Skip to content

AP Pre-Calculus Concept List

The following concepts form the learning graph for the AP Pre-Calculus course. Each concept is a node in the dependency graph, and learning dependencies connect them to form recommended learning pathways.

Foundation Concepts

  1. Real Number System
  2. Number Line
  3. Order of Operations
  4. Variables and Expressions
  5. Coordinate Plane
  6. Ordered Pairs
  7. Input and Output
  8. Function Definition
  9. Function Notation
  10. Domain
  11. Range
  12. Independent Variable
  13. Dependent Variable
  14. Interval Notation
  15. Set-Builder Notation

Function Fundamentals

  1. Vertical Line Test
  2. Function Evaluation
  3. Piecewise Functions
  4. Domain Restrictions
  5. Graphing Functions
  6. Intercepts
  7. X-Intercept
  8. Y-Intercept
  9. Increasing Functions
  10. Decreasing Functions
  11. Constant Functions
  12. Function Behavior
  13. Positive and Negative Regions
  14. Bounded Functions
  15. Even Functions
  16. Odd Functions
  17. Symmetry

Rates of Change

  1. Change in Tandem
  2. Average Rate of Change
  3. Slope
  4. Slope Formula
  5. Rate of Change Units
  6. Secant Line
  7. Linear Rate of Change
  8. Nonlinear Rate of Change
  9. Concavity from Rates
  10. Increasing Rate of Change
  11. Decreasing Rate of Change

Linear Functions

  1. Linear Function Definition
  2. Slope-Intercept Form
  3. Point-Slope Form
  4. Standard Form of a Line
  5. Parallel Lines
  6. Perpendicular Lines
  7. Linear Regression
  8. Residuals
  9. Correlation

Quadratic Functions

  1. Quadratic Function Definition
  2. Standard Form of Quadratic
  3. Vertex Form
  4. Factored Form
  5. Vertex
  6. Axis of Symmetry
  7. Parabola
  8. Completing the Square
  9. Quadratic Formula
  10. Discriminant
  11. Complex Numbers
  12. Imaginary Unit
  13. Complex Zeros

Polynomial Functions

  1. Polynomial Definition
  2. Degree of a Polynomial
  3. Leading Coefficient
  4. Monomial
  5. Binomial
  6. Trinomial
  7. Polynomial Addition
  8. Polynomial Multiplication
  9. Factoring Polynomials
  10. Factor Theorem
  11. Remainder Theorem
  12. Synthetic Division
  13. Long Division of Polynomials
  14. Zeros of Polynomials
  15. Multiplicity of Zeros
  16. Real Zeros
  17. Complex Conjugate Zeros
  18. Fundamental Theorem of Algebra
  19. Polynomial End Behavior
  20. Leading Term Test
  21. Turning Points
  22. Polynomial Graphs
  23. Local Maximum
  24. Local Minimum
  25. Global Maximum
  26. Global Minimum
  27. Intermediate Value Theorem

Rational Functions

  1. Rational Function Definition
  2. Rational Expressions
  3. Simplifying Rational Expr
  4. Vertical Asymptotes
  5. Horizontal Asymptotes
  6. Slant Asymptotes
  7. Holes in Graphs
  8. Rational Function Zeros
  9. Rational Function Domain
  10. End Behavior of Rationals
  11. Rational Function Graphs
  12. Rational Inequalities

Transformations

  1. Parent Functions
  2. Vertical Translation
  3. Horizontal Translation
  4. Vertical Stretch
  5. Vertical Compression
  6. Horizontal Stretch
  7. Horizontal Compression
  8. Reflection Over X-Axis
  9. Reflection Over Y-Axis
  10. Combined Transformations
  11. Transformation Order
  12. Writing Transformed Eqns

Function Modeling

  1. Function Model Selection
  2. Data Analysis for Models
  3. Regression Models
  4. Model Assumptions
  5. Model Validation
  6. Extrapolation
  7. Interpolation
  8. Residual Analysis
  9. Goodness of Fit
  10. Competing Models

Sequences

  1. Sequence Definition
  2. Arithmetic Sequence
  3. Common Difference
  4. Arithmetic Sequence Formula
  5. Geometric Sequence
  6. Common Ratio
  7. Geometric Sequence Formula
  8. Recursive Formulas
  9. Explicit Formulas
  10. Sequence Convergence
  11. Sequence Divergence

Exponential Functions

  1. Exponential Function Def
  2. Base of Exponential
  3. Growth Factor
  4. Decay Factor
  5. Exponential Growth
  6. Exponential Decay
  7. Natural Base e
  8. Continuous Growth
  9. Compound Interest
  10. Exponential Equations
  11. Exponential Graphs
  12. Exponential Transformations
  13. Exponential Modeling
  14. Half-Life
  15. Doubling Time
  16. Percent Rate of Change

Logarithmic Functions

  1. Logarithm Definition
  2. Common Logarithm
  3. Natural Logarithm
  4. Logarithmic Form
  5. Exponential-Log Conversion
  6. Properties of Logarithms
  7. Product Rule for Logs
  8. Quotient Rule for Logs
  9. Power Rule for Logs
  10. Change of Base Formula
  11. Logarithmic Equations
  12. Logarithmic Graphs
  13. Logarithmic Transformations
  14. Logarithmic Modeling
  15. Logarithmic Scale

Semi-Log Plots and Data

  1. Semi-Log Plot
  2. Linearizing Exp Data
  3. Log-Log Plots
  4. Exponential Regression
  5. Power Regression

Composition and Inverses

  1. Composition of Functions
  2. Domain of Compositions
  3. Decomposing Functions
  4. Inverse Function Definition
  5. One-to-One Functions
  6. Horizontal Line Test
  7. Finding Inverses Algebraically
  8. Inverse Function Graphs
  9. Restricting Domains

Angles and Radian Measure

  1. Angle Definition
  2. Degree Measure
  3. Radian Measure
  4. Degree-Radian Conversion
  5. Arc Length
  6. Sector Area
  7. Standard Position
  8. Terminal Side
  9. Reference Angle
  10. Coterminal Angles

Unit Circle

  1. Unit Circle Definition
  2. Unit Circle Coordinates
  3. Special Angles
  4. Quadrantal Angles
  5. Signs by Quadrant

Trigonometric Functions

  1. Sine Function
  2. Cosine Function
  3. Tangent Function
  4. Reciprocal Trig Functions
  5. Secant Function
  6. Cosecant Function
  7. Cotangent Function
  8. Trig Function Evaluation
  9. Exact Trig Values
  10. Right Triangle Trig
  11. SOH-CAH-TOA

Trigonometric Graphs

  1. Sine Graph
  2. Cosine Graph
  3. Amplitude
  4. Period
  5. Midline
  6. Frequency
  7. Phase Shift
  8. Vertical Shift of Trig
  9. Sinusoidal Functions
  10. Tangent Graph
  11. Period of Tangent
  12. Asymptotes of Tangent
  13. Secant Graph
  14. Cosecant Graph
  15. Cotangent Graph
  16. Graphing Trig Transformations

Sinusoidal Modeling

  1. Sinusoidal Modeling
  2. Periodic Data Analysis
  3. Tidal Models
  4. Temperature Models
  5. Daylight Hour Models
  6. Sinusoidal Regression
  7. Period from Data
  8. Amplitude from Data

Trigonometric Identities

  1. Pythagorean Identity
  2. Reciprocal Identities
  3. Quotient Identities
  4. Cofunction Identities
  5. Even-Odd Identities
  6. Sum and Difference Formulas
  7. Double Angle Formulas
  8. Verifying Identities
  9. Simplifying Trig Expr

Inverse Trig Functions

  1. Arcsine
  2. Arccosine
  3. Arctangent
  4. Inverse Trig Domains
  5. Inverse Trig Ranges
  6. Inverse Trig Graphs
  7. Composing Trig Inverses

Trig Equations and Inequalities

  1. Solving Trig Equations
  2. General Solutions
  3. Solutions in an Interval
  4. Trig Inequalities
  5. Multiple Angle Equations

Polar Coordinates

  1. Polar Coordinate System
  2. Polar Point Plotting
  3. Rectangular to Polar
  4. Polar to Rectangular
  5. Multiple Polar Represent

Polar Functions

  1. Polar Function Definition
  2. Polar Graphs
  3. Circles in Polar Form
  4. Cardioids
  5. Limaçons
  6. Rose Curves
  7. Petal Count of Roses
  8. Symmetry of Polar Graphs
  9. Polar Rate of Change
  10. Polar Graph Intersections

Parametric Functions

  1. Parametric Equations
  2. Parameter
  3. Parametric Graphs
  4. Eliminating the Parameter
  5. Parametric Motion
  6. Position Functions
  7. Velocity from Parametrics
  8. Direction of Motion
  9. Parametric Modeling
  10. Projectile Motion Model

Vectors

  1. Vector Definition
  2. Vector Notation
  3. Magnitude of a Vector
  4. Direction of a Vector
  5. Component Form
  6. Unit Vectors
  7. Vector Addition
  8. Vector Subtraction
  9. Scalar Multiplication
  10. Dot Product
  11. Vector Applications

Matrices

  1. Matrix Definition
  2. Matrix Dimensions
  3. Matrix Addition
  4. Matrix Subtraction
  5. Scalar Mult of Matrices
  6. Matrix Multiplication
  7. Identity Matrix
  8. Determinant
  9. Inverse of a Matrix
  10. Linear Transformations
  11. Rotation Matrix
  12. Reflection Matrix
  13. Matrix Applications

AP Exam Preparation

  1. Calculator Strategies
  2. Free Response Strategy
  3. Multiple Choice Strategy
  4. Time Management on Exams
  5. Showing Work on Free Resp