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STANDARDS

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US-WV

Math

West Virginia Math

High School Mathematics IV – Trigonometry/Pre-calculus: Building Relationships among Complex Numbers, Vectors, and Matrices

Perform arithmetic operations with complex numbers.

M.4HSTP.1

Fully covered
Find the conjugate of a complex number; use conjugates to find moduli (magnitude) and quotients of complex numbers.

Represent complex numbers and their operations on the complex plane.

M.4HSTP.2

Fully covered
Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

M.4HSTP.3

Fully covered
Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. (e.g., (–1 + √3 i)^3 = 8 because (–1 + √3 i) has modulus 2 and argument 120°.

M.4HSTP.4

Fully covered
Calculate the distance between numbers in the complex plane as the modulus of the difference and the midpoint of a segment as the average of the numbers at its endpoints.

Represent and model with vector quantities.

M.4HSTP.5

Fully covered
Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

M.4HSTP.6

Fully covered
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

M.4HSTP.7

Not covered
Solve problems involving velocity and other quantities that can be represented by vectors.
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Perform operations on vectors.

M.4HSTP.8

Add and subtract vectors.

M.4HSTP.8.a

Fully covered
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

M.4HSTP.8.b

Fully covered
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

M.4HSTP.8.c

Fully covered
Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.

M.4HSTP.9

Multiply a vector by a scalar.

M.4HSTP.9.a

Fully covered
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

M.4HSTP.9.b

Fully covered
Compute the magnitude of a scalar multiple cv using ||cv||=|c|*||v|| . Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Perform operations on matrices and use matrices in applications.

M.4HSTP.10

Not covered
Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
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M.4HSTP.11

Fully covered
Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled.

M.4HSTP.12

Not covered
Add, subtract and multiply matrices of appropriate dimensions.
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M.4HSTP.13

Not covered
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
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M.4HSTP.14

Partially covered
Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

M.4HSTP.15

Fully covered
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

M.4HSTP.16

Mostly covered
Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

Solve systems of equations.

M.4HSTP.17

Fully covered
Represent a system of linear equations as a single matrix equation in a vector variable.

M.4HSTP.18

Fully covered
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).