N-RN: The Real Number System
N-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.
Exponents and Power Rules
N-CN: The Complex Number System
N-CN.1: Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.
Points in the Complex Plane
N-CN.2: Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Points in the Complex Plane
N-CN.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Points in 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.
Points in the Complex Plane
N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.
Roots of a Quadratic
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., ??, |??|, ||??||, ??).
Vectors
N-VM.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Vectors
N-VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.
2D Collisions
Golf Range
N-VM.4: Add and subtract vectors.
N-VM.4.a: 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.
Adding Vectors
Vectors
N-VM.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
Adding Vectors
Vectors
N-VM.5: Multiply a vector by a scalar.
Dilations
N-VM.5.a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(???, ?? subscript y) = (c???, c?? subscript y).
Dilations
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.
Circles
Ellipses
Hyperbolas
Parabolas
Points, Lines, and Equations
N-VM.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Dilations
Translations
Correlation last revised: 12/27/2023