Learning Recommendations: C+ or higher average in Calculus or a C or higher average in IB Mathematics 2.

 

General Description: This one-year course further develops the topics of derivatives, integration, polynomial approximations and series, conics, coordinate systems, vectors, and their formulas for algebraic and transcendental functions. This class covers all topics typically covered during the second semester of college calculus.

Content:

I. Functions, Graphs, and Limits

1. Analysis of graphs

2. Limits of functions

3. Parametric, polar, and vector functions

II. Derivatives

1. Concept of the derivative

2. Derivative at a point

3. Derivative as a function

4. Second derivatives

5. Applications of derivatives

6. Computation of derivatives

III. Integrals

1. Interpretations and properties of definite integrals

2. Applications of integrals

3. Fundamental Theorem of Calculus

4. Techniques of anti-differentiation

5. Numerical approximations to definite integrals

IV. Polynomial Approximations and Series

1. Concept of Power Series

2. Taylor and Maclaurin Series

3. Convergence of Series

Strategies: Students will learn through a combination of:

  •  Teacher directed instruction
  •  Small group investigations
  •  Teacher-led investigations

Equipment to be provided by student: Graphing Calculator. TI-Nspire (Not CAS) is recommended.