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Illustrative Mathematics

Equivalent Expressions?

For Teachers 7th - 8th Standards
Pre-algebra pupils need to understand that two expressions are only equal if they have the same value. Show them that once the expression is multiplied by a number, the value of the expression changes. It makes for a good lead-in to...
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Linear Systems: Vector Spaces and Subspaces

For Students 12th - Higher Ed
In this vector space worksheet, students find the column space of given matrices, the identify the vector space and determine if the matrix is invertible. This four-page worksheet contains approximately six multi-step problems.
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Worksheet 6 - Vector

For Teachers Higher Ed
In this vector worksheet, students draw simple pictures, identify the positions of the vectors, write equations to describe vector location. This two-page worksheet contains four multi-step problems.
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Worksheet 13 - Implicit Differentiation

For Teachers Higher Ed
In this implicit differentiation worksheet, students differentiate expressions and identify the derivative of a function. This one-page worksheet contains six multi-step problems.
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Worksheet 32 - Antiderivative

For Teachers Higher Ed
In this antiderivative worksheet, students determine the antiderivative by using substitution. They evaluate integrals. This one-page worksheet contains approximately six multi-step problems.
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Equilibria 1

For Teachers 9th - 12th
In this equilibria worksheet, students answer 5 multi-step questions which pertain to equilibrium expressions and concentrations.
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Probability

For Students 7th - 9th
Middle schoolers explore independent probability. They identify mutually exclusive outcomes. This two-page instructional activity contains four multi-step problems.
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Worksheet 21 - Vector

For Teachers Higher Ed
In this vector worksheet students find the geometric interpretation of the change in a vector. They identify vector fields for specified functions. This two-page worksheet contains five multi-step problems.
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Worksheet 5 - Vectors & Physics

For Teachers Higher Ed
In this vectors worksheet, students determine the amount of work it takes to move objects, they determine if vectors are parallel or orthogonal and identify the displacement direction and the force direction. This one-page worksheet...
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Worksheet 15 - Differentiation

For Teachers Higher Ed
In this differentiation worksheet, students determine the seconds of motion, identify the constant, and speed of movement. This two-page worksheet contains five multi-step problems.
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Worksheet 7 - Asymptote

For Teachers Higher Ed
In this asymptote worksheet, students compute limits, graph vertical asymptotes, and find the slope of the secant line. This one-page worksheet contains six multi-step worksheets.
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Worksheet 8 - Limit of Slopes

For Teachers Higher Ed
For this limit of slopes worksheet, students compute the limit of slopes, find the slope of the secant line, and determine the slope of the tangent line. This one-page worksheet contains five multi-step problems.
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Worksheet 9 - Functions

For Teachers Higher Ed
For this function worksheet, students explain continuous and noncontinuous function and graph derivatives. This two-page worksheet contains seven multi-step problems.
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Worksheet 12 - Differentiable Functions

For Teachers Higher Ed
In this differentiable function worksheet, students identify differentiable functions and calculate the derivative of a function. This two-page worksheet contains eight multi-step problems.
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Curved Lines

For Students 10th - Higher Ed
In this curved lines worksheet, students examine equations that, when graphed, present a curved line. They explore specified points on the graphed line and write an equation for the tangent line at given points. This two-page worksheet...
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Stability of Equilibrium Values

For Students Higher Ed
In this stability of equilibrium values worksheet, students explore equilibrium solutions and classify them as asymptotically stable or not asymptotically stable. They justify their reasoning. This four-page worksheet contains five...
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Slope Fields and Euler's Method

For Students Higher Ed
In this slope field worksheet, students use a slope field for a rate equation. Using Euler's Method, they identify the piecewise linear function approximating the solution of the initial value problem. This four-page worksheet contains...
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Complex Analysis: Homework Set 5: Domain

For Students Higher Ed
In this domain worksheet, students determine the domain of analyticity for given functions. This one-page worksheet contains five multi-step equations.
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Complex Analysis: Homework Set 6 - Cauchy's Residue Theorem

For Students Higher Ed
In this residue theorem worksheet, students find the maximum and minimum values of functions. They use Cauchy's Residue Theorem to evaluate integrals of functions. This two-page worksheet contains eleven multi-step equations.
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Complex Analysis: Cauchy's Second Residue Theorem

For Students Higher Ed
In this residue theorem worksheet, students evaluate functions, they express functions in terms of a Laurent series, and recall the infinite sequence. This four-page worksheet contains explanations and examples. It includes three...
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Algebra Worksheet #5

For Students Higher Ed
In this linear equations worksheet, students solve fourteen multi-step linear equation problems. Answers are printed at the bottom of the page.
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Academic Algebra II 1st Semester Exam

For Students 9th - 12th
In the semester exam, students solve problems dealing the the discriminant of quadratic equations, systems of equations, linear equations and inequalities. Students also simplify radicals, complete squares, and find the inverse...
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Solutions of Initial Value Problems

For Students Higher Ed
In this initial value worksheet, students explore the best methods to solve rate problems. Students differentiate functions to check the initial value of problems. This two-page worksheet contains approximately ten multi-step problems.
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S-I-R Model of Disease

For Students Higher Ed
In this SIR model worksheet, students use the SIR method to determine the rate of change of people real life problems. They investigate the sequence of people infected with a disease, the number recovered, and the number of susceptible...

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