• 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