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world‑class calculus tutor
Pioneered by Stanford AI researchers and learning scientists, Aristotle is the world's first voice-based AI calculus tutor.
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The curriculum
Over 330 calculus 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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Limits and Continuity
Differentiation: Definition and Fundamental Properties
Differentiation: Composite, Implicit, and Inverse Functions
Contextual Applications of Differentiation
Analytical Applications of Differentiation
Integration and Accumulation of Change
Differential Equations
Applications of Integration
AP Calculus AB tutoring curriculum142 skills across 8 units
Limits and Continuity
AP Calculus AB exam weighting: 10-12%. Topics: Introducing Calculus: Can Change Occur at an Instant?, Defining Limits and Using Limit Notation, Estimating Limit Values from Graphs, Estimating Limit Values from Tables, Determining Limits Using Algebraic Properties of Limits, Determining Limits Using Algebraic Manipulation, Selecting Procedures for Determining Limits, Determining Limits Using the Squeeze Theorem, Connecting Multiple Representations of Limits, Exploring Types of Discontinuities, Defining Continuity at a Point, Confirming Continuity over an Interval, Removing Discontinuities, Connecting Infinite Limits and Vertical Asymptotes, Connecting Limits at Infinity and Horizontal Asymptotes, Working with the Intermediate Value Theorem (IVT).
Differentiation: Definition and Fundamental Properties
AP Calculus AB exam weighting: 10-12%. Topics: Defining Average and Instantaneous Rates of Change at a Point, Defining the Derivative of a Function and Using Derivative Notation, Estimating Derivatives of a Function at a Point, Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist, Applying the Power Rule, Derivative Rules: Constant, Sum, Difference, and Constant Multiple, Derivatives of cos x, sin x, ex, and ln x, The Product Rule, The Quotient Rule, Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions.
Differentiation: Composite, Implicit, and Inverse Functions
AP Calculus AB exam weighting: 9-13%. Topics: The Chain Rule, Implicit Differentiation, Differentiating Inverse Functions, Differentiating Inverse Trigonometric Functions, Selecting Procedures for Calculating Derivatives, Calculating Higher - Order Derivatives.
Contextual Applications of Differentiation
AP Calculus AB exam weighting: 10-15%. Topics: Interpreting the Meaning of the Derivative in Context, Straight-Line Motion: Connecting Position, Velocity, and Acceleration, Rates of Change in Applied Contexts Other Than Motion, Introduction to Related Rates, Solving Related Rates Problems, Approximating Values of a Function Using Local Linearity and Linearization, Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms.
Analytical Applications of Differentiation
AP Calculus AB exam weighting: 15-18%. Topics: Using the Mean Value Theorem, Extreme Value Theorem, Global Versus Local Extrema, and Critical Points, Determining Intervals on Which a Function Is Increasing or Decreasing, Using the First Derivative Test to Determine Relative (Local) Extrema, Using the Candidates Test to Determine Absolute (Global) Extrema, Determining Concavity of Functions over Their Domains, Using the Second Derivative Test to Determine Extrema, Sketching Graphs of Functions and Their Derivatives, Connecting a Function, Its First Derivative, and Its Second Derivative, Introduction to Optimization Problems, Solving Optimization Problems, Exploring Behaviors of Implicit Relations.
Integration and Accumulation of Change
AP Calculus AB exam weighting: 17-20%. Topics: Exploring Accumulationsof Change, Approximating Areas with Riemann Sums, Riemann Sums, Summation Notation, and Definite Integral Notation, The Fundamental Theorem of Calculus and Accumulation Functions, Interpreting the Behavior of Accumulation Functions Involving Area, Applying Properties of Definite Integrals, The Fundamental Theorem of Calculus and Definite Integrals, Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation, Integrating Using Substitution, Integrating Functions Using Long Division and Completing the Square, Selecting Techniques for Antidifferentiation.
Differential Equations
AP Calculus AB exam weighting: 6-12%. Topics: Modeling Situations with Differential Equations, Verifying Solutions for Differential Equations, Sketching Slope Fields, Reasoning Using Slope Fields, Finding General Solutions Using Separation of Variables, Finding Particular Solutions Using Initial Conditions and Separation of Variables, Exponential Models with Differential Equations.
Applications of Integration
AP Calculus AB exam weighting: 10-15%. Topics: Finding the Average Value of a Function on an Interval, Connecting Position, Velocity, and Acceleration of Functions Using Integrals, Using Accumulation Functions and Definite Integrals in Applied Contexts, Finding the Area Between Curves Expressed as Functions of x, Finding the Area Between Curves Expressed as Functions of y, Finding the Area Between Curves That Intersect at More Than Two Points, Volumes with Cross Sections: Squares and Rectangles, Volumes with Cross Sections: Triangles and Semicircles, Volume with Disc Method: Revolving Around the x- or y-Axis, Volume with Disc Method: Revolving Around Other Axes, Volume with Washer Method: Revolving Around the x- or y-Axis, Volume with Washer Method: Revolving Around Other Axes.
AP Calculus BC tutoring curriculum194 skills across 10 units
Limits and Continuity
AP Calculus BC exam weighting: 4-7%. Topics: Introducing Calculus: Can Change Occur at an Instant?, Defining Limits and Using Limit Notation, Estimating Limit Values from Graphs, Estimating Limit Values from Tables, Determining Limits Using Algebraic Properties of Limits, Determining Limits Using Algebraic Manipulation, Selecting Procedures for Determining Limits, Determining Limits Using the Squeeze Theorem, Connecting Multiple Representations of Limits, Exploring Types of Discontinuities, Defining Continuity at a Point, Confirming Continuity over an Interval, Removing Discontinuities, Connecting Infinite Limits and Vertical Asymptotes, Connecting Limits at Infinity and Horizontal Asymptotes, Working with the Intermediate Value Theorem (IVT).
Differentiation: Definition and Fundamental Properties
AP Calculus BC exam weighting: 4-7%. Topics: Defining Average and Instantaneous Rates of Change at a Point, Defining the Derivative of a Function and Using Derivative Notation, Estimating Derivatives of a Function at a Point, Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist, Applying the Power Rule, Derivative Rules: Constant, Sum, Difference, and Constant Multiple, Derivatives of cos x, sin x, ex, and ln x, The Product Rule, The Quotient Rule, Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions.
Differentiation: Composite, Implicit, and Inverse Functions
AP Calculus BC exam weighting: 4-7%. Topics: The Chain Rule, Implicit Differentiation, Differentiating Inverse Functions, Differentiating Inverse Trigonometric Functions, Selecting Procedures for Calculating Derivatives, Calculating Higher - Order Derivatives.
Contextual Applications of Differentiation
AP Calculus BC exam weighting: 6-9%. Topics: Interpreting the Meaning of the Derivative in Context, Straight-Line Motion: Connecting Position, Velocity, and Acceleration, Rates of Change in Applied Contexts Other Than Motion, Introduction to Related Rates, Solving Related Rates Problems, Approximating Values of a Function Using Local Linearity and Linearization, Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms.
Analytical Applications of Differentiation
AP Calculus BC exam weighting: 8-11%. Topics: Using the Mean Value Theorem, Extreme Value Theorem, Global Versus Local Extrema, and Critical Points, Determining Intervals on Which a Function Is Increasing or Decreasing, Using the First Derivative Test to Determine Relative (Local) Extrema, Using the Candidates Test to Determine Absolute (Global) Extrema, Determining Concavity of Functions over Their Domains, Using the Second Derivative Test to Determine Extrema, Sketching Graphs of Functions and Their Derivatives, Connecting a Function, Its First Derivative, and Its Second Derivative, Introduction to Optimization Problems, Solving Optimization Problems, Exploring Behaviors of Implicit Relations.
Integration and Accumulation of Change
AP Calculus BC exam weighting: 17-20%. Topics: Exploring Accumulationsof Change, Approximating Areas with Riemann Sums, Riemann Sums, Summation Notation, and Definite Integral Notation, The Fundamental Theorem of Calculus and Accumulation Functions, Interpreting the Behavior of Accumulation Functions Involving Area, Applying Properties of Definite Integrals, The Fundamental Theorem of Calculus and Definite Integrals, Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation, Integrating Using Substitution, Integrating Functions Using Long Division and Completing the Square, Integrating Using Integration by Parts bc only, Integrating Using Linear Partial Fractions bc only, Evaluating Improper Integrals bc only, Selecting Techniques for Antidifferentiation.
Differential Equations
AP Calculus BC exam weighting: 6-9%. Topics: Modeling Situations with Differential Equations, Verifying Solutions for Differential Equations, Sketching Slope Fields, Reasoning Using Slope Fields, Approximating Solutions Using Euler’s Method bc only, Finding General Solutions Using Separation of Variables, Finding Particular Solutions Using Initial Conditions and Separation of Variables, Exponential Models with Differential Equations, Logistic Models with Differential Equations bc only.
Applications of Integration
AP Calculus BC exam weighting: 6-9%. Topics: Finding the Average Value of a Function on an Interval, Connecting Position, Velocity, and Acceleration of Functions Using Integrals, Using Accumulation Functions and Definite Integrals in Applied Contexts, Finding the Area Between Curves Expressed as Functions of x, Finding the Area Between Curves Expressed as Functions of y, Finding the Area Between Curves That Intersect at More Than Two Points, Volumes with Cross Sections: Squares and Rectangles, Volumes with Cross Sections: Triangles and Semicircles, Volume with Disc Method: Revolving Around the x- or y-Axis, Volume with Disc Method: Revolving Around Other Axes, Volume with Washer Method: Revolving Around the x- or y-Axis, Volume with Washer Method: Revolving Around Other Axes, The Arc Length of a Smooth, Planar Curve and Distance Traveled bc only.
Parametric Equations, Polar Coordinates, and Vector-Valued Functions
AP Calculus BC exam weighting: 11-12%. Topics: Defining and Differentiating Parametric Equations, Second Derivatives of Parametric Equations, Finding Arc Lengths of Curves Given by Parametric Equations, Defining and Differentiating Vector-Valued Functions, Integrating Vector-Valued Functions, Solving Motion Problems Using Parametric and Vector-Valued Functions, Defining Polar Coordinates and Differentiating in Polar Form, Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve, Finding the Area of the Region Bounded by Two Polar Curves.
Infinite Sequences and Series
AP Calculus BC exam weighting: 17-18%. Topics: Defining Convergent and Divergent Infinite Series, Working with Geometric Series, The nth Term Test for Divergence, Integral Test for Convergence, Harmonic Series and p-Series, Comparison Tests for Convergence, Alternating Series Test for Convergence, Ratio Test for Convergence, Determining Absolute or Conditional Convergence, Alternating Series Error Bound, Finding Taylor Polynomial Approximations of Functions, Lagrange Error Bound, Radius and Interval of Convergence of Power Series, Finding Taylor or Maclaurin Series for a Function, Representing Functions as Power Series.
From our families
What parents are telling us
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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 the class they're taking
High school, AP, or college aligned
The standard calculus sequence
The courses follow the AP AB and BC frameworks, the same limits, derivatives, integrals, and series sequence taught in college Calculus I and II.
Your school or college class
Share the syllabus, textbook, or problem sets and sessions follow the actual course, whether that's a high school class, AP, or a university lecture.
Your own goals
Passing the class, a final exam next month, or getting ahead over the summer? Aristotle builds the path backwards from your goal.
FAQ
Common questions about online calculus tutoring
The full first-year calculus sequence, tracked as 336 individual skills: limits and continuity, derivatives and their applications, integrals and accumulation, differential equations, and infinite series. The curriculum is built on the AP Calculus AB and BC frameworks, which cover the same material as high school calculus classes and college Calculus I and II, so it fits whichever version of the course your student is taking.
Yes. The curricula are built on the AB and BC frameworks, which cover the core of college Calculus I and much of Calculus II: limits, derivatives, integrals, differential equations, and series. A college student working through problem sets or preparing for a midterm uses the same skill map, and sessions are available 24/7 with no scheduling, which matters when the exam is Monday morning.
Your student talks through problems out loud while working with Aristotle on a shared whiteboard: setting up an optimization problem, choosing a u-substitution, or testing a series for convergence. Aristotle asks questions, listens to the reasoning, and guides them to the answer instead of giving it away. There is no scheduling; sessions start whenever they are ready, at 9pm after homework or the night before an exam.
Calculus failures usually are not about calculus. Most trace back to shaky algebra or precalculus: factoring, exponent rules, trig identities, function composition. Each skill on Aristotle's map is linked to its prerequisites, so the tutor finds the exact earlier gap behind a wrong answer and rebuilds from there, then returns to the calculus. That is how a student who is lost in October catches up instead of falling further behind.
Calculus tutors charge $60 to $100 an hour, which comes to $720 to $1,200 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 will happily produce a worked solution, which is exactly the problem: your student copies it down and learns nothing. Aristotle works the other way. It asks the student to explain their approach, spots the misconception behind a wrong step, and guides them with questions until they can do it themselves. It also remembers every session, so the work builds instead of starting over each time.
Yes. Parents get a summary after every session, and the parent dashboard shows which skills have been mastered and where your child is stuck. Sessions are reviewed, and every tutor response is checked before it reaches your child.
Yes. The AB and BC courses follow the College Board's unit structure skill for skill, so class tutoring and exam review use the same map. Aristotle teaches at your child's frontier, which means review time goes to the units where skills are actually weakest rather than starting again from page one.
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