# High School Calculus Honors

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Suggested Prerequisites

Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.

Description

Follow in the footsteps of great mathematicians! This interactive course, with engaging text and graphing software, turns mathematics into an adventure. You will explore limits, continuity, differentiation, and integration of algebraic, trigonometric, and transcendental functions, along with their practical applications.

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