Calculus Honors
HonorsProblem 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.
Quiz to follow (review of selected topics).
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 (Part 1 & 2)
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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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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Lesson 6: Continuity
Define continuity, apply the three continuity criteria, classify discontinuities, and solve for values that ensure continuity.
Quiz/graded classwork and DeltaMath assignment follow Unit 2.
Unit 3 - Derivatives
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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 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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Lesson 2: The Derivative as a Function (Day 1)
Define differential notation, interpret derivative graphs, and compute derivative functions for polynomial, radical, and rational forms.
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Lesson 2: The Derivative as a Function (Day 2)
Infer behavior of f' from f and identify nondifferentiable points from graph shape.
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Lesson 3: Rules of Differentiation (Day 1 & 2)
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 (Day 1 & 2)
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 (Days 1-3)
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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Lesson 11: Related Rates
Solve applied rate-of-change word problems by relating derivatives of linked variables.
Additional resources: Desmos Applet #2, Derivative Skill Check (completed problems), quiz review, completed quiz review, and midterm review packet (blank/completed).