AP Precalculus
Build a strong foundation in functions, trigonometry, vectors, matrices, and complex numbers to prepare for calculus.
Start here
Take the free AP Precalculus diagnostic
It finds what you already know and builds your study plan: the topics to clear first, each a short lesson plus an exit quiz.
Take the free diagnosticCourse Overview
This AP Precalculus course on Study Mondo covers 21 topics organized across 4 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.
What You'll Learn
Unit 1: Polynomial and Rational Functions
Polynomials, rational functions, end behavior, zeros, and asymptotes
Unit 2: Exponential and Logarithmic Functions
Exponential growth/decay, logarithms, properties, and applications
Unit 3: Trigonometric and Polar Functions
Unit circle, trig graphs, identities, inverse trig, and triangle laws
AP Exam Preparation
Free-response strategies for the four 2027 FRQ types and a full-course review for the AP Precalculus exam.
Start with any category below, or jump to a specific topic that you need help with.
Study tools
📚 Study schedules & cram guides
Pick the schedule that matches your timeline — from a 1-month build-up to a night-before review.
A focused 72-hour rescue plan when the exam is almost here.
~12 hours total study
One full week to lock in the highest-leverage topics and FRQ patterns.
~25 hours total study
A structured 4-week plan that builds mastery without burning out.
~60 hours total over 4 weeks
How to attack free-response questions and earn easy partial credit.
~3-4 hours of focused work
The night-before checklist: top formulas, common traps, and what NOT to do.
~45 minutes to skim
Explore Related Topics
Jump into high-impact topics and keep your study momentum moving.
Polynomials, rational functions, end behavior, zeros, and asymptotes
Rates of Change
Average rate of change, secant lines, instantaneous rate of change, and tangent lines
Polynomial Functions
End behavior, zeros, multiplicity, graphing, and polynomial division
Complex Zeros and the Fundamental Theorem of Algebra
Apply the Fundamental Theorem of Algebra to find all roots of polynomials and completely factor polynomial expressions.
Polynomial Division and Equivalent Forms
Understanding polynomial long division, synthetic division, and the Remainder and Factor Theorems
Rational Functions
Vertical, horizontal, and slant asymptotes, graphing, and solving rational equations
Transformations of Functions
Translations, reflections, stretches, compressions, and piecewise functions
Function Model Selection and Construction
Choosing and building function models from data and context: polynomial, piecewise, and rational models, assumptions, and model validation (CED 1.13–1.14).
Exponential growth/decay, logarithms, properties, and applications
Sequences
Arithmetic and geometric sequences, partial sums, sigma notation, and infinite series
Exponential Functions
Exponential growth, decay, transformations, compound interest, and the number e
Function Composition and Inverses
Composing functions, finding and verifying inverse functions
Logarithmic Functions
Logarithm properties, solving equations, change of base, and logarithmic models
Exponential and Logarithmic Data Modeling and Semi-log Plots
Exponential and logarithmic regression, residual plots, competing function models, and semi-log plots (CED 2.6, 2.14–2.15).
Unit circle, trig graphs, identities, inverse trig, and triangle laws
The Unit Circle
Master the unit circle, special angles, reference angles, and the CAST rule.
Trigonometric Functions
Unit circle, sine/cosine/tangent graphs, amplitude, period, and phase shifts
Sinusoidal Functions and Modeling
Graph sine, cosine, and tangent functions and understand transformations including amplitude, period, phase shift, and vertical shift.
Inverse Trigonometric Functions
Inverse sine, cosine, tangent, compositions, and solving trig equations
Solving Trigonometric Equations and Inequalities
Solve trigonometric equations using algebraic techniques, inverse functions, and the unit circle.
Trigonometric Identities and Equivalent Forms
Pythagorean, sum/difference, double-angle, and half-angle identities
Polar Coordinates and Polar Functions
Explore the polar coordinate system, conversions, graphing polar curves, and classic polar equations.
Free-response strategies for the four 2027 FRQ types and a full-course review for the AP Precalculus exam.
Free-Response Strategies: the Four Question Types
How each of the four 2027 free-response questions is structured and scored (Function Concepts; Modeling a Non-Periodic Context; Modeling a Periodic Context; Symbolic Manipulations), with rubric walkthroughs, point-loss traps and the 35 + 35 minute budget.
AP Precalculus Exam Review
Cumulative review of Units 1–3 keyed to the exam weights, with AP-style mixed multiple-choice practice, the no-calculator Part A versus calculator Part B split, and pacing (29 questions in 65 minutes, 13 in 40).