Calculus Teacher Resources
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Students use the relationship between volume and surface area to construct a box out of a piece of paper that maximizes volume using a table and by using graphing and calculus techniques.
In this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts. The twenty-two page worksheet contains explanation of the topic, numerous worked examples, and sixteen multi-part practice problems. Answers are not provided.
There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true.
Students explore and create functions. In this calculus lesson, students create functions with the help of the Voyage 200 PLT. This assignment requires technology.
In this calculus worksheet, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant line to the curve and then using our knowledge of limits, defining the limit as _x approaches zero to get the slope of the tangent line to the curve. Along with the video, there is an interesting practice module that models the connection between the slopes of the tangent lines and the derivative of a function.
Students investigate integral calculus. In this calculus lesson, students investigate the relationship between the area above and below the curve using integral calculus. Students look for a general rule for area above: area below.
Students investigate integral calculus. In this calculus lesson, students explore an application of integrations through a leaking hot tub problem. The activity emphasizes using the integral of a rate of change to give the accumulated change.
Twelfth graders explore integral calculus. In this calculus lesson, 12th graders explore the volume and surface area of an ellipse in the context of an Easter egg problem.
Students explore integral calculus. In this calculus lesson, students explore the relationship between the area under the graph of a functions and the integral of the function. Students also discover the rule for the integral of f(x)=ax^n.
Students are introduced to a scenario of a beach race in which the equation to be figured out is should the contestant aim to land on the beach to minimize their total time for the race. They solve this optimization problem involving different levels of calculus.
Twelfth graders investigate slope fields. In this Calculus lesson, 12th graders identify whether a slope field appropriately reflects a differential equation by matching. TI-83 Plus/TI-84 Plus and appropriate programs are required to complete the lesson.
Students compute the longest piece of furniture that can be taken around a corner. In this application of calculus problem, students use their TI-84 calculator to compute the size of the largest piece of furniture that can be taken around two corners. They first ignore all measurements except length, then compute allowing for depth of an object. There are ten exercises with varying degrees of directions that lead the student through the process.
In a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how you can draw an approximate graph of the original function. He also does a quick explanation which proves that a quadratic function has no inflection point.
Using what one learned about finding the minimum and maximum of functions, the optimization problem to find two numbers whose product is -16 and whose sum of squares is a minimum is solved. Sal starts by writing the equations and defining them in terms of only one variable, then finds the minimum point by using the first derivative, and finally proves he has a minimum point by finding the second derivative.
Learn to solve functions by taking the derivatives. In this calculus lesson, students compare the graph of a derivative to that of the original function.
Learners investigate the slopes and parametric equations. In this calculus lesson, students solve parametric equations with specific parameters. They relate lines and slopes based on the derivative of the equation.
High schoolers graph polar graphs. In this calculus lesson, students convert between polar and rectangular coordinates. They graph their solution on the TI calculator and make observations.
Twelfth graders investigate limits. In this Calculus lesson, 12th graders use the Ti-89 calculator to explore limits. Students examine the tables and graphs to approach limits from a numerical point of view.
Twelfth graders investigate applications of integration. In this Calculus lesson, 12th graders use the TI-89 to explore various problem solving techniques including symbolic, graphical, and numeric methods of solving applications of integrals.