Course curriculum

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Problem Solving Document


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Unit 1: Limits & Continuity

Unit 1 Note Packet (Download)
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Section 1: Understanding Graphical Limits
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Section 2 Examples: Limits of Piecewise Functions
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Section 2: Limits of Piecewise Functions
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Section 3: Solving Limits Analytically
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Section 4: Strange Limits with Function Combinations

Section 5: Limits at Infinity (Horizontal Asymptotes)

Section 5B: Vertical Asymptotes

Section 6: Special Trig Limits

Section 7: Squeeze Theorem

Section 8: Continuity

Section 9: Intermediate Value Theorem

Section 10: Epsilon Delta Definition of Limit (Not an AP Topic)


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Unit 2: Differentiation

Unit 2 Note Packet (Download)

Section 1: Using the Definition of the Derivative

Section 1B: Differentiability

Section 2: Power Rule

Section 3: Derivatives of Other Functions

Section 4: Product Rule and Quotient Rule

Section 5: Chain Rule

Section 6: Tangent and Normal Lines

Section 7: Implicit Differentiation

Section 8: Derivatives of Inverse Functions

Section 9: Sketching f'(x)


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Unit 3: Applications of Differentiation

Unit 3 Note Packet (Download)

Section 1: Absolute and Relative Extrema

Section 2: Rolle's Theorem and Mean Value Theorem

Section 3: Concavity and The Second Derivative Test

Section 4: Related Rates

Section 5: Optimization

Section 6: Linear Approximation and Differentials

Section 7: L'Hospital's Rule

Section 8: Other Indeterminant Forms (BC Topic)


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Unit 4: Integration

Unit 4 Note Packet (Download)

Section 1: Riemann Sums

Section 2: Definition of the Integral

Section 3: Antiderivatives

Section 4: The Definite Integral

Section 5: Derivatives of Integrals

Section 6: USubstitution (Part 1)

Section 7: USubstitution (Part 2)


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Unit 5: Applications of Integration

Unit 5 Note Packet (Download)

Section 1: Average Value

Section 2: Area Between Curves

Section 3: Volume by Washer/Disk Method

Section 4: Volume by Shell Method (Not an AP Topic)

Section 5: Volume by CrossSectional Area


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Unit 6: Interpreting Graphs & Motion

Unit 6 Note Packet (Download)

Section 1: Interpreting Graphs

Section 2: Motion Problems


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Unit 7: Differential Equations

Unit 7 Note Packet (Download)

Section 1: Verifying Solutions

Section 2: Slope Fields

Section 3: Separation of Variables

Section 4: Euler's Method and The Logistic Equation (BC Topic)

Section 5: The Logistic Equation


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Unit 8: Additional Integration Techniques (BC Only)

Unit 8 Note Packet (Download)

Section 1: Integration by Parts

Section 2: Partial Fraction Decomposition

Section 3: Improper Integrals

Section 4: Arc Length

Section 5: Trig Integrals (Not a BC Topic)

Section 6: Trig Substitution (Not a BC Topic)


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Unit 9: Parametric & Polar Equations

Unit 9 Note Packet (Download)

Section 1: Parametric Equations

Section 2 & 3: Derivatives and Arc Length of Parametric Equations

Section 4: Polar Graphs

Section 5: Tangent Lines of Polar Equations

Section 6 & 7: Area and Arc Length


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Unit 10: Tests of Convergence & Series

Unit 10 Note Packet (Download)

Section 1: nth Term Test

Section 2: pSeries Test

Section 3: Geometric Series

Sections 4 & 5: Integral and Comparison Test

Sections 6 & 7: Ratio and Root Test

Section 8: Alternating Series Test and Absolute Convergence

Section 10: Practicing Tests of Convergence

Section 11: Radius and Interval of Convergence

Section 12: Taylor and Maclaurin Series

Section 13: Deriving Taylor Series


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Rate FRQs

Rate FRQs

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Data Table FRQs

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Data Table FRQ (2022 #4)

Data Table FRQ (2021 #1)

Data Table FRQ (2019 #2)


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