- Project Manager/Lead Writer: Kevin Quattrin
- Associate Writers: Najla (nee Fawal) Abrao and Paul Maychrowitz
- Chief Editor: Elizabeth Regalia
Solution Manual
Table of Contents and Introduction: General Overview of Calculus
Chapter 1: Review of Derivatives [Chapter 1 pdf]
- 1.1: The Power and Exponential Rules with the Chain Rule
- 1.2: Trig, Trig Inverse, and Log Rules
- 1.3: Product and Quotient Rules
- 1.4: Local Linearity, Euler’s Method, and Approximations
- 1.5: Intro to AP: Basic Derivatives Numerically and Graphically
- 1.6: Higher Order Derivatives
- 1.7: Implicit Differentiation
- 1.8: Related Rates
- 1.9: Logarithmic Differentiation
- Chapter 1 Test
- Chapter 1 Answer Key
Chapter 2: Anti-Derivatives [Chapter 2 pdf]
- 2.1: The Power and Transcendental Rules
- 2.2: Integration by Substitution--the Chain Rule
- 2.3: Separable Differential Equations
- 2.4: Integration by Substitution--Back Substitution
- 2.5: Powers of Trig Functions: Sine and Cosine
- 2.6: Powers of Trig Functions: Secant and Tangent
- 2.7: Slope Fields
- Chapter 2 Test
- Chapter 2 Answer Key
Chapter 3: Integrals [Chapter 4 pdf]
- 3.0: Limit Definition of the Definite Integral
- 3.1: The Fundamental Theorem of Calculus
- 3.2: Definite Integrals and Integration by Substitution
- 3.3: Context: Area, Displacement, and Net Change
- 3.4: Intro to AP: Accumulation of Rates
- 3.5: Approximate Integration – Riemann Sums
- 3.6: Approximate Integration – Table Problems and MVT (rewrite)
- Chapter 4 Test
- Chapter 4 Answer Key
- 4.1: Extremes and the Derivative Tests
- 4.2: Accumulation of Rates Revisited
- 4.3: The Second Derivative, Points of Inflection, and Concavity
- 4.4: Graphing with Derivatives
- 4.5: Graphical Analysis I
- 4.6: Graphical Analysis II
- 4.t: Intro to AP: Rectilinear Motion
- Chapter 4 Test
- Chapter 4 Answer Key
Chapter 5: Applications of Integrals [Chapter 5 pdf]
- 5.1: Area between Two Curves
- 5.2: Arc Length
- 5.3: Volume by Rotation about the x-Axis
- 5.4: Volume by Rotation about the y-Axis
- 5.5: Volume by Rotation about a Line not an Axis
- 5.6: Volume by Cross-section Method
- 5.7: AP Area and Volume Problems
- 5.8: Volume by Shell Method
- Chapter 5 Test
- Chapter 5 Answer Key
Chapter 6: Limits, Continuity and Differentiability [Chapter 6 pdf]
- 6.1: Limits, L’Hopital’s Rule, and The Limit Definitions of a Derivative
- 6.2: Continuity and One-sided Limits
- 6.3 Differentiability and Smoothness
- 6.4: Limits at Infinity and End Behavior
- 6.5: Type I Improper Integrals
- 6.6: Infinite Limits and Type II Improper Integrals
- Chapter 6 Test
- Chapter 6 Answer Key
Chapter 7: Sequences and Numerical Series [Chapter 7 pdf]
- 7.1: Sequences and series—Preliminary Algebra
- 7.2: Convergence and Divergence
- 7.3: The Integral Test
- 7.4: The Comparison Tests
- 7.5: The Ratio Test and Nth Root Tests
- 7.6: Alternating Series
- 7.7: General Series Summary
- Chapter 7 Test
- Chapter 7 Answer Key
Chapter 8: Advanced Integration [Chapter 8 pdf]
- 8.1: Integrals of Rational Functions
- 8.2: Partial Fractions I
- 8.3: Models of Growth
- 8.4: Integration by Parts
- 8.5: Trig Substitution (optional)
- 8.6: Partial Fractions II (optional)
- 8.7: Partial Fractions III (optional)
- 8.8: General Integration
- Chapter 8 Test
- Chapter 8 Answer Key
Chapter 9: Parametric and Polar Coordinates [Chapter 9 pdf]
- 9.1: Parametric Motion
- 9.2: Parametric Graphing
- 9.3: AP Parametric Problems
- 9.4: Polar and Cartesian Graphs
- 9.5: Polar Coordinates, Arc Length, and Simple Area
- 9.6: Area Involving Two Polar Graphs
- 9.7: Derivatives and Polar Graphs
- 9.8: AP Polar Problems
- Chapter 9 Test
- Chapter 9 Answer Key
Chapter 10: Power Series [Chapter 10 pdf]
- 10.1: Taylor and Maclaurin Series
- 10.2: Error Bound Problems
- 10.3: Power Series
- 10.4: Review of Numerical Series
- 10.5: Radius and Intervals of Convergence
- 10.6: AP Power Series Problems
- Chapter 10 Test
- Chapter 10 Answer Key
Chapter 11: AP Calculus BC FRQ Review [Chapter 11 pdf]
Overview: The last 10 years
- 11.1 Accumulation of Rates (AB1)
- 11.2 Reasoning from Tabular Data (AB2)
- 11.3 Graphical Analysis (AB3)
- 11.4 Power Series
- 11.5 Differential Equations (AB5)
- 11.6 Parametric Motion
- 11.7 Polar Coordinates
- 11.8 Area and Volume (AB6)
- 11.9 Related Rates (AB7)
- 11.10 Advanced Integration.
- 11.11 Miscellaneous AB Topics
Appendix B: Synthesis of PreCalculus [Chapter B pdf]
- Overview: Functions and Traits
- 0.1: Recognizing and Identifying Graphs, Graphing from Traits
- 0.2: Factoring Review and Zeroes of Functions
- 0.3: Sign Patterns and Domains
- 0.4: Calculator Review
- 0.5: Important Facts for Calculus