AP Calculus AB & BC

Covers Unit 1 (Limits and Continuity), Unit 2 (Differentiation: Definition and Fundamental Properties), and Unit 3 (Differentiation: Composite, Implicit, and Inverse Functions).

1. Lesson 1
   Core 1 / Unit 1 Limits from graphs, tables, and algebra; limit laws; one-sided limits; the Squeeze Theorem.
2. Lesson 2
   Core 2 / Unit 1 Continuity and types of discontinuity, limits at infinity and asymptotes, the Intermediate Value Theorem.
3. Lesson 3
   Core 3 / Unit 2 Definition of the derivative, differentiability and continuity, the power rule, derivatives of sin x, cos x, e^x, and ln x.
4. Lesson 4
   Core 4 / Unit 2 Product and quotient rules, derivatives of tangent, cotangent, secant, and cosecant.
5. Lesson 5
   Core 5 / Unit 3 Chain rule, implicit differentiation, derivatives of inverse and inverse trigonometric functions, higher-order derivatives.
6. Lesson 6
   FRQ Practice 1 Limits, continuity, and derivatives from tables and graphs; justifying answers in the wording AP readers expect.

Covers Unit 4 (Contextual Applications of Differentiation) and Unit 5 (Analytical Applications of Differentiation).

1. Lesson 7
   Core 6 / Unit 4 Rates of change in context, straight-line motion (position, velocity, acceleration), related rates.
2. Lesson 8
   Core 7 / Unit 4 Local linearity and linearization, L'Hospital's Rule for indeterminate forms.
3. Lesson 9
   Core 8 / Unit 5 Mean Value Theorem, Extreme Value Theorem, increasing and decreasing intervals, the first and second derivative tests, concavity.
4. Lesson 10
   Core 9 / Unit 5 Connecting the graphs of f, f', and f''; optimization problems; behavior of implicit relations.
5. Lesson 11
   FRQ Practice 2 Graph-of-f' analysis questions and particle motion questions.

Covers Unit 6 (Integration and Accumulation of Change), Unit 7 (Differential Equations), and Unit 8 (Applications of Integration).

1. Lesson 12
   Core 10 / Unit 6 Accumulation of change, Riemann sums, the definite integral, the Fundamental Theorem of Calculus, accumulation functions.
2. Lesson 13
   Core 11 / Unit 6 Antiderivatives and indefinite integrals, u-substitution, long division and completing the square.
3. Lesson 14
   Core 12 / Unit 6 (BC only) Integration by parts, partial fractions, improper integrals.
4. Lesson 15
   FRQ Practice 3 Rate-in/rate-out questions and questions based on tables of values (Riemann sums).
5. Lesson 16
   Core 13 / Unit 7 Slope fields, separable differential equations, exponential models. BC only: Euler's method and logistic models.
6. Lesson 17
   Core 14 / Unit 8 Average value of a function, motion problems with integrals, accumulation in applied contexts.
7. Lesson 18
   Core 15 / Unit 8 Area between curves, volumes by cross sections, disc and washer methods. BC only: arc length.
8. Lesson 19
   FRQ Practice 4 Area and volume questions and differential equation questions.

BC only. Covers Unit 9 (Parametric Equations, Polar Coordinates, and Vector-Valued Functions) and Unit 10 (Infinite Sequences and Series).

1. Lesson 20
   Core 16 / Unit 9 (BC only) Parametric equations, vector-valued functions, and polar curves: derivatives, arc length, area, and motion in the plane.
2. Lesson 21
   Core 17 / Unit 10 (BC only) Convergence of sequences and series; geometric, harmonic, and p-series; the convergence tests.
3. Lesson 22
   Core 18 / Unit 10 (BC only) Alternating series error bound, Taylor and Maclaurin polynomials, Lagrange error bound, power series, radius and interval of convergence.

Comprehensive exam practice for both sections of the exam.

1. Lesson 23
   Multiple Choice Practice Multiple-choice strategies for the non-calculator and calculator parts; the graphing-calculator skills the exam expects.
2. Lesson 24
   FRQ Practice 5 Full-scope mixed FRQ exam simulation (time management and scoring according to AP rubrics).
3. Lesson 25
   Evaluation Simulation analysis, addressing common mistakes, and course wrap-up.