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Courses
AP Calculus AB
2003 AP CALC AB EXAM
2014 AP Calculus AB Free Response Questions
2015 AP Calculus AB Sample Exam
Chapter 7: Applications of Integration
Chapter 7: Section 1: Area of a Region Between Two Curves
Chapter 7: Section 2: Volume: The Disk Method
Review: Applications of the Fundamental Theorem of Calculus
Review: Analysis of Particle Motion
Review: Functions that are Represented Graphically
Review: Functions that are Represented Numerically
Review: Problems with Functions Involving Rates of Change
AP Calculus BC
Chapter 6: Differential Equations
Chapter 6: Section 1: Slope Fields and Euler's Method
Chapter 6: Section 2: Differential Equations: Growth and Decay
Chapter 6: Section 3: Logistic Differential Equation Lessons
Chapter 7: Applications of Integration
Chapter 7: Section 1: Area of a Region Between Two Curves
Chapter 7: Section 2: Volume: The Disk Method
Chapter 7: Section 4: Arc Length and Surfaces of Revolution
Chapter 8: Integration Techniques, L'Hospital's Rule, and Improper Integrals
Chapter 8: Section 2: Integration by Parts
Chapter 8: Section 3: Trigonometric Integrals
Chapter 8: Section 4: Trigonometric Substitution
Chapter 8: Section 5: Partial Fractions
Chapter 8: Section 6: Integration by Tables
Chapter 8: Section 7: Indeterminate Forms and L'Hospital's Rule
Chapter 8: Section 8: Improper Integrals
Chapter 9: Infinite Series
Chapter 9: Section 1: Sequences
Chapter 9: Section 2: Series and Convergence
Chapter 9: Section 3: The Integral Test and p-Series
Chapter 9: Section 4: Comparisons of Series
Chapter 9: Section 5: Alternating Series
Chapter 9: Section 6: The Ratio and Root Tests
Chapter 9: Section 7: Taylor Polynomials and Approximations
Chapter 9: Section 8: Power Series
Chapter 9: Section 9: Representation of Functions by Power Series
Chapter 9: Section 10: Taylor and Maclaurin Series
Chapter 10: Parametric Equations and Polar Coordinates
Chapter 10: Section 2: Plane Curves and Parametric Equations
Chapter 10: Section 3: Parametric Equations and Calculus
Chapter 10: Section 4: Polar Coordinates and Polar Graphs
Chapter 10: Section 5: Area and Arc Length in Polar Coordinates
Chapter 12: Vector-Valued Functions
Chapter 12: Section 1: Vector-Valued Functions
Chapter 12: Section 2: Differentiation and Integration of Vector-Valued Functions
Chapter 12: Section 3: Velocity and Acceleration
Chapter 12: Section 4: Tangent Vectors and Normal Vectors
Chapter 12: Section 5: Arc Length
2003 AP Calculus BC Exam
2015 AP Calculus BC Sample Exam
2015 AP Calculus AB Sample Exam
2014 AP Calculus BC Free Response Questions
Other Free Response Questions
Calculus
Review
Chapter 1: Limits, Derivatives, Integrals, and Definite Integrals
Chapter 1: Section 1: The Concept of Instantaneous Rate
Chapter 1: Section 2: Rate of Change by Equation, Graph, or Table
Chapter 1: Section 3: One Type of Integral of a Function
Chapter 1: Section 4: Definite Integrals by Trapezoids, from Equations and Data
Chapter 2: Properties of Limits
Chapter 2: Sections 1 and 2: Numerical, Graphical, and Algebraic Approaches to the Definition of Limit
Chapter 2: Section 3: The Limit Theorems
Chapter 2: Section 4: Continuity and Discontinuity
Chapter 2: Section 5: Limits Involving Infinity
Chapter 2: Section 6: The Intermediate Value Theorem and Its Consequences
Chapter 3: Derivatives, Antiderivatives, and Indefinite Integrals
Chapter 3: Section 2: Difference Quotients and One Definition of Derivative
Chapter 3: Section 3: Derivative Functions, Numerically and Graphically
Chapter 3: Section 4: Derivative of the Power Function and Another Definition of Derivative
Chapter 3: Section 5: Displacement, Velocity, and Acceleration
Chapter 3: Section 7: Derivatives of Composite Functions - The Chain Rule
Chapter 3: Section 8: Application of Sine and Cosine Derivatives
Chapter 3: Section 9: Exponential and Logarithmic Functions
Chapter 4: Products, Quotients, and Parametric Functions
Chapter 4: Section 2: Derivative of a Product of Two Functions
Chapter 4: Section 3: Derivative of a Quotient of Two Functions
Chapter 4: Section 4: Derivatives of the Other Trigonometric Functions
Chapter 4: Section 5: Derivatives of Inverse Trigonometric Functions
Chapter 4: Section 6: Differentiability and Continuity
Chapter 4: Section 7: Derivatives of a Parametric Function
Chapter 4: Section 8: Graphs and Derivatives of Implicit Relations
Chapter 4: Section 9: Related Rates
Chapter 5: Definite and Indefinite Integrals
Chapter 5: Section 1: A Definite Integral Problem
Chapter 5: Section 2: Linear Approximations and Differentials
Chapter 5: Section 3: Formal Definition of Antiderivative and Indefinite Integral
Chapter 5: Section 4: Riemann Sums and the Definition of Definite Integral
Chapter 5: Section 5: The Mean Value Theorem and Rolle's Theorem
Chapter 5: Section 6: The Fundamental Theorem of Calculus
Chapter 5: Section 7: Definite Integral Properties and Practice
Chapter 5: Section 8: Definite Integrals Applied to Area and Other Problems
Chapter 5: Section 9: Volume of a Solid by Plane Slicing
Chapter 5: Section 10: Definite Integrals Numerically by Grapher and by Simpson's Rule
Chapter 6: The Calculus of Exponential and Logarithmic Functions
Chapter 6: Section 2: Antiderivative of the Reciprocal Function and Another Form of the Fundamental Theorem
Chapter 6: Section 3: The Uniqueness Theorem and Properties of Logarithmic Functions
Chapter 6: Section 4: The Number e, Exponential Functions, and Logarithmic Differentiation
Chapter 6: Section 5: Limits of Indeterminate Forms: l'Hospital's Rule
Chapter 6: Section 6: Derivative and Integral Practice for Transcendental Functions
Chapter 7: The Calculus of Growth and Decay
Chapter 7: Section 2: Exponential Growth and Decay
Other Differential Equations for Real-World Applications
Chapter 7: Section 4: Graphical Solution of Differential Equations by Using Slope Fields
IM3
Module 5: Polynomial Functions
Module 5: Section 1: Transformations of Function Graphs
Module 5: Section 3: Graphing Cubic Functions
Module 5: Section 2: Inverses of Functions
Module 5: Section 4: Graphing Polynomial Functions
Module 10: Radical Functions
Module 10: Section 1: Inverses of Simple Quadratic and Cubic Functions
Module 10: Section 2: Graphing Square Root Functions
Module 10: Section 3: Graphing Cube Root Functions
Module 6: Polynomials
Module 6: Section 1: Adding and Subtracting Polynomials
Module 6: Section 2: Multiplying Polynomials
Module 6: Section 4: Factoring Polynomials
Module 6: Section 5: Dividing Polynomials
Module 7: Polynomial Equations
Module 7: Section 1: Finding Rational Solutions of Polynomial Equations
Module 7: Section 2: Finding Complex Solutions of Polynomial Equations
Module 9: Rational Expressions and Equations
Module 9: Section 1: Adding and Subtracting Rational Expressions
Module 9: Section 2: Multiplying and Dividing Rational Expressions
Module 9: Section 3: Solving Rational Equations
Module 11: Radical Expressions and Equations
Module 11: Section 1: Radical Expressions and Rational Exponents
Module 11: Section 2: Simplifying Radical Expressions
Module 11: Section 3: Solving Radical Equations
Module 12: Sequences and Series
Module 12: Section 1: Arithmetic Sequences
Module 12: Section 2: Geometric Sequences
Module 12: Section 3: Geometric Series
Module 13: Exponential Functions
Module 13: Section 1: Exponential Growth Functions
Module 13: Section 2: Exponential Decay Functions
Module 13: Section 3: The Base e
Module 13: Section 4: Compound Interest
Module 14: Modeling with Exponential and Other Functions
Module 14: Section 1: Fitting Exponential Functions to Data
Module 14: Section 2: Choosing Among Linear, Quadratic, and Exponential Models
Module 15: Logarithmic Functions
Module 15: Section 1: Defining and Evaluating a Logarithmic Function
Module 15: Section 2: Graphing Logarithmic Functions
Module 16: Logarithmic Properties and Exponential Equations
Module 16: Section 1: Properties of Logarithms
Module 16: Section 2: Solving Exponential Equations
Module 18: Unit-Circle Definition of Trigonometric Functions
Module 18: Section 1: Angles of Rotation and Radian Measure
Module 18: Section 2: Defining and Evaluating the Basic Trigonometric Functions
Module 18: Section 3: Using a Pythagorean Identity
Module 19: Graphing Trigonometric Functions
Module 19: Section 1: Stretching, Compressing, and Reflecting Sine and Cosine Graphs
Module 19: Section 3: Translating Trigonometric Graphs
Module 20: Gathering and Displaying Data
Module 20: Section 1: Data-Gathering Techniques
Module 20: Section 2: Shape, Center, and Spread
Module 21: Data Distributions
Module 21: Section 1: Probability Distributions
Module 21: Section 2: Normal Distributions
Module 21: Section 3: Sampling Distributions
PRECALCULUS PROBLEMS
Chapter 1: Functions and Their Graphs
Chapter 1: Section 1: Graphs of Equations
Chapter 1: Section 2: Linear Equations in Two Variables
Chapter 1: Section 3: Functions
Chapter 1: Section 4: Analyzing Graphs of Functions
Chapter 1: Section 5: A Library of Functions
Chapter 1: Section 6: Shifting, Reflecting, and Stretching Graphs
Chapter 1: Section 7: Combinations of Functions
Chapter 1: Section 8: Inverse Functions
Chapter 1: Section 9: Mathematical Modeling
Benchmark One Review Problems
Chapter 2: Polynomial and Rational Functions
Chapter 2: Section 1: Quadratic Functions
Chapter 2: Section 2: Polynomial Functions of Higher Degree
Chapter 2: Section 3: Polynomial and Synthetic Division
Chapter 2: Section 4: Complex Numbers
Chapter 2: Section 5: Zeros of Polynomial Functions
Chapter 2: Section 6: Rational Functions
Chapter 2: Section 7: Partial Fractions
Benchmark 2 Review Problems
Chapter 3: Exponential and Logarithmic Functions
Chapter 3: Section 1: Exponential Functions and Their Graphs
Chapter 3: Section 2: Logarithmic Functions and Their Graphs
Chapter 3: Section 3: Properties of Logarithms
Chapter 3: Section 4: Exponential and Logarithmic Equations
Chapter 3: Section 5: Exponential and Logarithmic Models
Chapter 4: Trigonometry
Chapter 4: Section 1: Radian and Degree Measure
Chapter 4: Section 3: Right Triangle Trigonometry
Chapter 4: Section 2: Trigonometric Functions: The Unit Circle
Chapter 4: Section 4: Trigonometric Functions of Any Angle
Chapter 4: Review Exercises
Chapter 4: Section 5: Graphs of Sine and Cosine Functions
Chapter 4: Section 6: Graphs of Other Trigonometric Functions
Chapter 4: Section 7: Inverse Trigonometric Functions
Chapter 4: Section 8: Applications and Models
Semester One Review Problems
Chapter 5: Analytic Trigonometry
Chapter 5: Section 1: Using Fundamental Identities
Chapter 5: Section 2: Verifying Trigonometric Identities
Chapter 5: Section 3: Solving Trigonometric Equations
Chapter 5: Section 4: Sum and Difference Formulas
Chapter 5: Section 5: Multiple-Angle and Product-to-Sum Formulas
Chapter 5: Review Exercises
Chapter 6: Additional Topics in Trigonometry
Chapter 6: Section 1: Law of Sines
Chapter 6: Section 2: Law of Cosines
Chapter 6: Section 3: Vectors in the Plane
Chapter 6: Section 4: Vectors and Dot Products
Chapter 6: Section 5: Trigonometric Form of a Complex Number
Chapter 7: Systems of Equations and Inequalities
Chapter 7: Section 1: Solving Systems of Equations
Chapter 7: Section 2: Two-Variable Linear Systems
Chapter 7: Section 3: Multivariable Linear Systems
Chapter 7: Section 4: Systems of Inequalities
Chapter 7: Section 5: Linear Programming
Chapter 8: Matrices and Determinants
Chapter 8: Section 1: Matrices and Systems of Equations
Chapter 8: Section 2: Operations With Matrices
Chapter 8: Section 3: The Inverse of a Square Matrix
Chapter 8: Section 4: The Determinant of a Square Matrix
Chapter 8: Section 5: Applications of Matrices and Determinants
Chapter 9: Sequences, Series, and Probability
Chapter 9: Section 1: Sequences and Series
Chapter 9: Section 2: Arithmetic Sequences and Partial Sums
Chapter 9: Section 3: Geometric Sequences and Series
Spring Semester Review Problems
Precalculus with Limits 7e: Links to Similar Problems from the Sixth Edition
Chapter 1: Functions and Their Graphs
Chapter 1: Section 1: Lines in the Plane
Chapter 1: Section 2: Functions
Chapter 1: Section 3: Graphs of Functions
Chapter 1: Section 4: Shifting, Reflecting, and Stretching Graphs
Chapter 1: Section 5: Combinations of Functions
Chapter 1: Section 6: Inverse Functions
Chapter 2: Polynomial and Rational Functions
Chapter 2: Section 1: Quadratic Functions
Chapter 2: Section 2: Polynomial Functions of Higher Degree
Chapter 2: Section 3: Real Zeros of Polynomial Functions
Chapter 2: Section 4: Complex Numbers
Chapter 2: Section 5: Zeros of Polynomial Functions
Chapter 2: Section 6: Rational Functions and Asymptotes
Chapter 2: Section 7: Graphs of Rational Functions
Chapter 3: Exponential and Logarithmic Functions
Chapter 3: Section 1: Exponential Functions and Their Graphs
Chapter 3: Section 2: Logarithmic Functions and Their Graphs
Chapter 3: Section 3: Properties of Logarithms
Chapter 3: Section 4: Exponential and Logarithmic Equations
Chapter 3: Section 5: Exponential and Logarithmic Models
Chapter 4: Trigonometric Functions
Chapter 4: Section 1: Radian and Degree Measure
Chapter 4: Section 3: Right Triangle Trigonometry
Chapter 4: Section 2: Trigonometric Functions: The Unit Circle
Chapter 4: Section 4: Trigonometric Functions of Any Angle
Chapter 4: Section 5: Graphs of Sine and Cosine Functions
Chapter 4: Section 6: Graphs of Secant and Cosecant Functions
Chapter 4: Section 7: Inverse Trigonometric Functions
Chapter 4: Section 8: Applications and Models
Chapter 5: Analytic Trigonometry
Chapter 5: Section 1: Using Fundamental Identities
Chapter 5: Section 2: Verifying Trigonometric Identities
Chapter 5: Section 3: Solving Trigonometric Equations
Chapter 5: Section 4: Sum and Difference Formulas
Chapter 5: Section 5: Multiple-Angle and Product-to-Sum Formulas
Chapter 6: Additional Topics in Trigonometry
Chapter 6: Section 1: Law of Sines
Chapter 6: Section 2: Law of Cosines
Chapter 6: Section 3: Vectors in the Plane
Chapter 6: Section 4: Vectors and Dot Products
Chapter 6: Section 5: Trigonometric Form of a Complex Number
Chapter 7: Linear Systems and Matrices
Chapter 7: Section 1: Solving Systems of Equations
Chapter 7: Section 2: Two-Variable Linear Systems
Chapter 7: Section 3: Multivariable Linear Systems
Chapter 7: Section 4: Matrices and Systems of Equations
Chapter 7: Section 5: Operations with Matrices
Chapter 7: Section 6: The Inverse of a Square Matrix
Chapter 7: Section 7: The Determinant of a Square Matrix
Chapter 7: Section 8: Applications of Matrices and Determinants
Trigonometry Lessons
Mr. Oo's Math Links
Chapter 12: Section 5: Arc Length
Lesson 1: Arc Length of a Space Curve Given by a Vector-Valued Function
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