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
- Volume using the Disc Method
- Volume using the Washer Method
- Volumes with cross sections
- 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
- 25 days of structured review coursework
- Review activities
- Videos with AP Exam strategies
- Exam tips
Additional Resources
Complete Your Curriculum With Assessments
While lesson plans are always free, we also offer a full suite of assessments, including editable homework, quizzes, and tests that align with the AP Calculus framework. Our Assessment Platform allows teachers to customize assessments and deliver them digitally or on paper.
Have Questions? Let Us Know!
Moving to a new curriculum can be a big step, but we’re here to help! Reach out to our team to learn more about making the switch to Math Medic as seamless as possible.
Why Choose Math Medic?
Comprehensive Curriculum
Math Medic provides a structured, day-by-day schedule with all the materials you need to teach AP Calculus. Lessons are free, while homework, quizzes, and tests are available as add-on subscriptions.
Discovery-Based Learning
Our discovery-based lesson model encourages students to explore concepts before formalizing their understanding. Teachers guide discussions and respond to student discoveries, which creates a dynamic learning environment.
By Teachers, For Teachers.
Math Medic was founded by high school math teachers with years of classroom experience. We’re not a publishing company—we’re a community of educators dedicated to making math instruction more effective and engaging. Think of us as an extension of your math department.
The Numbers Don’t Lie
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Frequently Asked Questions
All of our lessons are free! Assessment resources are available through a subscription to the Math Medic Assessment Platform. Pricing depends on the number of courses.
The Math Medic AP Precalculus curriculum is perfectly aligned to the College Board’s Course and Exam Description (CED) for AP Calculus.
None! The Math Medic curriculum is not aligned with a textbook. We created the sequence of topics based on the College Board’s Course and Exam Description (CED) for AP Calculus. For homework, quizzes, and tests, we use the Math Medic Assessment Platform to supplement the lessons.