AP Calculus BC: Free Practice Exam and Lessons

The exam (May 2027)

Each section is 50% of the score. Multiple choice is taken in the Bluebook app, free response is written by hand. Checked on the College Board's AP Central, October 2026.

What to learn: the units and our lessons

1. Unit 1: Limits and continuity (5-10% of the multiple choice)
   • Limits from a table
   • Limits by algebra
   • Limits by the conjugate
   • One-sided limits
   • Limits at infinity
   • Continuity
   • L'Hôpital's rule
2. Unit 2: Derivatives: definition and basic rules (5-10% of the multiple choice)
   • The derivative from the definition
   • The power rule
   • Product and quotient rules
   • Derivatives of sin, cos, e and ln
   • Tangent lines
3. Unit 3: Composite, implicit and inverse functions (5-10% of the multiple choice)
   • The chain rule
   • Implicit differentiation
   • Derivatives of inverse trig functions
   • Derivatives of bˣ / Derivatives of logarithms
   • Logarithmic differentiation
4. Unit 4: Using derivatives in context (5-10% of the multiple choice)
   • Related rates
   • Linear approximation
   • Differentials
   • L'Hôpital's rule
   • Net change
5. Unit 5: Analysing functions with derivatives (10-15% of the multiple choice)
   • The mean value theorem / Rolle's theorem
   • Maximum, minimum and optimization
   • Absolute maximum and minimum
   • The second derivative test
   • Concavity and inflection points
   • Curve sketching
   • Optimization
6. Unit 6: Integration and accumulation of change (15-20% of the multiple choice)
   • Antiderivatives
   • Definite integrals and area
   • u-substitution
   • Riemann sums
   • The Fundamental Theorem, part 1
   • Integrals with e and ln
   • Integration by parts
   • Partial fractions
   • Improper integrals
7. Unit 7: Differential equations (5-10% of the multiple choice)
   • Check a solution
   • Integrals as solutions
   • Slope fields
   • Separable equations
   • Separable equations
   • Growth and decay
   • Euler's method
8. Unit 8: Applications of integration (5-10% of the multiple choice)
   • Average value of a function
   • Net change
   • Area below the x-axis
   • Area between two curves
   • Volumes by disks and washers
   • Volumes by shells
   • Arc length
9. Unit 9: Parametric, polar and vector-valued functions (10-15% of the multiple choice)
   • Parametric curves
   • Area in polar coordinates
   • Arc length
10. Unit 10: Infinite sequences and series (15-20% of the multiple choice)
    • Limits of sequences
    • The divergence test
    • The integral test and p-series
    • Comparison tests
    • Alternating series
    • The ratio and root tests
    • Power series
    • Taylor and Maclaurin series