High School Calculus Honors

Module One: Functions

-Determining domain and range

-The difference between a relation and a function

-Using technology to support understanding

-The difference between composition and combination functions

-Vertical and horizontal transformations of functions

-Transformations of trigonometric functions

-Recognizing functions as even, odd, or neither

Module Two: Limits and Continuity

-What a limit is

-Knowing when a limit exists

-Determine a limit graphically, tabularly, and algebraically 

-Common trigonometric limits

-Know and apply properties of limits

-Limits involving vertical and horizontal asymptotes

-Understanding removable and non-removable discontinuity

-Recognizing discontinuity graphically, tabularly, and algebraically

-Average and instantaneous rate of change

-Apply limits to real-world scenarios

Module Three: Differentiation

-Notation of both Newton and Leibniz

-Limit definition of the derivative and alternate

-Equation of a tangent line

-Differentiability of functions

-Basic derivative rule: constant, sum/difference, and power

-Use of the product, quotient, and chain rules

-Derivatives of trigonometric and inverse trigonometric functions

-Derivatives of inverse functions equation

-Derivatives of exponential and logarithmic functions

-Apply derivate rules to implicit differentiation 

Module Four: Applications of Derivatives 

-Apply the first and second derivative rules

-Use derivatives to analyze graph behavior

-Sketch graph using derivative rules

-Global vs. local extrema and candidates test

-Applications of maximum and minimum

-Rectilinear motion using derivatives

-Find rates of change using derivative

-Understand the mean value theorem and L'Hôpital's Rule 

-Linearization of curves to approximate values

Module Five: Integration

-Area approximation using left, right, and midpoint

-Use summation notation to represent Riemann Sums

-Recognize a definite integral from a limit

-Integral is the area under the function

-Determine indefinite integrals using anti-derivative rules

-Understand the Fundamental Theorem of Calculus

-Perform integration by substitution

-Change limit when the variable is changed

-Properties of definite integrals

Module Six: Applications of Integrals

-Find the area under and between curves

-Know when to use vertical or horizontal variables

-Volume using the disc or washer method

-Volume with cross-sections 

-Rectilinear motion with integrals

-Finding distance vs. displacement

-Average value using mean value theorem for integrals

Module Seven: Differential Equations and More Riemann Sums

-Particular and general solutions of differential equations

-Real-world application of differential equations

-Create and use slope fields

-Recognize possible slope field of differential equation

-Trapezoidal approximation of the area under the curve

-Unequal partitions area approximation

-Error implications of different approximation methods

Module Eight: Supplemental Topics

-Explore graphs of a function and its derivative

-Compare rates of growth of functions

-Define functions using integrals

-Use tables of values to approximate area sums

-Use accumulated change and rate of change

-Recognize functions defined by integrals