The visual guide to
AP® Precalculus
4 units, 125 topics. Each topic is explained in writing, drawn as a lesson you can watch, and checked with practice questions.
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Each unit is as wide as its share of the exam's multiple-choice section.Filled: topics you've opened.
Unit 1Polynomial and Rational Functions
- Change in Tandem
- Concavity and What It Means
- Average Rate of Change
- Rate of Change at a Point
- Rates of Change in Linear Functions
- Second Differences and Quadratics
- Polynomial Shape and Extrema
- Points of Inflection
- Zeros, Factors, and Multiplicity
- Complex Zeros and Conjugate Pairs
- Even and Odd Functions
- Finding Degree from a Table
- Polynomial End Behavior
- Rational Functions and End Behavior
- Slant Asymptotes
- Zeros of Rational Functions
- Rational Inequalities and Sign Charts
- Vertical Asymptotes
- Holes in Rational Graphs
- Factored Form Versus Standard Form
- Polynomial Long Division
- The Binomial Theorem
- Translating a Graph
- Dilations and Reflections
- Combining Transformations
- Choosing a Function Model
- Piecewise Models and Restrictions
- Building a Polynomial Model
- Rational Models and Inverse Proportion
Unit 2Exponential and Logarithmic Functions
- Arithmetic Sequences
- Geometric Sequences
- Linear Versus Exponential Change
- Building a Function from Two Points
- The Shape of an Exponential Function
- Growth, Decay, and End Behavior
- Exponent Rules as Graph Moves
- Negative and Fractional Exponents
- Building an Exponential Model
- Equivalent Forms and Percent Change
- The Natural Base e
- Comparing Competing Models
- Residual Plots
- Composition of Functions
- Domain of a Composite, and Decomposing
- Inverses as a Reversed Mapping
- Restricting a Domain to Invert
- Reflecting Over the Line y = x
- Logarithmic Expressions
- Logarithmic Scales
- Logs as Inverses of Exponentials
- The Graph of a Logarithmic Function
- Product and Power Properties of Logs
- Change of Base and the Natural Log
- Solving Exponential Equations
- Log Equations and Extraneous Solutions
- Inverting Transformed Exponentials and Logs
- Logarithmic Modeling
- Semi-log Plots
- Linearizing Exponential Data
Unit 3Trigonometric and Polar Functions
- Periodic Phenomena
- Period, Cycle, and Frequency
- Angles in Standard Position
- Radian Measure
- Sine and Cosine on the Unit Circle
- Tangent as the Slope of the Ray
- Coordinates on a Circle of Radius r
- Exact Values from Special Triangles
- Quadrants and Reference Angles
- Unwrapping the Circle into a Sine Wave
- The Cosine Graph
- Amplitude and Midline
- Period and Frequency of a Sinusoid
- Symmetry and Concavity of Sinusoids
- Vertical Shift and Amplitude
- Changing the Period
- Phase Shift
- Reading a Wave's Equation Off Its Graph
- Sinusoidal Modeling from Data
- The Tangent Graph
- Transforming the Tangent Function
- Inverse Trig and Restricted Domains
- Evaluating Inverse Trig Functions
- Solving Trigonometric Equations
- Trigonometric Inequalities
- Secant and Cosecant
- The Cotangent Function
- The Pythagorean Identity
- Sum, Difference, and Double-Angle
- Using Identities to Solve Equations
- Polar Coordinates
- Converting Polar and Rectangular
- Complex Numbers in the Plane
- Graphing Polar Functions
- Reading a Polar Curve from Its r-Graph
- Rates of Change in Polar Functions
Unit 4Functions Involving Parameters, Vectors, and Matrices
- Parametric Functions
- Tables and Graphs of Parametric Curves
- Parametric Motion in the Plane
- Extremes and Intercepts of a Path
- Direction of Motion
- Rates of Change Along a Path
- Different Parametrizations, Same Curve
- Parametrizing a Circle
- Parametrizing a Line Segment
- Implicitly Defined Functions
- How x and y Vary Together
- Parabolas
- Ellipses
- Hyperbolas
- Parametrizing an Implicit Curve
- Parametrizing Conic Sections
- Vectors, Magnitude, and Direction
- Adding and Scaling Vectors
- Unit Vectors and Components
- The Dot Product
- Triangles Made by Vector Addition
- Vector-Valued Functions
- Matrix Multiplication
- The Inverse of a 2 by 2 Matrix
- The Determinant as Area
- Linear Transformations of the Plane
- Finding the Matrix from Where i and j Go
- Rotation Matrices
- Composing and Inverting Transformations
- Transition Matrices and Steady States