District Curriculum Overview

 

Subject:   Mathematics                                            Course:  340 Calculus Honors                                                Grade Level: 9 – 12

 

Concepts

Topics/Units

Content/Skills

Essential Activities/Agreements

Understanding graphs of continuous functions and their limits

Limits & Continuity of Functions

·         Formal definition of limits using epsilon-delta approach

·         Estimiating Limits

·         Finding limits algebraically

·         Theorems of limits and one-sided limits

·         Continuous functions

 

Understanding derivatives of a function, graphically, numerically and algebraically using limits.

 

Derivatives

·         As velocity

·         As slope of tangent lines

·         Rules for finding derivatives

·         Increments and Differentials

·         Chain Rule

·         Implicit differentiation

·         Higher order derivatives

 

Using derivatives to solve real world problems based on rates of change and optimization

Applications of Derivatives

·         Local extrema of functions

·         Rolle’s theorem and Mean Value theorem

·         First and Second derivative tests

·         Horizontal and vertical asymptotes

 

Using Riemann Sums and trapezoidal sum to approximate a definite integral of a function.

Definite Integrals

 

·         Area under a curve

·         Properties of the definite integral

·         Mean Value theorem

·         Fundamental Theorem of Calculus

·         Indefinite Integrals

·         Numerical Integration

 

Using integrals to solve real world problems

 

 Application of Definite Integral

·            Area between two graphs

·            Volumes of solids of revolution

·            Finding volumes using cylindrical shells/slicing methods