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Composition of Functions
High schoolers solve problems using the composition of functions. In this algebra instructional activity, students analyze the graph of a quadratic equation for its vertex and intercepts. they find the inverse of the function using...
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The Chain Rule and Applications
In this chain rule worksheet, students use the chain rule to differentiate compositions, and determine the value of the limits. They give reasons justifying each step of the chain theorem. This six-page worksheet contains theorems,...
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Related Rates Problems: An Application of Implicit Differentiation and the Chain Rule
In this related rates problem worksheet, students use the chain rule and implicit differentiation to solve related rate problems, such an writing an expression relating to the ripple of a circle. This three-page worksheet contains...
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Integrating Special Functions
In this math activity, students practice reading the examples of integrating special functions. The examples have the formulas included.
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Applications of Derivatives: General Rules for Optimization
In this minima and maxima worksheet, students find the global and local maxima and minima of one function. They work in small groups to solve one optimization problem. Steps for solving are listed on the page.
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Basic Ideas of Functions
In this Algebra I/Algebra II worksheet, students determine whether or not a relation is a function. Students determine the domain of a function and express the answer in interval notation. The three page worksheet contains fifty-eight...
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Variables and Functions
In this algebra worksheet, 5th graders solve 6 word problems by finding the value of variable in function tables. They use the information to solve the problems.
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Differentiation of Functions
In this differentiation worksheet, students use differentiation rules to solve given functions. This four-page worksheet contains 8 problems.
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Differentiation of Inverse Functions
Students explore the concept of differentiating inverse functions. In this differentiating inverse functions lesson, students find the first derivative of the inverse of sine function in a lecture style lesson.
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Matter and Motion 3
For this matter and motion worksheet, students solve 3 different types of problems that relate to the chain rule for multivariable functions. First, they find the rate of increase of the volume of a can and the rate of increase of the...
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Worksheet 17-Fall 1995
In this math worksheet, students find y' both implicitly and explicitly for given relations. They find y' using implicit differentiation for a given relation. Students prove the Pythagorean Theorem
Illustrative Mathematics
Foxes and Rabbits 1
Here is where algebra learners begin to understand that a function is a rule, and for each input there is exactly one output. The commentary gets bogged down with information about the predator-prey relationship between the fox and...
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Arithmetic Patterns
Pupils experience math functions as they practice their addition and subtraction skills, and fill in each table based on a given rule. There are two columns in each of the four tables. The in column is already completed and the out...
Illustrative Mathematics
Oakland Coliseum
Help algebra learners relate a real-life function that happens at the Oakland Coliseum every time the Raiders play. The resource states that the revenue of the Oakland Raiders home games is a function of the number of seats sold and the...
Flipped Math
Quadratics in Vertex Form
It looks different, but yet the same. Scholars view a video that introduces them to the vertex form for a quadratic equation. Pupils realize that though the equation looks different, its graph is still a parabola, and the key features...
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Simpson's Rule
In this Simpson's Rule worksheet, students use the Fundamental Theorem of Calculus to determine the antiderivatives and evaluate integrals. They find the midpoint of given polygons and sketch the graph of the function. This nine-page...
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Differentiation of Trigonometry Functions
In this trigonometry activity, students differentiate the different trigonometric identities. They derive the sine, cosine, tangent and inverses of these trig identities. There are 18 questions with an answer key.
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Circular Trigonometric Functions
In this Pre-calculus/Trigonometry worksheet, students estimate the amplitude, period, and horizontal and vertical translations of a graph and find a rule that models the data. The three page worksheet contains fourteen problems. Answers...
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Exploring Derivatives Using Lists
Learners explore lists and determine the derivative for that list. They use regressions to discover equations.
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Limits of Functions as Undefined X-Values and L'Hopital's Rule
In this limits worksheet, students apply L'Hopital's rule to solve four limits problems. They solve a total of eleven short answer problems. The final seven problems ask students to find the asymptotes of functions.
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Elementary Derivatives and Rules of Differentiation
In this derivative instructional activity, students use the definition of limits and derivatives to find formulas with given conditions. They find derivatives of given equations. This four-page instructional activity contains...
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L'Hopital's Rule
Students solve limit problems. In this solving limit problems lesson, students use L'Hopital's Rule. Students apply L'Hopital's Rule to functions as long as the derivative of the top function and bottom function is zero. Students...
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The Chain Rule and an Interesting Derivative
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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Getting Started with the TI-Navigator™ System: What's My Rule?
Students explore linear relationships. In this sixth through eighth grade mathematics lesson, students explore the symbolic representation of verbal descriptions of mathematical rules defining the relationship between two variables.