AP Precalculus

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

Standard forms and key features of circles and parabolas

Standard forms and key features of ellipses and hyperbolas

Solving systems of linear and nonlinear equations using multiple methods

Understanding patterns in sequences and finding explicit and recursive formulas

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.

End behavior, zeros, multiplicity, graphing, and polynomial division

Vertical, horizontal, and slant asymptotes, graphing, and solving rational equations

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, transformations, compound interest, and the number e

Logarithm properties, solving equations, change of base, and logarithmic models

Composing functions, finding and verifying inverse functions

Translations, reflections, stretches, compressions, and piecewise functions

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.

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, 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

Matrix operations, multiplication, determinants, inverses, and systems

Arithmetic and geometric sequences, partial sums, sigma notation, and infinite series

Circles, parabolas, ellipses, hyperbolas, and identifying conic sections

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