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Math
Virginia Math
Mathematical Analysis: Analytic Geometry
Given a translation or rotation matrix, determine an equation for the transformed function or conic section.
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Convert between standard and general forms of conic equations by completing the square.
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Graph conic sections from equations written in general or standard form using transformations.
- Ellipse equation review
- Ellipse graph from standard equation
- Ellipse standard equation & graph
- Equation of a hyperbola not centered at the origin
- Foci of a hyperbola from equation
- Graphing hyperbolas (old example)
- Intro to ellipses
- Intro to hyperbolas
- Vertices & direction of a hyperbola
- Vertices & direction of a hyperbola
Identify characteristics of conic sections including center, vertices, axes, symmetry, foci, directrix, eccentricity, and asymptotes.
- Center & radii of ellipses from equation
- Ellipse features review
- Ellipse foci review
- Equation of a hyperbola not centered at the origin
- Foci of a hyperbola from equation
- Foci of a hyperbola from equation
- Foci of an ellipse from equation
- Foci of an ellipse from equation
- Foci of an ellipse from radii
- Graph & features of ellipses
- Graphing hyperbolas (old example)
- Intro to ellipses
- Intro to focus & directrix
- Intro to hyperbolas
- Parabola focus & directrix review
- Proof of the hyperbola foci formula
- Vertices & direction of a hyperbola
- Vertices & direction of a hyperbola
Represent applications of conic sections.
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Graph and analyze parametric equations and use the graph to determine solutions.
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Use parametric equations to model contextual problems, including motion over time.
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Perform the operations of addition, subtraction, and scalar multiplication, graphically and algebraically on vectors.
- Add & subtract vectors
- Add vectors: magnitude & direction
- Adding & subtracting vectors
- Analyzing scalar multiplication
- Graphically add & subtract vectors
- Graphically adding & subtracting vectors
- Graphically subtracting vectors
- Scalar multiplication
- Scalar multiplication of vectors
- Vector addition & magnitude
- Vector word problems
- Vectors word problem: hiking
Find the dot (inner) product of two vectors and use it to determine the angle between two vectors.
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Determine if two vectors are orthogonal.
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Express complex numbers in vector notation.
Verify properties of the dot product.
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Determine the components of a vector.
- Components of vectors
- Components of vectors
- Components of vectors (example 2)
- Direction of vectors from components: 1st & 2nd quadrants
- Direction of vectors from components: 3rd & 4th quadrants
- Vector components from magnitude & direction
- Vector components from magnitude & direction
- Vector components from magnitude & direction (advanced)
- Vector magnitude and direction review
- Vectors word problem: pushing a box
Determine the norm (magnitude) of a vector.
Find a unit vector in the same direction of a given vector.
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Apply vectors to problems in context.
Classify polar equations (rose, cardioid, limaçon, lemniscate, spiral, and circle), given the graph or the equation.
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Determine the effects of changes in the parameters of polar equations on the graph, using graphing technology.
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Convert between polar and rectangular forms of coordinates.
Convert between complex numbers written in rectangular form and polar form.
Convert equations between polar and rectangular forms.
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Determine and verify the intersection of the graphs of two polar equations, using graphing technology.
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Multiply matrices by a scalar.
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Add, subtract, and multiply matrices.
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Represent problems with a system of no more than three linear equations.
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Express a system of linear equations as a matrix equation.
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Solve a system of equations using matrices.
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Determine the inverse of a two-by-two or three-by-three matrix using paper and pencil.
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Verify two matrices are inverses using matrix multiplication.
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Verify the commutative and associative properties for matrix addition and multiplication.
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