Code Scholars Tutoring · AP Calculus AB
AP Calculus AB Course Outline
All eight units and 81 AB topic codes, mapped to 34 available study lessons and original unit practice.
Topic labels below are Code Scholars summaries; numbers match the College Board framework. Gaps in topic numbering identify BC-only topics omitted from the AB sequence. Every listed topic links to a study lesson that covers it.
Unit 1: Limits and Continuity10–15% of MCQ · 16 topics
- 1.1Change over shrinking intervalsStudy lesson
- 1.2One-sided and two-sided limit notationStudy lesson
- 1.3Limits read from graphsStudy lesson
- 1.4Limits estimated from tablesStudy lesson
- 1.5Limit laws and substitutionStudy lesson
- 1.6Algebraic simplification of limitsStudy lesson
- 1.7Choosing a limit methodStudy lesson
- 1.8Bounding a function with the squeeze theoremStudy lesson
- 1.9Switching among limit representationsStudy lesson
- 1.10Removable, jump, and infinite discontinuitiesStudy lesson
- 1.11Continuity at a pointStudy lesson
- 1.12Continuity over intervalsStudy lesson
- 1.13Repairing a removable discontinuityStudy lesson
- 1.14Unbounded behavior near a vertical asymptoteStudy lesson
- 1.15End behavior and horizontal asymptotesStudy lesson
- 1.16Intermediate values and existenceStudy lesson
Unit 2: Differentiation: Definition and Fundamental Properties10–15% of MCQ · 10 topics
- 2.1Secant and tangent slopesStudy lesson
- 2.2Derivative definitions and notationStudy lesson
- 2.3Numerical estimates of derivativesStudy lesson
- 2.4Continuity versus differentiabilityStudy lesson
- 2.5The power ruleStudy lesson
- 2.6Linearity of differentiationStudy lesson
- 2.7Basic trigonometric, exponential, and logarithmic derivativesStudy lesson
- 2.8Products of functionsStudy lesson
- 2.9Quotients of functionsStudy lesson
- 2.10Other trigonometric derivativesStudy lesson
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions5–10% of MCQ · 6 topics
- 3.1Nested functions and the chain ruleStudy lesson
- 3.2Implicit derivativesStudy lesson
- 3.3Derivatives of inverse functionsStudy lesson
- 3.4Inverse trigonometric derivativesStudy lesson
- 3.5Selecting and combining derivative rulesStudy lesson
- 3.6Higher derivativesStudy lesson
Unit 4: Contextual Applications of Differentiation10–15% of MCQ · 7 topics
- 4.1Interpreting a derivative and its unitsStudy lesson
- 4.2Position, velocity, acceleration, and speedStudy lesson
- 4.3Rates in scientific and economic modelsStudy lesson
- 4.4Building a related-rates equationStudy lesson
- 4.5Solving related-rates questionsStudy lesson
- 4.6Tangent-line estimates and local errorStudy lesson
- 4.7Indeterminate forms and L’Hospital’s ruleStudy lesson
Unit 5: Analytical Applications of Differentiation15–20% of MCQ · 12 topics
- 5.1Mean Value Theorem hypotheses and conclusionsStudy lesson
- 5.2Existence of extrema and critical pointsStudy lesson
- 5.3Increasing and decreasing intervalsStudy lesson
- 5.4Sign changes and the first derivative testStudy lesson
- 5.5Absolute extrema by candidate comparisonStudy lesson
- 5.6Concavity and inflection pointsStudy lesson
- 5.7Second derivative testsStudy lesson
- 5.8Graphing from derivative evidenceStudy lesson
- 5.9Connecting graphs of a function and its derivativesStudy lesson
- 5.10Constructing an optimization modelStudy lesson
- 5.11Solving and justifying optimizationStudy lesson
- 5.12Analyzing implicit curvesStudy lesson
Unit 6: Integration and Accumulation of Change15–20% of MCQ · 11 topics
- 6.1Signed accumulation from ratesStudy lesson
- 6.2Rectangular and trapezoidal approximationsStudy lesson
- 6.3Riemann sums and definite integralsStudy lesson
- 6.4Derivatives of accumulation functionsStudy lesson
- 6.5Behavior of integral-defined functionsStudy lesson
- 6.6Properties of definite integralsStudy lesson
- 6.7Evaluating definite integrals by antiderivativesStudy lesson
- 6.8Antiderivatives and constantsStudy lesson
- 6.9Substitution and changed boundsStudy lesson
- 6.10Polynomial division and completing the squareStudy lesson
- 6.14Choosing an AB integration methodStudy lesson
Unit 7: Differential Equations5–10% of MCQ · 7 topics
- 7.1Differential equations as modelsStudy lesson
- 7.2Checking a proposed solutionStudy lesson
- 7.3Slope fields from a rate lawStudy lesson
- 7.4Qualitative reasoning from slope fieldsStudy lesson
- 7.6Separation of variablesStudy lesson
- 7.7Initial-value problems and solution domainsStudy lesson
- 7.8Exponential growth and decayStudy lesson
Unit 8: Applications of Integration10–15% of MCQ · 12 topics
- 8.1Average value over an intervalStudy lesson
- 8.2Displacement and total distanceStudy lesson
- 8.3Net change and contextual accumulationStudy lesson
- 8.4Area between curves with vertical slicesStudy lesson
- 8.5Area between curves with horizontal slicesStudy lesson
- 8.6Splitting area at multiple intersectionsStudy lesson
- 8.7Volumes with square or rectangular sectionsStudy lesson
- 8.8Volumes with triangular or semicircular sectionsStudy lesson
- 8.9Disks around a coordinate axisStudy lesson
- 8.10Disks around shifted axesStudy lesson
- 8.11Washers around a coordinate axisStudy lesson
- 8.12Washers around shifted axesStudy lesson