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Mr. Stephen Lange » Calculus Worksheets

Calculus Worksheets

Mastermathmentor Collection - see www.mastermathmentor.com to order solutions

CollegeBoard Collection


University of Arizona Collection


  • 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 Math 124.  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 a Position Graph - Answer questions about motion using a position graph.  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
  • Alternate Related Rates Worksheet w Answers
  • 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

CHAPTER 7 - Integration

  • Derivative and Integral Rules - A compact list of basic rules.   pdf  doc
  • Trig Reference Sheet - List of basic identities and rules for trig functions.   pdf   doc
  • Recognizing Integrals - Similar looking integrals require different techniques. Determine if algebra or substitution is needed.   pdf   doc
  • U-Substitution - Practice with u-substitution, including changing endpoints.   pdf   doc
  • More Substitution - Substitution in symbolic form.   pdf   doc
  • Trig Substitution & Partial Fraction - These problems cannot be done using the table of integrals in the text.   pdf   doc
  • More Trig Sub & Partial Fractions - These problems should be done without the use of a table of integrals.   pdf   doc
  • Integral Table - Table of integrals.   pdf
  • Complete Square & Division - Algebra review of completion of the square and long division of polynomials.   pdf  doc
  • Integration Tables - Manipulate the integrand in order to use a formula in the table of integrals.   pdf   doc
  • Integration Techniques - A collection of problems using various integration techniques.   pdf   doc
  • Estimation Rules - Illustrating and using the Left, Right, Trapezoid, Midpoint, and Simpson's rules.   pdf   doc
  • More Estimation - Another worksheet illustrating the estimation of definite integrals.   pdf   doc
  • Intro to Improper Integrals - Introduction to evaluating an improper integral.   pdf   doc
  • Improper Integrals - Recognizing an improper integral and using a value of an integral to find other values.   pdf   doc
  • Intro to Comparing Improper Integrals - General relationships between functions and the idea behind comparison.   pdf   doc
  • Improper Integrals by Comparison - Using comparison to prove an integral converges/ diverges.   pdf   doc
  • Improper Integrals by Comparison - Additional practice. Antiderivatives cannot be expressed in closed form.   pdf   doc
  • Evaluating Limits - Additional practice. Evaluating limits. L'Hopital's Rule.   pdf   doc

CHAPTER 8 - Using the Definite Integral

  • Intro to Slicing - How slicing can be used to construct a Riemann sum or definite integral.  pdf   doc
  • Slicing a Solid - Additional practice. Slicing a solid in two ways to find volume.  pdf
  • Geometry - Additional practice. Find area, volume, and length. Includes using density.  pdf   doc
  • More Geometry - Additional practice. More applications to geometry.  pdf   doc
  • Density and Mass - Using density and slicing to find mass.  pdf   doc
  • Physics - Additional practice. Problems involve work.  pdf   doc
  • More Work - Additional practice. More problems involving work.  pdf   doc

CHAPTER 9 - Sequences and Series

  • Geometric Series - Additional practice with geometric series.  pdf   doc
  • Integral Test - Using the integral test to determine if series converge.  pdf   doc
  • Convergence Tests - Additional practice using convergence tests.  pdf   doc
  • More Convergence Tests - A summary of the available convergence tests.  pdf   doc
  • Power Series - Working with power series.  pdf   doc
  • More Power Series - Additional practice finding radius and interval of convergence.  pdf   doc

CHAPTER 10 - Approximating Functions Using Series

  • Taylor Polynomials & series - How well do Taylor polynomials approximate functions values?  pdf   doc
  • Series Table - List of Taylor Series for basic functions.   pdf
  • Using Taylor Series - Different ways to use Taylor series.  pdf   doc
  • Taylor Series - Additional practice.  pdf   doc
  • More Taylor Series - Collection of problems using Taylor series.  pdf   doc
  • More Taylor Series - Additional practice.  pdf   doc
  • Complex Numbers - Algebra of complex numbers and Euler's Form.   pdf   doc

CHAPTER 11 - Differential Equations

  • Slopefields - Matching slopefields with differential equations.  pdf
  • Separable Variables - Using the method of separation of variables to solve differential equations.  pdf   doc
  • Differential Equations - Collection of applications.  pdf   doc
  • Models - Comparing various models including Logistic.  pdf   doc

Calculus Maximus


The topics below are both AB and BC topics.  The topics preceded with an asterisk (*) are BC only topics.  All documents are .pdf


Open House Info: AB & BC


First Day Handouts

Note to Students (and Parents)

AP Calculus Course Outline: AB, BC

AP Calculus Survival Guide


Appendix: Precalculus stuff to know cold  (Notes)

Appendix: Parent Function Catalog  (Notes)

Appendix: The Unit Circle  (Notes)


1 Intro: What is Calculus?   (Notes)

1.1  What is AP Calculus? (Notes)


2 Intro: Calculus prerequisites  (Notes)

2.1  Parent Functions  (Notes, Worksheet)

2.2  Simplifying Expressions  (Notes, Worksheet)

2.3  Equations of Lines  (Notes, Worksheet)

2.4  Domain, Range, and Symmetry  (Notes, Worksheet)

2.5  Fun with Functions  (Notes, Worksheet)

2.6  Trigonometry  (Notes, Worksheet)


3 Intro: Limits (Notes)

3.1  Intro to Limits (Notes, Worksheet)

3.2  More Limits (Notes, Worksheet)

3.3  Limits and Infinity (Notes, Worksheet) Practice TEST 3.1-3.3

3.4  Algebraic Limits (Notes, Worksheet)

3.5  Continuity on Intervals (Notes, Worksheet) Practice TEST 3.1-3.5

"Calculus Maximus," by Robert Grigsby, Calculus class of 2011


4 Intro: Differentiation (Notes)

4.1  Tangent Line Problem & Differentiability (Notes, Worksheet) Practice TEST 3.4-4.1

4.2  Derivatives on the Calculator (Notes)

4.3  Basic Differentiation Rules (Notes, Worksheet)

4.4  Product & Quotient Rules (Notes, Worksheet)

4.5  Rates of Change and Particle Motion I (Notes, Worksheet Practice TEST 4.1-4.5

4.6  The Chain Rule (Notes, Worksheet)

4.7  Implicit Differentiation (Notes, Worksheet) Practice TEST 4.1-4.7

4.8  Derivatives of Inverse & Inverse Trig Functions (Notes, Worksheet)

4.9  Derivatives of Exponential Functions (Notes, Worksheet)

4.10 Derivatives of Log Functions & LOG DIFF (Notes, Worksheet) Practice TEST 4.1-4.10


5 Intro: Applications of Differentiation (Notes)

5.1   Extrema on an interval (Notes, Worksheet) Practice TEST 4.1-5.1

5.2   Rolle's Theorem and the MVT (Notes, Worksheet/KEY)

5.3   Increasing, Decreasing, and 1st Derivative Test (Notes, Worksheet)

5.4   Concavity and the Second Derivative Test (Notes, Worksheet Practice TEST 5.1-5.4

5.5   Curve Sketching (Notes, Worksheet

5.5B Summary Sheet (Notes)

5.6   Optimization (Notes, Worksheet/KEY)                    

5.7   Linearization and Differentials (Notes, Worksheet/KEY)

5.8   Related Rates (Notes, Worksheet/KEY Practice TEST 5.1-5.8


AB Fall Final Review HERE/KEY


6 Intro: Integration (Notes)

6.1  Antiderivatives and Indefinite Integration (Notes, Worksheet/KEY)

6.2  Definite Integrals & Area with Riemann Sums & Trapezoidal Rule (Notes, Worksheet/KEY)

6.3  The FTOC I & II, the MVT II, & Avg Value (Notes, Worksheet/KEY Practice TEST 6.1-6.3

6.4  Integration by u-Substitution and Pattern Recognition (Notes, Worksheet/KEY)


BC Fall Final Review HERE/KEY


7 Intro: Differential Equations & Modeling (Notes)

7.1  Slope Fields (Notes, Worksheet/KEY)

7.2  *Euler's Method (Notes, Worksheet/KEY)

7.3  Separable Differential Equations (Notes, Worksheet/KEY) Practice TEST 6.4-7.3

7.3B Mega Integration Practice (Worksheet/KEY)

7.4  *Integration by Parts (Notes, Worksheet/KEY)

7.5  *Partial Fractions & Logistic Growth (Notes, Worksheet/KEY)


8 Intro: Applications of Integration (Notes)

8.1  Integral as Net Change (Notes, Worksheet/KEY)

8.2  Area between Curves (Notes, Worksheet/KEY)

8.3  Volumes (Notes, Worksheet/KEY)

8.4  *Arc Length (Notes, Worksheet/KEY)

8.5  *L'Hôpital's Rule and Indeterminate Forms (Notes, Worksheet/KEY)

8.6  *Improper Integrals (Notes, Worksheet/KEY Practice TEST 8.1-8.6


9 Intro: Vector Calculus (Notes)

9.1  *Intro to Parametric & Vector Calculus (Notes, Worksheet/KEY)

9.2  *Parametric & Vector Accumulation (Notes, Worksheet/KEY) Worksheet II--review


10 Intro: Polar Calculus (Notes)

10.1 *Polar Intro & Derivatives (Notes, Worksheet/KEY)

10.2 *Polar Area (Notes, Worksheet/KEY)


11 Intro: Sequences & Series (Notes)

11.1 *Sequences & Series: Convergence & Divergence (Notes, Worksheet/KEY)

        Summary of Tests for Convergence and Series Flow Chart with practice problems

11.2 *Taylor Polynomials (Notes, Worksheet/KEY)

11.3 *Power Series I: Taylor & Maclaurin Series (Notes, Worksheet/KEY)

11.4 *Power Series II: Geometric Series (Notes, Worksheet/KEY)

11.5 *Lagrange Error Bound (Notes, Worksheet/KEY)




Calculus Review for AP examination (also called "exam" or "test").




Calculus Cheat Sheet (by Paul)

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Calculus Cheat Sheet (by Paul)