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AP Precalculus
Functions of every flavor — polynomial, exponential, trigonometric — on a live interactive grapher.
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Scored lab investigations
Unit 1 · 30–40%
Polynomial & Rational Functions
- End Behavior of Polynomials12 min · 3 objectives
- Zeros & Multiplicity13 min · 3 objectives
- Asymptotes of Rational Functions14 min · 3 objectives
- Transformations of Functions13 min · 3 objectives
- Average Rate of Change14 min · 3 objectives
- Rates of Change, Concavity & Inflection14 min · 3 objectives
- Polynomial Division & the Remainder Theorem14 min · 3 objectives
- Complex Zeros & the Fundamental Theorem of Algebra14 min · 3 objectives
- Polynomial & Rational Inequalities14 min · 3 objectives
- Holes, Asymptotes & Removable Discontinuities14 min · 3 objectives
- Slant Asymptotes & End-Behavior Models14 min · 3 objectives
- Composition of Functions & Domain Restrictions14 min · 3 objectives
- Even, Odd & Symmetry14 min · 3 objectives
- Choosing and Validating a Function Model15 min · 3 objectives
Unit 2 · 25–40%
Exponential & Logarithmic Functions
- Exponential Growth & Decay12 min · 3 objectives
- Properties of Logarithms13 min · 3 objectives
- Inverse Functions14 min · 3 objectives
- Modeling with Exponentials & Logs13 min · 3 objectives
- Arithmetic & Geometric Sequences14 min · 3 objectives
- Change of Base & Solving Exponential Equations14 min · 3 objectives
- The Number e and Continuous Growth14 min · 3 objectives
- Half-Life & Doubling Time14 min · 3 objectives
- Semi-Log Plots: Linearizing Exponential Data14 min · 3 objectives
- Logarithmic Scales: pH, Decibels & Magnitude14 min · 3 objectives
- Logarithmic Equations & Extraneous Solutions14 min · 3 objectives
- Transforming Exponential & Logarithmic Graphs14 min · 3 objectives
- Logistic Growth and the Limits of Exponentials15 min · 3 objectives
Unit 3 · 30–35%
Trigonometric & Polar Functions
- The Unit Circle12 min · 3 objectives
- Trigonometric Identities13 min · 3 objectives
- Sinusoidal Models14 min · 3 objectives
- Polar Coordinates13 min · 3 objectives
- Radians, Arc Length & Angular Speed14 min · 3 objectives
- Graphs of Sine & Cosine: Amplitude, Period, Phase14 min · 3 objectives
- Tangent, Cotangent, Secant & Cosecant Graphs14 min · 3 objectives
- Inverse Trigonometric Functions14 min · 3 objectives
- Solving Trigonometric Equations on an Interval14 min · 3 objectives
- Sum, Difference & Double-Angle Formulas14 min · 3 objectives
- Law of Sines & Law of Cosines14 min · 3 objectives
- Polar Graphs: Circles, Roses & Cardioids14 min · 3 objectives
- Rates of Change of Polar Functions14 min · 3 objectives
- Sinusoidal Regression & Model Fitting15 min · 3 objectives
Unit 4 · Not assessed on the exam
Functions Involving Parameters, Vectors & Matrices
- Parametric Equations12 min · 3 objectives
- Vectors13 min · 3 objectives
- Matrices14 min · 3 objectives
- Linear Transformations13 min · 3 objectives
- Implicitly Defined Curves & Conic Sections14 min · 3 objectives
- Parametric Motion: Direction, Speed & Orientation14 min · 3 objectives
- The Dot Product & Angles Between Vectors14 min · 3 objectives
- Matrix Inverses & Solving Linear Systems14 min · 3 objectives
- Transition Matrices & Long-Run Behavior15 min · 3 objectives