# AP® Calculus AB

## Course Summary

Gain skills used in careers such as electrical engineers, economists, and business managers, which use calculus on the job. Explore the basics of calculus including functions, graphs, integrals, and more. Study the theory and application of limits, change, implicit differentiation, integration and other calculus topics. In this course, students acquire valuable problem-solving skills by mastering the concepts of differential and integral calculus.

This course prepares students for the AP® Calculus AB exam.

## Curriculum

This is a 2-semester course. We do not recommend taking both semesters simultaneously.

##### Unit 0: Review

- Lines
- Functions and Graphs
- Exponential Functions
- Functions and Logarithms
- Trigonometric Functions

##### Unit 1: Limits and Continuity

- Finding Limits Graphically and Numerically
- Evaluating Limits Analytically
- One-sided Limits
- Continuity and Intermediate Value Theorem
- Infinite Limits
- Limits at Infinity

##### Unit 2: Differentiation Definition and Fundamental Properties

- The Derivative and the Tangent Line Problem
- Basic Differentiation Rules
- Equations of a tangent Line
- The Natural Logarithmic Functions: Differentiation
- The Product and Quotient Rules

##### Unit 3: Differentiation: Composite, Implicit and Inverse Functions

- The Chain Rule
- Implicit Differentiation
- Inverse Functions
- Inverse Trigonometric Functions and Differentiation

##### Unit 4: Contextual Applications of Differentiation

- Velocity and Acceleration
- Related Rates - Introduction
- Related Rates - Advanced Examples
- Indeterminate Forms and L'Hopital's Rule

##### Unit 5: Analytical Applications of Differentiation

- Rolle's Theorem
- The Mean Value Theorem
- Extrema on an Interval
- Extrema on a Closed Interval
- Increasing and Decreasing Functions and the First Derivative Test
- Concavity and the Second Derivative Test
- A Summary of Curve Sketching
- Optimization Problems

##### Unit 6: Integration and Accumulation of Change

- Left and Right Side Approximations
- Area - Midpoint and Trapezoidal Approximations
- Riemann Sums and Definite Integrals
- Antidifferentiation and Indefinite Integration
- The Fundamental Theorem of Calculus
- Integration by Substitution
- The Natural Logarithmic Functions: Integration
- Exponential Functions: Differentiation and Integration
- Bases Other Than e and Applications
- Inverse Trigonometric Functions and Integration
- Trigonometric Integrals
- Trigonometric Substitution

##### Unit 7: Differential Equations

- Slope Fields
- Separation of Variables
- Differential Equations: Growth and Decay

##### Unit 8: Applications of Integration

- Area of a Region Between Two Curves
- Area of a Region Between Two Curves - Advanced Examples
- Volume: Solids with Known Cross Sections
- Volume: The Disk Method
- Volume: The Shell Method