Extending their knowledge of linear, exponential, and quadratic functions to polynomial, rational, and radical functions, students in Algebra 2 model situations and solve equations, discovering how the rules they learned in arithmetic continue to apply as they work with polynomials. Students focus on the properties and factors of polynomials, learning to find the zeros of a polynomial and graph it as a function. Students use complex numbers to solve quadratic equations and exponential expressions, and learn how to rewrite rational expressions in different forms and solve simple rational and radical equations. The trigonometric concepts students learned previously are expanded as they focus on the unit circle and apply these concepts to models of periodic phenomena. Students then extend their knowledge of function families to model functions defined as square roots or cube roots, as well as piecewise-defined functions. A detailed look at exponential and logarithmic functions is applied to showing intercepts and end behavior. Students collect data through sample surveys, experiments, and simulations, and learn about the role of randomness in this process. Quantitative reasoning is emphasized as students compare the differences between sample surveys, experiments, and observations, and explain how randomization relates to each one
Population Comparision [Mastery Project]
HOW CAN YOU USE MATHEMATICS TO CATEGORIZE AND IDENTIFY POPULATIONS?
The US Department of Agriculture (USDA) is getting serious about managing invasive species, and is calling on citizen scientists to help them track numbers of specific organisms that are throwing ecosystems off balance. You work for a local nature center, and are in charge of creating an educational field guide that will help visitors identify and report species proliferating in your area. To create the field guide, you must select a species, research its population, and compare its numbers to a native species. To learn more, see the Action Project Rubric.
Game Play [Mastery Project]
HOW DOES PLAY ENRICH OUR LIVES?
You are a game tester, and you’ve been tasked with creating an exciting new twist on a classic game for a new generation of players. You have selected your first game and gone through multiple rounds of playtesting it to make improvements. For your final project, you will create your own game using information you gained from looking at classic games. This portfolio will show off the successful elements of the game and recommend strategies players can use to be successful. Your project should take the form of a product pitch slide show and include a demonstration of the mathematical probabilities involved in your game.
Characteristics of rational functions
Exponential and logarithmic functions
Transformations of functions
Conic sections Systems of nonlinear equations
Arithmetic and geometric sequences
Introduction to trigonometry
Foundations of probability
The normal distribution
Compare and contrast exponential and logarithmic functions.
Use exponential and logarithmic functions to categorize and identify populations, then create a field guide to compare and contrast two different growth models.
Find the inverse of a function graphically and algebraically. Explore the relationships between linear and exponential functions and arithmetic and geometric sequences.
Analyze the unit circle and its relationship to trigonometric functions.
Distinguish between mutually exclusive and inclusive events, as well as independent and dependent events.
Create a game and analyze its success, playability, and strategy.