Students explore the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function. They write a paragraph describing any...

In this calculus worksheet, 12th graders solve problems that cover a variety of topics, including limits, derivatives, integrals, and problem solving.  The one page interactive worksheet contains forty-eight questions and is self...

In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series.  The one page...

You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase...

Learners identify graphical relationships between a function and its inverse using a graphing calculator. They begin by declaring the function f(x) with formula definition sin(x), then plot this function. To finishing the lab, they check...

Take an abbreviated look at the exam. Class members review released items to prepare for the BC exam. The released questions are the six free-response questions from the 2001 exam. Three of the items have context, while the other three...

The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...

There's value in using a video to analyze a table of values. Pupils learn how to find the limit of a function from a table of values in the fourth of 18 lessons in Unit 1 - Limits and Continuity. An engaging video gives a tutorial on how...

A one-sided limit need not be half as interesting as a two-sided limit. Pupils learn the notation for one-sided limits and how to determine the value of a one-sided limit from graphs by watching a short video. They then see how to create...

There's no limit to what one can learn about limits. The second of 18 videos in Unit 1 - Limits and Continuity focuses on understanding the basic concept of a limit. Pupils learn the definition of limits and see how to determine a limit...

Sometimes a little manipulation goes a long way. The sixth of 18 videos in Unit 1 - Limits and Continuity shows viewers how to use algebraic manipulation to determine limits. They first use substitution and factoring, then apply special...

Sandwich the video in between lessons. Scholars learn about the Squeeze Theorem, or Sandwich Theorem, in the eighth of 18 videos in Unit 1 - Limits and Continuity. After seeing a few examples, they look at different situations to...

Knowing more strategies is always a plus. Pupils watch an engaging video to learn additional ways to algebraically determine the limit of a function at a specified value. The video covers multiplying radical expressions by their...

It's time to put it all together. Viewers of an informative video learn to connect multiple representations of limits. Given algebraic, tabular, and graphical representations of a linear piecewise function, they determine whether a limit...

Acquire expert-level knowledge in the Intermediate Value Theorem. Viewers of an informative video learn about the Intermediate Value Theorem. After learning the definition, they consider several examples where they must apply the theorem...

It's called a removable discontinuity for a reason. After reviewing the conditions for a removable discontinuity to exist, scholars watch an informative video to learn how to remove the discontinuity. They look at several examples...

Confirm one's expertise with confirming continuity over an interval. Pupils first review how to determine the domain of a function taking denominators, roots, and logarithms into account. They then connect this concept to continuity in...

Infinite limits just got infinitely more interesting. The 15th of 18 installments in Unit 1 - Limits and Continuity looks at infinite limits and vertical asymptotes of rational functions. Scholars review how to determine the locations of...

Learning about end behavior means it's close to the end of the unit. The 16th of 18 lessons in Unit 1 - Limits and Continuity has scholars watch a video to learn how limits at infinity can be used to determine horizontal asymptotes and...

It is critical to find all the extreme points. Pupils analyze graphs in the presentation to determine whether there are points that are either maximums and minimums. Using derivatives, learners find out how to find critical points from...

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...

Going up? Wait, it might be going down! Learners watch a video to see how to use the derivative and critical points to find where a function is either increasing or decreasing. Individuals use the rate of change to solve real-world...

Absolutely! Find the global maximum and minimums. Pupils watch a video showing how to find the absolute maximums and minimums of a function on an interval by testing critical points. The learners see how to determine whether a critical...

Take a second look at extrema of functions. Pupils learn how to use the second derivative to determine whether a critical point is a maximum or a minimum. Learners use concavity to identify critical points as either a max or a min and...