Content Standards
A.SSE.A.1: Interpret expressions that represent a quantity in terms of its context.
A.SSE.A.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.
Compound Interest
Exponential Growth and Decay
A.SSE.A.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
Compound Interest
Exponential Growth and Decay
A.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.
Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
A.SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.
A.SSE.B.3.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A.SSE.B.3.c: Use the properties of exponents to transform expressions for exponential functions.
A.APR.A.1: Demonstrate understanding that polynomials form a system analogous to the integers; namely, they are closed under certain operations.
A.APR.A.1.a: Perform operations on polynomial expressions (addition, subtraction, multiplication, division) and compare the system of polynomials to the system of integers when performing operations.
Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
A.APR.A.1.b: Factor and/or expand polynomial expressions, identify and combine like terms, and apply the distributive property.
Addition and Subtraction of Functions
Addition of Polynomials
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
A.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
A.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
A.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.
A.APR.D.6: Rewrite simple rational expressions in different forms using inspection, long division, or, for the more complicated examples, a computer algebra system.
Dividing Polynomials Using Synthetic Division
A.CED.A.1: Create one-variable equations and inequalities to solve problems, including linear, quadratic, rational, and exponential functions.
Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Roots of a Quadratic
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
A.CED.A.2: Interpret the relationship between two or more quantities.
A.CED.A.2.a: Define variables to represent the quantities and write equations to show the relationship.
Exponential Functions
Exponential Growth and Decay
Slope-Intercept Form of a Line
A.CED.A.2.b: Use graphs to show a visual representation of the relationship while adhering to appropriate labels and scales.
Exponential Growth and Decay
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
A.CED.A.3: Represent constraints using equations or inequalities and interpret solutions as viable or non-viable options in a modeling context.
A.CED.A.4: Represent constraints using systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.
A.CED.A.5: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Solving Formulas for any Variable
A.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 or refute a solution method.
Modeling One-Step Equations
Quadratics in Factored Form
Solving Algebraic Equations II
Solving Two-Step Equations
A.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
A.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A.REI.B.3.a: Solve linear equations and inequalities in one variable involving absolute value.
Absolute Value Equations and Inequalities
A.REI.B.4: Solve quadratic equations in one variable.
A.REI.B.4.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
A.REI.B.4.b: Solve quadratic equations by inspection (e.g., for x^2 = 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.
Quadratics in Factored Form
Roots of a Quadratic
A.REI.C.5: Verify 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 (Standard Form)
A.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)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
A.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)
A.REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
Solving Linear Systems (Matrices and Special Solutions)
A.REI.D.10: Demonstrate understanding that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. Show that any point on the graph of an equation in two variables is a solution to the equation.
Absolute Value Equations and Inequalities
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Linear Inequalities in Two Variables
Logarithmic Functions
Point-Slope Form of a Line
Quadratic Inequalities
Quadratics in Polynomial Form
Standard Form of a Line
A.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. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Absolute Value Equations and Inequalities
Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
A.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
Systems of Linear Inequalities (Slope-intercept form)
Correlation last revised: 2/28/2022