# Mathematics Algebra 2

Scope and Sequence: Mathematics

Course/Grade Algebra 2

 Quarter 1 Quarter 2 Quarter 3 Quarter 4 Unit Titles Unit 1: Families of Functions  Unit 2: Systems of Linear Equations and Inequalities Unit 3: Introduction to Quadratic Functions  Unit 4: Applications of Quadratic Functions Unit 5: Polynomial and Radical Functions  Unit 6: Exponential Functions Unit 7: Rational Equations and Functions  Unit 8: Trigonometry and Probability Learning Outcomes (grade level expectations or standards) Identify and sketch the graph of the parent functions   Determine the domain and range of each parent function   Describe the effect of horizontal and vertical phase shifts Describe the effect of the lead coefficient on the graph   Given the parent function, apply given transformations   Given the transformation, determine the representative equation   Determine the zeros of functions and describe how they relate to equations   Solve absolute value equations   Graphs piecewise, absolute value and greatest integer functions   Identify intervals of increasing, decreasing, constant, concave up and concave down   Solve all systems of linear equations graphically, algebraically, and with matrices   Graph linear inequalities   Describe the number of solutions to a systems problem as unique, infinite, or nonexistent   Calculate and graph the inverse of linear functions   Solve systems of linear inequalities algebraically and graphically   Solve linear programming problems   Model and solve other real life problems with more than one variable Define quadratic functions   Graph quadratic functions manually and with technology   Identify domain and range of quadratic functions   Completely analyze the graph of a quadratic function with regards to domain and range; x and y intercepts; vertex; line of symmetry; intervals of increasing and decreasing; and concavity   Solve quadratic equations using factoring, completing the square, quadratic formula, and graphically   Derive the quadratic formula by completing the square   Calculate the descriminant and use descriminant to describe roots   Define the family of complex numbers   Perform operations on complex numbers   Identify complex roots of quadratic functions   Solve and graph quadratic inequalities   Write quadratic functions in standard, intercept and vertex forms   Graph quadratic functions and describe from parent functions   Identify a quadratic function from its graph   Model real world data with quadratic functions   Solve real world problems that can be modeled with quadratic functions, included, but limited to profit, velocity, area Define a polynomial function   Completely analyze the graph of a polynomial function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity   Find zero’s of a polynomial function algebraically   Solve polynomial equations graphically and algebraically   Perform operations with polynomials   Perform transformations on the graphs of polynomial functions and identify the new function   Model data with polynomial functions   Solve real world problems that can be modeled with polynomial functions   Define a radical function   Completely analyze the graph of a radical function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity   Find zero’s of a radical function algebraically   Perform transformations on the graphs of radical functions and identify the new function   Solve radical equations graphically and algebraically   Perform operations with radicals   Model data with radical functions   Solve real world problems that can be modeled with radical functions   Define an exponential function   Completely analyze the graph of a exponential function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity   Find zero’s of an exponential function algebraically   Perform transformations on the graphs of exponential functions and identify the new function   Calculate and graph the inverse of exponential functions   Solve exponential equations graphically and algebraically   Model data with exponential functions   Solve real world problems that can be modeled with exponential functions Define a rational function   Completely analyze the graph of a rational function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity   Find zero’s of a rational function algebraically   Perform transformations on the graphs of rational functions and identify the new function   Solve rational equations graphically and algebraically   Model data with rational functions   Solve real world problems that can be modeled with rational functions   Develop trigonometric ratios from the right triangles   Solve problems using trigonometric ratios (distance, angle of elevation)   Analyze the graphs of the trigonometric functions   Convert angle measures (degrees to radians, radians to degrees)   Express trig ratios in both radians and degrees   Graph the trigonometric functions (sin x, cos x & tan x)   Use the Pythagorean theorem to develop the trigonometric identities   Identify and apply trigonometric identities   Identify and apply the inverse trigonometric identities   Use the trigonometric identities to solve real world problems Significant Task (names only) Linear Systems: Using Graphs and Tables  Linear Systems: Using Algebra  Maximizing Your Efforts Exploring the Vertex Form of the Quadratic Function  Rocket Science Exploring the Exponential Function Math TODAY: Humidity Makes Air Feel Hotter III  Hurricane Hunters: Tracking Katrina and Rita Content Supporting Materials (text, calcs, manips) Text  Visual Aids  Graphing Calculators  Graph paper Text  Visual Aids  Graphing Calculators  Graph paper Text  Visual Aids  Graphing Calculators  Graph paper Text  Visual Aids  Graphing Calculators  Graph paper