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AP Calculus AB
Jun 25 – Aug 22, every Wed & Fri @ 7:00-8:00pm ET
$315 for 18 hours or $19 per session
Lesson 1: Limits and Continuity (2 hours)
• One- and Two-Sided Limits
• Limits That DNE
• Indeterminate Form of 0/0
• Infinite Limits
• Squeeze Th. & Trig Limits
• Continuity
• IVT
• Problem Solving
Lesson 2: Derivatives (4 hours)
• The Tangent Line Problem
• Instantaneous Rate of Change
• The Definition of Derivative
• The Alternate Form of Derivative Definition
• Continuity vs. Differentiability
• Derivative Rules: Power, Constant & Sum/Difference
• Higher Order Derivatives
• The Product Rule
• The Quotient Rule
• The Chain Rule
• Derivatives of Trigonometric Functions
• Derivatives of Logarithms and e
• Derivatives of Piecewise & Absolute Value Functions
• Appendix of Proofs
• Equations of Tangent Lines
• Horizontal Tangent Lines
• Equations of Normal Lines
• Derivatives of Inverse Functions
• Interpreting Rules of Derivatives
Lesson 3: Applications of Derivatives (2 hours)
• L’Hopital’s Rule
• Implicit Differentiation
• Related Rates
• Differentials
• Linear Approx. & Motion
Lesson 4: Analyzing Functions using Derivatives (3 hours)
• Extreme Values - Graphically
• Critical Values - Algebraically
• Extreme Values - Algebraically (1st Derivative Test)
• Extreme Value Theorem
• Concavity - Graphically
• Concavity - Algebraically
• The 2nd Derivative Test
• Connecting Graphs of f, f’ and f”
• Curve Sketching
• Analyzing Implicit Functions
• Roller’s Theorem
• Mean Value Theorem
• Newton’s Method
• Optimization
Lesson 5: Integration (4 hours)
• Riemann Sums
• Riemann Sums with Tables
• Trapezoidal Approximation
• Review: Sigma Notation
• Area Approximation with Sigma Notation
• The Definite Integral
• Antiderivatives
• Indefinite Integrals
• The Fundamental Theorem of Calculus - Part II
• The Fundamental Theorem of Calculus - Part I
• Average Values of Integrals
• Mean Value Theorem for Integrals
• u-Substitution
• More work with u-Substitution
• u-Substitution with Definite Integrals
Lesson 6: Application of Integration (3 hours)
• Integral Defined Functions (Graphically)
• Integral Defined Functions (Algebraically)
• Net Change/Accumulation
• Rate In/Rate Out
• Particle Motion Revisited
• Area Between Two Curves
• Volume by Disk Method
• Volume by Disk Method with Other Axes
• Volume by Washer Method
• Volume by Known Cross-Sections
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