• The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.
• applying the laws of exponents to perform operations on expressions;
• adding, subtracting, multiplying, and dividing polynomials; and
• factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.
• solving literal equations (formulas) for a given variable;
• justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;
• solving quadratic equations algebraically and graphically;
• solving multistep linear equations algebraically and graphically;
• solving systems of two linear equations in two variables algebraically and graphically; and
• solving real-world problems involving equations and systems of equations.
• solving multistep linear inequalities algebraically and graphically;
• justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;
• solving real-world problems involving inequalities; and
• solving systems of inequalities.
• determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and
• writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.
• determining whether a relation is a function;
• domain and range;
• zeros of a function;
• x- and y-intercepts;
• finding the values of a function for elements in its domain; and
• making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.
• The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
• The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.
• The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.
• The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.