Differential Equations Teacher Resources

Find Differential Equations lesson plans and worksheets
Showing 1 - 197 of 197 resources
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Differential Equations Representing Growth and Decay: Rice Legend

For Students 11th - Higher Ed
The legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...
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Differential Equations

For Students 12th - Higher Ed
In this differential equations activity, learners solve and complete 3 different parts of a problem. First, they sketch a slope field for the given differential equation on the axes provided. Then, students write an equation for the line...
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Worksheet Seventeen: Differential Equations

For Students Higher Ed
For this differential equation worksheet, students solve differential equations and graph solutions. This two-page worksheet contains 8 multi-step problems.
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Approxiamte Solutions to Differential Equations-Slope Fields (graphical) and Euler's Method (numeric)

For Teachers 12th
Twelfth graders explore differential equations.  In this calculus lesson, 12th graders explore Euler’s Methods of solving differential equations.  Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric...
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The Spread of Disease with Differential Equations

For Teachers 12th
Twelfth graders solve problems using differential equations.  In this Calculus lesson, 12th graders analyze data regarding the spread of a flu virus.  Students use the symbolic capacity of the TI-89 to develop a model and analyze the...
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Logistic Growth, Differential Equations, Slope Fields

For Teachers 12th Standards
Investigate differential equations with your class. They use the TI-89 to explore differential equations analytically, graphically, and numerically as the examine the relationships between each of the three approaches.
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Differential Equations and Initial Value Problems

For Students 11th - Higher Ed
Demonstrate working an initial value problem with an AP Calculus video that verifies that a family of functions is a solution to a differential equation by substitution. The presentation goes on to find a particular solution that belongs...
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Linear Systems: Applications of Linear Algebra to Differential Equations

For Students 12th - Higher Ed
In this differential equations instructional activity, students solve systems of simultaneous differential equations using linear algebra. This six-page instructional activity contains approximately six problems, with explanations and...
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First Order Linear Differential Equations

For Students 12th - Higher Ed
In this linear differential equations worksheet, students solve 5 various types of problems that relate to first order linear differential equations. First, they find the general solution of the differential equation given in numbers 1...
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Coffee: Differential Equation

For Teachers Higher Ed
In this differential worksheet, students read a word problem and write a differential equation and solve it. They draw the slope field for given problems. This two-page worksheet contains 9 multi-step problems.
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Differential Equations

For Students 11th - Higher Ed
In this differential equations worksheet, students solve and complete 3 sets of various problems. First, they solve each of the differential equations. Then, students use the given information to evaluate the constant of integration....
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Differential Equations

For Students 11th - Higher Ed
In this differential equations learning exercise, students identify the slope and describe all points on the plane for the positive slope. This one-page learning exercise contains three problems.
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First-Order Differential Equations and Vector-Matrix Systems

For Students 11th - Higher Ed
In this differential equation worksheet, students answer seventeen problems related to first-order differential equations, vectors, systems of equations, and vector-matrix form of systems of equations.
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Linear Systems: Differential Equations

For Students Higher Ed
For this differential equations worksheet, students solve collections of simultaneous differential equations. This six-page worksheet contains examples, explanations, and approximately six problems.
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Differential Equation

For Students Higher Ed
In this differential worksheet, students answer three essay questions. They are presented a problem about the height of a tree being a function of the base diameter. Students write the equation for the differential equation, solve the...
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Linear Systems: Differential Equations

For Students Higher Ed
In this differential equations worksheet, students determine the stability of matrices and evaluate a matrix with an exponent. This two-page worksheet contains examples, explanations, and two problems to solve.
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Applying Linear Algebra to Differential Equations

For Students 11th - Higher Ed
In this math worksheet, students using linear algebra to find the solutions to the differential equations. The equations are listed in systems.
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Differential Equations

For Students 12th - Higher Ed
In this differential equation worksheet, students find the derivative of given equations and express their answers as Maclaurin series. This two-page worksheet contains examples and explanations. There are two problems in this worksheet.
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Differential Equations and Slope Fields

For Teachers 11th - Higher Ed
Students solve differential equations.  In this differential equations lesson, students use their TI-89 calculator to explore slope fields and find solutions to a differential equation.  They graph their solutions.
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Biological Models with Differential Equations

For Teachers 12th
Explore differential equations by using models representing growth and decline. Using calculus, learners will investigate exponential and logistic growth in the context of several models representing the growth or decline of a...
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An Introduction to Solving Differential Equations

For Teachers 12th
Twelfth graders investigate differential equations.  In this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem.  Students...
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Solving Differential Equations

For Teachers 12th
Twelfth graders explore differential equations.  In this calculus lesson, 12th graders solve differential equations graphically, numerically and analytically.
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Differential Equations on the TI-92 PLUS

For Teachers Higher Ed
Students identify and familiarize themself with the features and capabilities of the TI-92 Plus calculator. They also find symbolic solutions of differential equations and general solutions or to find particular solutions of...
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Differential Equations

For Teachers 10th - 12th
Need some help teaching differential equations? Here's a perfect resource for you. An analysis of differential equations gives instructors a better understanding of the concept. The resource gives suggestions on how to incorporate...
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The Domain of Solutions to Differential Equations

For Teachers 10th - 12th
It'd be a shame to get a question wrong just by not accounting for the domain. An article on AP® Calculus looks at the importance of considering the domain of solutions to differential equations by looking at examples from past AP®...
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Differential Equation

For Students 11th - Higher Ed
In this differential equation worksheet, students sketch a slope field for the given equation. They identify the solution to the equation under specified circumstances. This one-page worksheet contains two multi-step problems.
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Differential Equation

For Students 10th - 12th
In this differential equation worksheet, students sketch a slope field for a given differential. They identify the domain. This one-page worksheet contains two multi-step problems.
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Differential Equations

For Students 10th - Higher Ed
In this differential equation worksheet, students solve differential equations. They determine the domain and range of functions. This one-page worksheet contains two multi-step equations.
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Worksheet Two

For Teachers Higher Ed
In this math worksheet, pupils solve differential equations. Students use similar equations, and analyze ways they differ from one another. Pupils draw directional fields and sketch solutions. The final three questions are applications...
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Newton's Law of Cooling, Data Analysis, and Differential Equations

For Teachers 11th - 12th
Learners calculate the length of time to cool a hot drink. In this data analysis and differential equations lesson, students use a TI-89 or TI-92 calculator to find the length of time for a hot drink to cool to room temperature. Readings...
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Hot Coffee

For Teachers Higher Ed
Students investigate differential equations and slope fields.  In this differential equations and slope fields lesson, students determine how much time can pass before a cup of coffee is safe to drink.  Students use a differential...
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Using Slope Fields

For Teachers 12th
Twelfth graders investigate slope fields.  In this Calculus instructional activity, 12th graders identify whether a slope field appropriately reflects a differential equation by matching.  TI-83 Plus/TI-84 Plus and appropriate programs...
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It's Outta Here

For Teachers 11th - 12th
Young scholars use differential equations to determine the distance of a hit baseball.  In this using differential equations to determine the distance of a hit baseball lesson, students find the velocity and angle of a ball hit by a...
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Integrals

For Students 12th - Higher Ed
For this integrals worksheet, students solve and complete 22 various types of problems. First, they evaluate each of the listed integrals by using substitution. Then, students solve each of the given differential equations when given the...
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Integrals

For Students 12th - Higher Ed
In this integrals worksheet, students solve and complete 22 various types of problems. First, they evaluate each of the listed integrals on the sheet. Then, students solve each of the given differential equations by substituting the...
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Condensing Section 4.1

For Students 11th - 12th
For this differential equations worksheet, students solve three sets of questions. The first section is titled "Existence and Uniqueness." The second section is titled "Linear Independence and Dependence," and the third section is about...
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Solving Differential Equations via the Fundamental Theorem of Calculus

For Teachers 11th - 12th
Students use their TI-89 calculator to compute derivatives and anti-derivatives. In this differential equation lesson, students follow detailed directions to complete one table of derivative/anti-derivative values. They compute the...
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Differentiation Computations

For Students 11th
In this calculus worksheet, 11th graders solve problems using differential equations and computations. They apply properties of trig functions and simplify their answers. There are 9 questions.
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A.P. Calculus Integration Test

For Students 12th - Higher Ed
In this A.P. Calculus activity, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields.  Some of the problems are multiple choice, while others are...
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Recovering a Function from its Derivative: A Graphical Approach

For Teachers 9th - 12th
Students follow detailed instructions for using their TI-86 graphing calculator to find solutions to differential equations. In this instructional activity, students learn to use their graphing calculator to solve 12 differential equations.
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Slope Fields and Euler's Method for AP Calculus

For Teachers 12th
Twelfth graders investigate slope fields and Euler’s Method.  In this calculus lesson, 12th graders explore the steps for programming slope fields on the TI-83 and Euler’s method for achieving a numerical solution to differential...
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Sturm Liouville Theory

For Students 12th - Higher Ed
In this Sturm Liouville Theory worksheet, students solve one multi-step problem that transforms the original differential equation into the Sturm-Liouville form. First, they apply the ideas expressed for each equation given in...
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Variational Calculus 3

For Students 12th - Higher Ed
In this methods of applied mathematics worksheet, students solve 5 various types of problems that relate to variational calculus equations. First, they determine a second order differential equation for the geodesic. Then, students write...
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Population: Logistically Speaking

For Teachers Higher Ed
In this population worksheet, students read word problems relating to population growth. They write the problem as a differential equation, create models and graphs of the solution. This three-page worksheet contains 10 multi-step...
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Variational Calculus 1

For Students 12th - Higher Ed
In this methods of applied mathematics worksheet, students solve 4 different problems that relate to variational calculus. First, they determine a second order differential equation for the function y(x) for which the function given...
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Calculus Test

For Students 11th - Higher Ed
In this calculus activity, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
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Worksheet 8

For Students 11th - Higher Ed
In this math learning exercise, learners explore how the use of implicit differentiation does not give the solutions to the differential equation. Then they write the definitions to the vocabulary related to differential equations.
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Worksheet 4

For Students 11th - Higher Ed
In this math worksheet, students write down five exact differential equations in symmetric form. Then they test the statements concerning differential equations.
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Worksheet 16

For Students 11th - Higher Ed
For this math worksheet, students consider a constant coefficient linear second order differential equation. Then they solve the homogeneous equation.
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Worksheet 3

For Students 12th - Higher Ed
in this math learning exercise, students define the meaning of a differential equation. Then they examine the method of solving a separable equation.
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Worksheet 9 Practice Test 1

For Students 11th - Higher Ed
In this math instructional activity, students find the solutions to the differential equations. Then they examine the group of equations in order to determine the ones that are linear.
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Worksheet 31

For Students 12th - Higher Ed
In this math worksheet, students find the solutions to the differential equations. They also investigate the application of recognizing the parts of the equation.
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Worksheet 30

For Students 11th - Higher Ed
For this math worksheet, students solve the differential equation by means of a power series about the point x0 = 2. Then they find the recurrence relation and the first four terms.
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Worksheet 20

For Students 10th - 12th
In this math worksheet, they write down and solve a differential equation governing the motion of an underdamped spring. Then they find the solution to the initial value problem.
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Worksheet 19

For Students 6th - Higher Ed
In this math worksheet, students use the following descriptions of a spring system to write a differential equation of the form my + γy + ky = F(x).
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Worksheet 14 Spring 1996

For Students 11th - Higher Ed
In this math instructional activity, learners answer the questions in the context of either being true or false. The topics covered include derivatives and differential equations.
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Worksheet 33 Spring 1996

For Students 11th - Higher Ed
In this math worksheet, students find the solutions to the differential equations. Then they graph the solution and show if they are perpendicular.
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Worksheet 2

For Students Higher Ed
Directions in this learning exercise direct the students to use any method they can to solve the equations, which are all differential equations. This activity could be used as a homework assignment, a class project, or a quiz.
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The Method of Separation of Variables

For Students 11th - Higher Ed
In this math worksheet, students read the examples of the initial value problems. Then they write all the possible solutions for the differential equation.
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Separation of Variables and Initial Value Problem

For Students 11th - Higher Ed
Ap Calculus classes learn how to solve a differential equation by getting like variables together with a video that presents an example of how to solve a differential equation by using the method of separation of variables. The example...
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Slope Fields

For Teachers 11th - 12th
Young scholars sketch a slope field for a given differential equation, given a slope field. They also match a slope field to a differential equation and match a slope field to a solution of a differential equation. Finally, students use...
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Math 53 Worksheet

For Students Higher Ed
In this college level calculus instructional activity, students determine if a limit exists and if so, find it, and solve differential equations.  The one page instructional activity contains seven problems.  Answers are not provided. 
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Differentiable Equations

For Students 12th - Higher Ed
In this differentiable equations worksheet, students solve and complete 2 different types of problems. First, they find the differentiable function and evaluate it at a given point. Then, students find the function by solving the...
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Solving Differentiall Equations Using Euler's Method

For Teachers 12th
Twelfth graders explore differential equations.  In this calculus instructional activity, 12th graders investigate the process of solving differential equations using Euler’s method.  The instructional activity provides the steps used in...
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A.P. Exam Review

For Teachers 9th - 12th
Students engage in a lesson plan that is concerned with the cumulative concepts introduced in a Calculus course. They review exponential growth and how it is used to measure increase in values. Students also apply the use of the...
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Don't Forget the Differential Equations: Finishing 2005 BC4

For Teachers 10th - 12th
Not explaining reasoning falls short of perfect. The article covers problem number four on the 2005 AP® Calculus BC exam. Using a similar problem, the author discusses the Euler Method procedure to answer the question. With the...
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Drawing Slope Fields

For Students 11th - Higher Ed
Work through an example on slope fields. In a video geared for AP Calculus, viewers watch as an instructor uses a slope field generator to produce a slope field and draws particular solutions for a given differential equation.
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Space Math Differentiation-"Ch..Ch..Ch..Changes"

For Students 11th - Higher Ed
In this differentiation in space math worksheet, students use 6 different equations to solve 6 problems that involve differentiation related to astrophysics.
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Reductions of Order

For Students 11th - 12th
For this calculus worksheet, students identify functions as linear or nonlinear, homogeneous versus nonhomogeneous by using the reduction power theorem. There are 5 questions.
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2006 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...
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Slope Field Matching

For Teachers 11th - 12th
In this slope field worksheet, young scholars match the slope field with the matching differential equation. They sketch possible solution curves to match given initial conditions. This two-page worksheet contains approximately 14...
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Math 150 - Differentiation Applications

For Students 11th - 12th
In this differentiation worksheet, students solve 25 short answer word problems. Students solve application word problems by finding the derivatives of functions.
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AP Calculus: Slope Fields

For Teachers 10th - 12th
Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...
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Calculus at the Battle of Trafalgar

For Teachers 10th - 12th
All's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time.
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Differential Equations

For Teachers 11th - 12th
Learners solve derivatives of differential equations. In this calculus lesson, students solve equations using the derivative to obtain no differentials in the equation. They complete an assignment in the text book also.
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Four Matrix, Eigenvalue, and Eigenvector Problems

For Teachers 12th - Higher Ed
In this matrix worksheet, students solve a system of differential equations, find eigenvalues and eigenvector in two problems, and solve a word problem using a system. 
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Air Resistance

For Teachers 12th
Twelfth graders explore integral calculus.  In this Calculus lesson, 12th graders use the tools of integral calculus to investigate the motion of a free falling objet which is governed by both gravity and air resistance. 
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Variational Calculus 2

For Students 12th - Higher Ed
In this methods of applied mathematics worksheet, students solve 6 different types of problems related to variational calculus. First, they determine the first integrals of the Euler-Lagrange equations corresponding to the optimizations...
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Calculus and The Simpsons

For Students 12th - Higher Ed
In this calculus worksheet, students examine a situation form The Simpsons in whcih Bart falls from a tree house.  Students write and solve an differential equation that gives the height of the tree house. The one page worksheet...
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Differential Equations with the TI-86

For Teachers 10th - 12th
Students explore how to graph differential equations using a TI calculator.  In this math lesson, students solve systems of equations using the calculator. Students explore graphing and use it to interpret experimental data.
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Calculus Volume 2

For Students 11th - Higher Ed
Delve into the middle of calculus. The resource is the second eBook of three that covers the complete calculus content. Seven chapters begin with integrals and different methods of integration before moving on to differential equations....
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2003 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Take a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...
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2005 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Grab a peak inside the test. The 2005 free-response questions from the AP® Calculus exam allow learners to see how topics appear on the tests. Topics cover differential equations, bounded areas, particle motion, and slopes of tangent lines.
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2010 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Most say that practice makes perfect. Scholars use the released free-response questions to practice for the AP® Calculus AB exam. Each question comes with several parts and either do or do not allow calculators. Items include topics such...
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2003 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Get a better grasp of the intended content. The six free-response questions provide insight into the purpose of the AP® Calculus content. Two questions have real-world context while the remaining are void of context. The items range from...
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2012 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...
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2007 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
What do the questions look like? Six free-response questions provide pupils with knowledge of how calculus topics appear on the AP® Calculus exam. The questions involve calculator and non-calculator problems by providing mathematical and...
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Approximation

For Teachers 10th - 12th
Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...
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2010 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
What do a zoo, snow, and a moving particle have in common? The six free-response items from the 2010 AP® Calculus BC exam allow teachers and pupils see how items may show up in context. Three of the questions are from only the BC portion...
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Engineering in a Calculus Classroom

For Teachers 11th - 12th
Learners solve several differential equations. In this calculus lesson, students test their modulus calculation by testing different weights or beam lengths. They share their findings in class.
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Worksheet 13

For Students 11th - Higher Ed
In this math instructional activity, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.
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Worksheet 15 Computer Lab

For Students 11th - Higher Ed
In this math instructional activity, students discuss the natural frequency ω0 of the system and how it is the number of oscillations of the spring in 2π units of time.
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Worksheet 1

For Teachers Higher Ed
For this math worksheet, students describe the difference between a partial and an ordinary differential equation. They give examples of 1st, 2nd, and 3rd order differential equations. Students apply this information to predator/prey...
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Managing the National Debt

For Teachers 11th - 12th
Young scholars explore the national debt.  In this calculus lesson, students predict the national debt by using logistic growth.  The young scholars estimate the current national debt and use that figure to make their predictions. 
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Definition of Antiderivatives - Concept

For Teachers 11th - Higher Ed
Antiderivatives means being against doing homework on derivatives, right? The first installment of a 12-part video series on antiderivatives and differential equations takes viewers through the definition of an antiderivative. It uses a...
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Euler's Method Introduction

For Teachers 9th - 12th Standards
Young mathematicians define and use Euler's method to solve problems in this calculus lesson. Learners visualize graphs and solve differential equations. They create these visuals on the TI calculator.
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Slope Fields

For Teachers 9th - 12th Standards
Young scholars create and analyze slope fields. In this calculus lesson, students create a visual of differential equations. They use the Ti Navigator to create slope fields.
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Worksheet 31 - Doman & Range

For Teachers Higher Ed
In this function worksheet, students determine the domain and range of given functions. They use trigonometric ratios to determine if a statement is true or false. Students differentiate equations. In this one-page worksheet, students...
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Differential Equations and Population Growth Lesson

For Teachers 9th - 12th
Students calculate the size of the population at a given time, for a population that grows at a rate that is directly proportional to the number of members present in the population. They also calculate the time at which the population...
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Math Handbook: Calculus

For Students 10th - 12th
If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...
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Euler's Method

For Teachers 9th - 12th Standards
Learners identify Euler's method of graphing in this calculus lesson. They approximate values of a function and check their work using EM. They also differentiate equations at an exact point.
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Worksheet on Power Series

For Students Higher Ed
In this function worksheet, students identify the interval of convergence and write differential equations. This two-page worksheet contains five multi-step questions.
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Slope Fields

For Teachers Higher Ed
In this slope field worksheet, students match the slope field to its correct differential equation. This one-page worksheet contains six problems.
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Euler Encore 1

For Teachers 11th - 12th
In this math worksheet, students use Euler's Method to solve differential equations. They are given an equation to graph (y'). Students sketch that equation as well as the related equation (y). They find the area of given rectangles and...
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Integrals

For Students 12th - Higher Ed
In this integrals activity, learners solve and complete 22 different types of problems. First, they evaluate each of the listed integrals provided on the sheet. Then, students solve each of the differential equations. They also graph a...
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Evaporation Pans & Related Rates

For Teachers 11th - 12th
Pupils calculate evaporation rate using differential equations. In this calculus lesson, students explain how pan evaporation works. They complete a worksheet to sum up the lesson.
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Relative Rates of Growth

For Students 11th - Higher Ed
It's all relative! A video introduces the concept that the relative rate of growth is the rate of growth relative to the dependent variable, and then compares the equation of the standard model and the relative growth version.
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Challenge Discussion Sheet 9

For Students Higher Ed
In this limits instructional activity, students evaluate five limits using limit definitions. They solve differential equations by isolating one variable. Students determine the dimensions of a rectangle inscribed below the graph of a...
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Using Linear Algebra to Solve Systems of ODE's

For Students 11th - Higher Ed
In this math instructional activity, students examine the coupled differential equations. Then they find the eigenvalues and eigenvectors for the 2x2 matrix.
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A.P. Calculus Exam Prep

For Students 11th - Higher Ed
In this A.P. Calculus exam practice test, students answer 28 multiple choice questions. Questions cover a wide variety of topics. Students tell the position of a particle moving along a horizontal line. They identify the solution to a...
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Population Models and Qualitative Analysis

For Students Higher Ed
In this quantitative analysis worksheet, students explore the limits of a rate equation. They use quantitative analysis methods to determine the differential, plot graphs of their values, and describe the relationships between the...
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2006 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Go a little deeper. Learners use the released 2006 AP® Calculus BC free-response questions to review for the BC test, which covers content from Calculus AB and Calculus BC. Topics include volumes of revolution, particle motion,...
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Worksheet 16-Fall 1995

For Teachers Higher Ed
In this math worksheet, students compute the quotient of two differential amounts. They compute the trigonometric functions of a given variable. Students compute the derivatives of three functions.
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#3 Differential Calculus

For Teachers 12th - Higher Ed
Students create models of the Mean Value Theorem.  In this Mean Value instructional activity, students use their knowledge of derivatives and exponential functions to explore the Mean Value Theorem.  They illustrate the meaning of the...
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The Method of Integration by Parts

For Students 11th - 12th
In this calculus worksheet, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.
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Worksheet 35

For Teachers Higher Ed
In this math worksheet, students analyze two vector fields. They tell which of the vector fields is the scaler field for the given function. Students draw solution curves to match the differential equations represented in the illustrations.
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2016 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
The split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...
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2016 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Using the common errors and test taker responses, it's easy for teachers to see where to pinpoint instruction throughout the AP Calculus course. Pupils, using the released items, develop an understanding of how future exams assess the...
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2015 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
How will the topics be assessed? Using the six released items from the Calculus AB test, pupils see how the exam assesses content from the course. With the additional materials covering test taker's responses and scoring keys, teachers...
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2014 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Give classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....
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2010 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Is this going to be on the test? The resource contains the AP Calculus AB free-response questions that were on the 2010 test. Pupils use the six questions to prepare for their tests. Teachers use the included response resources to...
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2013 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Apply the skills to problems to ace the AP test. Free-response questions require scholars to take calculus skills and apply them to situations. Pupils use the questions to see how those situations appear on an upcoming exam. Teacher use...
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2018 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Pupils interact with six released questions from the 2018 AP Calculus AB exam. Teachers use the additional materials to determine where the class is in terms of readiness for the exam to help provide additional instruction as needed.
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2017 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What is the answer to this question? Pupils use six questions to practice for the AP Calculus AB test. The review questions are divided in two sections, calculator and non-calculator. Additional resources allow teachers to determine how...
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2017 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Pupils use the six released free-response questions from an AP Calculus BC exam to prepare for their own exam. The questions cover a range of topics from the BC curriculum, with half of the items coming strictly from AB material and the...
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2015 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How will the exam ask this question? The free-response questions from the 2015 AP Calculus BC exam demonstrate how questions appear on the test. Using the questions, pupils gain experience answering similar inquiries to what they see on...
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2009 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Dive into the exam review. Pupils use questions, including one about diving into a pool, to prepare for the AP® Calculus BC exam. Items include contextual and non-contextual questions with contextual examples requiring a calculator....
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2013 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What is the important stuff? The free-response questions from the 2013 Calculus AB exam highlight the topics in calculus assessed that year. Items provide pupils the opportunity to experience questions similar to what they will see on...
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A Simple Model for Atmospheric Carbon Dioxide

For Students 11th - Higher Ed
In this atmospheric carbon dioxide worksheet, students use two diagrams to solve 6 problems about atmospheric carbon dioxide. One diagram shows the Keeling Curve and the other shows sources of carbon and the natural and anthropogenic...
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Newton's Law of Cooling

For Teachers 12th
Twelfth graders investigate exponential decay.  In this Calculus lesson, 12th graders explore Newton’s Law of cooling which can be modeled by a differential equation.  Students use the model to solve a murder as they examine the...
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The Product and Quotient Rules

For Students Higher Ed
In this product and quotient rules worksheet, students use Taylor's Theorem to rewrite functions in a given form. They determine the derivatives of functions. This three-page worksheet contains explanations, examples, and seven problems.
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Introduction to Slope Fields

For Teachers 11th - 12th
Students plot slope fields. In this introduction to slope fields activity, students plot 12 slope fields for given differential equations.
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Challenge Discussion Sheet 8

For Students Higher Ed
In this differential worksheet, students compute the rate a boat is approaching a dock when given the height and length of a rope. They find the rate the angle formed when a rocket is launched at given distances above the ground....
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Worksheet 8: Rate, Differentials

For Students Higher Ed
In this rate worksheet, students read story problems, determine the necessary information, and solve the rate problem. They use differentials to estimate the value of a function at a given point and integrate functions. This three-page...
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Quiz 9: Newton's Method

For Students Higher Ed
In this Newton's method worksheet, students estimate the value of a solution and use a differential to estimate the value of a root. This one-page worksheet contains two problems.
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2004 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop a deeper understanding of calculus. The released item and support materials allows teachers and pupils to dig deeper into calculus topics. Scholars use the commentary and descriptions of the items to gain a better understanding...
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2005 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Differentiate between the exams. Using the Q&A document, teachers compare the free-response questions that BC test-takers see to those that AB test-takers see. The pupils see which questions come from AB content and also those that...
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2004 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
The test is not all about skills. The six free-response questions contain two real-world application problems. Those items deal with populations and velocities. The other four questions ask pupils to show their knowledge of calculus...
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2000 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Gain an upper hand in preparation for the exam. Teachers and pupils use six released questions to gain an understanding of the AP® Calculus exam. By answering the questions, scholars see how different concept of the course show up on the...
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2008 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Get the most out of released items. Teachers use the included materials to learn about test-takers' performance on released free-response questions. Pupils respond to the questions and compare their responses to sample scored responses...
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2000 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How are concepts divided? Pupils use the AP® Calculus free-response questions to see how the exam addresses concepts. The concepts are divided into those that use calculators and others that do not. Calculator items require finding...
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2008 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...
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2006 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
An exam divides the six free-response questions into calculator use and no calculator use items. The non-calculator items are conceptual in nature and test whether pupils understand the calculus concepts. Scholars explain their answers...
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2011 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Does the exam look pupils expected? Released free-response questions from the AP® Calculus BC exam allow teachers and pupils to see and practice with actual exam questions. Three of the questions come from the AB portion of the course...
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2002 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Become better at the test concepts. An educational resource presents six free-response questions from the AP® Calculus AB exam. Pupils use the items to practice the content, which contains concepts ranging from particle motion to ships...
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2010 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...
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2007 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
There is just a single real-world problem. Released free-response items from the 2007 AP® Calculus BC Form B contains only one real-world question. The question involves rate of change of wind chill scenario. The mathematical problems...
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2002 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Though the items may be older, they still provide information. Released free-response items from the 2002 AP® Calculus BC exam provide teachers and pupils with information about how topics appear on the exam. Questions come from the AB...
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2004 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Given a set of questions, pupils realize the way the Calculus BC free-response exam asks questions. The items include both contextual and non-contextual questions. Both types are split into the calculator and non-calculator sections for...
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2003 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
There are shaded areas, particles, polar equations, oh my! Teachers use the materials to see how their pupils compare to the AP® Calculus BC exam expectations. Scholars use the released items to practice on several BC topics and become...
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1998 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Take a peek into the exam. Released items from the Calculus AB exam provide pupils insight into how questions appear on the exam. The six questions range from finding the area under a curve and the volume of the revolution to working...
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2005 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop an awareness of the exam. Pupils and teachers use the six release free-response questions to see how the exam covers topics. The questions are divided among calculator and non-calculator items. Scholars see the importance of...
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1998 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Provide a test run. Pupils use the questions to practice taking the free-response section of the AP® Calculus BC exam. Teachers see the different ways questions appear on the exam to prepare individuals for whatever comes their way on...
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2001 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Take an abbreviated look at the exam. Class members review released items to prepare for the BC exam. The released questions are the six free-response questions from the 2001 exam. Three of the items have context, while the other three...
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2002 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Where do the questions come from? Individuals examine released items and see the topics included. Teachers use the materials to see the distribution between strictly BC content and that which is shared with AB. The 2002 Calculus BC is...
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2006 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Move along with the review. Teachers and scholars use the six released free-response questions to review for their upcoming AP® exam. Questions from the 2006 exam contain problems dealing with cars, objects moving along a curve, and...
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Differentials

For Teachers 11th - Higher Ed
Students investigate Differential equations using derivatives. In this calculus lesson, students solve problems of differential equations by taking the derivative and explaining the changes that occurred in the equation. They define the...
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Review for Test on Derivatives.

For Teachers 12th - Higher Ed
Students review derivatives and equations for their test. In this calculus lesson, students review average rate, parametric equations, tangent line to a curve and value of a derivative to prepare and show mastery on a chapter test. They...
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Slope Fields

For Teachers 12th
Twelfth graders define and sketch slope fields. In this calculus lesson plan, 12th graders investigate solving differential equations through slope field graphs and algebraic equations. They use slope fields to check their work for the...
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Mini Exam on Calculus

For Students 11th - 12th
In this calculus worksheet, students differentiate equations and calculate rate of change. They find the area and volume under a curve. There are 18 questions on this test.
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Differential Equations and Population Growth

For Teachers 9th - 10th
Learners determine the size of the population at a given time. They calculate the time at which the population will be a given number. They observe how the population grows at the rate that is directly proportional to the number of...
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Roller Coaster Robot

For Teachers 10th - 12th
Students calculate the area under a curve. In this calculus lesson, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
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Differentials

For Teachers 10th - 12th
Students investigate Differential equations using derivatives. For this calculus lesson, students solve problems of differential equations by taking the derivative and explaining the changes that occurred in the equation and circle. They...
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Worksheet 6

For Students 11th - Higher Ed
In this math worksheet, students solve the differential equations. They also investigate Newton's Law of Cooling. Then they consider the temperature of different substances like coffee.
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Worksheet 6 - Series

For Students Higher Ed
In this series learning exercise, students evaluate a series of functions, graph the points and express functions in terms of cosine and sine. They solve first-order linear equations and solve differential equations. This one-page...
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Slope Field Solutions

For Teachers 12th - Higher Ed
In this slope field worksheet, students draw possible solution curves to a differential equation. Three problems are provided on this on-page worksheet.
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Wind, Pressure, Force, Calculus and Engineering Connections

For Teachers 12th
Twelfth graders solve first order differential equations using the separation of variables technique. In this calculus lesson, 12th graders explain the connection between math and engineering. They brainstorm what engineers do in real life.
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Calculus Test

For Students 11th - 12th
In this calculus worksheet, students assess their understanding and knowledge of limits, derivatives, differential equations, and other calculus topics.  The one page worksheet contains twenty-eight multiple choice questions.  Answers...
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TI-Nspire™ CAS

For Students 8th - Higher Ed Standards
When it comes to rating educational calculators, this calculator is always near the top of this list. Now it's available as an app. There is a lot of calculator power wrapped up in this app. Not only is this a fully functioning...
1 In 1 Collection
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TI-Nspire™

For Students 6th - Higher Ed Standards
We landed on the moon with less computing capabilities than you can find in this app! Here is a multiple function calculator that takes all the power you get from a handheld and adds the wonderful large screen that only a tablet can...
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Calculus - Early Transcendentals

For Teachers 9th - Higher Ed Standards
This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...
EngageNY

The Graph of the Natural Logarithm Function

For Teachers 10th - 12th Standards
If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...
EngageNY

Newton’s Law of Cooling, Revisited

For Teachers 10th - 12th Standards
Does Newton's Law of Cooling have anything to do with apples? Scholars apply Newton's Law of Cooling to solve problems in the 29th installment of a 35-part module. Now that they have knowledge of logarithms, they can determine the decay...
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Torricelli's Law

For Teachers 9th - 12th Standards
Investigate velocity using Torricelli's Law! The class will have a blast solving problems involving velocity and their related equations. They create an equation to represent the flow of the water through a tank. Super helpful tips on...
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Infestation to Extermination

For Teachers 9th - 12th Standards
Students solve problems with exponential growth and decay. In this calculus lesson, students relate exponential functions to infestation and extermination. They take the derivative to find their answer.
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Limits and Derivatives

For Students 11th - 12th
In this calculus worksheet, students evaluate functions and solve problems using the derivative. They apply the rules of limits to solve functions where the limit of x approaches zero. There are 12 problems to solve.
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Representation of Complex Numbers

For Teachers 9th - 12th
Learners write complex numbers in standard form. They add, subtract, multiply and divide complex numbers correctly.
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Numerical Analysis: Polynomial Interpolation

For Students Higher Ed
In this polynomial worksheet, students find interpolating functions that can be expressed as a linear combination of basis functions. This four-page worksheet contains five multi-step problems.
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Methods of Applied Mathematics 2

For Students 11th - Higher Ed
In this chain rule and directional derivatives worksheet, students solve 4 different word problems related to determining points. First, they find the rate at which a trees volume grows per year when its radius is a particular number and...
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Math Ref

For Students 7th - 12th
Forgot how to multiply matrices? Well, this app can help. It is like a gigantic, well-organized reference card for all things math. Customize your personal reference material by adding your own notes and build up a personalized list of...
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Integration By Parts

For Teachers 11th - 12th
This lesson plan provides an introduction to integration by parts. It helps learners first recognize derivatives produced by the product rule and then continues with step-by-step instructions on computing these integrals. It also shows...
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Maxima and Minima Problems

For Teachers 11th - 12th
Learners calculate the maxima and minima of quadratic equations. In this calculus lesson, students apply the derivatives by finding the maxima and minima using real life application. They solve optimization using the derivative. 
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Pendulum Motion

For Teachers Higher Ed
Students explore questions which cannot be handled with simple pendulums, and examine both the usefulness and the limitations of approximations in science. A Java applet created from a Stella model is included.
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Worksheet 7. Sir Isaac Newton

For Students Higher Ed
For this Newton worksheet, students obtain parametric equations, graph them on a graphing calculator, plot the trajectory of an object and sketch conic sections, This three-page worksheet contains 16 problems.
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Complex Analysis: Analyticity and Harmonic Functions

For Students Higher Ed
In this harmonic function worksheet, students summarize the theorems on analyticity, differentiability and the Cauch-Rieman equation. They identify the characteristics of a harmonic function. This three-page worksheet contains...
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Even More Calculus

For Students 12th
In this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts.  The twenty-two page worksheet contains explanation of the topic,...
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Stability of Equilibrium Values

For Students Higher Ed
In this stability of equilibrium values worksheet, students explore equilibrium solutions and classify them as asymptotically stable or not asymptotically stable. They justify their reasoning. This four-page worksheet contains five...
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Math 53 - Midterm 1 Review

For Students 11th - Higher Ed
In this math worksheet, students eliminate the parameter to find a Cartesian equation of the curve given by the parametric equations.
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Continuous Growth and e

For Teachers 7th - 9th
Students estimate the value of e. In this algebra lesson, students write positive number using powers and approximate the value of e. They differentiate between nominal and effective interest rate.
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Trigonometric Models

For Teachers 10th - 11th
Learners solve trigonometric functions using the identity property. In this trigonometry lesson, students find the inverse of trig functions. They calculate horizontal shifts, the period, the midline and the amplitude.
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Features of the TI-89 that Maximize is Use

For Teachers 9th - 12th
High schoolers explore the TI-89.  In this secondary mathematics lesson, students explore special features of the TI-89 that maximize its effectiveness including folder, files and management techniques. 
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Linear Systems: Symmetric Matrices

For Students 12th - Higher Ed
In this symmetric matrices worksheet, students explore the characteristics of symmetric matrices. This two-page worksheet contains examples and explanations concerning symmetric matrices. Two problems are provided to solve.
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Calculus at the Battle of Trafalgar

For Teachers 12th - Higher Ed
Students read an article on how calculus is used in the real world. In this calculus instructional activity, students draw a correlation between the Battle of Trafalgar and calculus. The purpose of this article is the show everyday uses...
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NUMB3RS Activity: Up to Speed

For Teachers 10th - 12th
Students explore traffic flow theory.  In this secondary mathematics activity, students investigate a very basic traffic flow model that predicts the location of a single vehicle in a line of tragic.  Students use a spreadsheet to model...
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Comparing Exponential and Linear Functions

For Teachers 9th - 10th
Learners solve and graph exponential functions. In this algebra lesson, students identify function notations and discuss the different properties of exponential functions. They relate linear functions to the real world.
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Solving Initial Value Problems

For Teachers 12th - Higher Ed
Learners explore derivatives and antiderivatives using the TI. In this calculus lesson, students relate integrals to real life scenarios. They identify the antiderivative through graphing.
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Numerical Determination of Drag Coefficients

For Teachers 11th - 12th
Students create a video of an object falling with a drag. In this physics lesson, students calculate drag coefficient using data from Logger Pro. They calculate velocity and acceleration of the object.