Course Overview

Students begin the course with a study of sequences, which is also an opportunity to revisit linear and exponential functions. Students represent functions in a variety of ways while addressing some aspects of mathematical modeling. This work leads to looking at situations that are well modeled by polynomials before pivoting to a study of the structure of polynomial graphs and expressions. Students do arithmetic on polynomials and rational functions and use different forms to identify asymptotes and end behavior. Students also study polynomial identities and use some key identities to establish the formula for the sum of the first \(n\) terms of a geometric sequence.

Next, students extend exponent rules to include rational exponents. They solve equations involving square and cube roots before developing the idea of \(i\), a number whose square is −1, expanding the number system to include complex numbers. This allows them to solve quadratic equations with non-real solutions.

Building on rational exponents, students return to their study of exponential functions and establish that the property of growth by equal factors over equal intervals holds even when the interval has non-integer length. They use logarithms to solve for unknown exponents, and are introduced to the number \(e\) and its use in modeling continuous growth. Logarithm functions and some situations they model well are also briefly addressed.

Students learn to transform functions graphically and algebraically. In previous courses and units, students adjusted the parameters of particular types of models to fit data. Here, they consolidate and generalize this understanding. This work is useful in the study of periodic functions that comes next. Students work with the unit circle to make sense of trigonometric functions and use those functions to model periodic relationships.

The last unit, on statistical inference, focuses on analyzing data from experiments using normal distributions. Students learn to account for variability in data and estimate population mean, margin of error, and proportions using sampling and simulations. They develop skepticism about news stories that summarize data inappropriately.

Within the classroom activities, students have opportunities to engage in aspects of mathematical modeling. Additionally, modeling prompts are provided for use throughout the course. Modeling prompts offer opportunities for students to engage in the full modeling cycle.

Algebra 2: Family Support