A.1 Students expand and deepen their understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. They use the properties of real numbers to simplify algebraic expressions and equations, and convert between different measurement units using dimensional analysis.
A.1.1 Know equivalent forms of real numbers (including integer exponents and radicals, percents, scientific notation, absolute value, rational numbers, irrational numbers).
A.1.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real-world problems.
A.3.8 Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.
A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.
A.3.11 Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables.
A.4 Perform operations on polynomials. Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial.
A.4.1 Simplify monomials and monomial expressions using the laws of integral exponents.
A.4.5 Graph polynomial functions with and without technology and describe end behavior.
A.4.6 Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function.
A.4.7 Write a polynomial equation for a given set of real and/or complex roots.
A.4.8 Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression, with and without technology.
A.4.9 Use graphing technology to find approximate solutions for polynomial equations.
A.4.10 Use polynomial equations to solve real-world problems.
A.4.11 Solve a polynomial inequality by examining the graph with and without the use of technology.
A.4.12 Apply the Binomial Theorem.
A.5 Simplify rational expressions and solve rational equations using what they have learned about factoring polynomials.
A.6 Simplify and perform operations on radical expressions and equations. Rationalize square root expressions and understand and use the concepts of negative and rational exponents. Add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Solve radical equations and equations with terms that have rational exponents.
A.7 Draw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing the square and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations.
A.7.1 Graph quadratic equations with and without graphing technology.
A.7.2 Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.
A.7.7 Solve non-linear systems of equations with and without using technology.
A.7.8 Use quadratic equations to solve real-world problems.
A.7.9 Solve optimization problems.
A.7.10 Use graphing technology to find approximate solutions of quadratic equations.
A.8 Understand the concepts of logarithmic and exponential functions. Graph exponential functions and solve problems of growth and decay. Understand the inverse relationship between exponents and logarithms and use it to prove laws of logarithms and to solve equations. Convert logarithms between bases and simplify logarithmic expressions.
A.8.1 Define exponential and logarithmic functions and determine their relationship.
A.10 In a general sense, all of mathematics is problem solving. In all of mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results
A.10.1 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guessing- and-checking, solving a simpler problem, writing an equation, working backwards, and creating a table.
A.10.3 Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions).
A.10.4 Use counterexamples to show that statements are false.