Algebra+II+Home

__1. Rational Exponents__ a. Convert expressions from radical notations to rational exponents and vice versa. b. Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents. __2. Polynomial and Rational Expressions__ a. Divide polynomial expressions by lower degree polynomials. b. Add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. __3. Complex Numbers__ b. Add, subtract, multiply, divide, and simplify expressions involving complex numbers.
 * Standard 1: Number Systems and Algebraic Operations—The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.**

a. Recognize the parent graphs of polynomial, exponential, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators. b. Use function notation to add, subtract, multiply, and divide functions. c. Combine functions by composition. d. Use algebraic, interval, and set notations to specify the domain and range of functions of various types. e. Find and graph the inverse of a function, if it exists. __2. Systems of Equations__ a. Model a situation that can be described by a system of equations and inequalities, and use the model to answer questions about the situation. b. Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators. c. Use either one quadratic equation and one linear equation or two quadratic equations to solve problems. __3. Quadratic Equations and Functions__ a. Solve quadratic equations by graphing, factoring, completing the square, and quadratic formula. b. Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator. c. Model a situation that can be described by a quadratic function, and use the model to answer questions about the situation. 4. Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola). __5. Exponential and Logarithmic Functions__ a. Graph exponential and logarithmic functions. b. Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another. c. Model a situation that can be described by an exponential or logarithmic function, and use the model to answer questions about the situation. __6. Polynomial Equations and Functions__ a. Solve polynomial equations using various methods and tools which may include factoring and synthetic division. b. Sketch the graph of a polynomial function. c. Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator. d. Model a situation that can be described by a polynomial function, and use the model to answer questions about the situation. __7. Rational Equations and Functions__ a. Solve rational equations. b. Sketch the graph of a rational function. c. Given the graph of a rational function, identify the x- and y-intercepts, asymptotes, using various methods and tools which may include a graphing calculator. d. Model a situation that can be described by a rational function, and use the model to answer questions about the situation. __1. Analysis of Collected Data Involving Two Variables__ a. Display data on a scatter plot. b. Interpret results using a linear, exponential, or quadratic model/equation. c. Identify whether the model/equation is a curve of best fit for the data, using various methods and tools which may include a graphing calculator. __3. Identify and use arithmetic and geometric sequences and series to solve problems.__
 * Standard 2: Relations and Functions—The student will use the relationships among the solution of an equation, zero of a function, x -intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.** __1. Functions and Function Notation__
 * Standard 3: Data Analysis and Statistics—The student will use data analysis and statistics to formulate and justify predictions from a set of data.**