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Course Description

Students enrolled in Precalculus will extensively study operations on functions including solving equations,  graphing, and finding domain and range.  Specific functions to be studied include polynomials, rational, exponential, logarithmic and trigonometric functions.  Students will also apply their knowledge and skill to the study of analytic geometry.

Grade Levels: 10th - 12th

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

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 solve problems.
  • Students will recognize mathematical reasoning requires justification of both process and solution.
  • Students will use correct notation, language and mathematical conventions to classify concepts and communicate results or solutions.

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

Unit 1: Trigonometric Functions of Angles (degrees only)

  • Trigonometry of right triangles
  • Law of sines (ambiguous case included)
  • Law of cosines
  • Sector area and arc length 
  • Applications of trig

Unit 2: Trigonometric Functions of Real Numbers (across 2 half units)

  • The Unit Circle
  • Angle Measure – Degrees and Radians
  • Exact value 
  • Sector area and arc length 
  • Trigonometric Functions
  • Sine, Cosine & Tangent Graphs

Unit 3: Trigonometric Identities 

  • Trigonometric Identities
  • Addition and Subtraction Formulas
  • Double-Angle Formulas

Unit 4:  Trigonometric Equations

  • Inverse Trigonometric Functions
  • Trigonometric Equations

Unit 5: Intro to Analyzing Functions

  • Functions, domain, range
  • Graphs of Functions
  • Transformations of Functions
  • Extreme Values of Functions
  • Even and odd 
  • Increasing and decreasing 
  • End behavior 
  • Combining Functions and Composite Functions
  • One-to-One Functions and Their Inverses

Unit 6: Square Root, Quadratic and Rational Functions

  • Square Root Functions: Domain, range, difference quotient, rationalize, include quadratic inside radical, inverses
  • Quadratic inequalities
  • Quadratic functions: domain, range, difference quotient, extremes, end behavior, roots
  • Rational functions: domain only

Unit 7: Exponential and Logarithmic Functions

  • Exponential Functions
  • Logarithmic Functions
  • Laws of Logarithms
  • Exponential and Logarithmic Equations
  • Applications of exponential and logarithmic functions 

Unit 8: Polynomials Functions

  • Polynomial Functions and Their Graphs
  • Writing polynomial functions 
  • Extremes of polynomials
  • Real Zeros of Polynomials
  • Complex Numbers
  • Complex Roots

Unit 9: Rational Functions

  • Rational Functions: Asymptotes (Vertical, Horizontal and Slant) and holes
  • Domain and range of both

Course Resources & Materials: Math Medic, DeltaMath, Desmos