### N: Number and Quantity

#### N.VM: Vector and Matrix Quantities

N.VM.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.

Adding Vectors

Vectors

N.VM.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.

Adding Vectors

Vectors

N.VM.4: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum, including vectors in complex vector spaces.

Vectors

N.VM.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.

Adding Vectors

Vectors

N.VM.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 × 2.

Dilations

Reflections

Rotations, Reflections and Translations

N.VM.10: Work with 2 × 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.

Real Number Line - Activity B

### A: Algebra

#### A.APR: Arithmetic With Polynomials and Rational Functions

A.APR.15: Reduce the degree of either the numerator or denominator of a rational function by using partial fraction decomposition or partial fraction expansion.

General Form of a Rational Function

Rational Functions

### F: Functions

#### F.TF: Trigonometric Functions

F.TF.16: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Unit Circle

F.TF.18: Apply Euler?s and deMoivre?s formulas as links between complex numbers and trigonometry.

Points in the Complex Plane - Activity A

Correlation last revised: 3/17/2015