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Nebraska Math
High School Advanced Topics: NUMBER
Students will solve problems and reason with number concepts using multiple representations, make connections within math and across disciplines, and communicate their ideas.
Use domain and range restrictions to apply an appropriate viewing window while using graphing technology.
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Compare and contrast radians and degrees as measures of angles and the reason graphing utilities tend to use radians as the default setting.
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Perform arithmetic operations with complex numbers.
- Absolute value of complex numbers
- Absolute value of complex numbers
- Add & subtract complex numbers
- Adding complex numbers
- Angle of complex numbers
- Classifying complex numbers
- Complex number absolute value & angle review
- Complex number conjugates
- Complex number conjugates
- Complex number equations: x³=1
- Complex number operations review
- Complex number polar form review
- Divide complex numbers
- Dividing complex numbers
- Dividing complex numbers review
- Graphically add & subtract complex numbers
- Intro to complex number conjugates
- Multiply & divide complex numbers in polar form
- Multiply complex numbers
- Multiplying complex numbers
- Multiplying complex numbers
- Subtracting complex numbers
- Visualizing complex number multiplication
Represent complex numbers and their operations in the complex plane.
Use complex numbers in polynomial identities and equations.
Represent quantities using bases other than decimal such as binary (base 2) or hexadecimal (base 16) and convert numbers to and from base 10.
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Explain modular arithmetic and its role in computer programming.
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Represent and model vector quantities.
- Components of vectors
- Components of vectors
- Components of vectors (example 2)
- Direction of vectors
- Direction of vectors from components: 1st & 2nd quadrants
- Direction of vectors from components: 3rd & 4th quadrants
- Equivalent vectors
- Intro to vectors and scalars
- Magnitude of a vector from components
- Magnitude of a vector from graph
- Magnitude of vectors
- Vector components from magnitude & direction
- Vector components from magnitude & direction
- Vector components from magnitude & direction (advanced)
- Vector magnitude and direction review
- Vector magnitude from initial & terminal points
- Vector word problems
- Vectors word problem: hiking
- Vectors word problem: pushing a box
Perform operations 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
Perform operations on matrices and use matrices in applications.
- Add & subtract matrices
- Adding & subtracting matrices
- Adding & subtracting matrices
- Associative property of matrix multiplication
- Defined matrix operations
- Determine invertibile matrices
- Dimensions of identity matrix
- Find the inverse of a 2x2 matrix
- Finding inverse of a 2x2 matrix using determinant & adjugate
- Intro to identity matrices
- Intro to identity matrix
- Intro to matrix multiplication
- Intro to zero matrices
- Is matrix multiplication commutative?
- Matrices as transformations
- Matrices as transformations
- Matrix from visual representation of transformation
- Matrix multiplication dimensions
- Multiply matrices
- Multiply matrices by scalars
- Multiplying matrices
- Multiplying matrices
- Multiplying matrices by scalars
- Multiplying matrices by scalars
- Properties of matrix addition
- Properties of matrix multiplication
- Properties of matrix scalar multiplication
- Transform vectors using matrices
- Using identity & zero matrices
- Using properties of matrix operations
- Zero matrix & matrix multiplication
Use vectors to communicate the geometric relationships between complex numbers in the complex plane.