What AP Precalculus covers
The program develops students’ understanding of functions and their representations, rates of change, and mathematical modeling. It also covers exponential, logarithmic, trigonometric, polar, parametric, vector, and matrix concepts.
AP Precalculus is a College Board course on polynomial, rational, exponential, logarithmic, trigonometric and polar functions, and on functions involving parameters, vectors and matrices. The exam assesses the first three units; the fourth is taught but not assessed.
1 Polynomial and Rational Functions 14 topics · 30–40% of the multiple-choice section 6 h
What the exam asks for
- Read function behavior from graphs, tables, formulas, and contextual quantities, including how outputs vary across intervals.
- Connect polynomial degree, zeros, multiplicities, symmetry, rates of change, and end behavior.
- Analyze rational functions by distinguishing zeros, vertical asymptotes, holes, and end behavior from equivalent forms.
- Select and build polynomial, piecewise, or rational models; use models to answer contextual questions and interpret restrictions.
Common slips to watch for
- Confusing a rational-function zero with a hole or vertical asymptote, especially before canceling common factors.
- Using only one pair of values to claim a rate is constant, or reversing the input and output changes in a rate calculation.
- Inferring polynomial end behavior from a leading coefficient without considering degree parity.
- Giving a fitted model without stating domain restrictions or checking whether its assumptions fit the context.
Topics
- Change in Tandem
- Rates of Change
- Rates of Change in Linear and Quadratic Functions
- Polynomial Functions and Rates of Change
- Polynomial Functions and Complex Zeros
- Polynomial Functions and End Behavior
- Rational Functions and End Behavior
- Rational Functions and Zeros
- Rational Functions and Vertical Asymptotes
- Rational Functions and Holes
- Equivalent Representations of Polynomial and Rational Expressions
- Transformations of Functions
- Function Model Selection and Assumption Articulation
- Function Model Construction and Application
2 Exponential and Logarithmic Functions 15 topics · 25–40% of the multiple-choice section 7 h
What the exam asks for
- Distinguish arithmetic change from geometric change and compare linear and exponential outputs over equal input intervals.
- Interpret exponential and logarithmic behavior through formulas, tables, graphs, inverses, domains, and end behavior.
- Manipulate powers and logarithms equivalently, then solve equations while checking restrictions and contextual meaning.
- Construct and assess exponential or logarithmic models, including linear representations of exponential data on semi-log plots.
Common slips to watch for
- Treating a common additive change as evidence of exponential behavior, or a common multiplicative change as evidence of linear behavior.
- Applying logarithm or exponent rules incorrectly across sums, products, or powers.
- Accepting an equation solution outside the logarithm's domain or outside the context's allowed inputs.
- Reversing the roles of a function and its inverse, or overlooking that an inverse may require a restricted domain.
Topics
- Change in Arithmetic and Geometric Sequences
- Change in Linear and Exponential Functions
- Exponential Functions
- Exponential Function Manipulation
- Exponential Function Context and Data Modeling
- Competing Function Model Validation
- Composition of Functions
- Inverse Functions
- Logarithmic Expressions
- Inverses of Exponential Functions
- Logarithmic Functions
- Logarithmic Function Manipulation
- Exponential and Logarithmic Equations and Inequalities
- Logarithmic Function Context and Data Modeling
- Semi-log Plots
3 Trigonometric and Polar Functions 15 topics · 30–35% of the multiple-choice section 6.5 h
What the exam asks for
- Use the unit circle and exact special-angle values to connect angles, coordinates, and sine, cosine, and tangent.
- Read sinusoidal amplitude, vertical shift, period, and phase shift, and construct periodic models from extrema or data.
- Analyze tangent and reciprocal-trigonometric graphs through periods, asymptotes, intervals of behavior, and transformations.
- Solve trigonometric equations with periodicity and domain limits in view; use identities and polar representations to rewrite or interpret functions.
Common slips to watch for
- Mixing degrees and radians, or giving a single angle when periodicity calls for additional solutions in the stated interval.
- Confusing amplitude with maximum value, or period with the horizontal distance between neighboring extrema.
- Missing tangent or reciprocal-function asymptotes when the denominator is zero.
- Applying an identity or inverse-trigonometric function without respecting its domain or principal-value range.
Topics
- Periodic Phenomena
- Sine, Cosine, and Tangent
- Sine and Cosine Function Values
- Sine and Cosine Function Graphs
- Sinusoidal Functions
- Sinusoidal Function Transformations
- Sinusoidal Function Context and Data Modeling
- The Tangent Function
- Inverse Trigonometric Functions
- Trigonometric Equations and Inequalities
- The Secant, Cosecant, and Cotangent Functions
- Equivalent Representations of Trigonometric Functions
- Trigonometry and Polar Coordinates
- Polar Function Graphs
- Rates of Change in Polar Functions
4 Functions Involving Parameters, Vectors, and Matrices 14 topics 6.8 h
What the exam asks for
- Evaluate parametric component equations in parameter order and connect the resulting points to motion, direction, and rate.
- Represent circles, lines, conics, and implicit curves with equations or parametrizations suited to their geometry.
- Use vector components to describe position, velocity, magnitude, direction, and operations such as sums and dot products.
- Apply matrix products, inverses, determinants, and transition models to transformations and two-state systems.
Common slips to watch for
- Listing parametric points without preserving parameter order, or confusing a parameter interval with an x-coordinate interval.
- Using row-by-column multiplication in the wrong order or multiplying matrices with incompatible dimensions.
- Assuming every two-by-two matrix has an inverse, or omitting the nonzero-determinant condition.
- Treating vector magnitude as a signed component or confusing a transition step with a state value.
Topics
- Parametric Functions
- Parametric Functions Modeling Planar Motion
- Parametric Functions and Rates of Change
- Parametrically Defined Circles and Lines
- Implicitly Defined Functions
- Conic Sections
- Parametrization of Implicitly Defined Functions
- Vectors
- Vector-Valued Functions
- Matrices
- The Inverse and Determinant of a Matrix
- Linear Transformations and Matrices
- Matrices as Functions
- Matrices Modeling Contexts
Hours are hours of teaching at the Standard level. A unit's weight is its share of the multiple-choice section.
A class in AP Precalculus, opened
Every class works like this. The tutor asks, you answer in your own words, and it reads what you wrote while you are still in the room, then tells you what is missing and asks you to try again.
PixelAI tutor
Example
AP Precalculus · Unit 3 · Sinusoidal functions
State the period of y = 3 sin(2x).
Put a finger on one full cycle. The 2 tells you how many cycles fit in 2π, so the length of one cycle is 2π divided by 2.
A sample written to show how a class sounds. The scores show how the exam would credit each answer. Not a real learner.
How the AP Precalculus exam is built
The 2027 exam is on Tuesday, May 11, in the morning session. It has 42 multiple-choice questions in 105 minutes (62.5% of the score) and 4 free-response questions of 6 points each in 70 minutes (37.5%). A graphing calculator is required for part of each section.
Practice papers. The Full syllabus level includes 2 full practice papers, written for Tutix in the style of the real exam: 46 questions and 66 marks each. You can sit them as long homework, and a class can go over them afterwards.
How students score on AP Precalculus
The share of students scoring 3 or higher on AP Precalculus was 75.6% in 2024, the first year the College Board's tables list it, and 82% in 2026. The College Board reviews each exam's score standards every five to ten years, so a change from one year to the next can reflect a new standard as well as how students did. AP pass rates for every exam shows the whole table.
| Year | 5 | 4 | 3 | 2 | 1 | 3 or higher | Students | Mean score |
|---|---|---|---|---|---|---|---|---|
| 2026 | 29% | 29% | 24% | 11% | 7% | 82% | n/a | n/a |
| 2025 | 28.1% | 25.8% | 26.8% | 11.2% | 8.0% | 80.8% | 253,596 | 3.55 |
| 2024 | 25.9% | 23.9% | 25.9% | 14.6% | 9.8% | 75.6% | 184,394 | 3.42 |
How long does AP Precalculus take?
Every level covers the whole syllabus. A deeper level only adds classes, so you can go deeper later and keep everything you have done. Hours are hours of teaching, counted in classes of 45 or 60 minutes.
29.2hours of teaching
- 39 classes of 45 minutes
- About 20 weeks at 2 a week
The Programs page draws AP Precalculus beside the other eleven programs on one hours scale, with what a pass costs at each level.
Questions people ask
How many hours of teaching does AP Precalculus take on Tutix?
The Standard level takes 26.2 hours: 35 classes of 45 minutes, or 27 of 60. The Full syllabus level takes 52 hours (70 classes of 45 minutes). The Short level is 5 hours. Every level covers the whole syllabus; deeper levels add classes.
What does the AP Precalculus exam look like?
As the board publishes it, the exam has these parts: Multiple choice, no calculator (29 questions, 65 minutes); Multiple choice, graphing calculator (13 questions, 40 minutes); Free response, graphing calculator (2 questions, 35 minutes); Free response, no calculator (2 questions, 35 minutes). Check your board's current specification for the exact format of the year you sit it.
Which AP Precalculus units carry the most weight?
The heaviest units are Polynomial and Rational Functions (30–40%); Exponential and Logarithmic Functions (25–40%); Trigonometric and Polar Functions (30–35%), measured as a share of the multiple-choice section.
Are there practice papers for AP Precalculus?
Yes. The Full syllabus level includes 2 full practice papers written for Tutix in the style of the real exam (46 questions and 66 marks each). You can sit them as long homework, and a class can go over them afterwards.
Is this an official College Board AP course?
No. Tutix is not affiliated with College Board and its AP Precalculus classes are not endorsed by College Board. The lessons and questions are Tutix's own, prepared to follow the published AP Precalculus course description, and the real exam is set and marked by College Board.
Can I try AP Precalculus for free?
Yes. The Free plan includes 45 live class minutes a month, about one class of the default length, and no card is needed. Pro is $15 a month for 360 live minutes (6 hours), and Pro+ is $30 a month for 900 live minutes.
Is the AP Precalculus tutor a person?
No. The tutor is an AI. It talks with you in real time, teaches on a whiteboard, reads your answers and remembers what each earlier class covered. A parent can set up a child's classes and choose to get a recap after each one.
When is the AP Precalculus exam in 2027?
AP Precalculus is on Tuesday, May 11, 2027, in the morning session. The 2027 AP exam window runs from May 3 to May 7 and from May 10 to May 14, set by the College Board.
What is a good AP Precalculus score?
The College Board calls a 5 extremely well qualified, a 4 very well qualified and a 3 qualified. In 2026, 82% of students who sat AP Precalculus scored 3 or higher. What counts as good for you depends on the colleges you are aiming at.
Does AP Precalculus count for college credit?
It depends on the college. The College Board says many US colleges grant credit or advanced placement for scores of 3 and above, and that each college makes its own decisions about which scores it accepts. Check each college's credit policy before you rely on a score.
Sources
- AP Precalculus: the exam, College Board (accessed October 21, 2026)
- AP Precalculus: the course, College Board (accessed October 21, 2026)
- AP exam dates, College Board (accessed October 21, 2026)
- AP score distributions, 2026, College Board (2026 results)
- The AP score scale, College Board (accessed October 21, 2026)
- Getting credit and placement, College Board (accessed October 21, 2026)
- AP score distributions, by year (2021 to 2026), College Board (2021 to 2026 results)
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