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Transformations of Absolute Value Functions

Given an absolute value function, the student will analyze the effect on the graph when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values.

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Domain and Range: Graphs

Given a function in graph form, identify the domain and range using set notation, interval notation, or a verbal description as appropriate.

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Domain and Range: Function Notation

Given a function in function notation form, identify the domain and range using set notation, interval notation, or a verbal description as appropriate.

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Domain and Range: Verbal Description

The student will be able to identify and determine reasonable values for the domain and range from any given verbal description.

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Domain and Range: Contextual Situations

The student will be able to identify and determine reasonable values for the domain and range from any given contextual situation.

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Modeling Data with Linear Functions

Given a scatterplot where a linear function is the best fit, the student will interpret the slope and intercepts, determine an equation using two data points, identify the conditions under which the function is valid, and use the linear model to predict data points.

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Formulating Systems of Inequalities

Given a contextual situation, the student will formulate a system of two linear inequalities with two unknowns to model the situation.

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Solving Systems of Equations Using Substitution

Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of substitution.

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Solving Systems of Equations Using Elimination

Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of elimination.

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Solving Systems of Equations with Three Variables

Given a system of three linear equations, the student will solve the system with a unique solution.

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Solving Systems of Equations Using Matrices

Given a system of up to three linear equations, the student will solve the system using matrices with technology.

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Introducing Conic Sections

Given a verbal description or a pictorial representation, the student will describe a conic section as the intersection of a cone and a plane.

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Graphing Conic Sections: Ellipses

Given an equation, the student will use parameter changes to graph an ellipse and to identify the changes in the graph of an ellipse.

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Graphing Conic Sections: Hyperbolas

Given an equation, the student will use parameter changes to graph a hyperbola and to identify the changes in the graph of a hyperbola.

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Using Logical Reasoning to Prove Conjectures about Circles

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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Generalizing Geometric Properties of Ratios in Similar Figures

Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.

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Determining Area: Sectors of Circles

Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.

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Making Conjectures About Circles and Segments

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.

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Determining Area: Regular Polygons and Circles

The student will apply the formula for the area of regular polygons to solve problems.

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Making Conjectures About Circles and Angles

Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.