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Calculus pathway

Calculus BC

All AB material plus BC extensions embedded in earlier units and units 9–10: parametric, polar, vector calculus and series.
57 lessons18 BC extensions12 units

How learning works

Full AB content plus BC extensions; do not skip AB concepts.

No timers. Reviews come back after 1, 7, 21 days. Reading a lesson is not mastery; you finish after attempting core lessons, checked written work and a delayed review.

Lessons

Review editionNot yet human-reviewed

Unit C1Limits and continuity

  1. C01Limits: nearby behavior, graphs and tables
    45 min
  2. C02Limit laws, factoring and rationalization
    45 min
  3. C03Squeeze reasoning and asymptotes
    45 min
  4. C04Continuity and repairing piecewise functions
    45 min
  5. C05Intermediate Value Theorem and existence proofs
    45 min

Unit C2Derivative foundations

  1. C06Derivative definition and differentiability
    45 min
  2. C07Power rules, constants and elementary derivatives
    45 min
  3. C08Product, quotient and reciprocal trig rules
    45 min
  4. C09Derivatives from numerical and graphical evidence
    45 min

Unit C3Composite, implicit and inverse derivatives

  1. C10Chain rule and choosing a differentiation method
    45 min
  2. C11Implicit differentiation and higher derivatives
    45 min
  3. C12Inverse functions and inverse-trigonometric derivatives
    45 min

Unit C4Contextual derivatives

  1. C13Rates, motion and units
    45 min
  2. C14Related rates: differentiate the relationship
    45 min
  3. C15Local linearity and approximation error
    45 min
  4. C16L’Hospital’s rule and eligible forms
    45 min

Unit C5Function analysis and optimization

  1. C17Extreme Value and Mean Value Theorems
    45 min
  2. C18Critical points and first-derivative evidence
    45 min
  3. C19Concavity, inflection and curve reconstruction
    45 min
  4. C55Reading a derivative graph without a formula
    45 min
  5. C20Optimization with a feasible domain
    45 min

Unit C6Integration and accumulation

  1. C21Accumulation, Riemann sums and sigma notation
    45 min
  2. C50Turning a sum into an integral
    45 min
  3. C22Trapezoids and integral properties
    45 min
  4. C23Fundamental Theorem: differentiating accumulation
    45 min
  5. C24Antiderivatives and definite evaluation
    45 min
  6. C25Substitution and algebra before integration
    45 min
  7. C51Completing the square inside an integral
    45 min

Unit C3Composite, implicit and inverse derivatives

  1. C57Method selection and explaining a strategy
    45 min

Unit C6Integration and accumulation

  1. C26Integration by parts
    BC extension45 min
  2. C27Linear partial fractions
    BC extension45 min
  3. C28Improper integrals and convergence
    BC extension45 min

Unit C7Differential equations

  1. C29Differential equations, verification and slope fields
    45 min
  2. C56Slope-field interpretation with explicit coordinates
    45 min
  3. C30Separation and initial conditions
    45 min
  4. C49Exponential models and interpreting growth constants
    45 min
  5. C31Exponential and logistic models
    BC extension45 min
  6. C32Euler’s method and error direction
    BC extension45 min

Unit C8Applications of integration

  1. C33Average value and accumulated change
    45 min
  2. C34Displacement and total distance
    45 min
  3. C35Area between curves with x or y slices
    45 min
  4. C36Volumes by cross-sections, disks and washers
    45 min
  5. C52Non-square cross-sections
    45 min
  6. C53Vertical and shifted axes of rotation
    45 min
  7. C37Arc length and distance along a curve
    BC extension45 min

Unit C9Parametric, polar and vector calculus

  1. C38Parametric derivatives and second derivatives
    BC extension45 min
  2. C39Parametric arc length and vector derivatives
    BC extension45 min
  3. C40Vector integration and motion in the plane
    BC extension45 min
  4. C41Polar slopes and areas
    BC extension45 min
  5. C54Intersecting polar curves and shared regions
    BC extension45 min

Unit C10Sequences and series

  1. C42Sequences, series and the nth-term test
    BC extension45 min
  2. C43Geometric and p-series; the integral test
    BC extension45 min
  3. C44Direct and limit comparison
    BC extension45 min
  4. C45Alternating, absolute and conditional convergence
    BC extension45 min
  5. C46Ratio test and convergence intervals
    BC extension45 min
  6. C47Taylor polynomials and Lagrange error
    BC extension45 min
  7. C48Power-series representations and operations
    BC extension45 min