HSN.RN.A Extend the properties of exponents to rational exponents.
HSN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
HSN.RN.B Use properties of rational and irrational numbers.
HSN.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
HSN.Q.A Reason quantitatively and use units to solve problems.
HSN.Q.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.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.
HSN.VM.A Represent and model with vector quantities.
HSN.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?.
HSN.VM.4c Understand vector subtraction ?? – ?? as ?? + (–??), where – ?? is the additive inverse of ??, with the same magnitude as ?? and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
HSN.VM.5a 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).
HSN.VM.5b Compute the magnitude of a scalar multiple c?? using ||c?? || = |c| ??. Compute the direction of c?? knowing that when | c | ?? ≠ 0, the direction of c?? is either along ?? (for c > 0) or against ?? (for c < 0).
HSN.VM.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication analogous 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.