• Arithmetic Properties (CA Standard 1.0, 2.0)
o Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
o Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
• B.Functions (CA Standard 16.0, 17.0, 18.0)
o 16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
o 17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.
o 18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.
• Polynomials (CA Standard 10.0, 12.0)
o 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques.
o 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
• D.Factoring (CA Standard 11.0)
o 11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
• E.Rational Expressions (CA Standard 13.0)
o 13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
• F.Equations (CA Standard 3.0, 4.0, 8.0, 9.0)/Inequalities (CA Standard 3.0, 4.0)
o Students solve equations and inequalities involving absolute values.
o Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
o 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
o 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
• G.Quadratics Equations (CA Standard 140, 19.0, 20.0, 21.0, 22.0, 23.0)
o 14.0 Students solve a quadratic equation by factoring or completing the square.
o 19.0 Students know the quadratic formula and are familiar with its proof by completing the square.
o 20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
o 21.0 Students graph quadratic functions and know that their roots are the x- intercepts.
o 22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
o 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
• H.Graphs (CA Standard 6.0, 7.0)
o Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
o Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
• I.Axioms (CA Standard 24.0, 25.0)
o 24.0 Students use and know simple aspects of a logical argument:
25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:
• K. Word Problems (CA Standard 5.0, 15.0)
o 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
o 15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.