# Math 122B - First Semester Calculus and 125 - Calculus I Worksheets

The following is a list of worksheets and other materials related to Math 122B and 125 at the UA. Your instructor might use some of these in class. You may also use any of these materials for practice.

## INTRODUCTION

• Tools for Success -A list of resources including tutoring services. website
• Student Survey - A survey to provide background information to an instructor.  pdf   doc
• Calculator Checklist - A list of calculator skills that are required for Calculus.  pdf   doc
• Pixels and the calculator screen - An exercise to illustrate the sensitivity of the window settings.  pdf   doc
• Homework Sample - A few examples to illustrate how homework should be written.  pdf   doc

## CHAPTER 1 - A Library of Functions

• Interesting Graphs - A few equations to graph that have interesting (and hidden) features.  pdf   doc
• Functions - Properties of functions and the Rule of Four (equations, tables, graphs, and words).  pdf   doc
• Reading Graphs - Four graphs and questions using function notation.  pdf   doc
• Find a Function - Find an example of a function in the media.  pdf   doc
• INDY 500 - Sketch graphs based on traveling one lap along an oval racetrack.  pdf   doc
• Farenheit - The relationship between Farenheit and Celsius.  pdf   doc
• Linear Functions - Applications.  pdf   doc
• Exponential Functions - Recognizing exponential functions and their properties.  pdf   doc
• Inverse Functions - Relationships between a function and its inverse.  pdf   doc
• New Functions From Old - Transformations, compositions, and inverses of functions.  pdf   doc
• Transformations - A matching exercise using symbolic expressions and tables.  pdf   doc
• More Transformations - Graphing transformation.   pdf   doc
• Logarithms - Using logarithms to solve problems. Properties of logas.  pdf   doc
• Trig Reference Sheet - List of basic identities and rules.   pdf   doc
• Trig (part I) -Interpreting trig functions and practice with inverses.  pdf   doc
• Trig (part II) - More practice.  pdf   doc
• Denise & Chad - An illustration of the effects of changes in amplitude and period.  pdf   doc
• Polynomials & Rational Functions - Recognizing polynomials and rational functions and their properties.  pdf   doc
• Power Functions - Use graphs to explore power functions.  pdf   doc
• Limits and Continuity - Graphical and numerical exercises.  pdf   doc
• More Continuity - Basics about continuity.  pdf   doc

## CHAPTER 2 - The Derivative

• Introduction to Rates - Introduction to rates of change using position and velocity.   pdf   doc
• Representations - Symbolic recognition and illustration of rates. Practical interpretation of rates of change using the rule of four.   pdf   doc
• Practical Example - Reading information about rates from a graph.  pdf   doc
• Estimation - Estimation using tables and equations. Practice with notation and terminology.  pdf   doc
• Derivative Graphs - Graphing a derivative function given a graph.  pdf   doc
• More Derivative Graphs - Matching exercise.  pdf   doc
• Terminology - Fill in the blank exercise. Practice with terminology  pdf   doc
• Differentiability - Determine when a function is not differentiable at a point.  pdf   doc
• More Differentiability - More practice.   pdf   doc
• Practice - Additional practice covering this section.  pdf   doc

## CHAPTER 3 - Rules For Differentiation

• Product & Quotient Rules - Practice using these rules.   pdf   doc
• Chain Rule - Practice using this rule.   pdf   doc
• Base e - Derivation of e using derivatives.  pdf   doc
• Rules - Practice with tables and derivative rules in symbolic form.  pdf   doc
• More Practice - More practice using all the derivative rules.  pdf   doc
• More Practice - More practice using all the derivative rules.  pdf   doc
• Derivative (&Integral) Rules - A table of derivative and integral rules.   pdf   doc

## CHAPTER 4 - Using the Derivative

• Reading Graphs - Reading information from first and second derivative graphs.  pdf   doc
• Critical Points Part I - Terminology and characteristics of critical points.  pdf   doc
• Critical Points Part II - Finding critical points and graphing.  pdf   doc
• Families of Functions - Finding critical points for families of functions.  pdf   doc
• More Families of Functions - Finding values of parameters in families of functions.  pdf   doc
• Optimization Part I - Optimization problems emphasizing geometry.  pdf   doc
• Optimization Part II - More optimization problems.  pdf   doc
• Parametric Equations (Circles) - Sketching variations of the standard parametric equations for the unit circle.  pdf   doc
• Parametric Equations (Misc) - Fun graphs using parametric equations.   pdf   doc
• Parametric Equations - Finding direction of motion and tangent lines using parametric equations.  pdf   doc
• Holiday Parametric Equations - Halloween surprise.   pdf   doc
• L'Hopital's Rule - Practice in recognizing when to use L'Hopital's Rule.  pdf   doc
• Limit Practice -Additional practice with limits including L'Hopital's Rule.   pdf   doc
• Introduction to Related Rates - Finding various derivatives using volume of a sphere and surface area of a cylinder.  pdf   doc
• Related Rates - Additional practice.  pdf   doc
• More Related Rates -Additional practice.   pdf   doc

## CHAPTER 5 - The Definite Integral

• Intro to Velocity and Area - Relationship between velocity, position, and area.  pdf   doc
• Representations - Practice with notation, estimation, and interpretations.  pdf   doc
• Rocket - Application of velocity and position for a model rocket.  pdf   doc
• Mice - Application of velocity and position for two mice.  pdf   doc
• Cars - Application of velocity, position, and acceleration of two cars.  pdf   doc
• Fundamental Theorem Part I - Graphical approach.  pdf   doc
• Fundamental Theorem Part II - Illustrations and notation.  pdf   doc

## CHAPTER 6 - Constructing Antiderivatives

• Position, Velocity, & Acceleration - Graphical relationships between position, velocity, and acceleration.  pdf   doc
• Sketching Antiderivatives - Graphing antiderivatives.   pdf   doc
• Area Between Graphs - Using the Fundamental Theorem to find area between graphs.  pdf   doc
• Practice - Problems from chapters 5 and 6.  pdf   doc
• Integration - Recognizing when to use substitution. Integrands look similar.  pdf   doc
• Substitution - Practice, including definite integrals.  pdf   doc
• More Substitution - More practice.  pdf   doc