All's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time.

Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...

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...

This pre-calculus worksheet is short, yet challenging. High schoolers calculate the limit of piecewise functions, rational functions, and graphs as x approaches a number from the positive or negative side. There are four questions.

Algebra II classes solve problems relating to piecewise functions, step functions, and decomposition/composition of functions. They utilize links to work with real world examples. Mr. Pleacher has added humor to the lesson by including...

High schoolers factor polynomials and linear functions and apply concepts of the fundamental theorem of algebra to solve problems. They graph their solutions and analyze the graph.

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®...

See calculus to the end. The eBook is the last of a three-volume series covering college-level calculus topics. Scholars begin with parametric equations and polar coordinates before moving to vectors, finally ending with multi-variable...

It's time to take stock of the class's knowledge of derivatives. Individuals review how to take the derivatives of composite, implicit, and inverse functions. They complete some problems involving the Chain Rule, implicit...

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

Test the limits of one's knowledge on continuity. The last of 18 installments in Unit 1 - Limits and Continuity is an end-of-unit review learning exercise. Individuals identify and classify discontinuities, investigate continuity at a...

Tie up everything in one differentiable bow. Pupils work through 20 problems to review the concepts from the unit. The problems range from finding the average rate of change to finding the derivatives of various functions that require...

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 a closer look at continuous functions within given intervals. Using the parent cubic function, learners explore properties of continuous functions on intervals. Pupils interpret the Intermediate Value Theorem and the Extreme Value...

Strengthen your understanding of logistic functions. Young mathematicians change the carrying capacity of a logistic function and see how function values change. The function models the number of members in a gym over time.

Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...

There's no easier test than the vertical line test. Learners drag a vertical line across the graphs of several relations in an interactive. They answer a set of challenge questions that focus on whether the graphs represent functions.

There is zero reason not to use the resource. Given a graph with a polynomial function and a linear function, scholars move the line in an interactive. To wrap up the lesson, they note how zeros and intersection points change.

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...

Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...

What kind of functions have holes in their graphs? Here, the teacher guides the class on how to use the simplified function of a rational function to aid in the graphing of the original rational function. T-tables are used in order...

Don't let your class's heart rates rise as you introduce them to differentiation ... an inquiry-based lesson helps them keep it in check! The second lesson in a three-part series asks learners to analyze the rate of change of different...

Learners practice using their knowledge of how to interpret a function and use function notation. The activity includes two questions. Given an input of a function and its output, the first question asks learners to write the ordered...

If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...