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Worksheet 1, Basic Calculus Pre-Course Review

For Students 10th - 11th
In this calculus worksheet, students review topics they need to already understand in order to be successful in a basic calculus course. Topics include functions, linear equations, coordinate graphing, piece-wise formulation, exponents,...
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Finding Slope From Two Points

For Students 8th - 10th
In this finding a slope worksheet, students find the slope of a line from given points. This two-page worksheet contains 16 problems. Answers are provided on the last page of the worksheet.
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Worksheet 13

For Students 11th - Higher Ed
In this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.
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Multiple Choice Inequalities

For Students 9th - 12th
In this inequality worksheet, students solve 10 multiple choice inequality problems.  Students determine solutions to inequalities and write linear inequalities given word problems.
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Minima/Maxima

For Students 10th - 12th
In this minima/maxima worksheet, students solve systems of equations, identify the first derivative of a quadratic equation, and find the critical point in an equation. Using Excel worksheets, students graph four equations. There are...
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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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Algebra War

For Students 9th - 10th
In this algebra worksheet, students play a game of "Algebra War". They write linear equations and evaluate functions. They work in groups as they play the game to reinforce basic algebra skills.
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Linear Systems: LU Decomposition

For Students 12th - Higher Ed
In this LU decomposition worksheet, students multiply matrices, identify the elimination matrices, and the inverse of a matrix. This three-page worksheet contains approximately six problems.
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Linear Systems: Applications of Determinants

For Students 12th - Higher Ed
In this determinant worksheet, students explore determinants, area and volume. This two-page worksheet contains explanations and examples. It provides two problems for students to solve.
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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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Linear Systems: Definition of the Nullspace

For Students 11th - Higher Ed
For this nullspace worksheet, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page worksheet contains approximately 8 problems.
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Linear Systems: Reduced Row Echelon Matrix

For Students 12th - Higher Ed
In this echelon matrix worksheet, students find the nullspace of matrices by finding the reduced row echelon. This two-page worksheet contains explanations, examples and six problems to complete.
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Linear Systems: Projections

For Students 11th - Higher Ed
For this projection worksheet, students determine the projections of a given matrix. This four-page worksheet contains explanations and examples and approximately ten problems to complete.
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Linear Systems: Vector Spaces of a Matrix

For Students 11th - Higher Ed
In this vector space matrix instructional activity, students decompose given vectors into two orthogonal pieces--one from the nullspace and another from the row space. this two-page instructional activity contains examples and...
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Linear Systems: Projections

For Students 11th - Higher Ed
In this projection activity, students determine the projections if a given matrix. They take a vector and project it onto a line and subspace. This four-page activity contains examples and approximately seven problems.
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Linear Systems: Applications of Eigenvalues and Eigenvectors

For Students Higher Ed
In this Eigenvalue activity, students examine the applications of matrix exponentiation. This four-page activity contains examples, explanations and approximately three problems to complete.
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Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors

For Students Higher Ed
In this interpretation of eigenvalues and eigenvectors activity, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
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Linear Systems: Introduction to Vector Space

For Students 12th - Higher Ed
In this vector space worksheet, students find the column spaces of given matrices. This two-page worksheet contains examples, theorems, explanations, and approximately three problems.
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Linear Systems: Symmetric Matrices

For Students 12th - Higher Ed
In this symmetric matrices worksheet, students find the eigenvalues of a matrix and discover that symmetric matrices are diagonalizable. This two-page worksheet contains examples, explanations and two problems.
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Linear Systems: Vector Spaces and Subspaces

For Students Higher Ed
In this vector spaces and subspaces worksheet, students review column spaces of matrices. They determine if the set of all 2 by 2 matrices is a vector space. Students determine if the set of all invertible 2 by 2 matrices is a vector...
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Linear Systems: Rectangular Matrices

For Students Higher Ed
In this rectangular matrices activity, students complete solutions to given matrices. They identify the pivot columns and examine the nullspace of a matrix. This four-page activity contains examples, explanations and approximately...
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Linear Systems: Column Space and Nullspace of a Matrix

For Students Higher Ed
In this column space and nullspace of a matrix worksheet, students are give a three by three matrix. They describe the kind of subspace it is. Students find the nullspace of the matrix.
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Linear Systems: Properties of the Four Matrix Subspaces

For Students Higher Ed
In this four matrix subspaces activity, students identify statements which are always true for given matrices. Students are given five matrices and a list of ten statements.
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Linear Systems: Lengths and Dot Products

For Students Higher Ed
In this dot product worksheet, students explore the multiplication of vectors. This two-page worksheet contains explanations, examples, and approximately ten problems.

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