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Linear Systems
In this linear systems learning exercise, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the...
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Linear Systems: Graphical Interpretation of Vectors
For this graphical interpretation of vectors worksheet, students execute operations of addition and multiplication by a scalar. They sketch results and determine the commutativity of vector addition. This three-page worksheet contains...
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Linear Systems: Identifying Pivots and Multipliers
In this identifying pivots worksheet, students use algebra to find equivalent systems of equations. This four-page worksheet contains examples, explanations and approximately ten problems.
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Linear Systems: Graphical Interpretation of Vectors and Linear Systems
In this interpretation of vectors and linear systems worksheet, students describe the geometric appearance of two vectors. They add the two vectors and sketch the sum as well as the vectors to determine the commutativity of vector...
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Linear Systems: Review of Vectors
In this review of vectors worksheet, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page worksheet contains approximately ten problems.
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Linear Systems: Identifying Pivots and Multipliers
In this pivot instructional activity, students explore the elimination process, and write a matrix in upper triangular form. They identify equivalent systems. This four-page instructional activity contains examples, explanations, and...
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General Solution to Ax=b
In this math learning exercise, students practice finding the vector spaces associated with the rectangular matrices. Then they find the complete solutions to the given equation using a matrix.
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Properties of the Definite Integrals
For this math worksheet, students investigate the properties of definite integrals. Then they apply the properties and compare sets of two integrals to each other.
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Linear Functions and Piecewise Linear Functions
An activity that could function as a review or as a quiz, this worksheet prompts students to find two different linear functions that satisfy the given equation. Students sketch the graph of two linear equations. They identify the domain...
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Numerical Analysis: Systems of Linear Equations
In this linear equation worksheet, students use the iterative method to solve systems of equations. Explanations and examples are provided. This four-page worksheet contains approximately three problems.
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Linear Systems: The Determinant
In this determinant learning exercise, students find the determinants of matrices. They identify patterns and their relationship to the canonical matrix. This two-page learning exercise contains approximately nine problems, as well as ...
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Linear Systems: Vector Spaces
In this vector spaces worksheet, learners explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...
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Linear Systems: Independence, Basis and Dimension
In this basis and dimension worksheet, students explore vector spaces associated with rectangular matrices. The two-page worksheet contains approximately 20 short answer questions.
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Linear Systems Class Overview
In this math worksheet, students find the solutions to the problems using the linear systems of equations. The sheet is a list of review topics.
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Linear Systems: Matrix Operations
In this matrix operations worksheet, students find the dot product of matrices. They use the elimination method to solve linear equations. This two-page worksheet contains explanations, examples and three problems.
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Comparing Improper Integrals
In this math worksheet, students compare the improper integrals. They determine if each integral converges or diverges. The improper integral test is read and applied.
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Introduction to Accumulation
In this math worksheet, students work in groups to estimate the area of the ellipses using the grids. Then they estimate the arclengths of the ellipses.
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Implicit Differentiation
In this implicit differentiation worksheet, students solve problems using the chain rule and implicit differentiation. They explain the differences between the chain rule and the implicit differentiation. This two-page worksheet...
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Average Velocity, Instantaneous Velocity, and Slope
For this velocity worksheet, students determine the average velocity for given situations. They graph the distance traveled, and compute velocity at time intervals. This two-page worksheet contains eleven problems.
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Average and Instantaneous Velocity
In this velocity worksheet, students determine the average velocity for a trip, graph the distance traveled as a function of time, estimate the slope and identify the instantaneous rate of change of the function. This two-page worksheet...
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Sounds of the Wetlands
Students identify the sounds of different bird calls. In this biology lesson, students create a sound map. They explain how this method is important in tracking wildlife.
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Numerical Analysis
In this numerical analysis worksheet, students plot functions, predict the number of iterations, and identify the convergence criteria of the function. This two-page worksheet contains eight problems.
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Numerical Analysis: Nonlinear Equations
In this nonlinear equations worksheet, students use iterative methods for solving systems of nonlinear equations. This four-page worksheet contains eight multi-step problems.
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Complex Analysis: Harmonic Functions
In this harmonic function learning exercise, students explore harmonic functions and construct a harmonic conjugate. This three-page learning exercise contains three problems, with explanations and examples.
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