High School Calculus



Course Summary:

Calculus is a year-long course that is comparable to calculus courses at the college or university level. In this course, the technological tools required for exploring, learning, and communicating calculus concepts include Microsoft Word with Microsoft Equation (or its equivalent) for typing math assignments, an approved graphing calculator (see a list of acceptable calculators at College Board AP Central) for the AP Calculus exam, and some type of grapher for creating graphs online such as Graphmatica (Windows) or Grapher (MAC) or an online graphing utility of your choice.




Module 1 - Introduction to Calculus

Module 1 Pre-Test

Seminar 1 - What is Calculus?

Seminar 2 - Intervals

Seminar 3 - Rates of Change and Linear Equations

Seminar 4 - Functions

Seminar 5 - Trigonometric Functions

Seminar 6 - Mathematical Models from Real-Life Data

Module 1 Test

Challenge Problem #1

Module 2 – Limits and Continuity

Module 2 Pre-Test

Seminar 1 - Introduction to Limits

Seminar 2 - Estimating Limits Graphically and Numerically

Seminar 3 - Evaluating Limits Analytically

Seminar 4 - Continuity and Intermediate Value Theorem

Seminar 5 - Infinite Limits and Limits at Infinity

Module 2 Test

Challenge Problem #2

Module 3 - Applications of Differentiation

Module 3 Pre-Test

Background Seminar  - Related Rates

Seminar 1 - Extrema and the Extreme Value Theorem

Seminar 2 - Rolle's Theorem and the Mean Value Theorem

Seminar 3 - Increasing and Decreasing Functions

Seminar 4 - Concavity and the Second Derivative Test

Seminar 5 - Optimization Problems

Seminar 6 - Local Linearity, Linear Approximation, and Differentials

Module 3 Test

Challenge Problem #3

Module 4 – Integration

Module 4 Pre-Test

Background Seminar

Seminar 1 - Antiderivatives

Seminar 2 - Area

Seminar 3 - Riemann Sums and Numerical Integration

Seminar 4 - Definite Integrals

Seminar 5 - The Fundamental Theorem of Calculus

Seminar 6 - Integration by Substitution

Module 4 Test

Challenge Problem #4

Module 5 – Derivatives and Integrals of Transcendental Functions

Module 5 Pre-Test

Background Seminar

Seminar 1 - Natural Logarithmic Function and Differentiation

Seminar 2 - Natural Logarithmic Function and Integration

Seminar 3 - Differentiation and Integration of the Natural Exponential Function

Seminar 4 - Bases Other Than e and Applications

Seminar 5 - Relative Magnitudes of Functions and Their Rates of Change

Seminar 6 - Differentiation and Integration of Inverse Trigonometric Functions

Module 5 Test

Challenge Problem #5

Module 6 – Applications of Integration

Module 6 Pre-Test

Seminar 1 - Area Between Two Curves

Seminar 2 - Volume of Solids with a Known Cross Section

Seminar 3 - Volume by Disks and Washers

Seminar 4 - Volume by Cylindrical Shell

Module 6 Test

Challenge Problem #6

Module 7 – Differential Equations and Their Application

Module 7 Pre-Test

Seminar 1 - Differential Equations and General and Particular Solutions

Seminar 2 - Graphical Solution Using Slope Fields

Seminar 3 - Separable Differential Equations

Seminar 4 - Applications and Modeling with Differential Equations

Seminar 5 - Integration by Parts

Seminar 6 - Indeterminate Forms and L'Hopital's Rule

Module 7 Test

Challenge Problem #7

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