Flipped Math
Calculus AB/BC - Using the Mean Value Theorem
At some point the rate of change must be the average. Pupils first see the definition of the Mean Value Theorem and hear an explanation of it in simple terms. The helpful video then compares the Mean Value Theorem with the Intermediate...
CK-12 Foundation
Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
Curated OER
Mean Value Theorem - An Application
In this mean value learning exercise, students read a short story problem about driving from one city to another. They use the given information and the mean value theorem to determine why an officer stopped the driver and issued a...
Curated OER
Mean Value Theorem
In this Mean Value Theorem, students determine values of a function. They identify the domain, main, maximum and minimum values of a function. This two-page worksheet contains three problems.
Curated OER
Worksheet 15-Fall 1995
For this math worksheet students use the intermediate value theorem to solve two problems. They find parallel lines that will cut a convex shape into two pieces with equal areas. Students repeat this problem with a concave shape....
Texas Instruments
Mean Value Theorem
Young scholars 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.
Curated OER
Intervals
In this intervals worksheet, high schoolers determine the coordinates at a point of inflection. They compute the deritative of a function and sketch curves that satisfy given conditions. Students solve equations using the Mean Value...
Curated OER
Rolle's Theorem and the Mean Value Theorem
Twelfth graders investigate the applications of the mean value theorem. In this calculus instructional activity, 12th graders apply the concepts of the mean value theorem to real life scenarios problems and relate it to Rolle's theorem....
Flipped Math
Calculus AB/BC Mid-Unit 5 Review: Analytical Applications of Differentiation
It's time to put analytical applications to work. Learners use the eight questions of the mid-Unit 5 review to refresh their memories of the key points. Pupils apply what they have learned to use the Mean Value Theorem, find extrema...
Curated OER
Challenge Discussion Sheet 6
Learners are challenged to determine values that are guaranteed by the mean value theorem. They sketch the graph of a function and show that it satisfies the conditions of the mean value theorem over a given interval. Students determine...
Curated OER
MVT for Derivatives
Young scholars find the derivative using the mean value theorem in this calculus lesson plan. They find the slopes of secant and tangent lines, then analyze the function and identify the slope.
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...
Curated OER
AP Calculus Practice Exam
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.
Curated OER
#3 Differential Calculus
Students create models of the Mean Value Theorem. In this Mean Value lesson, students use their knowledge of derivatives and exponential functions to explore the Mean Value Theorem. They illustrate the meaning of the throrem, create...
College Board
Differentiability of Piecewise Defined Functions
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®...
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
MVT for Integrals
Students identify the meaning of the Mean Value Theorem. In this calculus lesson, students solve problems using the definite integral. They calculate the average value of a function.
EngageNY
Applications of the Pythagorean Theorem
Begin seeing the world through the lens of geometry! Use the 19th installment in a 25-part module to apply the Pythagorean Theorem to solve real-world problems. Individuals sketch situations resulting in right triangles such as the...
College Board
2018 AP® Calculus BC Free-Response Questions
Don't just rely on the textbook. Released items from the AP Calculus BC provide pupils and teachers insight on how topics appear on the exam. The six items are divided into calculator and non-calculator sets with half of them also...
Curated OER
Complex Analysis: Theorems Following Cauchy's Integral Formulas
In this integral formula, students explore how theorems are derived. They write proofs supporting Cauchy's Inequality, Liouville's Theorem, the Fundamental Theorem of Algebra, Gauss' Mean Value Theorem and Cauchy's Residue Theorem. ...
Curated OER
T Points from Directions
Here is a lesson that starts with having geometers translate points using compass directions into an accurate picture of the problem. Then they must use their knowledge of the Pythagorean theorem or similar triangles to solve. This makes...
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
2018 AP® Calculus AB Free-Response Questions
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.
College Board
2007 AP® Calculus AB Free-Response Questions
Grow your knowledge of Calculus AB. Items released from the 2007 AP® Calculus AB exam provide information to teachers about the importance of particular topics. Pupils use the questions to gain an understanding of ways the exam assesses...