AP Calculus BC

Note: We will begin by review what was taught in AP Calculus AB; this will be called Calculus AB Review. This information will be taken from Chapters 1-5 in the textbook. Then we will study the topics that are new to Calculus BC, Chapter 6-9
Calculus AB Review:

1. Limits and Their Properties (Chapter 1)

1. Finding Limits Graphically and Numerically
2. Evaluating Limits Analytically
3. Continuity and One-Sided Limits
4. Infinite Limits

2. Differentiation (Chapter 2)

1. Definition of Derivative and Rates of Change
2.  Differentiation Rules
3. Implicit Differentiation

3. Applications of Differentiation (Chapter 3)

1. Rolle’s Theorem and Mean Value Theorem
2. First Derivative Test
3. Concavity and Second Derivative test
4. Limits at Infinity
5. Optimization Problems

4. Integration (Chapter 4)

5. Antiderivatives and Indefinite Integration
6. Riemann Sums and Definite Integrals
7. The Fundamental Theorem of Calculus
8. Integration by Substitution
9. Numerical Integration

10. Differential Equations (Chapter 5)

1. Slope field and Euler’s Method
2. Differential Equations: Growth and Decay
3. Separation of Variables and Logistic Equation

1. Applications of Integration (Chapter 6)

1. Area of a region between two curves
2. Volume: Disk and Shell Method
3. Arc Length and Surfaces of  Revolution

III. Integration Techniques, L’Hopital’s Rule and Improper Integrals (Chapter 7)

1. Integration Rules
2. Integration by Parts
3. Trigonometric Integrals
4. Trigonometric Substitution
5. Partial Fractions
6. Integration by Tables, and Other Techniques
7. Indeterminate Form and L’Hopital’s Rule
8. Improper Integrals

1. Infinite Series (Chapter 8)

1. Sequences
2. Series and Convergence
3. The Integral Test and p-series
4. Comparisons of Series
5. Alternating Series
6. The Ratio and Root Tests
7. Taylor Polynomials and Approximations
8. Power Series
9. Representations of Functions by Power Series
10. Taylor and Maclaurin Series

1. Conics, Parametric Equations, and Polar Coordinate (Chapter 9)

1. Conics and Calculus
2. Planes Curves and Parametric Equations
3. Parametric Equations and Calculus
4. Polar Coordinates and Polar Graphs
5. Area and Arc Length in Polar Coordinates
6. Polar Equations of Conics and Kepler’s Laws

This course is offered as dual credit through University of Missouri: St. Louis.^*

University Course Number:	MATH 1900
University Course Name:	Analytic Geometry & Calculus II
College Credit Earned:	5 hours
Course Fee:	$350

* Course offerings are dependent on enrollment and instructor availability.

Download the AP Calculus BC - Dual Credit Information Sheet | Download the AP Calculus BC - Dual Credit Syllabus

Find out more information about dual credit or email [email protected] if you have questions.