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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....
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AP Calculus Practice Exam

For Students 12th
In this calculus worksheet, 12th graders assess their knowledge of functions, integrals, trigonometric functions, derivatives, and limits.  The four page worksheet contains twenty-eight multiple choice questions.  Answers are...
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Computation of Limits

For Teachers 11th - Higher Ed
Students discuss the importance of limits as it relates to calculus. For this calculus lesson, students define limit and memorize the three rules of limits. They work problems to enhance their understanding of how limits function.
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Worksheet 18

For Students 11th - Higher Ed
In this math worksheet, students solve the problems using the rules of Calculus. They focus upon using trigonometric rules to investigate the functions.
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Worksheet 36

For Students 11th - Higher Ed
In this math instructional activity, learners apply the rules of Calculus to determine if each statement is true or false. If it is false they rewrite the mathematical proof to make it true.
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Enumeration

For Teachers 8th - 11th
In this calculus lesson, students review counting using the principles of Enumeration. They use random selections to count and convert word problems and count. There are 21 problems with an answer key.
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The Substitution Rule

For Students Higher Ed
In this college level Calculus worksheet, students use the Substitution Rule to evaluate the given integrals.  The one page worksheet contains nineteen problems.  Answers are not provided. 
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Intuitive Approach to Limits

For Teachers 11th - 12th
Students view examples of art work that illustrate limits in calculus. Students will lecture on limits and then complete practice drill. This lesson does not include a defined procedure or practice problems. All the art links work but...
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Limits with a Calculator

For Teachers 11th - 12th
Students investigate Limits using a graphing calculator or TI. In this calculus lesson, students solve limit problems through modeling and relation to the real world. They use correct notation and solve problems involving more than one...
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Test on Limits and Continuity

For Teachers 11th - 12th
Students review concepts of logarithms for their test. In this calculus lesson, students review inverse function, limits, derivatives and solving logs equations. They review the chain rule and domain and range of inverse logs.    
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Product Rule

For Teachers 11th - Higher Ed
Students define the product rule and use it to solve problems. In this calculus lesson, students review rules they learned and memorize the new rules as it relates to derivatives. They solve problems through differentiation by proving...
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Differentials

For Teachers 10th - 12th
Students investigate Differential equations using derivatives. In this calculus lesson, students solve problems of differential equations by taking the derivative and explaining the changes that occurred in the equation and circle. They...
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Implicit Differentiation

For Teachers 11th - 12th
Students define and use implicit differentiation to solve equations. In this calculus instructional activity, students take the derivative implicitly to find x and y values. They apply this knowledge to real life scenarios.
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Logariths

For Teachers 11th - Higher Ed
Students analyze, discuss and memorize the properties of logs. In this calculus lesson, students apply the rules of logs while playing a timed game to see which group can write the equations correctly. They walk away from this lesson...
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Related Rates

For Teachers 12th
Twelfth graders define and investigate problems involving rates. In this calculus lesson, 12th graders complete worksheets with word problems dealing with related rates, distance and time. They complete review problems on the board...
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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....
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Find the Average Value of a Function

For Students 11th
In this calculus worksheet, 11th graders calculate the average value of a function. They find the line tangent to a curve and graph the equation. There are 15 questions.
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Average Value of a Function

For Students 12th
In this calculus worksheet, 12th graders calculate the line tangent to a curve and find the average value of a function. There are 12 questions.
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Matrices

For Students 9th - 10th
In this calculus worksheet, students practice solving equations of area and integrals. There are 14 multi-step problems.
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Power and Maclaurin Series

For Students 11th - 12th
In this calculus worksheet, students solve 4 problems by finding the Power and Maclaurin series for different terms. They take the derivative and simplify functions.
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Limit Comparison Test

For Students 11th
In this calculus instructional activity, 11th graders solve 7 problems where they determine the convergence and divergence properties using the limit comparison test.
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Sherlock Holmes' Real Train Adventure

For Students 11th - 12th
In this calculus learning exercise, students use the trapezoid and Simpson's rule to calculate the midpoint sum. They use a specific interval to perform their integration. There are 12 questions.
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Barehands Integration

For Students 11th - 12th
In this calculus worksheet, students use integration to calculate the solution of functions. They use the correct notation and formula to calculate where the derivative is constant. There are 10 questions.
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The Chain Rule and an Interesting Derivative

For Students 11th - 12th
In this calculus worksheet, students use the chain rule to derive functions. They use function notations correctly as they solve word problems using the derivative. There are 3 questions.

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