### 1: The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.

#### 1.1: The student will model and interpret real-world situations, using the language of mathematics and appropriate technology.

1.1.1: The student will determine and interpret a linear function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.1.A: The majority of these items should be in context.

1.1.1.B: Essential characteristics are any points on the line, x- and y-intercepts, and slope.

1.1.1.a: Given one or more of the following:

1.1.1.a.1: a verbal description

1.1.1.a.2: a graph

1.1.1.a.3: a table of values

1.1.1.a.4: an equation

1.1.1.a.5: two or more essential characteristics

1.1.1.a.6: an absolute value equation

1.1.1.b: the student will be able to do each of the following:

1.1.1.b.1: write and/or solve an equation or an inequality that models the situation

1.1.1.b.2: graph the function

1.1.1.b.3: find and/or interpret the meaning of any essential characteristics in the context of the problem.

1.1.1.c: Students should be able to perform these skills with and without the use of a graphing calculator.

1.1.2: The student will determine and interpret a quadratic function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.2.A: The majority of the items should be in context.

1.1.2.B: Essential characteristics are zeros, vertex (maximum or minimum), y-intercept, increasing and decreasing behavior.

1.1.2.C: A table of values must include rational zeros and at least one other point.

1.1.2.D: All have real zeros.

1.1.2.a: Given one or more of the following:

1.1.2.a.1: a verbal description

1.1.2.a.2: a graph

1.1.2.a.3: a table of values

1.1.2.a.4: a function in equation form

1.1.2.b: the student will be able to do each of the following:

1.1.2.b.1: find one or more of the essential characteristics

1.1.2.b.2: write the function in equation form

1.1.2.b.3: graph the function

1.1.2.b.4: approximate the value of f(x) for a given number x

1.1.2.b.5: determine x for a given value of f(x).

1.1.2.0: The student will determine and interpret information from models of simple conic sections.

1.1.2.0.B: Ellipses and hyperbolas will have axes parallel to the x and y axes and centers at the origin.

1.1.2.1.1.2.02.a: Given its center and radius, the student will write an equation of a circle.

1.1.2.1.1.2.02.b: Given an equation of a circle, the student will find the center and radius of the circle.

1.1.2.1.1.2.02.d: The student will graph ellipses and hyperbolas.

1.1.3: The student will determine and interpret an exponential function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.

1.1.3.A: The majority of the items should be in context.

1.1.3.B: Essential characteristics are y-intercepts, asymptotes, increasing or decreasing.

1.1.3.C: For f(x) = ab to the x power, b > 0, a and b are rational numbers, b is not 1.

1.1.3.D: The y-values for x =0 and x = 1 will be given.

1.1.3.a: Given one or more of the following:

1.1.3.a.1: a verbal description

1.1.3.a.2: a graph

1.1.3.a.3: a table of values

1.1.3.a.4: a function in equation form

1.1.3.b: the student will be able to do each of the following:

1.1.3.b.1: find one or more of the essential characteristics

1.1.3.b.2: write the function in equation form

1.1.3.b.3: graph the function

1.1.3.b.4: approximate the value of f(x) for a given number x

1.1.3.b.5: determine x for a given value of f(x).

1.1.4: The student will be able to use logarithms to solve problems that can be modeled using an exponential function.

1.1.4.A: The majority of the items should be in context.

1.1.4.B: Properties used to solve problems may include the product, quotient, and/or power properties of logarithms.

1.1.4.a: Given verbal descriptions and formulas in exponential form, the student will be able to use the properties of logarithms to solve problems such as exponential growth and decay.

#### 1.2: Given an appropriate real-world situation, the student will choose an appropriate linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential model and apply that model to solve the problem.

1.2.A: The majority of the items should include a verbal description of a real-world situation.

1.2.a: Given a scatter plot of approximately linear data, the student will write an equation of best fit and/or use that equation to find values for x or f(x) using a graphing calculator.

1.2.b: Given a verbal description and/or a table of values of a function, the students will recognize that the function is linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential and/or write the appropriate equation that models the situation.

#### 1.3: The student will communicate the mathematical results in a meaningful manner.

1.3.0.1: The student will compute and interpret summary statistics for distributions of data including measures of center (mean, median, and mode) and spread (range, percentiles, variance, and standard deviation).

### 2: The student will demonstrate the ability to analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

#### 2.1: The student will be familiar with basic terminology and notation of functions.

2.1.1: The student will identify and use alternative representations of linear, piecewise-defined, quadratic, polynomial, simple rational and exponential functions.

2.1.1.A: These items are not in context.

2.1.1.a: Given one or more of the following:

2.1.1.a.1: a verbal description

2.1.1.a.2: a graph

2.1.1.a.3: a table of values

2.1.1.a.4: an equation

2.1.1.a.5: two or more essential characteristics

2.1.1.b: the student will be able to do each of the following:

2.1.1.b.1: find a value for x or f(x)

2.1.1.b.2: find real roots

2.1.1.b.3: find maximum and/or minimum

2.1.1.b.4: find intervals on which the function is increasing and/or decreasing.

2.1.1.c: Given an absolute value function, the student will graph the function and/or calculate a numeric value of the function.

2.1.2: The student will identify the domain, range, the rule or other essential characteristics of a function.

2.1.2.A: Vertical and horizontal lines are included.

2.1.2.B: Functions with restricted domain and/or range are included.

2.1.2.D: Rational functions should have denominators that are:

2.1.2.D.1: linear

2.1.2.D.3: sum and/or difference of two cubes in factored form.

2.1.2.E: Essential characteristics of a polynomial function include degree, intercepts, end behavior and symmetry of even or odd power functions.

2.1.2.a: Given one or more of the following:

2.1.2.a.1: a graph of a linear or non-linear function or relation including polynomial functions

2.1.2.a.2: an equation over a specified interval

2.1.2.a.3: a written description of a real-world situation with a restricted domain

2.1.2.a.4: a simple rational function

2.1.2.b: the student will be able to do each of the following:

2.1.2.b.3: describe the end behavior of a polynomial function

2.1.2.b.4: describe the symmetry of even or odd power functions

2.1.2.b.5: describe the interrelationship between the degree of a polynomial function and the number of intercepts

2.1.2.c: Given the equation of a function, the student will produce the graph and describe the domain and range using inequalities.

#### 2.2: The student will perform a variety of operations and geometrical transformations on functions.

2.2.1: The student will add, subtract, multiply, and divide functions.

2.2.1.A: Items involving factoring will be restricted to quadratics or the sum or difference of two cubes.

2.2.1.B: Long division is restricted to linear, binomial, or monomial terms in the denominator.

2.2.2: The student will find the composition of two functions and determine algebraically and/or graphically if two functions are inverses.

2.2.2.A: Functions given in equation form can include linear, quadratic, exponential, logarithmic, or rational functions such as f(x) = (ax+b)/(cx+d).

2.2.2.a: Given a function in equation form, the student will find the inverse function in equation form.

2.2.2.b: Given a one-to-one function as a graph, the student will graph the inverse of the function.

2.2.2.c: Given a function as a table of values, the student will determine the domain and/or range of the inverse of the function.

2.2.3: The student will perform translations, reflections, and dilations on functions.

2.2.3.A: Translations are either vertical or horizontal shifts.

2.2.3.B: Dilations either shrink or stretch a function.

2.2.3.C: This indicator assesses recognition of translations, reflections, and dilations on functions.

2.2.3.D: Transformations for absolute value functions are restricted to translations and reflections. They do not include dilations.

2.2.3.E: Exponential functions are restricted to translations.

2.2.3.a: The student will describe the effect that changes in the parameters of a linear, quadratic or exponential function have on the shape and position of its graph.

2.2.3.b: Given a verbal description of a transformed linear, quadratic, or exponential function, the student will write the function in equation form.

2.2.3.c: Given a transformed linear, quadratic, or exponential function in equation form, the student will give a verbal description of the transformation.

#### 2.3: The student will identify linear and nonlinear functions expressed numerically, algebraically, and graphically.

2.3.A: Functions can include linear, quadratic, exponential, logarithmic or functions such as f(x) = (ax + b)/(cx + d)

2.3.B: The items may have no real world context given.

2.3.C: Graphs may include piece-wise functions.

2.3.a: Given one or more of the following:

2.3.a.1: a table of values

2.3.a.2: a graph

2.3.b: the student will be able to do each of the following:

2.3.b.1: choose the correct equation or graph from the same family of functions

2.3.b.2: choose the correct equation or graph from a variety of families of functions.

#### 2.4: The student will describe or graph notable features of a function using standard mathematical terminology and appropriate technology.

2.4.A: Essential characteristics of a linear, quadratic, or exponential function are those listed for 1.1.1, 1.1.2, and 1.1.3.

2.4.B: Transformations for an absolute value function in one variable are restricted to translations and reflections. They do not include dilations.

2.4.a: Given one or more of the essential characteristics of a function, the student will graph the function.

2.4.b: Given the equation form of a linear, quadratic, or exponential function, the student will find one or more required essential characteristic and/or graph the function.

#### 2.5: The student will use numerical, algebraic, and graphical representations to solve equations and inequalities.

2.5.A: Equations may be in one or two variables.

2.5.B: Quadratic equations and inequalities are included.

2.5.C: Higher-order polynomial equations will be factorable.

2.5.D: Absolute value equations and inequalities are single variable and may be linear or quadratic.

2.5.G: Simple rational inequalities will lead to a linear inequality.

2.5.H: Exponential equations are either of the form f(x) = ab to the x power, b > 0, a and b are rational numbers, b is not 1 or the form c to the power (nx+d) = g to the power (mx + f), where c and g are powers of the same base.

2.5.a: Given an equation or inequality, the student will find the solution and express the solution algebraically and graphically. For constructed response items the student will also justify their method and/or solution.

#### 2.6: The student will solve systems of linear equations and inequalities.

2.6.A: Systems of linear equations will be 2 x 2 or simple 3 x 3 that do not take too much time to solve without a calculator.

2.6.B: Systems of linear inequalities will be 2 x 2.

2.6.a: Algebraically and graphically solve 2 x 2 systems of linear equations and algebraically solve simple 3 x 3 systems of linear equations.

2.6.b: Solve systems of two linear inequalities in two variables and graph the solution set.

2.6.c: Interpret the solution(s) to systems of equations and inequalities in terms of the context of the problem.

#### 2.7: The student will use the appropriate skills to assist in the analysis of functions.

2.7.1: The student will add, subtract, multiply, and divide polynomial expressions.

2.7.1.A: Rational expressions may include monomials, quadratics, and the sum and difference of two cubes.

2.7.2: The student will perform operations on complex numbers.

2.7.2.a: The student will represent the square root of a negative number in the form bi, where b is real; simplify powers of pure imaginary numbers.

2.7.2.c: The student will simplify rational expressions containing complex numbers in the denominator.

2.7.3: The student will determine the nature of the roots of a quadratic equation and solve quadratic equations of the form y = ax² + bx + c by factoring and the quadratic formula.

2.7.3.A: The solutions may be real or complex numbers.

2.7.5: The student will perform operations on radical and exponential forms of numerical and algebraic expressions.

2.7.5.a: The student will convert between and among radical and exponential forms of expressions.

2.7.5.A: Denominators in problems requiring rationalizing the denominator are restricted to square roots.

2.7.5.d: Radicals containing a numerical coefficient are restricted to square roots and cube roots.

2.7.6: The student will simplify and evaluate expressions and solve equations using properties of logarithms.

2.7.6.A: Properties of logarithms include the Change of Base Formula, property of equality for logarithmic functions, and the product, quotient, and power properties of logarithms.

#### 2.8: The student will use literal equations and formulas to extract information.

2.8.A: Problems may include addition/subtraction and multiplication/division properties of equality, factoring a common factor, and terms that are rational.

2.9.0.1: The student will represent the general term of an arithmetic or geometric sequence and use it to determine the value of any particular term.

2.9.0.2: The student will represent partial sums of an arithmetic or geometric sequence and determine the value of a particular partial sum.

2.9.0.4: The student will recognize and solve problems that can be modeled using a finite arithmetic or geometric series.

Correlation last revised: 3/5/2015

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