#### A2.1: Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

A2.1.1: Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

A2.1.2: Use function notation. Add, subtract, multiply, and divide pairs of functions.

A2.1.3: Understand composition of functions and combine functions by composition.

A2.1.4: Graph relations and functions with and without graphing technology.

A2.1.5: Find the zeros of a function.

A2.1.6: Solve an inequality by examining the graph.

A2.1.7: Graph functions defined piece-wise.

A2.1.8: Interpret given situations as functions in graphs, formulas, and words.

#### A2.2: Students solve systems of linear equations and inequalities and use them to solve word problems. They model data with linear equations.

A2.2.1: Graph absolute value equations and inequalities.

A2.2.2: Use substitution, elimination, and matrices to solve systems of two or three linear equations in two or three variables.

A2.2.3: Use systems of linear equations and inequalities to solve word problems.

A2.2.4: Find a linear equation that models a data set using the median fit method and use the model to make predictions.

#### A2.3: Students solve quadratic equations, including the use of complex numbers. They interpret maximum and minimum values of quadratic functions. They solve equations that contain square roots.

A2.3.1: Define complex numbers and perform basic operations with them.

A2.3.2: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

A2.3.3: Solve quadratic equations in the complex number system.

A2.3.4: Graph quadratic functions. Apply transformations to quadratic functions. Find and interpret the zeros and maximum or minimum value of quadratic functions.

A2.3.6: Solve equations that contain radical expressions.

#### A2.4: Students write equations of conic sections and draw their graphs.

A2.4.1: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

A2.4.2: Graph conic sections.

#### A2.5: Students use the binomial theorem, divide and factor polynomials, and solve polynomial equations.

A2.5.2: Divide polynomials by others of lower degree.

A2.5.3: Factor polynomials completely and solve polynomial equations by factoring.

#### A2.6: Students use negative and fractional exponents. They simplify algebraic fractions and solve equations involving algebraic fractions. They solve problems of direct, inverse, and joint variation.

A2.6.1: Understand and use negative and fractional exponents.

A2.6.4: Solve equations involving algebraic fractions.

A2.6.6: Solve problems of direct, inverse, and joint variation.

#### A2.7: Students graph exponential functions and relate them to logarithms. They solve logarithmic and exponential equations and inequalities. They solve word problems using exponential functions.

A2.7.1: Graph exponential functions.

A2.7.4: Solve logarithmic and exponential equations and inequalities.

#### A2.8: Students define and use arithmetic and geometric sequences and series.

A2.8.1: Define arithmetic and geometric sequences and series.

A2.8.2: Find specified terms of arithmetic and geometric sequences.

#### A2.9: Students use fundamental counting principles to compute combinations, permutations, and probabilities.

A2.9.1: Understand and apply counting principles to compute combinations and permutations.

A2.9.2: Use the basic counting principle, combinations, and permutations to compute probabilities.

#### A2.10: Mathematical Reasoning and Problem Solving

A2.10.1: Use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

A2.10.4: Use the properties of number systems and the order of operations to justify the steps of simplifying functions and solving equations.

A2.10.5: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously. .

A2.10.6: Use counterexamples to show that statements are false.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.