Lesson Plan
West Contra Costa Unified School District

The Extreme Value Theorem

For Teachers 11th - Higher Ed
Finding the critical numbers of a function can be extreme. The lesson introduces the Extreme Value Theorem to the class with a graph. Pupils then have an opportunity to practice determining the values using an algebraic function.
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...
Handout
Curated OER

Study Guide for the Advanced Placement Calculus AB Examination

For Teachers 11th - 12th Standards
Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and...
Activity
Houston Area Calculus Teachers

Collecting Driving Data

For Students 11th - Higher Ed
Give AP Calculus classes the opportunity to check the accuracy of their calculations! A calculus activity involves the collection of data, the application of mathematics, and the analysis of the accuracy of results. Young mathematicians...
Lesson Plan
Curated OER

The First Fundamental Theorem of Calculus

For Teachers 9th - 12th Standards
Solve problems using the fundamental theorem. In this calculus lesson, students solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.
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...
Worksheet
Curated OER

AP Calculus Practice Exam

For Students 11th - 12th
In this practice exam worksheet, students solve 17 multiple choice problems. Students find derivatives, points of continuity, maximums, minimums, integrals, and area of enclosed regions.
Lesson Plan
Texas Instruments

Mean Value Theorem

For Teachers 9th - 12th Standards
Students calculate the slopes of secant lines. In this calculus lesson, students graph tangent and secant lines using the coordinate plane. They use the Ti calculator to graph and observe the lines.
Lesson Plan
Curated OER

The Second Fundamental Theorem of Calculus

For Teachers 10th - 12th Standards
Young scholars investigate the fundamental theorem of calculus. In this calculus lesson, students derive the fundamental theorem of calculus. They differentiate between the first and second theorem.
Worksheet
Curated OER

AP Calculus Practice Exam

For Students 11th - 12th
In this Calculus worksheet, learners are provided with questions that are reflective of the content of their exam.  Topics covered include derivatives, volume of a solid of rotation, local maximum and minimum, and integration. ...
AP Test Prep
College Board

Differentiability of Piecewise Defined Functions

For Teachers 10th - 12th
Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...
Worksheet
Curated OER

AP Calculus Practice Exam

For Students 11th - 12th
In this Calculus activity, students are provided with practice problems for their exam.  Topics covered include derivatives, area bounded by a curve, local maximum, instantaneous rate of change, and the volume of a solid of...
Lesson Plan
Curated OER

MVT for Derivatives

For Teachers 9th - 12th Standards
Young scholars find the derivative using the mean value theorem in this calculus lesson. They find the slopes of secant and tangent lines, then analyze the function and identify the slope.
AP Test Prep
College Board

Seeing Is Believing

For Teachers 11th - Higher Ed
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
Activity
Houston Area Calculus Teachers

Area and Volume

For Students 11th - Higher Ed
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created...
Worksheet
Curated OER

A.P. Calculus Practice Exam AB Version- Section I- Part B

For Students 11th - Higher Ed
In this A. P. Calculus AB instructional activity, students solve seventeen multiple-choice problems with a graphing calculator.  This instructional activity is designed as a practice test for the A.P. Exam and should be timed.
Worksheet
Curated OER

Applying the Fundamental Theorem of Calculus

For Students Higher Ed
In this fundamental theorem worksheet, students identify the anti-derivative and write equations as an explicit function. This two-page worksheet contains two multi-step problems.
Lesson Plan
Curated OER

AP Exam Rubrics/ Four Color Theorem

For Teachers 12th
Twelfth graders review free response questions that are present on the AP exam. In this calculus lesson, 12th graders analyze the 4 color theorem that proved 4 colors were enough to color a map while still separating adjacent countries....
Worksheet
Curated OER

Worksheet 7

For Students 11th - Higher Ed
In this math instructional activity, students examine the values of the series and determine how they could be defined as divergent. They also evaluate the Squeeze Theorem.
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...
Lesson Plan
Curated OER

Four Color Theorem

For Teachers 11th - 12th
Students identify and interpret how the Free Response questions are graded on an AP Exam. They also discuss coloring the included map, placing several examples on the board to determine the number of colors necessary to color each....
Lesson Plan
Curated OER

Gateway Arc Length

For Teachers 9th - 12th Standards
Learners differentiate and calculate the length of an arc. They define an arc and relate it to the area of a circle and integrate the function to solve the equations. Students use their TI calculators to graph the equation.