Free AP Calculus Lesson Plans
Get a free AP Calculus curriculum created by teachers, for teachers
Free Lesson Plans
Math Medic AP Calculus Units
Our AP Calculus curriculum is built for teachers who want to engage students in meaningful, discovery-based learning. Each lesson follows the Experience First, Formalize Later (EFFL) approach, which empowers students to explore key concepts before solidifying their understanding through a structured whole-class discussion.
This course is aligned with College Board’s AP Calculus framework and covers limits, derivatives, integrals, and applications of calculus in a logical, student-friendly progression. Each unit includes daily lesson plans, practice problems, quizzes, and assessments to help students be fully prepared for the AP exam.
- Defining limits and using limit notation
- Estimating limits from graphs
- Algebraic approaches to evaluating limits
- Squeeze theorem
- Continuity and discontinuity
- Limits involving infinity
- Intermediate Value Theorem
- Instantaneous rates of change
- Defining the derivative
- Continuity and differentiability
- Derivative shortcuts
- Derivatives of sin x, cos x, e^x, and ln x
- The product and quotient rules
- Derivatives of trig functions
- The chain rule
- Implicit differentiation
- Derivatives of inverse functions
- Higher-order derivatives and derivative strategies
- Interpreting derivatives in context
- Connecting position, velocity, and acceleration
- Rates of change in applied contexts
- Related rates
- Tangent line approximations
- L’Hôpital’s rule
- The Mean Value Theorem
- The Extreme Value Theorem
- Critical points and extrema
- Determining function behavior from the first derivative
- Candidate’s test
- Analyzing function behavior with the second derivative
- Connecting features of f, f’, and f”
- Optimization
- Exploring behaviors of implicit relations
- Exploring accumulation of change
- Approximating areas with Riemann sums and trapezoids
- Infinite Riemann sums and definite integrals
- The Fundamental Theorem of Calculus
- Accumulation functions
- Applying properties of definite integrals
- The FTC and definite integrals
- Finding antiderivatives and indefinite integrals
- Integration using u-substitution
- Other integration techniques
- Modeling differential equations and verifying solutions
- Slope fields
- Finding general and particular solutions using separation of variables
- Exponential models with differential equations
- Average value of a function
- Connecting position, velocity, and acceleration using integrals
- Using accumulation and definite integrals in applied contexts
- Finding areas between curves expressed as functions of x and y
- Volumes with cross sections
- Volume using the Disc Method
- Volume using the Washer Method
- Integration by parts
- Evaluating improper integrals
- Approximating solutions with Euler’s Method
- Defining and differentiating parametric equations
- Solving parametric and vector motion problems
- Areas of polar curve regions
- The series toolbox
- Ratio test for convergence
- Finding Taylor polynomial approximations
- Radius and interval of convergence
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Comprehensive Curriculum
Math Medic is an all-in-one package for your classroom. We provide a day-by-day schedule with all the supplemental materials you need. The lessons are free, while homework, quizzes, and tests are available as add-on services.
Discovery-Based Learning
We use a discovery- or inquiry-based lesson model that uses activities to enable students to guide the lessons. Teachers don’t lecture but respond to the students.
By Teachers, For Teachers.
Math Medic was created by high school math teachers based on years of experience in the classroom. We’re not a publishing company, we’re your colleagues—an extension of your math department.
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