Segment A of Pre-Calculus teaches that basic operations and transformations apply to all functions. There are several types of functions, and all functions have graphical and algebraic applications. Functions can be used to solve real-life problems. Any type of equation can be reduced to a simple linear equation. There are many applications that can be solved by using linear and quadratic equations, and many similarities between equations and inequalities. All common graphs can be transformed using the same basic transformations. Polynomial functions can be solved using techniques similar to those of other types of equations. There are numerous theorems that can be useful when solving polynomial equations. The graphs of rational functions involve the use of vertical, horizontal and slant asymptotes. There is a relationship between exponential and logarithmic equations.

Segment B of Pre-Calculus teaches that graphs of trigonometric functions model various real-world phenomena. Many situations that involve right triangles can be solved using trigonometric ratio and the Unit Circle is a tool that can help solve those problems. Numeric patterns can be modeled with explicit or recursive functions. Sums of numbers can be found using a variety of formulas. The similarities and differences between the equations of conic sections as well as their practical real-world uses. Limit and continuity is essential to the study of calculus.

 

PRE-REQUISITES: Algebra  2 recommended

ESTIMATED COMPLETION TIME: For both segments 32-36 weeks or approximately 125 – 135 hours

 

MAJOR TOPICS AND CONCEPTS — SEGMENT A

Equations and Inequalities

  • Linear Equations
  • Fractional Coefficients
  • Special Cases
  • Quadratics by Factoring and Square Roots
  • Quadratics by Completing the Square and Quadratic Formula
  • Compound Inequalities
  • Inequalities with Absolute Value

Functions

  • Introduction to Functions
  • Linear Functions and Their Graphs
  • Finding the Equation of a Line
  • Parallel and Perpendicular Lines
  • Graphs of Functions
  • Transformation of Functions
  • Composite Functions
  • Inverse Functions

Polynomial and Rational Functions

  • Quadratic Functions
  • Rational Functions
  • Polynomial Functions
  • Remainder and Factor Theorems
  • Rational Zero Theorem
  • Fundamental Theorem of Algebra
  • Direct and Inverse Variation

Exponential and Logarithmic Functions

  • Exponential Functions
  • Logarithmic Functions
  • Logarithmic Properties and Graphs
  • Solving Logarithmic Equations
  • Real-World Application: Compound Interest
  • Real-World Application: Half-Life and Logistic Growth

MAJOR TOPICS AND CONCEPTS — SEGMENT B

Trigonometric Functions and Graphs

  • Inverses of Trigonometric Functions
  • Solving Trigonometric Equations
  • Sum and Difference Identities
  • Double and Half Angle Identities
  • Law of Sines
  • Law of Cosines

Series and Sequences

  • Sequences
  • Series and Sigma Notation
  • Arithmetic Sequences
  • Arithmetic Series
  • Geometric Sequence
  • Geometric Series

Conic Sections

  • Midpoint and Distance Formulas
  • Circles
  • Hyperbolas
  • Parabolas
  • Ellipses
  • Solving Systems of Equations
  • Identifying the General Form of a Conic Section

Introduction to Calculus

  • Limits with Tables and Graphs
  • Limits with Algebra
  • One Sided Limits
  • Continuity

 

LINKS TO FULL COURSE CURRICULUM MAPS

SEGMENT A

SEGMENT B