College Board
2003 AP® Calculus AB Free-Response Questions
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...
College Board
2012 AP® Calculus BC Free-Response Questions
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,...
College Board
2008 AP® Calculus AB Free-Response Questions
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...
College Board
Vectors: A Curriculum Module for AP® Calculus BC
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...
PBL Pathways
Lake Pollution
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.
Curated OER
Understanding the Fundamental Theorem of Calculus
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.
PBL Pathways
Total Cost to Produce the Turbo Blender
Class members blend their knowledge of functions and problem-solving skills to provide business advice to the Turbo Blender manufacturers. Through a project-based approach, learners examine marginal cost data to produce a function....
Flipped Math
Calculus AB/BC - Unit 6 Review: Integration and Accumulation of Change
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...
Curated OER
The Fundamental Theorem
In this calculus worksheet, students solve equations and functions by taking the derivative of each equation. They apply the Fundamental Theorem of Calculus to their problems, as they solve for the limit and identify different graphs....
College Board
2006 AP® Calculus BC Free-Response Questions
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...
College Board
2003 AP® Calculus BC Free-Response Questions Form B
Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...
College Board
2011 AP® Calculus BC Free-Response Questions
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...
College Board
2005 AP® Calculus AB Free-Response Questions Form B
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.
College Board
2003 AP® Calculus BC Free-Response Questions
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...
College Board
2005 AP® Calculus BC Free-Response Questions Form B
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...
College Board
2002 AP® Calculus BC Free-Response Questions Form B
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...
Curated OER
Polynomials Functions
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.
Curated OER
Functions
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...
College Board
Why We Use Theorem In Calculus
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...
Curated OER
The Fundamental Theorem and IVP's
For this math worksheet, students practice solving the problems concerning the concept of energy consumption. They also review the Fundamental Theorem of Calculus.
Curated OER
Fundamental Theorem of Calculus
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.
Curated OER
Lesson #100 The Fundamental Theorem of Calculus and Area Under the Curve
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....
Curated OER
Linear Systems
In this linear systems learning exercise, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the...
College Board
2005 AP® Calculus BC Free-Response Questions
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...