, motion, and optimization.
  3. Applications of Derivatives:
    • Analyzing curves and motion with parametric equations.
    • Using derivatives to evaluate slope and concavity in polar functions.
    • Solving optimization problems in diverse contexts.
  4. Integration:
    • Techniques of integration: substitution, integration by parts, and partial fractions.
    • Evaluating improper integrals and their applications.
    • Integrating parametric and polar functions.
  5. Applications of Integrals:
    • Calculating area and volume using advanced techniques.
    • Solving problems involving arc length and surface area of solids of revolution.
    • Modeling with differential equations, including logistic growth.
  6. Sequences and Series:
    • Understanding and analyzing infinite sequences and series.
    • Working with convergence and divergence of series.
    • Mastering Taylor and Maclaurin series for approximations.
    • Understanding the radius and interval of convergence.
  7. Polar and Parametric Equations:
    • Graphing and analyzing polar functions.
    • Converting between Cartesian and polar coordinates.
    • Exploring motion in parametric equations.
  8. Vector-Valued Functions:
    • Differentiating and integrating vector-valued functions.
    • Analyzing motion in two dimensions using vectors.
  9. AP Exam Preparation:
    • Extensive practice with multiple-choice and free-response questions.
    • Focused review sessions for mastering advanced calculus concepts.
    • Strategies for managing time and accuracy on the AP exam.

Why Take This Course?

  • Earn College Credit: Scoring well on the AP Calculus BC exam can result in more college credit than AP Calculus AB.
  • Prepare for Advanced Studies: Gain essential skills for mathematics, engineering, and physics courses.
  • Challenge Yourself: Explore deeper and more complex calculus concepts to enhance problem-solving abilities.

Course Outcome:

Students will develop a thorough understanding of advanced calculus topics, prepare confidently for the AP Calculus BC exam, and gain the skills necessary for future academic success in STEM fields.

Who Should Enroll:

  • High school students who have completed AP Calculus AB or equivalent coursework.
  • Learners seeking a deeper understanding of calculus concepts.
  • Students planning to pursue mathematics, engineering, physics, or other STEM fields.

1 on 1 Class

  • Custom Schedule

  • UnDivided Attention

  • Flexible Schedules

  • Focused Learning Speed

$25/class

Book a Demo

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You will need a stable internet connection, a webcam, and a microphone for participating in the live video sessions. A quiet environment and a laptop or desktop are recommended for the best learning experience.

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If you need to cancel or reschedule a class, please do so at least 24 hours in advance. Missed classes without notice may not be eligible for rescheduling or refunds.

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