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Build a strong foundation in functions, trigonometry, vectors, matrices, and complex numbers to prepare for calculus.
This AP Precalculus course on Study Mondo covers 61 topics organized across 12 categories. Each topic includes detailed written explanations, worked examples, practice problems with step-by-step solutions, flashcards for review, and interactive lessons to help you master the material.
All content is completely free. Start with any category below, or jump to a specific topic that you need help with.
Take a diagnostic test covering all AP Precalculus units. Identify gaps and get a targeted study plan.
Pick the plan that matches your timeline — from a 1-month build-up to a night-before review.
Jump into high-impact topics and keep your study momentum moving.
Foundational concepts: transformations, compositions, inverses, and rates of change
Understanding how to shift, stretch, compress, and reflect functions
Combining functions through composition and finding inverse functions
Defining and evaluating functions with different rules on different intervals
Understanding how functions change over intervals and at specific points
A structured 4-week plan that builds mastery without burning out.
~60 hours total over 4 weeks
Standard forms and key features of circles and parabolas
Understanding polynomial and rational functions, their graphs, and behavior
Analyze polynomial functions, their zeros, multiplicity, and end behavior.
Understanding polynomial functions, their graphs, and how to determine end behavior
Analyze rational functions including vertical, horizontal, and slant asymptotes.
Apply transformations including shifts, reflections, stretches, and compositions.
Understanding rational functions, vertical asymptotes, horizontal asymptotes, and holes
Understanding polynomial long division, synthetic division, and the Remainder and Factor Theorems
Breaking down rational expressions into simpler fractions for integration and analysis
Understand complex numbers, perform operations with complex numbers, and solve equations involving complex solutions.
Apply the Fundamental Theorem of Algebra to find all roots of polynomials and completely factor polynomial expressions.
Solve polynomial inequalities using sign analysis, test points, and graphical methods.
Solve rational inequalities by finding critical values from zeros and vertical asymptotes, then using sign analysis.
Polynomials, rational functions, end behavior, zeros, and asymptotes
Properties and applications of exponential and logarithmic functions
Model growth and decay with exponential functions using various bases.
Evaluate logarithms, apply properties, and solve logarithmic equations.
Understanding exponential functions, exponential growth, and exponential decay models
Understanding logarithms as inverse of exponentials, logarithmic properties, and solving logarithmic equations
Techniques for solving equations involving exponentials and logarithms
Real-world applications including compound interest, population growth, and radioactive decay
Exponential growth/decay, logarithms, properties, and applications
Composition, inverses, and transformations of functions
Unit circle, trigonometric functions, identities, and equations
This topic has been split into three focused topics: Degrees and Radians, Arc Length and Sector Area, and The Unit Circle.
Learn how to convert between degrees and radians, and understand radian measure.
Calculate arc lengths and sector areas using radian measure.
Fundamental trigonometric identities including Pythagorean, reciprocal, quotient, and even-odd identities
Master the unit circle, special angles, reference angles, and the CAST rule.
Understand negative angles and coterminal angles, and learn how to find them.
Graph sine, cosine, and tangent functions and understand transformations including amplitude, period, phase shift, and vertical shift.
Use sum and difference formulas for trig functions
Solve trigonometric equations using algebraic techniques, inverse functions, and the unit circle.
Apply double and half angle formulas
Understand inverse trigonometric functions, their domains, ranges, and how to evaluate and use them to solve equations.
Apply the Law of Sines and Law of Cosines to solve oblique triangles and find missing sides and angles.
Parametric equations, vectors, and matrix operations
Understanding parametric equations and how to convert between parametric and rectangular forms
Master parametric equations: graphing curves, eliminating the parameter, derivatives, and motion applications.
Understanding vectors, vector operations, and magnitude and direction
Learn vector operations, magnitude, unit vectors, dot product, projections, and real-world applications.
Explore the polar coordinate system, conversions, graphing polar curves, and classic polar equations.
Convert between polar and rectangular coordinates, graph polar equations, and understand polar curves.
Perform matrix addition, multiplication, find determinants and inverses, and solve systems using matrices.
Unit circle, trig graphs, identities, inverse trig, and triangle laws
Unit circle, sine/cosine/tangent graphs, amplitude, period, and phase shifts
Pythagorean, sum/difference, double-angle, and half-angle identities
Inverse sine, cosine, tangent, compositions, and solving trig equations
Law of Sines, ambiguous case, Law of Cosines, and triangle area formulas
Polar coordinates, vector operations, and matrix algebra
Arithmetic/geometric sequences, series, sigma notation, and conic sections
Limits, continuity, rates of change, and systems of equations
Intuitive limits, notation, one-sided limits, limits at infinity, and evaluation
Continuity, types of discontinuity, IVT, and piecewise functions
Average rate of change, secant lines, instantaneous rate of change, and tangent lines
Linear and nonlinear systems, substitution, elimination, and inequalities