Specification points

College Board AP Precalculus precalculus

152 points in 4 topics, with College Board's codes and titles.

Codes and titles are read by a script from College Board's published specification and have not been checked by a person. What each point covers is in the specification itself: College Board’s specification.

1 Polynomial and Rational Functions

1.1 Change in Tandem
1.1.A How inputs and outputs vary together
1.1.B Graphing two related quantities in context
1.2 Rates of Change
1.2.A Comparing rates of change at two points
1.2.B How quantities vary over intervals
1.3 Rates of Change in Linear and Quadratic Functions
1.3.A Average rates of change of functions and sequences
1.3.B Change in average rates of change
1.4 Polynomial Functions and Rates of Change
1.4.A Polynomial rates of change
1.5 Polynomial Functions and Complex Zeros
1.5.A Zeros of polynomial functions
1.5.B Even and odd polynomial functions
1.6 Polynomial Functions and End Behavior
1.6.A End behaviour of polynomials
1.7 Rational Functions and End Behavior
1.7.A End behaviour of rational functions
1.8 Rational Functions and Zeros
1.8.A Zeros of rational functions
1.9 Rational Functions and Vertical Asymptotes
1.9.A Vertical asymptotes
1.10 Rational Functions and Holes
1.10.A Holes in rational function graphs
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.11.A Equivalent polynomial and rational expressions
1.11.B Polynomial long division
1.11.C The binomial theorem
1.12 Transformations of Functions
1.12.A Transformations of functions
1.13 Function Model Selection and Assumption Articulation
1.13.A Choosing a function type for a model
1.13.B Assumptions and restrictions in modelling
1.14 Function Model Construction and Application
1.14.A Polynomial and piecewise function models
1.14.B Rational function models
1.14.C Applying function models

2 Exponential and Logarithmic Functions

2.1 Change in Arithmetic and Geometric Sequences
2.1.A Arithmetic sequences as functions
2.1.B Geometric sequences as functions
2.2 Change in Linear and Exponential Functions
2.2.A Linear and exponential functions from sequences
2.2.B Comparing linear and exponential functions
2.3 Exponential Functions
2.3.A Characteristics of exponential functions
2.4 Exponential Function Manipulation
2.4.A Equivalent exponential expressions
2.5 Exponential Function Context and Data Modeling
2.5.A Exponential models for proportional change
2.5.B Applying exponential models
2.6 Competing Function Model Validation
2.6.A Linear, quadratic and exponential models from data
2.6.B Validating a model
2.7 Composition of Functions
2.7.A Evaluating composite functions
2.7.B Representing composite functions
2.7.C Decomposing functions
2.8 Inverse Functions
2.8.A Input–output pairs of inverse functions
2.8.B Inverse functions on invertible domains
2.9 Logarithmic Expressions
2.9.A Evaluating logarithms
2.10 Inverses of Exponential Functions
2.10.A Inverses of exponential functions
2.11 Logarithmic Functions
2.11.A Characteristics of logarithmic functions
2.12 Logarithmic Function Manipulation
2.12.A Equivalent logarithmic expressions
2.13 Exponential and Logarithmic Equations and Inequalities
2.13.A Exponential and logarithmic equations and inequalities
2.13.B Inverses of exponential and logarithmic functions
2.14 Logarithmic Function Context and Data Modeling
2.14.A Logarithmic function models
2.15 Semi-log Plots
2.15.A Semi-log plots
2.15.B Linearising exponential data

3 Trigonometric and Polar Functions

3.1 Periodic Phenomena
3.1.A Graphing periodic relationships
3.1.B Characteristics of periodic functions
3.2 Sine, Cosine, and Tangent
3.2.A Sine, cosine and tangent on the unit circle
3.3 Sine and Cosine Function Values
3.3.A Coordinates of points on a circle
3.4 Sine and Cosine Function Graphs
3.4.A Sine and cosine from the unit circle
3.5 Sinusoidal Functions
3.5.A Characteristics of sine and cosine
3.6 Sinusoidal Function Transformations
3.6.A Amplitude, shifts and period of sinusoids
3.7 Sinusoidal Function Context and Data Modeling
3.7.A Sinusoidal models
3.8 The Tangent Function
3.8.A The tangent function from the unit circle
3.8.B Characteristics of the tangent function
3.8.C Transformations of the tangent function
3.9 Inverse Trigonometric Functions
3.9.A Inverse trigonometric functions
3.10 Trigonometric Equations and Inequalities
3.10.A Trigonometric equations and inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.11.A Quotients of sine and cosine
3.12 Equivalent Representations of Trigonometric Functions
3.12.A The Pythagorean identity
3.12.B Sum identities
3.12.C Solving equations with trigonometric identities
3.13 Trigonometry and Polar Coordinates
3.13.A Rectangular and polar coordinates
3.14 Polar Function Graphs
3.14.A Graphs of polar functions
3.15 Rates of Change in Polar Functions
3.15.A Characteristics of polar graphs

4 Functions Involving Parameters, Vectors, and Matrices

4.1 Parametric Functions
4.1.A Graphs and tables of parametric functions
4.2 Parametric Functions Modeling Planar Motion
4.2.A Parametric motion: position
4.3 Parametric Functions and Rates of Change
4.3.A Parametric motion: direction and rate of change
4.4 Parametrically Defined Circles and Lines
4.4.A Parametric motion on circles and segments
4.5 Implicitly Defined Functions
4.5.A Graphs of equations in two variables
4.5.B Implicitly defined functions
4.6 Conic Sections
4.6.A Conic sections
4.7 Parametrization of Implicitly Defined Functions
4.7.A Parametric curves
4.7.B Conic sections parametrically
4.8 Vectors
4.8.A Characteristics of vectors
4.8.B Vector sums and products
4.8.C Unit vectors
4.8.D Angles and magnitudes in vector addition
4.9 Vector-Valued Functions
4.9.A Vector-valued functions and motion
4.10 Matrices
4.10.A Matrix multiplication
4.11 The Inverse and Determinant of a Matrix
4.11.A Inverse of a 2 × 2 matrix
4.11.B Determinants, invertibility and vectors
4.12 Linear Transformations and Matrices
4.12.A Linear transformations with 2 × 2 matrices
4.13 Matrices as Functions
4.13.A Linear transformations and matrices
4.13.B Composing linear transformations
4.13.C Inverse linear transformations
4.14 Matrices Modeling Contexts
4.14.A Matrix models of state transitions
4.14.B Predicting states with matrix models