Change in Tandem
Explore how two quantities change together across tables, graphs, formulas and contexts.
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AP Precalculus
Scroll through Units 1–3, then choose the topic you are studying.
Units 1–3 are split directly into the guide’s 44 topics. Every topic opens its own Questions & Solutions page with temporary sample content ready to replace later.
3 exam units
44 topics
44 resource files
Unit 1
Polynomial and Rational Functions
Study change, polynomial and rational functions, equivalent representations, transformations and contextual modeling.
Rates of Change
Calculate and interpret average rates of change from different representations.
Rates of Change in Linear and Quadratic Functions
Compare constant and changing rates in linear and quadratic functions.
Polynomial Functions and Rates of Change
Use rates of change to analyse intervals and key features of polynomial functions.
Polynomial Functions and Complex Zeros
Connect polynomial factors and zeros with real and complex solutions.
Polynomial Functions and End Behavior
Describe polynomial end behavior from degree and leading coefficient.
Rational Functions and End Behavior
Analyse rational-function end behavior and horizontal or slant asymptotes.
Rational Functions and Zeros
Find zeros and intercepts of rational functions and interpret multiplicity.
Rational Functions and Vertical Asymptotes
Locate vertical asymptotes and describe behavior on either side.
Rational Functions and Holes
Identify holes, removable discontinuities and their coordinates.
Equivalent Representations of Polynomial and Rational Expressions
Move between equivalent polynomial and rational forms to reveal useful features.
Transformations of Functions
Apply shifts, stretches and reflections and describe their effects.
Function Model Selection and Assumption Articulation
Select suitable function models and state the assumptions behind the choice.
Function Model Construction and Application
Construct and apply polynomial or rational models in context.
Unit 2
Exponential and Logarithmic Functions
Study multiplicative change through sequences, exponential and logarithmic functions, composition, inverses, equations and data modeling.
Change in Arithmetic and Geometric Sequences
Compare additive and multiplicative change in arithmetic and geometric sequences.
Change in Linear and Exponential Functions
Distinguish linear and exponential change from tables, graphs and contexts.
Exponential Functions
Analyse exponential domains, ranges, asymptotes, growth, decay and rates.
Exponential Function Manipulation
Rewrite exponential expressions and functions using exponent laws and equivalent bases.
Exponential Function Context and Data Modeling
Construct and apply exponential models to contextual data.
Competing Function Model Validation
Compare competing models using fit, residuals and stated assumptions.
Composition of Functions
Compose functions and interpret the result in context.
Inverse Functions
Determine inverse functions, needed restrictions and their graphical relationship.
Logarithmic Expressions
Rewrite and simplify logarithmic expressions using logarithm properties.
Inverses of Exponential Functions
Use logarithms as inverse operations for exponential functions.
Logarithmic Functions
Analyse logarithmic domains, ranges, asymptotes and rates of change.
Logarithmic Function Manipulation
Rewrite and transform logarithmic functions using equivalent forms.
Exponential and Logarithmic Equations and Inequalities
Solve exponential and logarithmic equations and inequalities.
Logarithmic Function Context and Data Modeling
Construct and apply logarithmic models to data and contexts.
Semi-log Plots
Use semi-log plots to identify and model exponential relationships.
Unit 3
Trigonometric and Polar Functions
Model periodic behavior with trigonometric functions, then extend those ideas to polar coordinates, graphs and rates of change.
Periodic Phenomena
Recognise and describe periodic phenomena using key features and repeated behavior.
Sine, Cosine, and Tangent
Connect angles, coordinates and the unit circle to sine, cosine and tangent.
Sine and Cosine Function Values
Evaluate sine and cosine using reference angles, symmetry and the unit circle.
Sine and Cosine Function Graphs
Analyse sine and cosine graphs, including period, zeros and extrema.
Sinusoidal Functions
Determine amplitude, midline, period and phase shift in sinusoidal functions.
Sinusoidal Function Transformations
Apply transformations to sine and cosine functions and models.
Sinusoidal Function Context and Data Modeling
Construct and apply sinusoidal models to contextual data.
The Tangent Function
Analyse the tangent function, including its period and vertical asymptotes.
Inverse Trigonometric Functions
Define and evaluate inverse trigonometric functions with restricted domains.
Trigonometric Equations and Inequalities
Solve trigonometric equations and inequalities over specified intervals.
The Secant, Cosecant, and Cotangent Functions
Analyse reciprocal trigonometric functions and their graphs.
Equivalent Representations of Trigonometric Functions
Use identities and equivalent forms to rewrite and solve trigonometric problems.
Trigonometry and Polar Coordinates
Convert between rectangular and polar coordinates and connect them to trigonometry.
Polar Function Graphs
Graph and analyse polar functions and their key features.
Rates of Change in Polar Functions
Calculate and interpret rates of change for polar functions.
Unit 4
Coming Soon
Content for Unit 4 will be added later.
Coming SoonHow to use this course map
Scroll to the unit you are studying, then open a topic. Each topic has a separate page so questions, quick answers and worked solutions can be added without changing the course structure.
Folder structure
- 14 topic pages in Unit 1
- 15 topic pages in Unit 2
- 15 topic pages in Unit 3