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Course Description

In Calculus, the student brings together all the skills learned in Algebra through Precalculus and applies them to the study of limits.  Students will find themselves in a course traditionally taken by first and second  semester college students.  During the first semester, the student will engage in a complete analysis of limits of ratios (derivatives).  During the second semester, the student will perform the same analysis on limits of sums (integrals).

Grade Levels: 11th - 12th

Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards

Essential Questions: 

  • How can I evaluate limits, the definition of continuity, and the Intermediate Value Theorem?
  • How can I find derivatives, equations of tangent lines and test for differentiability?
  • How can I find derivatives of specific types of functions?
  • How can I apply derivative techniques to analyze graphs of functions and select applications?
  • How can I apply derivative techniques to select applications to deepen my understanding of how derivatives can be used further in other problem-solving processes?
  • How can I find antiderivatives?
  • How can I use definite integration as an application to determine area?
  • How can I use definite integration as an application to determine area between curves, volume, average values of functions and accumulating amounts?

Enduring Understanding/Big Ideas:

  • Students will determine expressions and values using mathematical operations, procedures and rules.
  • Students will translate mathematical information from a single representation or across multiple representations in order to develop processes to problem solve.
  • Students will recognize mathematical reasoning requires justification of both process and solution.
  • Students will use correct notation, language and mathematical convention to classify concepts and communicate results or solutions.

Course Level Scope & Sequence (Units &/or Skills):

Unit 1: Limits

  • Evaluating limits using graphs or tables
  • Limits at Infinity
  • Formal Definition of a Limit
  • Evaluating Limits Algebraically
  • Justifying Limits that do not exist
  • Limits of Trigonometric Functions
  • Continuity
  • Intermediate Value Theorem
  • Tangent/Velocity

Unit 2: Derivatives

  • Definition of a Derivative
  • Derivative Rules (Power, Product, Quotient)
  • Derivatives of Trig Functions
  • Chain Rule
  • Differentiability
  • Higher Order Derivatives

Unit 3: Inverse Functions

  • Exponential Functions & Their Derivatives
  • Derivatives of Logarithmic Functions

Unit 4: Applications of Derivatives (part 1)

  • Maximum & Minimum Function Values
  • Mean Value Theorem
  • First Derivative Test (finding Relative Extrema)
  • Using the First Derivative to determine where a function increases or decreases
  • Second Derivative Test (finding Relative Extrema)
  • Using the Second Derivative to determine the concavity of a function and inflection points
  • Graphs of Functions & Their Derivatives

Unit 5: Applications of Derivatives (part 2)

  • Rectilinear Motion
  • Implicit Differentiation
  • Related Rates
  • Linear Approximations
  • L’Hopital’s Rule
  • Newton’s Method

Unit 6: Antiderivatives

  • Antiderivatives
  • Antiderivatives by Substitution
  • Differential Equations

Unit 7: The Definite Integral

  • Sigma Notation
  • Approximating Area (Riemann Sums)
  • Exact Area using Limit of Riemann Sums
  • The Definite Integral
  • The Fundamental Theorems of Calculus

Unit 8: Area & Volume

  • Area Between Curves
  • Volumes by Slicing
  • Volumes using Disk/Washer
  • Average Value of a Function

Course Resources & Materials: Calc (Math) Medic, Desmos

Date Last Revised/Approved: 2011