Students at the End of

Students at the end of this grade level must be able to investigate and solve step and piecewise functions. This means that they must be able to write absolute value functions as piecewise functions. Piecewise functions that students must be able to explain include domain, range, vertex, axis of symmetry, intercepts, extrema, and points of discontinuity. Students must show the ability to solve absolute value equations and inequalities analytically and graphically. Standard 2: Students must be able to explore exponential functions.

This includes the ability to extend properties of exponents to include all integer exponents. They must also be able to solve exponential equations and inequalities of relative simplicity both analytically and graphically. Students must demonstrate an understanding and ability to use basic exponential functions to model reality. Standard 3: Students must be able to solve quadratic equations and inequalities in one variable. This involves finding real and complex solutions to mathematical equations by means of processes such as factoring, square roots, and the application of the quadratic formula.

They must be able to analyze the nature of roots by means of technology and the discriminant. They must be able to describe their solutions by means of linear inequalities. Standard 4: Students must be able to explore inverses of functions. This includes a discussion of functions and their inverses, by means of concepts such as one-to-oneness, domain, and range. Students must demonstrate an ability to determine the inverses of linear, quadratic and power functions, including restricted domains.

They must also be familiar with the use of graphs to determine functions and their inverses. Composition must be used to verify the relationship between functions and their inverses. Standards for Grade Level 10 Standard 1: Students must be able to analyze a higher degree of polynomial function graphs. This means that they must be able to graph simple polynomial functions and understand the effects of elements such as degree, lead coefficient, and multiplicity of real zeros on the graph.

Students must also be able to determine the symmetry of polynomial functions in terms of their nature as even, odd, or neither. They must also demonstrate an ability to explain polynomial functions by referring to elements such as domain and range, intercepts, zeros, relative and absolute extreme, and end behavior. Standard 2: Students at the end of this grade level must show an ability to explore and understand logarithmic functions as inverses of exponential functions.

This includes the definition and understanding of nth root functions, as well as extending the properties of exponents to include rational exponents. Students must be able to extend the laws of exponents in order to understand and use the properties of logarithms. Standard 3: Students must be able to penetrate various equations and inequalities by finding real and complex roots of higher degree polynomial equations. They must demonstrate an ability to use the factor theorem, remainder theorem, and rational root theorem in order to accomplish this.

They must also solve polynomial, exponential and logarithmic equations both analytically and graphically. Standard 4: Students must be able to understand and use matrices to perform basic operations. This includes addition, subtraction, multiplication and inversion of matrices. They must also be able to identify the appropriate methods and technology to accomplish this. In addition, students must demonstrate the ability to find the inverses of two-by-two matrices without only with the use of pencil and paper, without additional technology.

Standards for Grade Level 11 Standard 1: At the end of this grade level, students must be able to explore rational functions in terms of investigating and explaining the characteristics of rational functions. Elements such as domain, range, zeros, points of discontinuation, and intervals of increase and decrease must be included in this ability. They must also find the inverses of rational functions with discussions of domain and range, symmetry, and function composition. Standard 2: Students must demonstrate an ability to use the circle for the purpose of defining trigonometric functions.

In order to do this, they must define and understand angles as measured in both degrees and radians. They must understand and apply the trigonometric functions and find their values by using points on angles in the standard position. Standard 3: Students must be able to investigate and use graphs relating to the six trigonometric functions, as well as understanding and applying these functions as functions of real numbers. They must also demonstrate an ability to identify the characteristics of trigonometric graphs representing the six basic functions.

Students must be able to understand graph transformations of trigonometric functions.