NUMBER AND QUANTITY
 
Vector and Matrix Quantities
 
Represent and model with vector quantities.
 

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 eigenvalues and eigenvectors. [NVM1] (Alabama) 


2 ) (+) Solve problems involving velocity and other quantities that can be represented by vectors, including navigation (e.g., airplane, aerospace, oceanic). [NVM3] (Alabama) 


3 ) (+) Add vectors endtoend, componentwise, 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. [NVM4a] (Alabama) 


4 ) (+) Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces. [NVM4b] (Alabama) 


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 componentwise, including vectors in complex vector spaces. [NVM4c] (Alabama) 

Perform operations on matrices and use matrices in applications.
 

6 ) (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network, including linear programming. [NVM6] (Alabama) 


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. [NVM7] (Alabama) 


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. [NVM10] (Alabama) 


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. [NVM11] (Alabama) 


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. [NVM12] (Alabama) 

Complex Numbers
 
Use complex numbers in polynomial identities and equations.
 

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. [NCN9] (Alabama) 

Limits
 
Understand limits of functions. (Alabama)
 

12 ) Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) 

ALGEBRA
 
Seeing Structure in Expressions
 

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) 


14 ) Use logic symbols to write truth tables. (Alabama) 

Arithmetic With Polynomials and Rational Functions
 

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.
 

16 ) (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [FTF4]. 

Apply trigonometry to general triangles.
 

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. [GSRT10] (Alabama) 


18 ) Apply Euler's and deMoivre's formulas as links between complex numbers and trigonometry. (Alabama) 