AP Pre-Calculus
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Updated November 8th, 2024

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   AP Pre-Calculus is designed for serious students who want to learn challenging mathematics content to prepare them for calculus. In doing so, this course will look at mathematical properties through algebraic, graphical, and numerical lenses.

Use this link to gain College Board Course Information: link (opens a new tab).


   Welcome Pre-Calculus students!

   See your Teams page to sign up for Remind and Khan Academy.

   Keep in mind, the course is divided into three large units, which are each divided into two sections for the purposes of testing student ability. Here are several MATHguide resources to help you throughout the year.

Unit 1: Polynomial and Rational Functions

  Slope (Rates of Change)
      Slope
      Rates of Change

  Domain and Range
      Domain and Range

  Functions
      Even and Odd Functions
  Polynomials

  End Behavior
      End Behavior
      End Behavior 2

  Translations/Transformations
      Translations (of Parabolas): From Equations to Statements

  Rational Expressions
      Graphing Basic Rational Expressions
      Graphing Basic Rational Expressions as Transformations
      Graphing Intermediate Rational Expressions
      Graphing Advanced Rational Expressions

  Rational Expressions: Asymptotes
  Rational Expressions: Asymptotes and Holes

  Binomial Theorem
      Expanding Binomials
      Expanding Binomials
      Finding the nth Term
      Finding the nth Term




Unit 2: Exponential and Logarithmic Functions

  Power Rules of Exponents

  Arithmetic Sequences and Series
      Finding a Formula
      Finding the Number of Terms of a Sequence
      Finding the Sum of a Series 1
      Finding the Sum of a Series 2
      Sum of First N Multiples of M
      Sum of First N Multiples of M 2

  Geometric Sequences and Series
      Finding a Formula
      Finding the Sum of a Finite Series
      Finding the Sum of an Infinite Series

  Recognizing Functions

  Composition of Functions

  Inverses
      Finding Inverses

  Exponential Functions
  Translating Exponential Functions
      Exponential Functions: Translations

  Logarithmic Functions
      Logarithmic Functions: Translations

  Properties of Logarithms





Unit 3: Trigonometric and Polar Functions

  Sine, Cosine, and Tangent Functions

  Trigonometry Basics: SOH CAH TOA
  Right Triangle Trigonometry
      Sine Problem
      Cosine Problem
      Tangent Problem

  Trigonometric Angles: Reference Angles, Radians, Unit Circle

  Graphing Sinusoids
      Graphs to Equations

  Trigonometric Equations

  Trigonometric Expressions
      Simplifying Trigonometric Expressions
      Simplifying Trigonometric Expressions: Common Denominator
      Verifying Trigonometric Identities
      Trigonometric Expressions: Steps
      Trigonometric Expressions: Multiple Choice




Unit 4: Functions Involving Parameters, Vectors, and Matrices

  Parametric Equations
      Parametric Equations 1
      Parametric Equations 2
      Parametric Equations 3

  Polar Coordinates
      Polar Conversions
      Polar Conversions 2

  Rectangular Equations to Polar Equations
  Polar Equations to Rectangular Equations

  Conic Sections (all)

      Conic Sections: Equations of Circles

      Parabolas: Directrix, Focus, Vertex
      Parabolas: Graphing
      Parabolas: Building Equations
      Parabolas

      Graphing Ellipses
      Equations of Ellipses Given Foci and Vertices
      Graphing Ellipses

      Graphing Hyperbolas
      Graphing Hyperbolas

      Identify the Conic Section
      Conic Sections: General Form to Standard Form
      General Form to Standard Form [with help]
      General Form to Standard Form

  Vectors: Notation, Add/Subtract, Magnitude, Direction
      Horizontal and Vertical Components
      Adding Vectors
      Subtracting Vectors
      Finding Magnitude
      Finding Direction

  Engineering Notation

  Unit Vectors
      Creating Unit Vectors
      Finding Unit Vectors

  Dot Product
      Finding Vector Dot Products
      Finding Vector Dot Products

  Angle Between Two Vectors
      Calculating the Angle Between Two Vectors
      Calculating the Angle Between Two Vectors

  Word Problems
      Work Problem: Force times a Distance
      Vectors: Work Problems
      Vectors: Inclined Planes
      Vectors: Inclined Plane Problems

  Matrices: Add, Subtract, Multiply
      Adding Matrices
      Subtracting Matrices
      Scalar Multiplication
      Multiplying Matrices

  Inverse Matrices
      Inverse Matrices
      Inverse Matrices

  Matrix Equations

  Solving Systems of Equations by RREF

  Interpreting RREF Augmented Matrices