Calculus Honors
Problem sets, AP-style practice, and enrichment materials.
Course Documents
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Opening Day Handout
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General Timeline (Drill-Down Topics)
Unit 1 - Functions (Review)
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Lesson 1: Function Notation and Rates of Change
Interpret and use function notation, write and simplify difference quotients, calculate average rate of change over an interval, define a secant line, and write secant line equations in point-slope form.
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Lesson 2: Representing Functions
Sketch parent functions, classify function families, identify key features (domain/range, intervals, extrema, end behavior), and graph transformations.
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Quiz Review, 1-1 through 1-2
Quiz review resource covering Unit 1, lessons 1-1 through 1-2.
Unit 2 - Limits
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Lesson 2: Definitions of Limits
Define limits, one-sided limits, and non-existent limits; evaluate limits from graphs, by substitution, and using TI-Nspire.
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Lesson 3: Techniques for Computing Limits
Apply limit laws, identify indeterminate forms, and evaluate 0/0 limits using factoring, division, rationalization, complex fraction simplification, and basic trig identities.
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Quiz to follow (Lessons 2-2 and 2-3).
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Lesson 4: Infinite Limits
Identify infinite limits visually, define vertical asymptotes with limits, and evaluate rational-function behavior near asymptotes.
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Lesson 5: Limits at Infinity
Connect Algebra II end behavior to limits at infinity and identify horizontal asymptotes through limit reasoning.
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Quiz to follow (Lessons 2-4 and 2-5).
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Lesson 6: Continuity
Define continuity, apply the three continuity criteria, classify discontinuities, and solve for values that ensure continuity.
DeltaMath assignment to follow Unit 2-6.
Unit 3 - Derivatives
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Lesson 1: Introducing the Derivative
Build derivative meaning from average to instantaneous rate of change and compute derivatives from the limit definition (both forms).
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Desmos Applet #1: Secant Line to Tangent Line
Explore how a secant line approaches a tangent line as points get closer.
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Lesson 2: The Derivative as a Function
Define differential notation, interpret derivative graphs, compute derivative functions, infer behavior of f' from f, and identify nondifferentiable points from graph shape.
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Desmos Applet #2: Evaluating f'(x) at Various a-values
Visualize tangent lines at selected a-values and use f'(a) to verify slope behavior directly from the graph.
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Lesson 3: Rules of Differentiation
Develop constant, power, constant multiple, sum rules, natural exponential derivatives, and higher-order derivatives.
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Lesson 4: Product and Quotient Rules
Differentiate products/quotients and practice with class and homework problems.
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Lesson 5: Derivatives of Trigonometric Functions
Use trig limits to derive sine/cosine derivatives, extend to all trig functions, and apply product/quotient/higher-order rules.
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Lesson 6: Derivatives as Rates of Change
Connect position, velocity, and acceleration using analytical and graphical models.
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Lesson 7: The Chain Rule
Differentiate compositions of functions using chain rule strategies.
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Lesson 8: Implicit Differentiation
Differentiate implicitly defined relationships when y is not isolated.
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Lesson 9: Exponential and Logarithmic Derivatives
Review exponent/log properties and differentiate exponential and logarithmic functions with chain/product/quotient/implicit rules.
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Lesson 10: Derivatives of Inverse Trigonometric Functions
Differentiate inverse trig functions and apply combined derivative rules.
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Quiz Review, 3-9 through 3-10
Blank quiz review copy for Unit 3 topics covering lessons 3-9 through 3-10.
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Lesson 11: Related Rates
Solve applied rate-of-change word problems by relating derivatives of linked variables.
Blank Notes Completed Notes (coming soon) Video Walkthrough Graded Assignment, Related Rates (due Monday)
Related Rates quiz for class p8 is Tuesday, February 24.
Unit 4 - Applications of Derivatives
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Lesson 1: Maxima and Minima
Identify and justify local/absolute extrema from functions and derivative behavior.
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Lesson 2: Mean Value Theorem
Apply the Mean Value Theorem to connect average and instantaneous rates of change.
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Lesson 3: What Derivatives Tell Us
Interpret derivative information to understand function behavior and key graph features.
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Lesson 4: Graphing Functions
Use derivative information to sketch and analyze function graphs.
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Lesson 5: Optimization
Apply derivatives to optimize quantities and justify maximum or minimum values in context.
Additional resources: Derivative Skill Check (completed problems), quiz review, completed quiz review, and midterm review packet (blank/completed).