AP Calculus BC

Jump Start Class

Tuesdays and Thursdays
June 9th - August 1st, 2025
5:30pm-7:30pm

Concept Overview

1. Limits and Continuity

  • Understanding the concept of a limit.

  • Limits at infinity.

  • Continuity and the Intermediate Value Theorem.

  • Limits of indeterminate forms (L'Hopital’s Rule).

2. Differentiation

  • Definition of the derivative.

  • Basic differentiation rules (power, product, quotient, chain rule).

  • Implicit differentiation.

  • Derivatives of trigonometric, exponential, logarithmic, and inverse functions.

  • Applications of the derivative:

    • Related rates.

    • Optimization problems.

    • Linear approximation and differentials.

3. Integration

  • Definition of the integral (antiderivative).

  • Fundamental Theorem of Calculus.

  • Techniques of integration:

    • Substitution.

    • Integration by parts.

    • Trigonometric integrals.

    • Partial fractions.

  • Improper integrals.

  • Numerical methods for integration (e.g., trapezoidal rule, Simpson's rule).

4. Applications of Integrals

  • Area under curves.

  • Volume of solids of revolution (disk and washer methods).

  • Work, fluid pressure, and other physical applications.

  • Average value of a function.

  • Arc length and surface area.

5. Series

  • Sequences and series.

  • Convergence and divergence.

  • Power series.

  • Taylor and Maclaurin series, including their radius and interval of convergence.

  • Error bounds for approximating functions using series.

6. Polar Coordinates and Parametric Equations

  • Parametric equations and their derivatives.

  • Polar coordinates and graphs.

  • Calculus with parametric and polar equations (area, length, etc.).

7. Differential Equations

  • Solving separable differential equations.

  • Slope fields.

  • Euler’s method.

8. Applications of Derivatives and Integrals

  • Analyzing functions using the first and second derivatives (increasing/decreasing, concavity, and points of inflection).

  • Optimization and motion problems.

  • Work and related physical applications.

These topics make up the majority of what is assessed on the AP Calculus BC exam. The test consists of multiple-choice questions and free-response questions, with a focus on problem-solving, conceptual understanding, and mathematical reasoning.

Schedule: June 9th – August 1st, 2025 (Tuesdays and Thursdays, 5:30 PM – 7:30 PM)

Week 1: Limits & Continuity

  • ✅ Tuesday, June 10, 2025 – Understanding the Concept of a Limit & Limits at Infinity
    Introduction to the concept of limits, evaluating limits, and limits at infinity.

  • ✅ Thursday, June 12, 2025 – Continuity & Intermediate Value Theorem + L'Hopital's Rule
    Exploring the continuity of functions and the Intermediate Value Theorem, plus an introduction to L'Hopital's Rule for indeterminate forms.

Week 2: Differentiation Basics

  • ✅ Tuesday, June 17, 2025 – Definition of the Derivative & Basic Differentiation Rules (Power, Product, Quotient, Chain)
    Covering the formal definition of the derivative and the key differentiation rules.

  • ✅ Thursday, June 19, 2025 – Implicit Differentiation & Derivatives of Trigonometric, Exponential, Logarithmic, and Inverse Functions
    Implicit differentiation and applying differentiation rules to trigonometric, exponential, logarithmic, and inverse functions.

Week 3: Advanced Derivative Applications

  • ✅ Tuesday, June 24, 2025 – Related Rates & Optimization Problems
    Introduction to related rates problems and optimization techniques.

  • ✅ Thursday, June 26, 2025 – Linear Approximation & Differentials
    Exploring linear approximation and using differentials for error estimation.

Week 4: Introduction to Integration

  • ✅ Tuesday, July 1, 2025 – Definition of the Integral & Fundamental Theorem of Calculus
    Understanding the definition of the integral and the relationship between integration and differentiation via the Fundamental Theorem of Calculus.

  • ✅ Thursday, July 3, 2025 – Integration by Substitution
    Learning the method of integration by substitution for simplifying integrals.

Week 5: Integration Techniques

  • ✅ Tuesday, July 8, 2025 – Integration by Parts & Trigonometric Integrals
    Mastering integration by parts and applying techniques to integrate trigonometric functions.

  • ✅ Thursday, July 10, 2025 – Partial Fractions & Improper Integrals
    Exploring partial fraction decomposition and how to evaluate improper integrals.

Week 6: Applications of Integrals

  • ✅ Tuesday, July 15, 2025 – Area Under Curves & Volume of Solids of Revolution (Disk and Washer Methods)
    Applying integrals to find the area under curves and calculating volumes of solids of revolution using disk and washer methods.

  • ✅ Thursday, July 17, 2025 – Work, Fluid Pressure, Average Value of a Function, Arc Length, and Surface Area
    Using integrals to calculate work, fluid pressure, average values, arc length, and surface area.

Week 7: Series & Polar Coordinates

  • ✅ Tuesday, July 22, 2025 – Sequences and Series: Convergence & Divergence
    Introduction to sequences and series, with a focus on determining convergence or divergence.

  • ✅ Thursday, July 24, 2025 – Power Series, Taylor & Maclaurin Series, Error Bounds, Polar Coordinates & Parametric Equations
    Learning about power series, Taylor and Maclaurin series expansions, error bounds, and polar coordinates and parametric equations.

Week 8: Differential Equations & Review

  • ✅ Tuesday, July 29, 2025 – Solving Separable Differential Equations & Euler’s Method
    Methods for solving separable differential equations and using Euler’s method for numerical approximation.

  • ✅ Thursday, July 31, 2025 – Review of Derivative & Integral Applications, Optimization, Motion, & Physical Applications
    A comprehensive review of derivative and integral applications, including optimization, motion, and other physical applications.

Notes:

  • Concept Focus: Each week is dedicated to a particular concept or topic, with enough time for practice questions and review.

  • Review & Practice: Some weeks may focus on review and practice from the previous weeks, especially towards the end of the schedule.

  • Advanced Practice: The final week is used to simulate a full practice test, addressing any remaining weak areas before the exam.

AP Calculus BC Jump Start Class – Purchase Information

Class Schedule:

  • Every Tuesdays and Thursdays from 5:30 PM to 7:30 PM

  • Start Date: June 9th. 2025

  • End Date: August 1st, 2025

Location:

  • In-person sessions will take place at 21150 Box Springs Rd. Suit 201, Moreno Valley, CA 92557

  • Online enrollment available on Zoom.

What’s Included in the Fee:

  • Taxes and Fees Included

  • Access to all class materials:

    • Practice worksheets and handouts

    • Access to online practice problems and resources

    • AP Calculus BC practice tests

  • In-class support and guidance from experienced instructors

Payment Policy:

  • Total Cost: $960 per student ($30/hour for 32 hours)

  • A non-refundable payment is required to secure your spot in the class.

  • Payments can be made via cash or card.

  • Once payment is successfully processed, you will receive an email confirmation with all class details.

Class Size:

  • Classes will be conducted in small groups with a maximum of 5 students per class to ensure individual attention and engagement.

Materials Needed:

  • Calculator (Scientific or Graphing recommended for practice)

  • Notebook or paper for note-taking and solving problems during sessions

  • Pen/Pencil for practice exercises

By purchasing this class, you agree to the terms and conditions outlined above. We look forward to helping your child succeed on the SAT!

Contact us.