AP Calculus AB
Jump Start Class
Weekly Sessions: June 16 through August 9, 2025
In-Center : Every Tuesday and Thursday from 1:00 PM to 2:00 PM
Online: Every Tuesday and Thursday from 2:00 PM to 3:00 PM
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.
Weekly Sessions: June 16 through August 9, 2025
In-Center : Every Tuesday and Thursday from 1:00 PM to 2:00 PM
Online: Every Tuesday and Thursday from 2:00 PM to 3:00 PM
Week 1: Foundations & Limit Concepts
✅Introduction & Diagnostic Test (1 hr) + Limit Concepts: Understanding and Evaluating Limits (1 hr)
Introduction to the course, diagnostic test, and understanding basic limit concepts.✅ 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
✅ Definition of Derivative and Basic Techniques (Power, Product, Quotient Rules)
Understanding the definition of the derivative and applying basic differentiation rules.✅ Chain Rule, Derivatives of Trig, Exponential, Logarithmic Functions
Learning the chain rule and differentiating trigonometric, exponential, and logarithmic functions.
Week 3: Advanced Derivative Applications
✅ Implicit Differentiation, Higher-Order Derivatives
Exploring implicit differentiation and calculating higher-order derivatives.✅ Critical Points, Extrema, and Mean Value Theorem
Identifying critical points, determining extrema, and applying the Mean Value Theorem.
Week 4: Optimization & Related Rates
✅ Concavity, Inflection Points, Second Derivative Test
Understanding concavity, identifying inflection points, and using the second derivative test for concavity and extrema.✅ Optimization Problems & Related Rates
Solving optimization problems and applying related rates techniques.
Week 5: Integration & Fundamental Theorem of Calculus
✅ Antiderivatives and Fundamental Theorem of Calculus
Learning about antiderivatives and understanding the Fundamental Theorem of Calculus.✅ Integration Techniques: Substitution & Integration by Parts
Mastering integration by substitution and integration by parts.
Week 6: Advanced Integration & Applications
✅ Integration by Partial Fractions & Numerical Methods
Applying partial fraction decomposition for integration and using numerical methods for approximating integrals.✅ Applications of Integration: Area, Volume, Work
Using integrals to calculate areas, volumes, and work in physical contexts.
Week 7: Differentiation and Slope Fields
✅ Practice: Integration & Differentiation Problems
Timed practice session on integration and differentiation problems.✅ Slope Fields
Learning to draw and interpret slope fields for differential equations.
Week 8: Advanced Topics
✅ Differential Equations
Introduction to solving differential equations and applying techniques to solve simple separable equations.✅ 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:
In-Center : Every Tuesday from 1:00 PM to 2:00 PM
Online: Every Tuesday from 2:00 PM to 3:00 PM
Start Date: June 16th. 2025
End Date: August 8th, 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!