HSN.RN.B Use properties of rational and irrational numbers
HSN.RN.B.3 Explain why the sum/difference or product/quotient (where defined) of two rational numbers is rational; the sum/difference of a rational number and an irrational number is irrational; the product/quotient of a nonzero rational number and an irrational number is irrational; and the product/quotient of two nonzero rationals is a nonzero rational.
HSN.RN.B.4 Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators.
HSN.Q.A Reason quantitatively and use units to solve problems
HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems. Choose and interpret units consistently in formulas. Choose and interpret the scale and the origin in graphs and data displays.
HSN.CN.B Represent complex numbers and their operations on the complex plane
HSN.CN.B.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). Explain why the rectangular and polar forms of a given complex number represent the same number.
HSN.VM.A Represent and model with vector quantities
HSN.VM.A.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).
HSN.VM.A.3 Solve problems involving velocity and other quantities that can be represented by vectors.
HSN.VM.B Perform operations on vectors
HSN.VM.B.4 Add and subtract vectors. 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. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. 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. Perform vector subtraction component-wise.
HSN.VM.B.5 Multiply a vector by a scalar. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; Perform scalar multiplication component-wise, e.g., as c(vx, v subscript y) = (cvx, cv subscript y). 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).
HSN.VM.C Perform operations on matrices and use matrices in applications
HSN.VM.C.6 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
HSN.VM.C.7 Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).
HSN.VM.C.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.