Conquering AP Calculus 1
We are offering a 10 session package to help high schoolers improve their grades and understanding within their Calculus 1 (or Calculus AB) math classes. This tutoring package provides personalized support to strengthen core calculus skills, enhance problem-solving techniques, and prepare students for top performance in class exams and the AP Exam.
Each session includes:
-Comprehensive review of school lessons, homework, and exam material
-Extra practice problems and AP-style questions
-Personalized study strategies based on each student’s learning style
-Ongoing progress assessments and reports after each session
Students will also build critical academic habits such as time management, effective memorization, and the strategic use of online learning resources to support their long-term success.
Curriculum Overview:
1. Limits and Continuity
Understanding and evaluating limits, including at infinity
One-sided limits and asymptotic behavior
Continuity and types of discontinuities
Intermediate Value Theorem
2. Derivatives
Definition of the derivative (limit definition)
Basic derivative rules (power, sum, difference, product, quotient, chain rule)
Derivatives of trigonometric, exponential, logarithmic, and inverse functions
Higher-order derivatives
3. Applications of Derivatives
Motion (position, velocity, acceleration)
Related rates problems
Optimization problems (absolute extrema and relative extrema)
Curve sketching:
Increasing/decreasing intervals
Concavity and points of inflection
Sketching graphs based on first and second derivatives
Mean Value Theorem and Rolle’s Theorem
4. Integrals and Accumulation of Change
Antiderivatives and indefinite integrals
Definite integrals and properties
Fundamental Theorem of Calculus (Parts 1 and 2)
Integrating functions involving u-substitution
5. Applications of Integration
Area under a curve and between curves
Accumulated change problems (growth/decay models)
Volume of solids of revolution (disk and washer methods)
Average value of a function
6. Differential Equations and Slope Fields
Solving simple separable differential equations
Sketching slope fields
Modeling with differential equations (growth and decay models)
By the end of the program, students will have built a strong, confident foundation in AP Calculus AB, equipped with the skills needed to excel in both their school coursework and the AP Exam.
