This course contains problem sets that accompany each section and module. In these problem sets, students are given an opportunity to apply the quantitative-reasoning skills they learned throughout the module.
Answers are only available to the problems with “Show Solution” links below the question prompt.
Module 1: Functions and Graphs
- Problem Set: Review of Functions
- Problem Set: Basic Classes of Functions
- Problem Set: Trigonometric Functions
- Problem Set: Inverse Functions
- Problem Set: Exponential and Logarithmic Functions
- Module 1 Review Problems
Module 2: Limits
- Problem Set: A Preview of Calculus
- Problem Set: The Limit of a Function
- Problem Set: The Limit Laws
- Problem Set: Continuity
- Problem Set: The Precise Definition of a Limit
- Module 2 Review Problems
Module 3: Derivatives
- Problem Set: Defining the Derivative
- Problem Set: The Derivative as a Function
- Problem Set: Differentiation Rules
- Problem Set: Derivatives as Rates of Change
- Problem Set: Derivatives of Trigonometric Functions
- Problem Set: The Chain Rule
- Problem Set: Derivatives of Inverse Functions
- Problem Set: Implicit Differentiation
- Problem Set: Derivatives of Exponential and Logarithmic Functions
- Module 3 Review Problems
Module 4: Applications of Derivatives
- Problem Set: Related Rates
- Problem Set: Linear Approximations and Differentials
- Problem Set: Maxima and Minima
- Problem Set: The Mean Value Theorem
- Problem Set: Derivatives and the Shape of a Graph
- Problem Set: Limits at Infinity and Asymptotes
- Problem Set: Applied Optimization Problems
- Problem Set: L’Hôpital’s Rule
- Problem Set: Newton’s Method
- Problem Set: Antiderivatives
- Module 4 Review Problems
Module 5: Integration
- Problem Set: Approximating Areas
- Problem Set: The Definite Integral
- Problem Set: The Fundamental Theorem of Calculus
- Problem Set: Integration Formulas and the Net Change Theorem
- Problem Set: Substitution
- Problem Set: Integrals Involving Exponential and Logarithmic Functions
- Problem Set: Integrals Resulting in Inverse Trigonometric
- Module 5 Review Problems
Module 6: Applications of Integration
- Problem Set: Areas Between Curves
- Problem Set: Determining Volumes by Slicing
- Problem Set: Volumes of Revolution: Cylindrical Shells
- Problem Set: Arc Length of a Curve and Surface Area
- Problem Set: Physical Applications
- Problem Set: Moments and Centers of Mass
- Problem Set: Integrals, Exponential Functions, and Logarithms
- Problem Set: Exponential Growth and Decay
- Problem Set: Calculus of the Hyperbolic Functions
- Module 6 Review Problems
