Common Core State Standards

CCSS.Math.Content.HSN.RN: The Real Number System

CCSS.Math.Content.HSN.RN.A: Extend the properties of exponents to rational exponents.

CCSS.Math.Content.HSN.RN.A.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.

CCSS.Math.Content.HSN.CN: The Complex Number System

CCSS.Math.Content.HSN.CN.A: Perform arithmetic operations with complex numbers.

CCSS.Math.Content.HSN.CN.A.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.

CCSS.Math.Content.HSN.CN.A.2: 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.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

CCSS.Math.Content.HSN.CN.B: Represent complex numbers and their operations on the complex plane.

CCSS.Math.Content.HSN.CN.B.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.

CCSS.Math.Content.HSN.CN.C: Use complex numbers in polynomial identities and equations.

CCSS.Math.Content.HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.

CCSS.Math.Content.HSN.VM: Vector and Matrix Quantities

CCSS.Math.Content.HSN.VM.A: Represent and model with vector quantities.

CCSS.Math.Content.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).

CCSS.Math.Content.HSN.VM.A.2: 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.3: Solve problems involving velocity and other quantities that can be represented by vectors.

CCSS.Math.Content.HSN.VM.B: Perform operations on vectors.

CCSS.Math.Content.HSN.VM.B.4a: 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.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

CCSS.Math.Content.HSN.VM.B.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).

CCSS.Math.Content.HSA.SSE: Seeing Structure in Expressions

CCSS.Math.Content.HSA.SSE.A: Interpret the structure of expressions

CCSS.Math.Content.HSA.SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

Exponential Growth and Decay

Simple and Compound Interest

Unit Conversions

CCSS.Math.Content.HSA.SSE.A.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Exponential Growth and Decay

Simple and Compound Interest

Translating and Scaling Functions

Using Algebraic Expressions

CCSS.Math.Content.HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

CCSS.Math.Content.HSA.SSE.B: Write expressions in equivalent forms to solve problems

CCSS.Math.Content.HSA.SSE.B.3a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

CCSS.Math.Content.HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions.

CCSS.Math.Content.HSA.APR: Arithmetic with Polynomials and Rational Expressions

CCSS.Math.Content.HSA.APR.A: Perform arithmetic operations on polynomials

CCSS.Math.Content.HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

CCSS.Math.Content.HSA.APR.B: Understand the relationship between zeros and factors of polynomials

CCSS.Math.Content.HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

CCSS.Math.Content.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomials and Linear Factors

Quadratics in Factored Form

CCSS.Math.Content.HSA.APR.C: Use polynomial identities to solve problems

CCSS.Math.Content.HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (𝘹 + 𝘺)ⁿ in powers of 𝘹 and y for a positive integer 𝘯, where 𝘹 and 𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle.

CCSS.Math.Content.HSA.CED: Creating Equations

CCSS.Math.Content.HSA.CED.A: Create equations that describe numbers or relationships

CCSS.Math.Content.HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Exponential Growth and Decay

Geometric Sequences

Modeling and Solving Two-Step Equations

Quadratic Inequalities

Simple and Compound Interest

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

CCSS.Math.Content.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2D Collisions

Air Track

Determining a Spring Constant

Golf Range

Points, Lines, and Equations

Simple and Compound Interest

Slope-Intercept Form of a Line

CCSS.Math.Content.HSA.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

CCSS.Math.Content.HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

CCSS.Math.Content.HSA.REI: Reasoning with Equations and Inequalities

CCSS.Math.Content.HSA.REI.A: Understand solving equations as a process of reasoning and explain the reasoning

CCSS.Math.Content.HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

CCSS.Math.Content.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

CCSS.Math.Content.HSA.REI.B: Solve equations and inequalities in one variable

CCSS.Math.Content.HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Exploring Linear Inequalities in One Variable

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Linear Inequalities in One Variable

CCSS.Math.Content.HSA.REI.B.4b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

CCSS.Math.Content.HSA.REI.C: Solve systems of equations

CCSS.Math.Content.HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

CCSS.Math.Content.HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

CCSS.Math.Content.HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

CCSS.Math.Content.HSA.REI.D: Represent and solve equations and inequalities graphically

CCSS.Math.Content.HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Circles

Ellipses

Hyperbolas

Parabolas

Points, Lines, and Equations

CCSS.Math.Content.HSA.REI.D.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Solving Equations by Graphing Each Side

Solving Linear Systems (Slope-Intercept Form)

CCSS.Math.Content.HSA.REI.D.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities in Two Variables

CCSS.Math.Content.HSF.IF: Interpreting Functions

CCSS.Math.Content.HSF.IF.A: Understand the concept of a function and use function notation

CCSS.Math.Content.HSF.IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).

Introduction to Functions

Points, Lines, and Equations

CCSS.Math.Content.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions

Translating and Scaling Functions

CCSS.Math.Content.HSF.IF.B: Interpret functions that arise in applications in terms of the context

CCSS.Math.Content.HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

CCSS.Math.Content.HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function

Introduction to Functions

Radical Functions

Rational Functions

CCSS.Math.Content.HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

CCSS.Math.Content.HSF.IF.C: Analyze functions using different representations

CCSS.Math.Content.HSF.IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Linear Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

CCSS.Math.Content.HSF.IF.C.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

CCSS.Math.Content.HSF.IF.C.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions

Polynomials and Linear Factors

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