MP: These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

MP.2A.1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.

MP.2A.1.A: apply mathematics to problems arising in everyday life, society, and the workplace;

Determining a Spring Constant
Estimating Population Size

MP.2A.1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Estimating Population Size

MP.2A.1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

Biconditional Statements
Using Algebraic Expressions

MP.2A.1.E: create and use representations to organize, record, and communicate mathematical ideas;

Describing Data Using Statistics
Stem-and-Leaf Plots
Using Algebraic Expressions

MP.2A.1.G: display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Using Algebraic Expressions

1: The student will demonstrate an understanding of how to use algebraic methods to manipulate numbers, expressions, and equations.

1.2A.7: The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.

1.2A.7.A: add, subtract, and multiply complex numbers;

Points in the Complex Plane

1.2A.7.B: add, subtract, and multiply polynomials;

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

1.2A.7.C: determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two;

Dividing Polynomials Using Synthetic Division

1.2A.7.D: determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form

1.2A.7.E: determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping;

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

1.2A.7.G: rewrite radical expressions that contain variables to equivalent forms;

Simplifying Radical Expressions

2: The student will demonstrate an understanding of how to describe and graph various functions and their inverses.

2.2A.2: The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

2.2A.2.A: graph the functions f(x)= the square root of x, f(x)=1/x, f(x)=x³, f(x)= ³ the square root of x, f(x)=b to the x power, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;

Absolute Value with Linear Functions
Compound Interest
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Translating and Scaling Functions

2.2A.2.B: graph and write the inverse of a function using notation such as f-¹ (x);

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

2.2A.2.C: describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions
Radical Functions

2.2A.8: The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.

2.2A.8.B: use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and

Least-Squares Best Fit Lines
Solving Using Trend Lines

2.2A.8.C: predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

Correlation
Solving Using Trend Lines

3: The student will demonstrate an understanding of how to write and solve systems of equations and inequalities.

3.2A.3: The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.

3.2A.3.A: formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic;

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

3.2A.3.E: formulate systems of at least two linear inequalities in two variables;

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

3.2A.3.F: solve systems of two or more linear inequalities in two variables; and

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

3.2A.3.G: determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

4: The student will demonstrate an understanding of how to describe, write, and solve quadratic and square root functions, equations, and inequalities.

4.2A.4: The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.

4.2A.4.B: write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;

Addition and Subtraction of Functions
Parabolas
Zap It! Game

4.2A.4.C: determine the effect on the graph of f(x) = the square root of x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d;

Radical Functions

4.2A.4.D: transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x - h)² + k to identify the different attributes of f(x);

Circles
Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Zap It! Game

4.2A.4.E: formulate quadratic and square root equations using technology given a table of data;

Radical Functions

4.2A.4.F: solve quadratic and square root equations;

Radical Functions
Roots of a Quadratic

4.2A.4.G: identify extraneous solutions of square root equations; and

Operations with Radical Expressions
Radical Functions

4.2A.4.H: solve quadratic inequalities.

Quadratic Inequalities

5: The student will demonstrate an understanding of how to describe, write, and solve exponential and logarithmic functions and equations.

5.2A.5: The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.

5.2A.5.A: determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions: Translating and Scaling

5.2A.5.B: formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;

Arithmetic Sequences
Compound Interest
Geometric Sequences

5.2A.5.C: rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;

Logarithmic Functions

5.2A.5.D: solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and

Exponential Functions

6: The student will demonstrate an understanding of how to describe, write, and solve cubic, cube root, absolute value, and rational functions, equations, and inequalities.

6.2A.6: The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.

6.2A.6.A: analyze the effect on the graphs of f(x) = x³ and f(x) = ³ the square root of x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Radical Functions
Translating and Scaling Functions

6.2A.6.C: analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Absolute Value with Linear Functions
Translating and Scaling Functions

6.2A.6.D: formulate absolute value linear equations;

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

6.2A.6.E: solve absolute value linear equations;

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

6.2A.6.F: solve absolute value linear inequalities;

Absolute Value Equations and Inequalities
Compound Inequalities

6.2A.6.G: analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

General Form of a Rational Function
Rational Functions

6.2A.6.H: formulate rational equations that model real-world situations;

Rational Functions

6.2A.6.K: determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and

General Form of a Rational Function
Rational Functions

6.2A.6.L: formulate and solve equations involving inverse variation.

Direct and Inverse Variation