AP Precalculus Study Guide: Unit-by-Unit Plan with Free Practice Drills

By Brian Stewart, Barron’s SAT, ACT & PSAT Author & Perfect SAT/ACT Scorer
Updated August 27, 2026 for the 2027 AP® Precalculus Exam

Preparing for the 2027 AP® Precalculus exam requires more than reviewing formulas and function rules. The exam asks students to solve symbolically, move among graphical, numerical, analytical, and verbal representations, build and evaluate models, and explain why conclusions follow from the mathematics. This guide breaks the tested course down unit by unit, explains the new 2027 exam format, highlights what the 2026 released free-response questions show about the recurring task types, and links to 30 free AP Precalculus practice drills with full answer explanations.

In more than 20 years of working with students on standardized tests, I have found that short practice sets are most useful when students study the explanations as carefully as the questions. That is the idea behind these drills: practice a focused skill, identify exactly why each wrong answer fails, and then apply that reasoning when the same function appears in a different representation.

Want the drill-first version? Go directly to the AP® Precalculus Strategy Guide & All 30 Practice Drills.

2027 AP® Precalculus Exam Format and Changes

Beginning with the May 2027 exam, College Board is changing the AP® Precalculus timing and question counts while keeping the course content the same. The exam remains hybrid digital: students complete multiple-choice questions and view free-response prompts in Bluebook, then handwrite their free-response answers in paper booklets. The 2027 exam has 42 multiple-choice questions in 105 minutes and 4 free-response questions in 70 minutes, for a total testing time of 2 hours 55 minutes.

The calculator split still matters. MCQ Part A and FRQ Part B are no-calculator portions. MCQ Part B and FRQ Part A use a graphing calculator, and College Board specifies radian mode for the calculator-active portions. Practice both ways: you should be able to manipulate expressions and reason from function structure by hand, but also use graphing, tables, regression, and numerical solving efficiently when technology is available.

The AP Precalculus Course Framework

The AP Precalculus framework is built around three mathematical practices: procedural and symbolic fluency, multiple representations, and communication and reasoning. Throughout the course, students study function types through the lenses of modeling and covariation and work with them in graphical, numerical, analytical, and verbal forms. Understanding how these pieces fit together is more useful than treating each unit as a standalone topic list.

Covariation (how output values change as input values change) is a thread that runs from the very first topic in Unit 1 all the way through rates of change in polar functions in Topic 3.15. Average rate of change isn’t just a Unit 1 concept; it’s an analytical tool used to describe and compare function behavior across all three tested units. Similarly, modeling runs throughout the course: polynomial and rational models in Unit 1, exponential and logarithmic models in Unit 2, and sinusoidal models in Unit 3. The multiple representations practice (moving fluently between graphical, numerical, analytical, and verbal forms of the same function) is how the exam tests whether those modeling and covariation skills are genuinely flexible or only work when the function shows up in one particular form.

Keeping these lenses in mind while working through unit content is what turns content review into actual exam preparation.

What the 2026 AP® Precalculus Free-Response Questions Show

The 2026 released free-response questions are useful because they show the four recurring AP Precalculus task types in concrete form. The exact functions and contexts change, but the underlying jobs students are asked to perform are highly recognizable from year to year.

Unit-by-Unit AP Precalculus Review and Free Practice

Unit 1: Polynomial and Rational Functions

Unit 1 builds the covariation framework and then applies it to polynomial and rational functions specifically. The first few topics (change in tandem, rates of change, and rates of change in linear and quadratic functions) are about developing the conceptual vocabulary you’ll use throughout the entire course. Knowing that a function whose average rate of change is constant is linear, that a function whose average rate of change changes at a constant rate is quadratic, and that a function whose successive output ratios are constant is exponential: these are the distinctions that show up in model selection questions and that students most often get wrong by rushing.

The polynomial topics in Unit 1 (Topics 1.4 through 1.6) focus on zeros, end behavior, points of inflection, and complex zeros, and on what each of those features looks like across different representations. A question about whether a polynomial has a zero at a given x-value based on a table of values is testing a different skill than a question about identifying a repeated zero from a graph, even though both involve the same underlying concept. The rational function topics (1.7 through 1.10) extend end behavior analysis to include horizontal and vertical asymptotes and holes, with particular attention to how the degree and leading coefficients of numerator and denominator determine long-run behavior.

Topics 1.11 through 1.14 (equivalent representations, transformations, function model selection, and function model construction) are where Unit 1 content connects most directly to the three mathematical practices. Model selection questions (Topic 1.13) are a topic many students rush through because they seem qualitative. Correctly selecting between function types requires checking specific quantitative properties of the data: constant first differences, constant second differences, constant ratios, or periodic behavior. Naming the property that confirms your answer, and ruling out the alternatives, is part of what the question is testing.

• Unit 1 — Change in Tandem — Drill 1→
• Unit 1 — Rates of Change — Drill 2→
• Unit 1 — Polynomial Functions & Rates of Change — Drill 3→
• Unit 1 — Polynomial Functions & Complex Zeros — Drill 4→
• Unit 1 — Polynomial End Behavior — Drill 5→
• Unit 1 — Rational Functions: End Behavior & Zeros — Drill 6→
• Unit 1 — Rational Functions: Asymptotes & Holes — Drill 7→
• Unit 1 — Equivalent Representations — Drill 8→
• Unit 1 — Transformations of Functions — Drill 9→
• Unit 1 — Function Model Selection — Drill 10→

Unit 2: Exponential and Logarithmic Functions

Unit 2 can account for 25–40% of the multiple-choice section, so it deserves serious review time. It opens with arithmetic and geometric sequences (Topic 2.1), which is a natural bridge from Unit 1’s covariation framework (constant differences versus constant ratios) before moving into the broader comparison of change in linear and exponential functions (Topic 2.2). The distinction between additive and multiplicative change is central to understanding why exponential growth and decay behave the way they do, and it’s the conceptual hook that makes the rest of Unit 2 easier to organize.

Topics 2.3 through 2.6 build out exponential functions in full: their properties, their models, their transformations, and the question of competing function model types (when exponential fits and when polynomial fits better). Composition and inverse functions (Topics 2.7 and 2.8) are directly relevant to FRQ 1, which focuses on function concepts from Units 1 and 2 and may include composition, inverse functions, transformations, and interpretation across representations. These topics reward students who have practiced working through compositions and inverses in all representations, not just algebraically but from graphs and tables.

Topics 2.9 through 2.14 cover logarithms in depth: logarithmic expressions and their properties, logarithmic functions and their graphs, the inverse relationship between exponential and logarithmic functions, and solving equations that involve both. Topic 2.15 (semi-log plots) is the kind of topic students often skip in review because it feels niche, but it connects the analytical properties of logarithms to a graphical representation and is the kind of multi-representation question that appears in the calculator-active portions of both sections.

• Unit 2 — Arithmetic & Geometric Sequences — Drill 11→
• Unit 2 — Change in Linear and Exponential Functions — Drill 12→
• Unit 2 — Exponential Functions — Drill 13→
• Unit 2 — Exponential Models — Drill 14→
• Unit 2 — Composition of Functions — Drill 15→
• Unit 2 — Inverse Functions — Drill 16→
• Unit 2 — Logarithmic Expressions — Drill 17→
• Unit 2 — Logarithmic Functions — Drill 18→
• Unit 2 — Exponential & Logarithmic Equations — Drill 19→
• Unit 2 — Semi-log Plots — Drill 20→

Unit 3: Trigonometric and Polar Functions

Unit 3 is one of the heaviest-tested parts of the exam at 30–35% of the multiple-choice section, and it is also the unit that generates the most anxiety. Part of that anxiety is earned (the unit is long and the content is dense), but a lot of it comes from students who approach Unit 3 as a pure memorization task. Radian measure, unit circle values, sinusoidal parameters, the tangent function, inverse trig functions, trig equations, identities, and polar coordinates are all easier to learn and retain when you understand the covariation logic connecting them, not just the formulas.

Topics 3.1 and 3.2 establish periodic phenomena and connect sine, cosine, and tangent to angles and circles. Radian measure is not just a replacement for degrees to be memorized; it is a natural way to measure angles through arc length. Topics 3.3 and 3.4 develop sine and cosine function values and graphs, building toward the sinusoidal function work in Topics 3.5, 3.6, and 3.7.

The sinusoidal topics are directly connected to FRQ 3, the periodic-modeling question. The parameters of a sinusoidal model (amplitude, period, vertical shift, and phase shift) each correspond to something specific in a real-world context: the amplitude is half the range of output values, the period is the length of one complete cycle, the vertical shift is the midline value, and the phase shift is determined by where in the cycle the input begins. Students who have built and analyzed sinusoidal models from context, not just identified parameter values from a given formula, are significantly faster and more accurate on FRQ 3 than students who have only practiced the algebra end of it.

Topics 3.8 through 3.12 extend the trigonometric work to the tangent function, inverse trigonometric functions, trigonometric equations and inequalities, the secant/cosecant/cotangent functions, and equivalent representations of trigonometric functions. FRQ 4 is the no-calculator Symbolic Manipulations question and can draw on Unit 2 and Unit 3 symbolic skills. The 2026 version required exact exponential and logarithmic equation solving, rewriting exponential and trigonometric expressions, and solving a trigonometric equation. That is a good reason to know exact unit-circle values and identities without relying on technology.

Topics 3.13 and 3.14 introduce trigonometry and polar coordinates and then polar function graphs. Topic 3.15 is Rates of Change in Polar Functions: students reason about how the signed radius changes as the angle changes, including whether the distance from the origin is increasing or decreasing and how to interpret average rate of change in radius per radian. Polar content is easy to underweight because it comes at the end of the course, but it is part of the tested Unit 3 framework and deserves real review time.

• Unit 3 — Periodic Phenomena & Unit Circle — Drill 21→
• Unit 3 — Sine & Cosine Function Values — Drill 22→
• Unit 3 — Sinusoidal Functions: Amplitude, Period & Midline — Drill 23→
• Unit 3 — Sinusoidal Function Models — Drill 24→
• Unit 3 — The Tangent Function — Drill 25→
• Unit 3 — Inverse Trigonometric Functions — Drill 26→
• Unit 3 — Trigonometric Equations — Drill 27→
• Unit 3 — Equivalent Trigonometric Expressions — Drill 28→
• Unit 3 — Polar Coordinates & Polar Graphs — Drill 29→
• Unit 3 — Rates of Change in Sinusoidal Functions — Drill 30 (Supplemental Covariation Practice)→

The Unit-by-Unit Study Plan at a Glance

The three tested units are not weighted equally in the multiple-choice section. Use this table to guide how you allocate review time, with links to the drills for each unit clustered by function type.

Note that Unit 1 and Unit 2 have overlapping ranges that can reach 40%, so no unit can be safely deprioritized. Within the MCQ section, questions also include a general functions category (covering covariation, composition, inverses, and transformations across function types) drawn from Units 1 and 2 content but tested through graphical, numerical, and verbal representations rather than purely analytical ones. If you find yourself slowing down on graph-based or table-based questions during drill practice, that’s the signal to spend extra time on the equivalent representations and transformations drills.

A Realistic 5-Week AP Precalculus Study Plan for 2027

Five weeks is a workable timeline for focused review if you’re targeting the AP Precalculus exam in May. The 2027 AP® Precalculus exam is scheduled for Tuesday, May 11, 2027, during Session 1. Starting in early April gives you a realistic runway to review all three tested units and practice each free-response task type under the new 2027 timing.

Week 1: Unit 3, Topics 3.1–3.7. The unit circle, sine and cosine function values, and sinusoidal function parameters. These are the conceptual building blocks for everything else in Unit 3, and they take time to internalize. Do Drills 21–24 this week. Don’t move on until you can read the four sinusoidal parameters (amplitude, period, vertical shift, phase shift) directly from a context description, a graph, and a formula, in either direction.

Week 2: Unit 3, Topics 3.8–3.15. Review tangent, inverse trig, trig equations, reciprocal trig functions, equivalent trig expressions, polar coordinates, polar graphs, and rates of change in polar functions. Do Drills 25–30; note that Drill 30 is supplemental sinusoidal rate-of-change practice, so use College Board examples or AP Classroom to make sure you also practice Topic 3.15 in its actual polar-function form. Practice your first FRQ 3 and FRQ 4 attempts this week using released AP Precalculus free-response questions. These are the two no-calculator FRQs. For 2027, Part B gives you 35 minutes total for both questions, so eventually practice the pair together under that full-section time limit.

Week 3: Unit 2, all topics. Arithmetic and geometric sequences through semi-log plots. Do Drills 11–20. Pay particular attention to the composition and inverse function drills if FRQ 1 practice revealed gaps there, and to the equation-solving drill if FRQ 4 practice did. This is the week to get your logarithm algebra fast and reliable without a calculator.

Week 4: Unit 1, all topics. Covariation through function model construction. Do Drills 1–10. Because Unit 1 builds the conceptual vocabulary for the whole course, reviewing it after Units 2 and 3 often clicks faster than students expect, since the ideas feel familiar from their applications. Spend extra time on the model selection drill (Drill 10). Do your first complete timed attempt at FRQ 1 and FRQ 2 (both calculator-required) this week. For 2027, Part A gives you 35 minutes total for the two questions.

Week 5: Targeted review of your two weakest areas from drill practice, a full timed run of all four free-response question types using the 2027 split (35 minutes for calculator Part A and 35 minutes for no-calculator Part B), and at least one session working through the Bluebook interface so the exam environment is familiar on test day. Use the final week to make your weakest algebraic, modeling, and reasoning skills reliable under time pressure rather than trying to learn large amounts of new material.

Three Mathematical Practices to Build Throughout Your Review

College Board currently weights the three AP Precalculus mathematical practices across the overall exam as follows: Procedural and Symbolic Fluency, 35–50%; Multiple Representations, 20–30%; and Communication and Reasoning, 30–40%. Those ranges are a useful reminder that content knowledge alone is not enough: a large share of the exam asks you to represent, interpret, or justify mathematics rather than merely execute a procedure.

Practice 1 (Procedural and Symbolic Fluency) includes solving equations and inequalities, rewriting expressions in equivalent forms, and constructing functions through transformations, compositions, inverses, and regressions. Build fluency across all three tested units so that symbolic work does not become the bottleneck on the no-calculator portions.

Practice 2 (Multiple Representations) requires moving among graphical, numerical, analytical, and verbal forms. A function may be given as a graph in one question, a table in another, and an equation in the next. During review, deliberately translate among representations instead of practicing each function type only in algebraic form.

Practice 3 (Communication and Reasoning) asks you to describe function behavior, interpret numerical results in context, and support conclusions with a mathematical rationale. On FRQs, pay close attention to task verbs such as explain, justify, and give a reason. A correct numerical result may not be sufficient when the prompt explicitly asks for reasoning.

How to Use the AP Precalculus Practice Drills

The 30 drills linked throughout this post cover skills from all three tested units. Each one presents a function, data set, graph, or modeling scenario followed by five questions that mix procedural fluency, multiple representations, and reasoning tasks. The most productive way to use them is to work each drill under something close to exam conditions: decide whether you’re in a calculator or no-calculator section before you start, identify what each question is asking before you look at the choices, and eliminate wrong answers with a specific reason rather than on instinct. For Topic 3.15 specifically, add polar rate-of-change practice from College Board materials; Drill 30 reinforces the broader covariation skill with sinusoidal functions rather than polar functions.

After each drill, read every explanation, including for the questions you got right. The explanations describe the exact flaw in each wrong answer choice, which is where most of the learning happens. A wrong answer on an AP Precalculus question is usually wrong for a precise mathematical reason, not a random one. Training yourself to name that reason is the skill that pays off on the questions where two choices both look plausible and the difference comes down to something specific. Doing this consistently across the drills helps you recognize recurring distractor patterns and representation changes more quickly.

Your Complete Practice Resource

All 30 drills referenced in this post are free, organized by unit, and built around the multi-representation reasoning the exam uses. The complete collection with a full strategy guide covering exam structure, the three mathematical practices, the four free-response task types, and specific preparation strategies is available at the AP® Precalculus strategy and drills hub.

• AP® Precalculus Strategy Guide & All 30 Drills→
• Unit 3 — Sinusoidal Function Models (directly tied to FRQ 3)→
• Unit 2 — Exponential & Logarithmic Equations (directly relevant to FRQ 4)→
• Unit 3 — Equivalent Trigonometric Expressions (directly relevant to FRQ 4)→
• Unit 1 — Function Model Selection (a topic many students rush through)→
• Unit 3 — Polar Coordinates & Polar Graphs (a topic students sometimes underprepare for)→

The 2027 AP® Precalculus exam is scheduled for Tuesday, May 11, 2027, during Session 1. A strong review plan should combine content practice with the three mathematical practices: symbolic fluency, movement among representations, and clear reasoning. The goal is not simply to recognize a function type, but to use it flexibly in the format the question demands.

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