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MATH 221
Calculus I
Dale Buske
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Front Matter
Syllabus
Course Information
Topics and Learning Outcomes
Calendar
Assessments and Grades
Frequently Asked Questions
Daily Prep
Daily Prep 1.1 - Average Velocity
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Daily Prep 1.2 - The Notion of a Limit
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 1.3 - The Derivative of a Function at a Point
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Additional suggestions
Daily Prep 1.4 - The Derivative Function
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
Additional suggestions
Daily Prep 1.5 - Interpreting, Estimating, and Using the Derivative
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Answers
Daily Prep 1.6 - The Second Derivative
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 1.7 - Limits, Continuity, and Differentiability
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 1.8 - The Tangent Line Approximation
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 2.1 - Elementary Differentiation Rules
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 2.2 - The Sine and Cosine Functions
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Daily Prep 2.3 - The Product and Quotient Rules
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 2.4 - Derivatives of the Other Trig Functions
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Daily Prep 2.5 - The Chain Rule
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Additional suggestions
Daily Prep 2.6 - Derivatives of Inverse Functions
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
Additional suggestions
Daily Prep 2.7 - Implicit Differentiation
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 3.1 - Related Rates
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Answers
To prepare for class
After class
Daily Prep 3.2 - Using Derivatives to Evaluate Limits
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Additional suggestions
Daily Prep 3.3 - Using Derivatives to Identify Extreme Values
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Additional suggestions
Daily Prep 3.5 - Global Optimization
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 3.6 - Applied Optimization
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
Daily Prep 4.1 - Determining Distance from Velocity
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 4.2 - Riemann Sums
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
Additional suggestions
Daily Prep 4.3 - The Definite Integral
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
Additional suggestions
And yet additional suggestions
Daily Prep 4.4 - The Fundamental Theorem of Calculus
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
More to prepare for class
Additional suggestions
Daily Prep 5.1 - Constructing Accurate Graphs of Antiderivatives
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
Daily Prep 5.2 - The Second Fundamental Theorem of Calculus
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
Additional suggestions
Daily Prep 5.3 - Integration by Substitution
Overview
Basic learning objectives
To prepare for class
After class
Advanced learning objectives
Additional suggestions
Answers
To prepare for class
After class
In-Class Activities
Average Velocity - Activity 1.1.2
Average Velocity - Activity 1.1.3
Average Velocity - Activity 1.1.4
The Notion of a Limit - Activity 1.2.2
The Notion of a Limit - Activity 1.2.3
The Notion of a Limit - Activity 1.2.4
The Derivative of a Function at a Point - Activity 1.3.2
The Derivative of a Function at a Point - Activity 1.3.5
The Derivative Function - Activity 1.4.2
The Derivative Function - Activity 1.4.3
The Derivative Function - Activity 1.4.5
Interpreting, Estimating, and Using the Derivative - Activity 1.5.2
Interpreting, Estimating, and Using the Derivative - Activity 1.5.3
Interpreting, Estimating, and Using the Derivative - Activity 1.5.5
The Second Derivative - Activity 1.6.3
The Second Derivative - Activity 1.6.5
Limits, Continuity, and Differentiability - Activity 1.7.2
Limits, Continuity, and Differentiability - Activity 1.7.3
Limits, Continuity, and Differentiability - Activity 1.7.4
The Tangent Line Approximation - Activity 1.8.2
The Tangent Line Approximation - Activity 1.8.3
Elementary Derivative Rules - Activity 2.1.2
Elementary Derivative Rules - Activity 2.1.3
Elementary Derivative Rules - Activity 2.1.4
Sine and Cosine - Activity 2.2.4
The Product Rule - Activity 2.3.2
The Quotient Rule - Activity 2.3.4
Derivatives of Other Trigonometric Functions - Activity 2.4.5
The Chain Rule - Activity 2.5.0
The Chain Rule - Activity 2.5.2
The Chain Rule - Activity 2.5.3
Derivatives of Inverse Functions - Activity 2.6.2
Derivatives of Inverse Functions - Activity 2.6.5
Implicit Differentiation - Activity 2.7.2
Implicit Differentiation - Activity 2.7.4
Related Rates - Activity 3.1.0
Related Rates - Activity 3.1.2
Related Rates - Activity 3.1.4
Related Rates - Activity 3.1.5
Using Derivatives to Evaluate Limits - Activity 3.2.3
Using Derivatives to Evaluate Limits - Activity 3.2.4
Using Derivatives to Identify Extreme Values - Activity 3.3.2
Using Derivatives to Identify Extreme Values - Activity 3.3.3
Global Optimization - Activity 3.5.3
Global Optimization - Activity 3.5.4
Applied Optimization - Activity 3.6.0
Applied Optimization - Activity 3.6.2
Applied Optimization - Activity 3.6.3
Determining Distance Traveled from Velocity - Activity 4.1.2
Determining Distance Traveled from Velocity - Activity 4.1.3
Determining Distance Traveled from Velocity - Activity 4.1.4
Riemann Sums - Activity 4.2.2
Riemann Sums - Activity 4.2.5
The Definite Integral - Activity 4.3.2
The Definite Integral - Activity 4.3.3
The Fundamenatal Theorem of Calculus - Activity 4.4.2
The Fundamental Theorem of Calculus - Activity 4.4.3
The Fundamental Theorem of Calculus - Activity 4.4.5
Constructing Accurate Graphs of Antiderivatives - Activity 5.1.3
Constructing Accurate Graphs of Antiderivatives - Activity 5.1.4
The Second Fundamental Theorem of Calculus - Activity 5.2.3
The Second Fundamental Theorem of Calculus - Activity 5.2.4
Integration by Substitution - Activity 5.3.2
Integration by Substitution - Activity 5.3.3
Integration by Substitution - Activity 5.3.4
Past Exams
Exam 1 - Spring 2026
Topics
Questions
Exam 1 - Fall 2025
Topics
Questions
Exam 1 - Fall 2024
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Exam 2 - Spring 2026
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Exam 2 - Fall 2025
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Questions
Exam 3 - Spring 2026
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Questions
Exam 3 - Fall 2025
Topics
Questions
MATH 221
Calculus I
Dale Buske
Mathematics and Physics
Saint Cloud State University
Last Updated: August 11, 2026
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