Algebra 2 Curriculum

Unit 1: Parent Functions and Data Regression

Descriptions: Students survey functions studied in this course, identify their attributes, and use data regression to connect real world data to selected functions.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1E Create and use representations to organize, record, and communicate mathematical ideas.

Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:

ALGII.2A Graph the functions, f (x) = x, f(x)=1/x, f (x)=x^3, f(x)=b^x, f (x) = x , and f(x)=logbx 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.

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.

Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:

ALGII.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.

ALGII.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.

ALGII.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

Unit 2: Transformation of Functions

Descriptions: Students apply the properties of functions to their graphs and transformations using multiple representations.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Quadratic and Square Root Functions, Equations, and Inequalities. 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. The student is expected to:

ALGII.4C Determine the effect on the graph of f (x) = x when f(x) is replaced by a f(x), f(x) + d, f(bx), and f(x − c) for specific positive and negative values of a, b, c, and d.

Exponential and Logarithmic Functions and Equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:

ALGII.5A Determine the effects on the key attributes on the graphs of f(x) = b^x and f(x) = logb(x), where b is 2, 10 and e when f(x) is replaced by a f(x), f(x) + d, and f(x − c) for specific positive and negative real values of a, c, and d.

Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:

ALGII.6A Analyze the effect on the graphs of f(x) = x^3 and f (x) =cubic square root of x when f(x) is replaced by a· f(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d.

ALGII.6G Analyze the effect on the graphs of f(x)= 1/x, when f(x) is replaced by a· f(x), f(bx), f(x − c), and f(x) + d for specific positive and negative real values of a, b, c, and d.

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.

Unit 3: Composition and Inverse of Functions

Descriptions: Students connect the relationship between a function and its inverse and use composition of functions to determine if functions are inverses of each other.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:

ALGII.2A Graph the functions, f (x) = 1/x, f(x)=x^3, f(x)=b^x, f (x) = x , and f(x)=logbx 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.

ALGII.2B Graph and write the inverse of a function using notation such as f -1(x).

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

ALGII.2D Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.

Unit 4: Absolute Value Functions

Descriptions: Students solve absolute value equations and inequalities and apply attributes of transformations to absolute value functions.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1B 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.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is

expected to:

ALGII.2A Graph the functions f(x) =|x|, f(x)=x^3, f(x)=b^x, and f(x)=logbx 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.

ALGII.2B Graph and write the inverse of a function using notation such as f -1(x).

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

Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be

used to model situations, solve problems, and make predictions. The student is expected to:

ALGII.6C Analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by a· f(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c and d.

ALGII.6D Formulate absolute value linear equations.

ALGII.6E Solve absolute value linear equations.

ALGII.6F Solve absolute value linear inequalities

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.

Unit 5: Matrices & Systems of Equations and Inequalities

Descriptions: In real-world situations, students solve and analyze systems of linear equations with two or more variables using graphs, tables, matrices, and algebraic methods.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

ALGII.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:

ALGII.3A 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.

ALGII.3B Solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution (including inverse matrices).

ALGII.3E Formulate systems of at least two linear inequalities in two variables.

ALGII.3F Solve systems of two or more linear inequalities in two variables.

ALGII.3G Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.

Unit 6: Transformations and Attributes of Quadratic Functions

Descriptions: Students analyze the transformation of a quadratic function through multiple representations.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:

ALGII.2A Graph the functions, f (x) = 1/x, f(x) = |x| f(x)=x^3, f(x) = cubic square root of x, f(x)=b^x, and f(x)=logbx 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.

Quadratic and Square Root Functions, Equations, and Inequalities. 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. The student is expected to:

ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.

ALGII.4D Transform a quadratic function f(x) = ax^2 + bx + c to the form f(x) = a(x – h)^2 + k to identify the different attributes of f(x).

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.

Unit 7: Factoring and Complex Numbers

Descriptions: Students explore various methods of factoring polynomials and introduction of complex numbers.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1B 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.

ALGII.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ALGII.1F Analyze mathematical relationships to connect and communicate mathematical idea.

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7A Add, subtract, and multiply complex numbers.

ALGII.7D Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.

ALGII.7E 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.

Unit 8: Solving Quadratic Equations and Inequalities

Descriptions: Students analyze solutions of quadratic equations and inequalities using multiple representations.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1B 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.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Quadratic and Square Root Functions, Equations, and Inequalities. 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. The student is expected to:

ALGII.4F Solve quadratic and square root equations.

ALGII.4H Solve quadratic inequalities.

Unit 9: Applications of Quadratic Equations and Inequalities

Descriptions: Students analyze quadratic functions and connect attributes to real world situations.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

ALGII.1B 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.

ALGII.1E Create and use representations to organize, record, and communicate mathematical ideas.

ALGII.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Quadratic and Square Root Functions, Equations, and Inequalities. 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. The student is expected to:

ALGII.4A Write the quadratic function given three specified points in the plane.

ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.

ALGII.4E Formulate quadratic and square root equations using technology given a table of data.

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.

Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:

ALGII.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.

ALGII.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.

ALGII.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

Unit 10: Systems of Linear and Quadratic Equations

Descriptions: Students analyze a system of equations in two variables consisting of a linear equation and a quadratic equation.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:

ALGII.3A 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.

ALGII.3C Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation.

ALGII.3D Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables.

Unit 11: Radicals and Rational Exponents

Descriptions: Students simplify radical expressions and rational exponents and explore the relationship to laws of exponents.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.

ALGII.7H Solve equations involving rational exponents.

Unit: 12 Root Equations and Functions

Descriptions: Students explore transformations and attributes of square root and cube root functions.

Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

ALGII.1B 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.

ALGII.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

ALGII.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:

ALGII.2A Graph the functions, f (x) =1/x, f(x)=x^3, f(x)=b^x, f(x) = x , and f(x) = logbx 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.

ALGII.2B Graph and write the inverse of a function using notation such as f^ -1(x).

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

ALGII.2D Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.

Quadratic and Square Root Functions, Equations, and Inequalities. 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. The student is expected to:

ALGII.4C Determine the effect on the graph of f (x) = 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.