N-Q.IA.3 Understand, analyze, apply, and evaluate some common voting and analysis methods in addition to majority and plurality, such as runoff, approval, the so-called instant-runoff voting (IRV) method, the Borda method and the Condorcet method.
Understand and apply some basic mathematics of information processing and the Internet.
N-Q.IA.4 Describe the role of mathematics in information processing, particularly with respect to the Internet.
N-Q.IA.5 Understand and apply elementary set theory and logic as used in simple Internet searches.
N-Q.IA.6 Understand and apply basic number theory, including modular arithmetic, for example, as used in keeping information secure through public-key cryptography.
N-CN The Complex Number System
Perform arithmetic operations with complex numbers.
N-CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Represent complex numbers and their operations on the complex plane.
N-CN.4 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.
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||, v).
N-VM.4.c 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.
N-VM.5.b 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).
N-VM.10 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.
Extend the domain of trigonometric functions using the unit circle
F-TF.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
Explain volume formulas and use them to solve problems
G-GMD.2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
Visualize relationships between two-dimensional and three-dimensional objects
G-GMD.IA.7 Plot points in three-dimensions.
G-MG Modeling with Geometry
Use diagrams consisting of vertices and edges (vertex-edge graphs) to model and solve problems related to networks.
G-MG.IA.8 Understand, analyze, evaluate, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings.
G-MG.IA.9 Model and solve problems using at least two of the following fundamental graph topics and models: Euler paths and circuits, Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, vertex coloring.
G-MG.IA.10 Compare and contrast vertex-edge graph topics and models in terms of: properties, algorithms, optimization, types of problems that can be solved.
S Statistics and Probability
S-MD Using Probability to Make Decisions
Calculate expected values and use them to solve problems
S-MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.