Unit 1 – Reasoning with Geometry
1.1 Construct logical arguments and explain reasoning with two dimensional figures to prove geometric theorems about parallelograms and solve problems. Demonstrate an understanding of the properties of three of a triangle’s points of concurrency.
1.2 Understand properties of circles and how to apply them algebraically and geometrically. Demonstrate understanding that within circles, segments, lines, and angles create special relationships and use these to solve geometric problems
Unit 2 – Functions and their Inverses
2.1 Compare functions using multiple representations of and understand key features to interpret, analyze, and find solutions.
2.2 Understand inverse relationships, describe them algebraically, and use these relationships to solve, analyze and interpret.
Unit 3 – Exponential and Logarithmic Functions
3.1 Understand how to create exponential equations and graphs with one or two variables, and be able to identify the different parts of an exponential equation and relate them to the real world.
3.2 Recognize the relationship between exponential and logarithmic equations as inverses using multiple representations, interpret the key features of the graph, and use them to solve equations and model real world phenomena.
Unit 4 – Polynomial Functions
4.1 Students understand surface area and volume of geometric figures can be modeled by polynomial functions.
4.2 Recognize parts of a polynomial, and apply the Fundamental Theorem of Algebra to determine the types and number of solutions.
4.3 Understand and apply the Remainder Theorem, the Factor Theorem, and the Division Algorithm. Create polynomial equations in one or two variables and use them to solve problems algebraically and graphically
4.4 Recognize key features, zeros, and transformations of polynomial functions. Analyze a polynomial function and compare two or more functions by using their key features. Given solutions or a graph, write the equation of polynomial function. Graph transformations. Compare the relative rates of growth of exponential and polynomial functions.
Unit 5 – Modeling with Geometry
5.1 Derive the equation of a circle as well as distinguishing the center and radius of a circle from an equation.
5.2 Implement surface area and volume of geometric figures and model using polynomial functions. Furthermore, relating cross sections with two dimensional and three dimensional figures.
Unit 6 – Rational Functions
6.1 Recognize rational expressions as the division of two polynomials and use properties of simple fractions to analyze, perform arithmetic operations, create and solve equations that model real world phenomena.
6.2 Understand and interpret the key features, uses and limitations of multiple representations of a rational function.
Unit 7 - Trigonometric Functions
7.1 Understand that triangular trigonometric functions are related to circular trigonometric functions in the coordinate plane.
7.2 Understand and interpret the key features, uses and limitations of multiple representations of trigonometric functions that model real world periodic behavior.
Unit 8 - Statistics
8.1 Understand statistics as a process of making inferences about a population (parameter) based on results from a random sample (statistic). Acknowledge the role of randomization in using sample surveys, experiments, and observational studies to collect data and understand the limitations of generalizing results to populations (related to randomization).
8.2 Understand simulation is useful for using data to make decisions. Know how to carry out a simulation with data for the purposes of: estimating population means or proportions, determining the margin of error for those estimates, and determining statistical significance.
8.3 Understand that samples can differ by chance.
8.4 Understand not all data that is reported is valid. Reports should be evaluated based on source, design of the study, and data displays.