Precalculus

Avon Lake City Schools

Curriculum Framework

Precalculus

Course Overview:

This course is to prepare students for college level mathematics. The course begins with a review of the number system and the graphs of simple functions. Emphasis is placed upon trigonometric analysis by verifying identities and solving equations. Logarithms, complex numbers and inverse functions are included in the study. This course further develops the fundamentals of algebra, coordinate geometry, complex numbers and topics in an effort to bridge the mathematics and the beginning college courses. A graphing calculator is required (TI-83 or TI-84, approximate cost: $100-$110).

Textbook (Title and Publishing Company):

Pre-Calculus, 7th Edition, James Stewart, Lothar Redlin, and Saleem Watson

Online/Supplemental Materials:

  • Delta Math
  • Desmos

Assessments:

Common assessments will be given by the entire Precalculus team

Content/Topics/Learning Goals

Subject to Pacing and Schedules

1st Quarter

Algebra and Geometry Review

The algebra review covers areas including:

  • Exponents and Radicals
  • Algebraic Expressions
  • Rational Expressions
  • Solving Equations
  • Solving Inequalities
  • Modeling
  • Lines in the Coordinate Plane
  • Distance Formula
  • Pythagorean Theorem
  • Equations of Circles
  • Classifying Triangles

Trigonometric Functions - Right Triangle Trig, Applications, Unit Circle, Trig Identities

Topics in this unit include:

  • The Unit Circle
  • Trigonometry of Right Triangles
  • Trigonometric Functions of Angles
  • Trigonometric Identities

2nd Quarter

Trigonometric Functions - Right Triangle Trig, Applications, Unit Circle, Trig Identities (continued from quarter 1)

Trigonometric Functions

  • Trigonometric Graphs
  • More Trigonometric Identities (Double-Angle Identities, Half-Angle Identities, etc.)
  • Solving Basic Trigonometric Equations
  • Using Trigonometric Identities to Solve Trigonometric Equations

3rd Quarter

Functions

Topics covered in this unit include:

  • Graphs of Functions
  • Interpreting Graphs of Functions
  • Average Rate of Change
  • Linear Functions
  • Transformations of Functions
  • Combining Functions
  • One-to-One Functions and their Inverses
  • Intro to Limits

Writing and Optimizing Functions, Polynomial Functions, Rational Functions

Topics in this unit include:

  • Quadratic Functions
  • Graphing Polynomial Functions
  • Dividing Polynomials
  • Real Zeros of Polynomials
  • Rational Functions
  • More limits

4th Quarter

Exponential and Logarithmic Functions

Topics in this unit include:

  • Graphing Exponential and Logarithmic Functions
  • The Natural Exponential Function
  • Laws of Logarithms
  • Solving Exponential and Logarithmic Equations
  • Modeling with Exponential and Logarithmic Equations
  • Logarithmic scales
  • Logistic functions
  • Compound Interest Project

Intro to Calculus

  • Limits
    • Graphically, algebraically, and with a table
  • Limit properties
  • Tangent Lines
  • Secant Lines
  • Intro to Derivatives

Conic Sections (when time permits)

Last updated: September, 2023