Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...

Undo a function to create a new one. The inverse of a function does just that. An inquiry-based lesson examines the result of reversing the variables of a function, beginning with linear patterns and advancing to quadratic and...

Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...

In this math worksheet, pupils determine if the definite integral of given functions exist. They use a Taylor polynomial to approximate given values. Students express the arc length of a graph on a polar coordinate system as an integral.

In this math worksheet, students give examples of functions that will satisfy given conditions. Students tell the tabulations for a given function. Students use the definition of a derivative to compute the inverse of a function. they...

Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...

Natural human interest in patterns and algebraic study of function notation are linked in this introductory unit on the properties of sequences. Once presented with a pattern or situation, the class works through how to justify...

How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...

If you have ever injured your shoulder, you know it takes a while to improve your arm's range of motion. For this real-world example, young mathematicians gain insight into the world of physical therapy while they analyze a case study...

In this algebra worksheet, students use the summation notation correctly as they solve problems. They define the integral of a function and solve problems involving i. There are 14 questions with an answer key.

With just a little work, integrals can become much easier. The 11th of 16 installments in Unit 6 - Integration has viewers watch a video to learn different ways to rewrite an integrand before determining the integral. They use polynomial...

Properly apply the properties of integrals. By watching a video, scholars learn about the properties of definite integrals. They see how to use the area under a curve and the properties to determine the value of a given definite integral.

Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...

How do reverse transcriptase inhibitors work? Young virologists examine the function of azidothymidine, a drug doctors use to treat HIV patients, during a hands-on modeling activity. Groups create a strand of DNA from an HIV RNA strand...

Take the next step in separating. Pupils pick up from the previous lesson to now find the particular solution of a differential equation at a given point. Scholars watch three examples of finding the particular solution and hear the...

Turn your classroom into a greenhouse with a lesson plan on plant growth. First, investigate the different parts of seeds, identifying the seed coat, cotyledon, and embryo. Then plant the seeds and watch them grow! Measure the new...

How did Europe transition from a period of conflict to a period of sustained peace? As class members continue their study of the history and development of the European Union, groups examine the events in six time periods, from the...

In this graphing rational functions worksheet, students answer 18 multiple choice problems about rational functions.  Students determine values for a which a function is undefined given the equation of the function.

In this graphing functions worksheet, students solve four problems where they graph given functions, find the sum related to the area under the curve and determine an integral.

For this calculus worksheet, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.

In this integral learning exercise, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page learning exercise contains approximately 40...

This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...

What an impressive task it is to make dental impressions! Pupils learn how dentists use proportional reasoning, unit conversions, and systems of equations to estimate the materials needed to make stone models of dental impressions....