# Academic standards list

### High School: Number and Quantity — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### The Real Number System

CCSS.Math.Content.HSN-RN

Extend the properties of exponents to rational exponents

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values,…

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Use properties of rational and irrational numbers.

### Quantities

CCSS.Math.Content.HSN-Q

Reason quantitatively and use units to solve problems

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas;…

### The Complex Number System

CCSS.Math.Content.HSN-CN

Perform arithmetic operations with complex numbers

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.

Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

(+) 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

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the…

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of…

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of…

Use complex numbers in polynomial identities and equations

(+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).

### Vector & Matrix Quantities

CCSS.Math.Content.HSN-VM

Represent and model with vector quantities.

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use…

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Perform operations on vectors.

Perform operations on matrices and use matrices in applications.

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still…

(+) 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…

(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as…

(+) Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

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