Best fit
Students enrolled in AP Precalculus who want the reasoning marks, not just the arithmetic
AP Precalculus
AP Precalculus Tutoring
A College Board AP course built around functions, modeling, and reasoning: three exam-assessed units, a fourth course unit beyond the exam, and the three AP mathematical practices that decide how answers are graded.
AP Precalculus is not Algebra 2 with trigonometry attached. Almost every question asks the same underlying thing: how do two quantities change together, which family of functions captures that, and can you defend the choice. Sessions are built around that habit, because it is what separates a correct answer from a scoring one.
Starting point
College Board describes AP Precalculus as intended for students who have completed Geometry and Algebra 2, or Integrated Math 3
Session style
One-on-one or small group tutoring
Student outcome
Describe how two quantities vary together and name the function family that behavior implies
Course Menu
Study guide and practice links
Course Overview
Four units, three of them on the exam
College Board organizes AP Precalculus into four units. Units 1 through 3 are assessed on the AP Exam and carry published weightings. Unit 4 is part of the course but is not assessed, so it is taught here as real course content rather than as exam preparation.
Functions are the whole course
Polynomial, rational, exponential, logarithmic, trigonometric, and polar families are studied as models of how quantities vary together, not as separate chapters of formulas.
Modeling is graded, not optional
Students are expected to choose a function family, build a model, interpret its parameters, and say where it stops being reasonable. Two of the four free-response questions are modeling tasks.
Three practices decide the marks
Procedural and Symbolic Fluency, Multiple Representations, and Communication and Reasoning are weighted across the exam, so how an answer is justified matters as much as the value.
Unit 4 is course content, not exam content
Parametric functions, vectors, and matrices are taught because they are part of the course and because they matter later, but College Board does not assess them.
Official resources referenced
Student Fit
Who this course is for
- Students enrolled in AP Precalculus who want the reasoning marks, not just the arithmetic
- Students who can compute confidently but lose points explaining why a model fits
- Students who find the shift from solving equations to analyzing functions unfamiliar
- Students preparing for the AP Exam who want deliberate MCQ and free-response practice
- Students who want a stronger function foundation before college mathematics, whether or not calculus follows
- Students moving between representations slowly, and losing time on the exam because of it
Prerequisites
What students should know before starting
- College Board describes AP Precalculus as intended for students who have completed Geometry and Algebra 2, or Integrated Math 3
- College Board states that students who took those courses at any level have covered the content needed to start
- Comfort with factoring, exponent rules, radicals, and function notation makes the first unit far easier
- Familiarity with the coordinate plane, transformations, and right-triangle trigonometry is useful rather than required
- A graphing calculator, since parts of the course and the exam assume one
Questions
Frequently asked questions
What is AP Precalculus?
It is a College Board Advanced Placement mathematics course centered on functions and modeling. Students study how quantities change together, build function models from situations, move among algebraic, graphical, numerical, and verbal representations, and justify their conclusions. It ends in an AP Exam each May.
What are the four AP Precalculus units?
Unit 1 Polynomial and Rational Functions, Unit 2 Exponential and Logarithmic Functions, Unit 3 Trigonometric and Polar Functions, and Unit 4 Functions Involving Parameters, Vectors, and Matrices.
Is Unit 4 on the AP Precalculus Exam?
No. College Board assigns Unit 4 no exam weighting, so none of its content is assessed. We still teach it, because parametric functions, vectors, and matrices carry directly into calculus, physics, and linear algebra, but we label it clearly so exam preparation time is spent where the marks are.
How are the exam-assessed units weighted?
College Board publishes approximate ranges for the multiple-choice section: Unit 1 accounts for 30 to 40 percent, Unit 2 for 25 to 40 percent, and Unit 3 for 30 to 35 percent. Unit 4 is not assessed.
What is the AP Precalculus Exam format?
Section I is 42 multiple-choice questions in 1 hour 45 minutes, worth 62.5 percent: 29 questions in 65 minutes without a calculator, then 13 questions in 40 minutes with a graphing calculator. Section II is 4 free-response questions in 1 hour 10 minutes, worth 37.5 percent: two questions in 35 minutes with a calculator, then two in 35 minutes without. This format takes effect with the May 2027 exam.
Is the exam on paper or on a computer?
It is a hybrid. Students answer the multiple-choice section in the Bluebook application and read the free-response questions there as well, but they handwrite their free-response answers in a paper booklet.
How is AP Precalculus different from Precalculus Honors?
AP Precalculus follows one national College Board framework, is organized around function modeling and the three AP mathematical practices, and ends in a standardized exam. A Precalculus Honors course follows whatever sequence the school sets, so its scope varies, and it often includes topics such as limits and continuity that are not AP Precalculus units. There is real overlap in the function and trigonometry content, but they are not interchangeable, and neither is universally harder. The difficulty depends on the school and the teaching.
Does AP Precalculus include calculus?
No. It develops the function fluency and reasoning that later calculus work assumes, and Unit 1 spends real time on rates of change, but limits, derivatives, and integrals are not part of the AP Precalculus framework.
Is AP Precalculus required before AP Calculus AB or BC?
No. College Board states plainly that the course is not a prerequisite for AP Calculus and does not have to be followed by it. It can still be a strong foundation for calculus and other quantitative college coursework.
What calculator is needed?
A graphing calculator, since one section of the multiple-choice questions and one part of the free-response section require it. Just as important is working fluently without one, because the other parts forbid it. We practice both conditions deliberately.
How does Code Scholars prepare students for the free-response questions?
By working the four question types separately, since they reward different things. Students practice identifying precisely what a prompt asks, showing enough supporting work, interpreting results in context, using correct notation, and connecting representations. All practice problems are written by Code Scholars rather than taken from released exams.
Will this help with college credit or placement?
That depends entirely on the individual college. Credit and placement policies for AP Precalculus vary by institution, so check the policy of the specific colleges a student is considering. We do not promise a score, a grade, or a credit outcome.
Curriculum
AP Precalculus curriculum
Unit order, topic placement, and exam weightings follow the current College Board framework. Every topic listed below is an official course topic; the surrounding explanation is written by Code Scholars.
1
Unit 1: Polynomial and Rational Functions
Exam assessed, 30 to 40 percent of the multiple-choice section. The unit opens with how two quantities change together and builds toward choosing and defending a function model. Rate of change, end behavior, and the difference between a hole and an asymptote all trace back to reading a function rather than manipulating it.
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 1.7 Rational Functions and End Behavior
- 1.8 Rational Functions and Zeros
- 1.9 Rational Functions and Vertical Asymptotes
- 1.10 Rational Functions and Holes
- 1.11 Equivalent Representations of Polynomial and Rational Expressions
- 1.12 Transformations of Functions
- 1.13 Function Model Selection and Assumption Articulation
- 1.14 Function Model Construction and Application
2
Unit 2: Exponential and Logarithmic Functions
Exam assessed, 25 to 40 percent of the multiple-choice section. The organizing idea is proportional change: what it looks like in a sequence, in a function, in a table, and on a semi-log plot. Logarithms arrive as the inverse that makes those relationships solvable rather than as a separate set of rules.
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 2.15 Semi-log Plots
3
Unit 3: Trigonometric and Polar Functions
Exam assessed, 30 to 35 percent of the multiple-choice section. Periodic behavior is introduced as something to model before it is something to compute, so amplitude, period, and shifts are read as facts about a situation. Polar functions close the unit by describing position with distance and direction instead of coordinates.
- 3.1 Periodic Phenomena
- 3.2 Sine, Cosine, and Tangent
- 3.3 Sine and Cosine Function Values
- 3.4 Sine and Cosine Function Graphs
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions
- 3.13 Trigonometry and Polar Coordinates
- 3.14 Polar Function Graphs
- 3.15 Rates of Change in Polar Functions
4
Unit 4: Functions Involving Parameters, Vectors, and Matrices — additional course content, not assessed on the AP Exam
College Board includes this unit in the course and assigns it no exam weighting, so nothing here appears on the AP Exam. It is still taught: parametric motion, vectors, and matrices are exactly the ideas that reappear in calculus, physics, linear algebra, and computer graphics. Students preparing only for the exam can treat it as optional; students continuing in mathematics should not.
- 4.1 Parametric Functions
- 4.2 Parametric Functions Modeling Planar Motion
- 4.3 Parametric Functions and Rates of Change
- 4.4 Parametrically Defined Circles and Lines
- 4.5 Implicitly Defined Functions
- 4.6 Conic Sections
- 4.7 Parametrization of Implicitly Defined Functions
- 4.8 Vectors
- 4.9 Vector-Valued Functions
- 4.10 Matrices
- 4.11 The Inverse and Determinant of a Matrix
- 4.12 Linear Transformations and Matrices
- 4.13 Matrices as Functions
- 4.14 Matrices Modeling Contexts
5
Running throughout: the three AP mathematical practices
College Board weights these across the exam, which means they are not study advice but scoring criteria. Roughly 35 to 50 percent of the exam rests on Procedural and Symbolic Fluency, 20 to 30 percent on Multiple Representations, and 30 to 40 percent on Communication and Reasoning.
- Procedural and Symbolic Fluency: rewriting an expression because a different form answers the question
- Choosing the equivalent form that exposes zeros, asymptotes, or a rate
- Solving equations and inequalities with and without a calculator
- Multiple Representations: reading the same function as an equation, a graph, a table, and a description
- Knowing which representation answers which question fastest
- Building a missing representation from the ones you were given
- Communication and Reasoning: stating what a parameter means in context
- Justifying a model choice with evidence rather than preference
- Describing function behavior with the precision the question calls for
- Saying when a result is unreasonable, and why
6
Modeling and multiple representations
This is the part of AP Precalculus that surprises students arriving from a computation-heavy course. A modeling question is not finished when a number appears. It is finished when the model has been chosen, justified, interpreted, and bounded.
- Identifying which quantities in a situation actually vary
- Deciding whether change is additive, proportional, or periodic
- Choosing the function family that behavior implies
- Estimating or computing parameters from data or from given conditions
- Explaining what each parameter means in the situation, not in the formula
- Using the model to predict, then checking the prediction for sense
- Comparing two candidate models and defending the better fit
- Stating the limitations and assumptions a model carries
- Moving deliberately among equation, graph, table, context, and description
- Recognizing that each representation hides something the others show
7
Technology and graphing calculator skills
Part of the exam requires a graphing calculator and part forbids one, so students need both fluencies. The aim is not calculator tricks: it is knowing what to ask the machine, and being able to tell when the answer it gives is meaningless.
- Choosing a viewing window that shows the behavior in question
- Finding zeros, intersections, and extrema and interpreting them
- Generating and reading tables of values
- Solving equations numerically when an exact method is impractical
- Fitting a model to data and judging whether the fit is appropriate
- Exploring exponential, logarithmic, trigonometric, and polar behavior
- Recognizing a misleading window, a rounding artifact, or a false intersection
- Working the same problem again without technology, since a whole section forbids it
8
The AP Exam and how sessions prepare for it
The exam is a hybrid digital administration: multiple-choice questions are answered in Bluebook, free-response questions are read in Bluebook, and free-response answers are handwritten in a paper booklet. The format below takes effect with the May 2027 exam.
- Section I, multiple choice: 42 questions, 1 hour 45 minutes, 62.5 percent of the score
- Part A: 29 questions in 65 minutes, no calculator
- Part B: 13 questions in 40 minutes, graphing calculator required
- Section II, free response: 4 questions, 1 hour 10 minutes, 37.5 percent of the score
- Part A: 2 questions in 35 minutes, graphing calculator required
- Part B: 2 questions in 35 minutes, no calculator
- Question 1: Function Concepts
- Question 2: Modeling a Non-Periodic Context
- Question 3: Modeling a Periodic Context
- Question 4: Symbolic Manipulations
Practice
Practice that matches how the exam actually asks
Sessions alternate between the two calculator conditions and between the four free-response types, because fluency in one does not transfer automatically to the other.
No-calculator symbolic work
Calculator-required analysis
Reading graphs for behavior
Reading tables for rate
Function family selection
Non-periodic modeling
Periodic modeling
Parameter interpretation
Equivalent-form rewriting
Written justification
Multi-part free response
Timing and triage
Outcomes
By the end of this course, students will be able to
- Describe how two quantities vary together and name the function family that behavior implies
- Analyze a polynomial or rational function completely: zeros, multiplicity, end behavior, asymptotes, holes
- Distinguish additive from proportional change and model each correctly
- Use logarithms as the inverse that makes exponential relationships solvable
- Build a periodic model from a situation and interpret amplitude, period, and shift in context
- Move between polar and rectangular descriptions and read a polar graph
- Rewrite an expression into the form that answers the question being asked
- Interpret every parameter in a model in the language of the situation
- Justify a model choice and state the assumptions it depends on
- Work confidently both with a graphing calculator and without one
Learning Format
How sessions are structured
- One-on-one or small group tutoring
- Unit-paced review matched to your school calendar
- Free-response walkthroughs with written justification
- Calculator and no-calculator drill sets
- Assessment post-mortems
- Modeling practice on original contexts
- Progress tracking
Why Code Scholars
Support that builds real understanding
Built From the Current Framework
Unit order, topic placement, and exam weightings follow the College Board framework, and the exam format reflects the changes taking effect with the May 2027 administration.
Reasoning Is Taught, Not Assumed
Because roughly a third of the exam rests on Communication and Reasoning, students practice writing justifications rather than only producing values.
Modeling From First Principles
Students learn to choose a function family from the behavior of a situation, which is the skill two of the four free-response questions are built on.
Both Calculator Conditions
Every topic is practiced with and without technology, since the exam separates the two and rewards different habits in each.
Unit 4 Handled Honestly
It is taught as course content and clearly labeled as not assessed, so students preparing for the exam can allocate their time accurately.
Clear About the Two Precalculus Courses
Families choosing between AP Precalculus and a school Precalculus Honors course get a straight comparison rather than a sales pitch.
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