Course Documents
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Opening Day Handout
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General Timeline (Drill-Down Topics)
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Midterm Review
Blank review and completed review for the Calculus Honors midterm.
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Final Exam Review
Blank review and completed review for the Calculus Honors final exam.
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)
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.
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Lesson 6: Local Linearity
Use tangent lines and linear approximations to estimate function values near a point.
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Lesson 7: L'Hôpital's Rule
Use L'Hôpital's Rule to evaluate indeterminate forms by differentiating numerator and denominator.
Additional resources: Derivative Skill Check (completed problems), quiz review, and completed quiz review.
Unit 5 - Integration
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Lesson A: Antidifferentiation
Introduce antidifferentiation and connect derivative rules to finding families of original functions.
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Lesson B: Substitution Rule
Use substitution to rewrite and evaluate antiderivatives by reversing the chain rule.
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Lesson 1: Riemann Sums and Trapezoidal Rule
Approximate area under a curve using Riemann sums and the Trapezoidal Rule.
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Lesson 2: Definite Integrals
Interpret definite integrals as accumulated change and signed area over an interval.
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Lesson 3: The Fundamental Theorem of Calculus
Connect accumulation functions, derivatives, and definite integrals through the Fundamental Theorem of Calculus.
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Lesson 4: The Average Value of a Function
Use definite integrals to find and interpret the average value of a function over an interval.
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Lesson 5: u-Substitution with Definite Integrals
Apply u-substitution to evaluate definite integrals and adjust bounds of integration.
Unit 6 - Applications of Integration
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Lesson 2: Area Between Two Curves
Use definite integrals to find the area enclosed between two curves.