Mathematics - AP Calculus Semester 1

Mathematics

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Curriculum Guides 2003-2004

Mathematics - AP Calculus Semester 1

Printable Version

Goals and Descriptions

Calculus and Pre-Calculus | Functions

Calculus and Pre-Calculus

Differential Equations: Solution Methods
The learner will be able to understand the solution methods of certain elementary differential equations, as well as their use in many different situations, including growth and decay problems.

Strand	Source	Activities
Differential Equations	CA: Content Standards, 1998, Calculus, 27.0	Classroom

Derivatives: Formulas
The learner will be able to use formulas to determine the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 4.4	Classroom

Limit: Knowledge
The learner will be able to display an understanding of the formal and graphical definitions or interpretations of limits of function values, including one sided limits, limits at infinity, and infinite limits.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.0	Classroom

Calculus Concepts: Intermediate Value
The learner will be able to illustrate an understanding of the intermediate value theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 3.0	Classroom

Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 3.0	Classroom

Calculus Concepts: Rolle's Theorem
The learner will be able to understand Rolle's Theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Calculus Concepts: Understand/L'Hopital
The learner will be able to understand L'Hopital's Rule.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Apply Calculus Concepts: L'Hopital's
The learner will be able to apply L'Hopital's Rule.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Intermediate Value Theorem: Application
The learner will be able to apply an understanding of the intermediate value theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 3.0	Classroom

Extreme Value Theorem: Application
The learner will be able to apply an understanding of the extreme value theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 3.0	Classroom

Calculus Concepts: Apply/Rolle's Theorem
The learner will be able to apply Rolle's Theorem.

Strand	Source	Activities
Applying Calculus Concepts	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Derivatives: Mean Value Theorem
The learner will be able to comprehend the Mean Value Theorem.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Derivatives: Chain Rule/Proof
The learner will be able to understand the chain rule and its proof.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 5.0	Classroom

Derivatives: Higher Order
The learner will be able to calculate higher order derivatives (second derivative, third derivative, etc.).

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 7.0	Classroom

Derivatives: Composite/Chain Rule
The learner will be able to calculate the derivative of composite functions using the chain rule.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 5.0	Classroom

Derivatives: Mean Value Theorem
The learner will be able to use the Mean Value Theorem.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 8.0	Classroom

Derivatives: Sketch Graphs
The learner will be able to apply derivatives in manually sketching function graphs.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 9.0	Classroom

Derivatives: Implicit Differentiation
The learner will be able to apply the concept of implicit differentiation in many different problem types originating in a variety of curriculum areas.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 6.0	Classroom

Derivatives: Derive Formulas
The learner will be able to derive formulas for determining derivatives.

Strand	Source	Activities
Derivatives/Antiderivatives	CA: Content Standards, 1998, Calculus, 4.4	Classroom

Limits: Apply Theorems
The learner will be able to apply theorems used for evaluating the limits of sums, products, quotients, and function compositions.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.1	Classroom

Limits: Estimate/Graphing Calculator
The learner will be able to make estimates of limits with the application of graphing calculators.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.2	Classroom

Limits: Verify/Graphing Calculator
The learner will be able to verify limits with the application of graphing calculators.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.2	Classroom

Limits: Apply
The learner will be able to apply special limits such as the limit of (sin(x))/x and/or (cos(x))/x as the value of x approaches zero.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.3	Classroom

Limits: Prove Theorems
The learner will be able to create proofs of theorems that relate to the evaluating the limits of sums, products, quotients, and function composition.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.1	Classroom

Limits: Prove
The learner will be able to create proofs for special limits such as (sin(x))/x and/or (cos(x))/x as the value of x approaches zero.

Strand	Source	Activities
Limits	CA: Content Standards, 1998, Calculus, 1.3	Classroom

Problem Solving: Derivative
The learner will be able to apply the derivative to obtain solutions to problems in a variety of curriculum areas involving the rate of change of a function.

Strand	Source	Activities
Problem Solving	CA: Content Standards, 1998, Calculus, 4.2	Classroom

Differentiation: Understand/Definition
The learner will be able to understand the formal definition of the derivative of a function at a point.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 4.0	Classroom

Differentiation: Understand/Concept
The learner will be able to understand the concept of differentiability.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 4.0	Classroom

Differentiation: Understand/Slope
The learner will be able to illustrate an understanding of the derivative of a function as the slope of the line tangent to the curve.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 4.1	Classroom

Differentiation: Understand/Rate
The learner will be able to illustrate an understanding of the interpretation of the derivative of a function as the instantaneous rate of change.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 4.2	Classroom

Differentiation: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 4.3	Classroom

Differentiation: Solve/Related Rates
The learner will be able to apply differentiation in obtaining solutions to related rates problems in both theoretical and real world contexts.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 12.0	Classroom

Differentiation: Solve Optimization Prob
The learner will be able to apply differentiation in obtaining solutions to optimization problems in both theoretical and real world contexts.

Strand	Source	Activities
Differentiation	CA: Content Standards, 1998, Calculus, 11.0	Classroom

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Functions

Functions: Continuity/Definition
The learner will be able to display a comprehension of the formal definition and graphical interpretation of the concept of continuity of a function.

Strand	Source	Activities
Functions	CA: Content Standards, 1998, Calculus, 2.0	Classroom

Functions: Identify Attributes
The learner will be able to identify the various attributes of a given function, including maxima/minima, points of inflection, and increasing/decreasing intervals.

Strand	Source	Activities
Functions	CA: Content Standards, 1998, Calculus, 9.0	Classroom

Functions: Convergence/Divergence
The learner will be able to comprehend the definition of convergence and divergence of a function as the domain variable approaches a fixed number or infinity.

Strand	Source	Activities
Functions	CA: Content Standards, 1998, Calculus, 1.0	Classroom

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