AP Calculus AB

Jump Start Class

Mondays and Wednesdays
June 9th - August 1st, 2025
5:30pm-7:30pm

Concept Overview

1. Limits and Continuity

  • Understanding the concept of a limit and applying limit properties.

  • Evaluating limits analytically (including one-sided limits and limits at infinity).

  • Continuity of functions and the Intermediate Value Theorem.

2. Differentiation

  • Definition of the derivative and interpreting it as a rate of change.

  • Techniques of differentiation, including the power, product, quotient, and chain rules.

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

  • Implicit differentiation.

  • Higher-order derivatives.

  • Applications of the derivative:

    • Critical points and extrema (local and global).

    • Mean Value Theorem and its application.

    • Concavity, inflection points, and the second derivative test.

    • Optimization problems and related rates.

3. Integration

  • Antiderivatives and the Fundamental Theorem of Calculus.

  • Techniques of integration, including substitution, integration by parts, and partial fractions.

  • Definite integrals and properties of definite integrals.

  • Applications of integrals:

    • Area under curves.

    • Average value of a function.

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

    • Work, area between curves, and other applied problems.

4. Applications of Differentiation and Integration

  • Slope fields and differential equations.

  • Mathematical modeling using calculus.

  • Numerical methods (such as the Trapezoidal Rule and Simpson’s Rule).

5. Differential Equations

  • Solving basic differential equations, including separable equations and growth/decay models.

  • Slope fields and their relationship to differential equations.

The AP Calculus AB exam also emphasizes:

  • Conceptual Understanding: Understanding the principles behind the mathematics.

  • Problem Solving: Applying mathematical concepts to solve real-world problems.

  • Communication: Clearly explaining reasoning and work in the context of calculus.

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

Week 1: Foundations & Limit Concepts

  • ✅ Monday, June 9th, 2025 – Introduction & Diagnostic Test (1 hr) + Limit Concepts: Understanding and Evaluating Limits (1 hr)
    Introduction to the course, diagnostic test, and understanding basic limit concepts.

  • ✅ Wednesday, June 11, 2025 – One-Sided Limits, Limits at Infinity, and Continuity
    Exploring one-sided limits, limits at infinity, and the concept of continuity.

Week 2: Derivatives & Differentiation Techniques

  • ✅ Monday, June 16, 2025 – Definition of Derivative and Basic Techniques (Power, Product, Quotient Rules)
    Understanding the definition of the derivative and applying basic differentiation rules.

  • ✅ Wednesday, June 18, 2025 – Chain Rule, Derivatives of Trig, Exponential, Logarithmic Functions
    Learning the chain rule and differentiating trigonometric, exponential, and logarithmic functions.

Week 3: Advanced Derivative Applications

  • ✅ Monday, June 23, 2025 – Implicit Differentiation, Higher-Order Derivatives
    Exploring implicit differentiation and calculating higher-order derivatives.

  • ✅ Wednesday, June 25, 2025 – Critical Points, Extrema, and Mean Value Theorem
    Identifying critical points, determining extrema, and applying the Mean Value Theorem.

Week 4: Optimization & Related Rates

  • ✅ Monday, June 30, 2025 – Concavity, Inflection Points, Second Derivative Test
    Understanding concavity, identifying inflection points, and using the second derivative test for concavity and extrema.

  • ✅ Wednesday, July 2, 2025 – Optimization Problems & Related Rates
    Solving optimization problems and applying related rates techniques.

Week 5: Integration & Fundamental Theorem of Calculus

  • ✅ Monday, July 7, 2025 – Antiderivatives and Fundamental Theorem of Calculus
    Learning about antiderivatives and understanding the Fundamental Theorem of Calculus.

  • ✅ Wednesday, July 9, 2025 – Integration Techniques: Substitution & Integration by Parts
    Mastering integration by substitution and integration by parts.

Week 6: Advanced Integration & Applications

  • ✅ Monday, July 14, 2025 – Integration by Partial Fractions & Numerical Methods
    Applying partial fraction decomposition for integration and using numerical methods for approximating integrals.

  • ✅ Wednesday, July 16, 2025 – Applications of Integration: Area, Volume, Work
    Using integrals to calculate areas, volumes, and work in physical contexts.

Week 7: Differentiation and Slope Fields

  • ✅ Monday, July 21, 2025 – Practice: Integration & Differentiation Problems
    Timed practice session on integration and differentiation problems.

  • ✅ Wednesday, July 23, 2025 – Slope Fields
    Learning to draw and interpret slope fields for differential equations.

Week 8: Advanced Topics

  • ✅ Monday, July 28, 2025 – Differential Equations
    Introduction to solving differential equations and applying techniques to solve simple separable equations.

  • ✅ Wednesday, July 30, 2025 – Advanced Applications
    Review of advanced calculus applications, including optimization, motion, and physical problems.

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 AB Jump Start Class – Purchase Information

Class Schedule:

  • Every Monday and Wednesday 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 AB 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.