AP Precalculus
Build a strong foundation in functions, trigonometry, vectors, matrices, and complex numbers to prepare for calculus.
Foundational concepts: transformations, compositions, inverses, and rates of change
Function Transformations
Understanding how to shift, stretch, compress, and reflect functions
Composite and Inverse Functions
Combining functions through composition and finding inverse functions
Piecewise Functions
Defining and evaluating functions with different rules on different intervals
Average and Instantaneous Rates of Change
Understanding how functions change over intervals and at specific points
Systems of Equations
Solving systems of linear and nonlinear equations using multiple methods
Arithmetic and Geometric Sequences
Understanding patterns in sequences and finding explicit and recursive formulas
Circles and Parabolas
Standard forms and key features of circles and parabolas
Ellipses and Hyperbolas
Standard forms and key features of ellipses and hyperbolas
Understanding polynomial and rational functions, their graphs, and behavior
Polynomial Functions and End Behavior
Understanding polynomial functions, their graphs, and how to determine end behavior
Rational Functions and Asymptotes
Understanding rational functions, vertical asymptotes, horizontal asymptotes, and holes
Polynomial Division and Remainder Theorem
Understanding polynomial long division, synthetic division, and the Remainder and Factor Theorems
Partial Fraction Decomposition
Breaking down rational expressions into simpler fractions for integration and analysis
Complex Numbers and Operations
Understand complex numbers, perform operations with complex numbers, and solve equations involving complex solutions.
Fundamental Theorem of Algebra and Factoring
Apply the Fundamental Theorem of Algebra to find all roots of polynomials and completely factor polynomial expressions.
Polynomial Inequalities
Solve polynomial inequalities using sign analysis, test points, and graphical methods.
Rational Inequalities
Solve rational inequalities by finding critical values from zeros and vertical asymptotes, then using sign analysis.
Polynomial Inequalities
Solve polynomial inequalities using sign analysis, test points, and graphical methods.
Rational Inequalities
Solve rational inequalities by finding critical values from zeros and vertical asymptotes, then using sign analysis.
Properties and applications of exponential and logarithmic functions
Exponential Functions and Growth/Decay
Understanding exponential functions, exponential growth, and exponential decay models
Logarithmic Functions
Understanding logarithms as inverse of exponentials, logarithmic properties, and solving logarithmic equations
Solving Exponential and Logarithmic Equations
Techniques for solving equations involving exponentials and logarithms
Logarithmic and Exponential Models
Real-world applications including compound interest, population growth, and radioactive decay
Unit circle, trigonometric functions, identities, and equations
Degrees and Radians
Learn how to convert between degrees and radians, and understand radian measure.
Trigonometric Identities
Fundamental trigonometric identities including Pythagorean, reciprocal, quotient, and even-odd identities
Arc Length and Sector Area
Calculate arc lengths and sector areas using radian measure.
The Unit Circle
Master the unit circle, special angles, reference angles, and the CAST rule.
Graphing Trigonometric Functions
Graph sine, cosine, and tangent functions and understand transformations including amplitude, period, phase shift, and vertical shift.
Solving Trigonometric Equations
Solve trigonometric equations using algebraic techniques, inverse functions, and the unit circle.
Negative and Coterminal Angles
Understand negative angles and coterminal angles, and learn how to find them.
Inverse Trigonometric Functions
Understand inverse trigonometric functions, their domains, ranges, and how to evaluate and use them to solve equations.
Law of Sines and Law of Cosines
Apply the Law of Sines and Law of Cosines to solve oblique triangles and find missing sides and angles.
Sum and Difference Identities
Use sum and difference formulas for trig functions
Double Angle and Half Angle Identities
Apply double and half angle formulas
Parametric equations, vectors, and matrix operations
Parametric Equations
Understanding parametric equations and how to convert between parametric and rectangular forms
Vectors in the Plane
Understanding vectors, vector operations, and magnitude and direction
Polar Coordinates and Graphs
Convert between polar and rectangular coordinates, graph polar equations, and understand polar curves.
Matrix Operations and Applications
Perform matrix addition, multiplication, find determinants and inverses, and solve systems using matrices.