The student will identify and extend geometric and arithmetic sequences.
The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.
the identity properties for addition and multiplication;
the multiplicative property of zero; and
the inverse property for multiplication.
The student will graph inequalities on a number line.
The student will represent relationships with tables, graphs, rules, and words.
write verbal expressions as algebraic expressions and sentences as equations and vice versa; and
evaluate algebraic expressions for given replacement values of the variables.
solve one- and two-step linear equations in one variable; and
solve practical problems requiring the solution of one- and two-step linear equations.
solve one-step inequalities in one variable; and
graph solutions to inequalities on the number line.
the commutative and associative properties for addition and multiplication;
the distributive property;
the additive and multiplicative identity properties;
the additive and multiplicative inverse properties; and
the multiplicative property of zero.
The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship.
solve multistep linear equations in one variable with the variable on one and two sides of the equation;
solve two-step linear inequalities and graph the results on a number line; and
identify properties of operations used to solve an equation.
The student will graph a linear equation in two variables.
The student will identify the domain, range, independent variable, or dependent variable in a given situation.
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.
The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form.
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.
local and absolute maxima and minima;
domain and range;
intervals in which the function is increasing/decreasing;
end behaviors; and
The student will use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic).
The student will collect data and generate an equation for the curve (linear, quadratic, exponential, and logarithmic) of best fit to model real-world problems or applications. Students will use the best fit equation to interpolate function values, make decisions, and justify conclusions with algebraic and/or graphical models.
The student will transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and words. Students will select and use appropriate representations for analysis, interpretation, and prediction.
The student will determine optimal values in problem situations by identifying constraints and using linear programming techniques.
add, subtract, multiply, divide, and simplify rational algebraic expressions;
add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents;
write radical expressions as expressions containing rational exponents and vice versa; and
factor polynomials completely.
The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include "Sigma" and a subscript n.
The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.
absolute value equations and inequalities;
quadratic equations over the set of complex numbers;
equations containing rational algebraic expressions; and
equations containing radical expressions.
The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. Graphing calculators will be used as a tool to visualize graphs and predict the number of solutions.
The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.
domain and range, including limited and discontinuous domains and ranges;
x- and y-intercepts;
intervals in which a function is increasing or decreasing;
inverse of a function; and
composition of multiple functions.
The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.
The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.
The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.
The student will identify properties of a normal distribution and apply those properties to determine probabilities associated with areas under the standard normal curve.
The student will compute and distinguish between permutations and combinations and use technology for applications.