# Courses of Study : Mathematics

Number of Standards matching query: 18
NUMBER AND QUANTITY
Vector and Matrix Quantities
Represent and model with vector quantities.
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
1 ) (+) 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| |), including the use of eigen-values and eigen-vectors. [N-VM1] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
2 ) (+) Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). [N-VM3] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
3 ) (+) 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. Find the dot product and the cross product of vectors. [N-VM4a] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
4 ) (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [N-VM4b] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
5 ) (+) 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, including vectors in complex vector spaces. [N-VM4c] (Alabama)

Perform operations on matrices and use matrices in applications.
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
6 ) (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network, including linear programming. [N-VM6] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
7 ) (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled, including rotation matrices. [N-VM7] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
8 ) (+) 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. Solve matrix equations using augmented matrices. [N-VM10] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
9 ) (+) 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, including matrices larger than 2 x 2. [N-VM11] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
10 ) (+) Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Solve matrix application problems using reduced row echelon form. [N-VM12] (Alabama)

Complex Numbers
Use complex numbers in polynomial identities and equations.
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
11 ) (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understand the importance of using complex numbers in graphing functions on the Cartesian or complex plane. [N-CN9] (Alabama)

Limits
Understand limits of functions. (Alabama)
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
12 ) Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)

ALGEBRA
Seeing Structure in Expressions
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
13 ) Use the laws of Boolean Algebra to describe true/false circuits. Simplify Boolean expressions using the relationships between conjunction, disjunction, and negation operations. (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
14 ) Use logic symbols to write truth tables. (Alabama)

Arithmetic With Polynomials and Rational Functions
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
15 ) Reduce the degree of either the numerator or denominator of a rational function by using partial fraction decomposition or partial fraction expansion. (Alabama)

FUNCTIONS
Trigonometric Functions
Extend the domain of trigonometric functions using the unit circle.
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
16 ) (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [F-TF4].

Apply trigonometry to general triangles.
 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
17 ) (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. Understand Law of Sines = 2r, where r is the radius of the circumscribed circle of the triangle. Apply the Law of Tangents. [G-SRT10] (Alabama)

 Mathematics (2016) Grade(s): 9 - 12 Analytical Mathematics All Resources: 0
18 ) Apply Euler's and deMoivre's formulas as links between complex numbers and trigonometry. (Alabama)