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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.

1
Unit 1: Intro to Calculus
  • 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
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2
Unit 2: Differentiation
  • 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
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3
Unit 3: Differentiating Composite, Implicit, and Inverse Functions
  • The chain rule
  • Implicit differentiation
  • Derivatives of inverse functions
  • Higher-order derivatives and derivative strategies
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4
Unit 4: Contextual Applications of Differentiation
  • Interpreting derivatives in context
  • Connecting position, velocity, and acceleration
  • Rates of change in applied contexts
  • Related rates
  • Tangent line approximations
  • L'Hôpital's rule
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5
Unit 5: Analytical Applications of Derivatives
  • 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
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6
Unit 6: Integration and Accumulation of Change
  • 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
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7
Unit 7: Differential Equations
  • Modeling differential equations and verifying solutions
  • Slope fields
  • Finding general and particular solutions using separation of variables
  • Exponential models with differential equations
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8
Unit 8: Applications of Integration
  • 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
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9
Unit 9: Selected BC Lessons
  • 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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10
Unit 10: AP Calculus Exam Review
  • 25 days of structured review coursework
  • Review activities
  • Videos with AP Exam strategies
  • Exam tips
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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

We’ve helped thousands of teachers, schools, and districts bring the joy of learning to mathematics students.
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