AP Test Prep
College Board

2005 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...
Worksheet
Curated OER

Part 3 of the Fundamental Theorem of Calculus

For Students Higher Ed
In this Fundamental Theorem of Calculus worksheet, students find the solution of given functions. This one-page worksheet contains five problems.
Worksheet
Curated OER

Applying the Fundamental Theorem of Calculus

For Students Higher Ed
In this fundamental theorem learning exercise, students identify the anti-derivative and write equations as an explicit function. This two-page learning exercise contains two multi-step problems.
AP Test Prep
1
1
Flipped Math

Calculus AB/BC Mid-Unit 6 Review: Integration and Accumulation of Change

For Students 10th - 12th
Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...
Worksheet
Curated OER

Nine Definite Integrals and Fundamental Theorem Of Calculus Problems

For Students 11th - Higher Ed
In this definite integral worksheet, student find the value of five definite integrals.  Student then explain why a definite integral inequality holds true.  Finally, students are given the graph of a functions and asked to...
AP Test Prep
College Board

Why We Use Theorem In Calculus

For Teachers 11th - Higher Ed
Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they...
Lesson Plan
Curated OER

Applied Fundamental Theorem of Calculus

For Teachers 9th - 12th
Students apply the Fundamental Theorem of Calculus. For this calculus lesson, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.
Lesson Plan
Curated OER

Polynomials Functions

For Teachers 9th - 12th
High schoolers factor polynomials and linear functions and apply concepts of the fundamental theorem of algebra to solve problems. They graph their solutions and analyze the graph.
Unit Plan
College Board

Vectors: A Curriculum Module for AP® Calculus BC

For Students 10th - 12th
It is all in a matter of time. The model curriculum module uses parametric equations and vectors to solve problems dealing with particle motion along a curve. At the beginning of the lesson, the unit reviews parametric equations and...
AP Test Prep
College Board

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...
AP Test Prep
1
1
Flipped Math

Calculus AB/BC - Unit 6 Review: Integration and Accumulation of Change

For Students 10th - 12th
Sometimes it's important to stop and take the time to review. Pupils look back at the second half of the unit and consider what they have learned about integration. They complete a instructional activity of review problems that assesses...
Worksheet
Curated OER

Challenge Sheet 2: Evaluate Functions

For Students Higher Ed
In this function worksheet, students evaluate integrals using the fundamental theorem of calculus. They identify the maxima and minima on intervals. This one-page worksheet contains seven problems.
Worksheet
Curated OER

Functions

For Students 12th - Higher Ed
In this functions worksheet, students solve and complete 5 different sets of problems that include determining functions on intervals. First, they define a definite integral and the Fundamental Theorem of Calculus. Then, students draw a...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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...
AP Test Prep
College Board

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...
Worksheet
Curated OER

Worksheet 2

For Students 11th - Higher Ed
In this math instructional activity, students state the definition of a definite integral. Then they describe the Fundamental Theorem of Calculus.
Worksheet
Curated OER

Understanding the Fundamental Theorem of Calculus

For Students Higher Ed
In this Fundamental Theorem of Calculus worksheet, students demonstrate their understanding of the theorem by identifying the derivative and anti-derivative of given functions. This two-page worksheet contains ten problems.
Worksheet
Curated OER

Fundamental Theorem of Calculus

For Students Higher Ed
In this fundamental theorem worksheet, students give antiderivatives of functions, find the area under a curve, and evaluate continuous functions. This two-page worksheet contains ten problems.
Lesson Plan
Curated OER

Fundamental Theorem of Calculus

For Teachers 9th - 12th Standards
High schoolers, with the assistance of their TI-84 Plus / TI-83 Plus calculators, explore and assess the connections between an accumulation function, one defined by a definite integral, and the integrand. They summarize that the...
Activity
PBL Pathways

Lake Pollution

For Students 11th - Higher Ed
Explain the timing of a lake cleanup to the EPA using calculus. A project-based learning opportunity has learners compare rate functions to compute a total change. Their solutions explain the time needed to rid a lake of pollutants.
Worksheet
Curated OER

Worksheet 25

For Students 11th - Higher Ed
In this math worksheet, students state the Fundamental Theorem of Calculus. Then they evaluate the functions and test them against the theorem.
Lesson Plan
Curated OER

Lesson #100 The Fundamental Theorem of Calculus and Area Under the Curve

For Teachers 11th - 12th
Learners explore the Fundamental Theorem of Calculus and apply the properties of definite integrals to solving equations. As a class, they explore formulas to use in evaluating integral yields in regions above and below the x-axis....