Calculus

GENERAL STUDIES

Calculus

Course Description:

The Calculus course is a comprehensive look at the study of differential and integral calculus concepts including limits, derivative and integral computation, linearization, Riemann sums, the Fundamental Theorem of Calculus, and differential equations. Applications include graph analysis, linear motion, average value, area, volume, and growth and decay models.

 

Course Objectives:

    • Evaluate limits, including those involving infinity.
    • Define and apply numerical and function derivatives.
    • Understand the relationship between continuity and differentiability.
    • Differentiate a variety of functions written in explicit and implicit form.
    • Analyze the behavior of a function using limits and derivatives.
    • Apply differential calculus to linear approximations, motion along a line, related rate problems, and optimization.
    • Define and apply ant derivatives and indefinite integrals.
    • Define and apply Riemann sums and definite integrals.
    • Understand the consequences of the Fundamental Theorem of Calculus.
    • Integrate a variety of functions.
    • Apply integral calculus to average value, total change, and motion along a line, initial value problems, area, and volume.
    • Model and solve problems involving differential equations.

 

Assessments:

Attendance and participation: 10%

Assignments and homework: 10%

  • Nightly homework will be given as a review of what was covered in class

Tests and quizzes: 60%

  • Quizzes will be given half way through each unit.
  • Tests will be given at the end of each unit.

Midterm or final: 20%

 

Scope and Sequence:

 

Exploring Expressions, Equations, and Functions

  • Variables and Patterns
  • Order of Operations
  • Properties
    • Identity and Equality
    • Distributive
    • Associative and Commutative

 

Exploring Rational Numbers

  • Integers and Number Line
  • Rational Numbers
    • Adding/Subtracting
    • Multiplying/Dividing
    • Square Roots and Real Numbers

 

Solving Linear Equations

  • With Addition/Subtraction
  • With Multiplication/Division
  • Multi-Step Equations and with Variables on Both Sides
  • Formulas

 

Proportional Reasoning

  • Ratios and Proportions
  • Percent and Percent Change
  • Probability and Odds
  • Direct and Inverse Variation

 

Graphing Relations and Functions

  • The Coordinate Plane
    • Relations and Functions
    • Graphing Linear Equations
    • Writing Equations from Patterns

 

Analyzing Linear Equations

  • Slope
  • Writing Linear Equations
    • Point Slope and Standard Form
    • Slope Intercept From
    • Graphing Linear Equations
      • Midpoints
      • Perpendicular and Parallel Lines

 

Solving Linear Inequalities

  • With Addition/Subtraction
  • With Multiplication/Division
  • Multi-Step
  • Compound Inqualities
  • Absolute Value
  • Graphing Inequalities with Two Variables

 

Solving Systems of Linear Equations and Inequalities

  • Using Graphing
  • Using Substitution
  • With Elimination Using Addition/Subtraction and Multiplication
  • Graphing Systems of Inequalities

 

Exploring Polynomials

  • Multiplying and Dividing Monomials
  • Scientific Notation
  • Polynomials
    • Addition/Subtraction
    • Multiplying by a Monomial
    • Multiplying by another Polynomial
    • Special Products

 

 

Using Factoring

  • GCF and Distributive Property
  • Factoring Trinomials
  • Difference of Squares and Perfect Squares
  • Solving Equations by Factoring

 

Exploring Quadratic and Exponential Functions

  • Graphing Quadratic Functions
  • Solving Quadratics by Graphing
  • The Quadratic Formula
  • Exponential Functions and Growth and Decay

 

Exploring Rational Expressions and Equations

  • Simplifying
  • Multiplying/Dividing
  • Dividing Polynomials
  • Rational Expressions with Like and Unlike Denominators
  • Mixed Expressions and Complex Fractions
  • Solving Rational Equations

 

 

Exploring Radical Expressions and Equations

  • Simplifying
  • Operations with Radical Expressions
  • Radical Equations
  • Completing the Square