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High School


Course Description:

Designed for the serious and motivated college bound student. It consists of the basic topics in Calculus that includes limits, differentiation, and integration. *Graphing calculators are required. See instructor for recommendations.

Semester 1

Topic 1: Limits: Graphically and Numerically
Topic 2: Limits Analytically (Including Trigonometry)
Topic 3: Continuity
Topic 4: Intermediate Value Theorem

Derivative Rules & Tangent/Normal Lines
Topic 1: Limit Definition of a Derivative
Topic 2: Rules of Derivatives 1 (Power Rule, Product Rule, Quotient Rule, and Trig Rules)
Topic 3: Rules of Derivatives 2 (Chain Rule and Implicit Differentiation)
Topic 4: Tangent Line
Topic 5: Average Rate of Change vs. Instantaneous Rate of Change

Applications of Derivatives
Topic 1: First Derivatives Applications: Max, Min, Extreme Value Theorem, Increasing/Decreasing Intervals
Topic 2: Second Derivatives: Concavity, Points of Inflection, Second Derivative Test
Topic 3: Graphing Implications
Topic 4: Mean Value Theorem

Semester 2

Note: if the following section is blank the course is 1 semester long

Topic 1: Riemann Sums
Topic 2: Areas Under Curves
Topic 3: Rules of Integration - Definite and Indefinite
Topic 4: Second Fundamental Theorem
Topic 5: Integration as Accumulation
Topic 6: Rectilinear Motion

Transcendental Functions
Topic 1: Differentiating y=lnx and integrate y= 1/x
Topic 2: Logarithmic Differentiation
Topic 3: Differentiate and Integrate y=e ͯ
Topic 4: Differentiate and Integrate y=a ͯ and y=log a ͯ
Topic 5: Differentiate Inverse Functions
Topic 6: Differential Equations and Slope Fields

Areas and Volumes
Topic 1: Area Between Two Curves
Topic 2: Volume of Solids of Revolution
Topic 3: Volume of Solids with Known Cross-Sections

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