AP Precalculus is designed to prepare students for college-level Mathematics and science through deep work with modelling and functions across multiple representations. College Board’s 2026–27 framework contains four units, but only Units 1–3 are assessed on the AP Exam.
- Unit 1: Polynomial and Rational Functions
- Unit 2: Exponential and Logarithmic Functions
- Unit 3: Trigonometric and Polar Functions
- Unit 4: Functions Involving Parameters, Vectors, and Matrices — not assessed on the AP Exam
The May 2027 exam uses a hybrid digital format. Students complete multiple-choice questions and view free-response questions in Bluebook, then handwrite free-response answers. The exam duration is 2 hours 55 minutes.
Technology and symbolic fluency must coexist
A graphing calculator is required for designated parts of the AP Precalculus exam, and Bluebook includes a built-in Desmos graphing calculator. College Board also states that technology should not replace symbolic manipulation when an equation or expression is accessible with precalculus algebra.
The mathematical spine
Preparation
- Build function language: domain, range, composition, inverse and transformations.
- Move between equation, graph, table and context.
- Practise symbolic work without technology.
- Use Desmos for exploration, regression, intersections and verification.
- Explain conclusions with precise mathematical language.
Official source checked 26 September 2026: College Board AP Precalculus course and current exam/calculator guidance.
World Mathematics route: return to the World Mathematics Atlas for the wider map across examinations, curricula, competitions, mathematical objects and university routes.
AP Precalculus: build function modelling before calculus
The course is organised around functions
Polynomial/rational, exponential/logarithmic and trigonometric/polar-style relationships under the current framework should be treated as families with behaviours, parameters and modelling uses.
Representations should translate
Move among equations, graphs, tables and verbal contexts. A model is stronger when the student can explain what parameters mean.
Rates of change prepare calculus
Average rate, difference quotients and changing behaviour develop the language later used for derivatives.
Polynomial and rational functions need structural landmarks
Zeros, end behaviour, asymptotes and factors should guide graphs before calculator display.
Exponential and logarithmic functions model multiplicative change
Interpret growth/decay rates and inverse relationships.
Trigonometric functions model periodicity
Amplitude, period and phase should come from context and unit-circle understanding.
Technology supports modelling
Graphing tools can fit or solve models, but the student must choose a sensible window and interpret results.
Domain matters
A mathematically valid function may make sense only on part of its domain in a real model.
AP exam format is year-specific
Use College Board’s current exam page for 2027 date, digital/paper details and calculator arrangements rather than relying on an old article.
Official practice should anchor preparation
Use current course/exam descriptions and sample/released material where available.
Transition to calculus
The goal is not to pre-teach every derivative. It is to make functions, rates, graphs and algebra sufficiently stable for calculus.
Review
Classify errors by algebra, function concept, modelling, technology and interpretation.