Interactive
CK-12 Foundation

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...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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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Flipped Math

Calculus AB/BC - Sketching Slope Fields

For Students 10th - 12th
Frolic through a field of slopes. Learners watch a video describing slope fields and how to create one. Scholars use given slope fields to determine the equation of a tangent line and the possible differential equation. Pupils continue...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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.
AP Test Prep
College Board

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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Flipped Math

Calculus AB/BC - Connecting Differentiability and Continuity

For Students 10th - 12th
Despite what you thought, you can differentiate between continuity and differentiability. Using a short lesson, pupils learn how differentiability and continuity relate to each other. It provides three descriptions of when a function is...
eBook
Rice University

Calculus Volume 1

For Students 11th - Higher Ed
Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...
AP Test Prep
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Flipped Math

Calculus AB/BC - Unit 7 Review: Differential Equations

For Students 10th - 12th
Differentiate everyone's knowledge. Pupils work through nine review questions to highlight key concepts from Unit 7. Items range from finding slope fields and reasoning with them to finding general and particular solutions of...
AP Test Prep
College Board

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.
AP Test Prep
College Board

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...
AP Test Prep
College Board

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.
AP Test Prep
College Board

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...
AP Test Prep
College Board

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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Flipped Math

Calculus AB/BC - Verifying Solutions for Differential Equations

For Students 10th - 12th
Find out if it is truly the solution. An informative presentation provides viewers with multiple examples of finding the particular solution to a differential equation. Learners find out how to verify the solution by differentiating the...
AP Test Prep
College Board

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...
AP Test Prep14:45
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Flipped Math

Calculus AB/BC - Implicit Differentiation

For Students 10th - 12th
It's implied that implicit differentiation is important. Viewers of an engaging video learn the process of implicit differentiation. After watching several examples, they see how to apply implicit differentiation to find the vertical and...
AP Test Prep
College Board

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...
AP Test Prep12:31
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Calculus AB/BC - General Solutions Using Separation of Variables

For Students 10th - 12th
Viewers to learn how to solve a differential equation written implicitly. Pupils find out that they must first separate the variables to take the integral of each side before solving for y to arrive at a general solution for the...
AP Test Prep16:31
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Flipped Math

Calculus AB/BC - Exponential Models with Differential Equations

For Students 10th - 12th
Exponential models come with a shortcut. Pupils watch an example of how to determine if a differential equation is an exponential model. Learners realize the solution is in the same formula, allowing for a quick way to determine the...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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....
AP Test Prep
College Board

2014 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...