Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to lowest terms. Students are able to add, subtract, multiply, and divide rational expressions and functions. Students are able to solve both computationally and conceptually challenging problems using these techniques. Represent simultaneous linear situations with tables, graphs and equations, understanding the connections among the representations. Students are able to apply algebraic techniques to rate problems, work problem percent mixture problems, and direct and indirect variations.
Students can solve equations and inequalities involving absolute values.
Solve a system of two linear equations and inequalities, relate the solution to the graph of the system and interpret it in terms of the context from which the equations arose. Solve linear equations and inequalities, interpret the reasonableness and meaning of the solutions, represent solutions and methods for finding solutions as graphs and tables, and understand the relationship between these representations and algebraic techniques. 3.4.8 Use algebraic expressions, equations and inequalities to model linear and nonlinear situations, including direct and inverse variation, exponential growth and quadratic behavior. 3.4.10 Students are able to solve a quadratic equation by factoring or completing the square. 3.4.11 Students know the quadratic formula and are familiar with its proof using completing the square.