# Government Standards

## Common Core

Assessment Exam - Common Core Math - High School: Number and Quantity
The Real Number System eTAP Lesson
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, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
CCSS.Math.Content.HSN.RN.A.1
Real Numbers

Square Roots
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
CCSS.Math.Content.HSN.RN.A.2
Simplifying Square Roots
Use properties of rational and irrational numbers.
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.
CCSS.Math.Content.HSN.RN.B.3

Quantities eTAP Lesson
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; choose and interpret the scale and the origin in graphs and data displays.
CCSS.Math.Content.HSN.Q.A.1
Word Problems of Measurements & Four Operations
Define appropriate quantities for the purpose of descriptive modeling.
CCSS.Math.Content.HSN.Q.A.2
Cubic Units for Volume
Interpreting Categorical and Quantitative Data eTAP Lesson
Summarize, represent, and interpret data on two categorical and quantitative variables
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
CCSS.Math.Content.HSS.ID.B.5
Data Classification, Range, and Midrange
Quantities eTAP Lesson
Reason quantitatively and use units to solve problems.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
CCSS.Math.Content.HSN.Q.A.3
The Complex Number System eTAP Lesson
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.
CCSS.Math.Content.HSN.CN.A.1
Complex Numbers
Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
CCSS.Math.Content.HSN.CN.A.2
Commutative and Associative Property
Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
CCSS.Math.Content.HSN.CN.A.3

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 rectangular and polar forms of a given complex number represent the same number.
CCSS.Math.Content.HSN.CN.B.4
Complex Plane
Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.
CCSS.Math.Content.HSN.CN.B.5

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 the numbers at its endpoints.
CCSS.Math.Content.HSN.CN.B.6
Complex Numbers
Use complex numbers in polynomial identities and equations.
Solve quadratic equations with real coefficients that have complex solutions.
CCSS.Math.Content.HSN.CN.C.7

Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).
CCSS.Math.Content.HSN.CN.C.8
Multiplying and Dividing Polynomials
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
CCSS.Math.Content.HSN.CN.C.9
De Moivre’s Theorem
Vector and Matrix Quantities eTAP Lesson
Represent and model with vector quantities.
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).
CCSS.Math.Content.HSN.VM.A.1
Two Dimensional Vectors
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
CCSS.Math.Content.HSN.VM.A.2

Solve problems involving velocity and other quantities that can be represented by vectors.
CCSS.Math.Content.HSN.VM.A.3
One Dimensional Motion Problems (Newton's Second Law)
Perform operations on 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.
CCSS.Math.Content.HSN.VM.B.4.a

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
CCSS.Math.Content.HSN.VM.B.4.b
Two Dimensional Trajectory Problems
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.
CCSS.Math.Content.HSN.VM.B.4.c

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
CCSS.Math.Content.HSN.VM.B.5.a
Two Dimensional Problems Involving Balanced Forces
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).
CCSS.Math.Content.HSN.VM.B.5.b

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.
CCSS.Math.Content.HSN.VM.C.6
What are Matrices
Add, subtract, and multiply matrices of appropriate dimensions.
CCSS.Math.Content.HSN.VM.C.7

Subtracting Matrices
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
CCSS.Math.Content.HSN.VM.C.9

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.
CCSS.Math.Content.HSN.VM.C.10
Solving Linear Systems with Matrices
Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
CCSS.Math.Content.HSN.VM.C.11

Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
CCSS.Math.Content.HSN.VM.C.12
Determinant