“Aristotle is so impressive. It explained a math problem to my daughter that ChatGPT couldn't figure out.”
Akshay
parent of Tara, 15
Grades 10–12Your child's own
Your child's own
world‑class precalculus tutor
Pioneered by Stanford AI researchers and learning scientists, Aristotle is the world's first voice-based AI precalculus tutor.
From functions and trigonometry through their first limits, Aristotle has improved thousands of grades over 22% within a week.
Trusted by families at
The curriculum
Over 460 precalculus skills, personalized to your child
Aristotle is designed to always know what to teach at exactly the right time.
Sample curriculum
+ 8 more math subjects available
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* Click a topic to see the skills inside
Algebra and Function Foundations
Functions and Their Graphs
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Trigonometry
Analytic Trigonometry
Applications of Trigonometry
Systems of Equations and Inequalities
Matrices and Determinants
Sequences, Series, and Probability
Analytic Geometry: Conics, Parametric, and Polar
Limits and the On-Ramp to Calculus
Precalculus tutoring curriculum164 skills across 12 units
Algebra and Function Foundations
A lean diagnostic on-ramp covering the algebraic grammar precalculus assumes: real-number properties and notation, exponent and radical fluency, rewriting polynomial and rational expressions, and solving equations and inequalities. Topics: Real Numbers and Algebraic Properties, Exponents and Radicals, Polynomial and Rational Expressions, Solving Equations and Inequalities.
Functions and Their Graphs
The central object of the course: the coordinate plane and graphs of equations, lines and their slopes and forms, the definition and notation of functions, reading graph features, the library of parent functions, transformations, combinations and composition, and inverse functions. Topics: Coordinate Plane and Graphs, Linear Equations in Two Variables, Functions and Function Notation, Analyzing Graphs of Functions, Library of Parent Functions, Transformations of Functions, Combinations and Composition of Functions, Inverse Functions.
Polynomial and Rational Functions
Functions defined by polynomials and ratios of polynomials: quadratics and their graphs, the end behavior and zeros of higher-degree polynomials, polynomial division and the zero theorems, complex numbers, and the graphs, asymptotes, and inequalities of rational functions. Topics: Quadratic Functions, Polynomial Functions of Higher Degree, Polynomial and Synthetic Division, Complex Numbers, Zeros of Polynomial Functions, Rational Functions, Nonlinear Inequalities.
Exponential and Logarithmic Functions
The inverse pair of exponential and logarithmic functions: their graphs and key features, the definition of the logarithm, the properties used to rewrite logarithmic expressions, solving exponential and logarithmic equations, and growth, decay, and other models. Topics: Exponential Functions and Graphs, Logarithmic Functions and Graphs, Properties of Logarithms, Exponential and Logarithmic Equations, Exponential and Logarithmic Models.
Trigonometry
Trigonometry from angles to applications: angle measure in degrees and radians, the unit-circle and right-triangle definitions of the six trigonometric functions, trig functions of any angle, the graphs of all six functions and their inverses, and right-triangle and periodic applications. Topics: Angles and Their Measure, Trigonometric Functions: The Unit Circle, Right Triangle Trigonometry, Trigonometric Functions of Any Angle, Graphs of Sine and Cosine, Graphs of Other Trigonometric Functions, Inverse Trigonometric Functions, Applications and Models.
Analytic Trigonometry
Working symbolically with trigonometric expressions and equations: simplifying with the fundamental identities, verifying identities, solving trigonometric equations, and applying the sum and difference, double-angle, half-angle, and product-to-sum formulas. Topics: Using Fundamental Identities, Verifying Trigonometric Identities, Solving Trigonometric Equations, Sum and Difference Formulas, Multiple-Angle and Product-to-Sum Formulas.
Applications of Trigonometry
Trigonometry beyond the right triangle: solving oblique triangles with the Laws of Sines and Cosines, vector operations and the dot product in the plane, and the trigonometric (polar) form of complex numbers with DeMoivre's Theorem. Topics: Law of Sines, Law of Cosines, Vectors in the Plane, Vectors and Dot Products, Trigonometric Form of Complex Numbers.
Systems of Equations and Inequalities
Solving systems of equations and inequalities: linear and nonlinear systems by substitution, elimination, and Gaussian methods, decomposing rational expressions into partial fractions, and graphing systems of inequalities and solving linear programming problems. Topics: Two-Variable Systems, Multivariable Linear Systems, Partial Fractions, Systems of Inequalities and Linear Programming.
Matrices and Determinants
Matrix methods for linear systems: representing and row-reducing augmented matrices, matrix algebra, inverses for solving systems, determinants, and Cramer's Rule. Topics: Matrices and Systems of Equations, Operations with Matrices, Inverse of a Square Matrix, Determinants and Cramer's Rule.
Sequences, Series, and Probability
Discrete patterns and counting: sequence and series notation, arithmetic and geometric sequences and their sums, mathematical induction, the Binomial Theorem, counting principles, and basic probability. Topics: Sequences and Series, Arithmetic Sequences and Series, Geometric Sequences and Series, Mathematical Induction, The Binomial Theorem, Counting and Probability.
Analytic Geometry: Conics, Parametric, and Polar
Curves in the plane beyond function graphs: the conic sections and their equations, rotation of axes, parametric representations of curves, and polar coordinates with the graphs and conic equations they enable. Topics: Parabolas, Ellipses, Hyperbolas, Rotation of Conics, Parametric Equations, Polar Coordinates and Graphs.
Limits and the On-Ramp to Calculus
An introduction to the limit concept that motivates calculus: estimating limits graphically and numerically, evaluating them algebraically, and using limits to find instantaneous rate of change as the slope of a tangent line and to approximate the area under a curve. Topics: Introduction to Limits, Limits and Rates of Change.
AP Precalculus tutoring curriculum303 skills across 4 units
Polynomial and Rational Functions
AP Exam weighting: 30-40%. 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.
Exponential and Logarithmic Functions
AP Exam weighting: 27-40%. 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.
Trigonometric and Polar Functions
AP Exam weighting: 30-35%. 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.
Functions Involving Parameters, Vectors, and Matrices
AP Exam weighting: not assessed on the AP Exam. 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.
From our families
What parents are telling us
“My son told me yesterday that we should cancel his human tutor, Aristotle is doing a better job. The human tutor was $250/hour.”
Kim
parent of Andy, 13
“Sam got an A+. So it def worked!!!”
Tina
parent of Sam, 14
Why families switch
Everything an hourly tutor can't be
On demand, 24/7
No scheduling, no weekly slot. Help is there during homework at 9pm and the morning before the test.
A fraction of the cost
Unlimited sessions on a flat plan instead of paying a human tutor by the hour.
Truly personalized
Aristotle tracks every skill your child has mastered and teaches at their exact frontier: never too easy, never too far ahead.
Driven by science
How Aristotle works
Dialogue over lectures
Your child speaks — the tutor listens and responds.
Interactive engagement is the highest level of learning · ICAP Framework
Misconceptions over mistakes
Finds the conceptual gap underneath the wrong answer.
Models the reasoning pattern, not just the error · MISTAKE
Expert-level error handling
Follows the same 3-step process expert tutors use.
Novice tutors skip to correction — experts don't · Bridge
Verified every turn
Every response is checked before it reaches your child.
Turn-by-turn verification improves outcomes · TRAVER
Gets them to think
Asks your child to explain, then guides them until they get there themselves.
Socratic dialogue outperforms GPT-4 by 12% · SocraticLM
Fits your child's precalculus class
Common Core, AP, and school aligned
Common Core and AP standards
Precalculus skills are aligned to Common Core high school standards and the AP course follows the College Board framework, so tutoring matches what your child is graded on.
Your child's school
Share the syllabus or textbook and sessions follow your child's actual class, whether that's public, private, or homeschool.
Your own goals
Working toward calculus next year, a placement test, or getting a grade up? Aristotle builds the path backwards from your goal.
FAQ
Common questions about online precalculus tutoring
Two full courses, with 467 individually tracked skills between them: general Precalculus and AP Precalculus. The Precalculus course runs from functions and their graphs through trigonometry, matrices, conics, and an on-ramp to limits. The AP course follows the College Board's four units, from polynomial and rational functions through parameters, vectors, and matrices. Aristotle always knows which skills your child has mastered and what comes next.
That is the whole point of the course, and it is where Aristotle focuses. Calculus assumes instant fluency with functions, exponentials, logarithms, and trigonometry, and students who memorized their way through precalculus hit a wall in the first month. Aristotle teaches for that fluency, working across graphs, tables, and equations, and the final unit of the course is a direct on-ramp to limits, the first idea of calculus.
Trigonometry is where most precalculus students get stuck, usually because the unit circle never clicked or because earlier algebra and geometry gaps surface all at once. Each skill on Aristotle's map is linked to its prerequisites, so the tutor traces a wrong answer back to the exact earlier skill that is missing and rebuilds from there, instead of drilling the same identities again.
Your child talks through problems out loud while working with Aristotle on a shared whiteboard, whether that's graphing a rational function, proving an identity, or setting up a system of equations. Aristotle asks questions, listens to their reasoning, and guides them to the answer. Sessions start whenever your child is ready, with no scheduling: during homework at 9pm, or the morning before a test.
Math tutors at this level charge $45 to $75 an hour, and AP-level tutors often add a premium, which comes to $540 to $900 or more a month at three hours a week. Aristotle costs $299 a month for unlimited sessions across every subject, or $49 for a single session.
Chatbots hand your child the answer and forget them when the chat ends. Aristotle teaches the way expert tutors do: it asks your child to explain their thinking, finds the misconception underneath a wrong answer, and guides them with questions until they can solve it themselves. It also remembers every session, tracking what your child has mastered and planning what to teach next.
Yes. Parents get a summary after every session, and the parent dashboard shows which skills your child has mastered and where they are stuck. Sessions are reviewed, and every tutor response is checked before it reaches your child.
Yes. The Precalculus course is aligned to Common Core high school standards and the AP Precalculus course follows the College Board's framework, so tutoring matches what your child is graded on. Share the syllabus, textbook, or upcoming test topics and sessions will follow what is happening in their class.
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