Questions by unit, scored like the exam
Before calculus
- P01 Function notation, composition, inverse, and domain
- P02 Factorization, rational expressions, exponents, and equations
- P03 Graph transformations, intercepts, and asymptotes
- P04 Radians, unit circle, identities, and inverse trig
- P05 Exponential and logarithm algebra
- P06 Graphing, numerical roots, derivatives, and integrals
Unit 1: Limits and Continuity
- T1.1 Instantaneous changeFree
- T1.2 Limit notationFree
- T1.3 Reading limits from graphsFree
- T1.4 Reading limits from tables
- T1.5 Limit laws
- T1.6 Rewrite before taking a limit
- T1.7 Choose a limit method
- T1.8 Squeeze arguments
- T1.9 Translate limit representations
- T1.10 Classify discontinuities
- T1.11 Test point continuity
- T1.12 Continuity intervals
- T1.13 Repair a discontinuity
- T1.14 Vertical asymptotes
- T1.15 End behavior and horizontal asymptotes
- T1.16 Intermediate Value Theorem
Unit 2: Differentiation: Definition and Fundamental Properties
- T2.1 Secant and instantaneous rates
- T2.2 Derivative definition and tangent line
- T2.3 Estimate a derivative
- T2.4 Continuity versus differentiability
- T2.5 Power rule
- T2.6 Linearity and polynomial derivatives
- T2.7 Elementary derivatives and derivative-definition limits
- T2.8 Product rule
- T2.9 Quotient rule
- T2.10 Reciprocal trig derivatives
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
- T5.1 Mean Value Theorem
- T5.2 Extreme Value Theorem and critical points
- T5.3 Increasing and decreasing intervals
- T5.4 First-derivative extrema test
- T5.5 Global extrema and endpoints
- T5.6 Concavity and inflection
- T5.7 Second-derivative extrema test
- T5.8 Sketch from derivative evidence
- T5.9 Connect f and derivative graphs
- T5.10 Build an optimization model
- T5.11 Solve and interpret optimization
- T5.12 Analyze implicit curves
Unit 6: Integration and Accumulation of Change
- T6.1 Signed accumulation
- T6.2 Riemann and trapezoidal approximations
- T6.3 Integral as a limiting sum
- T6.4 Differentiate accumulation
- T6.5 Analyze accumulation graphs
- T6.6 Integral properties and geometry
- T6.7 FTC endpoint evaluation
- T6.8 Antiderivatives and constant families
- T6.9 Substitution
- T6.10 Long division and completed squares
- T6.11 Integration by partsBC only
- T6.12 Linear partial fractionsBC only
- T6.13 Improper integralsBC only
- T6.14 Choose integration methods
Unit 7: Differential Equations
Unit 8: Applications of Integration
- T8.1 Average value
- T8.2 Displacement and distance
- T8.3 Net change in context
- T8.4 Area using vertical slices
- T8.5 Area using horizontal slices
- T8.6 Regions requiring multiple integrals
- T8.7 Square and rectangular cross sections
- T8.8 Triangular and semicircular cross sections
- T8.9 Disks about coordinate axes
- T8.10 Disks about shifted axes
- T8.11 Washers about coordinate axes
- T8.12 Washers about shifted axes
- T8.13 Cartesian arc lengthBC only
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- T9.1 Parametric first derivativesBC only
- T9.2 Parametric second derivativesBC only
- T9.3 Parametric arc lengthBC only
- T9.4 Vector derivativesBC only
- T9.5 Vector antiderivativesBC only
- T9.6 Motion in the planeBC only
- T9.7 Polar slope and derivativesBC only
- T9.8 Area enclosed by one polar curveBC only
- T9.9 Area between polar curvesBC only
Unit 10: Infinite Sequences and Series
- T10.1 Partial sums and series convergenceBC only
- T10.2 Geometric seriesBC only
- T10.3 Term test for divergenceBC only
- T10.4 Integral testBC only
- T10.5 Harmonic and p-seriesBC only
- T10.6 Direct and limit comparisonBC only
- T10.7 Alternating seriesBC only
- T10.8 Ratio testBC only
- T10.9 Absolute and conditional convergenceBC only
- T10.10 Alternating remainderBC only
- T10.11 Taylor polynomial and approximationBC only
- T10.12 Lagrange remainderBC only
- T10.13 Radius and endpoint testsBC only
- T10.14 Taylor and Maclaurin seriesBC only
- T10.15 Transform power seriesBC only