Students extend their understanding of irrational numbers, expand their knowledge of exponents to include any rational number, and expand their knowledge fo the number system to include imaginary and complex numbers and explore how these numbers behave under famiilar operations.
Students develop structures and patterns for negative and rational exponents, they write and interpret percent growth and decay functions, and they learn to fit an exponential function to a scatterplot (where the domain is not in the integers). Students derive a formula for the sum of a geometric series.
Students develop an understanding of logs as an inverse for exponentiation, and they model and solve problems using logarithms.
Students work with polynomials, interpret graphs of polynomial functions, and model using polynomial functions. They also work with contexts that can be modeling using rational functions and interpret vertical and horizontal asymptotes.
Students connect the unit circle behavior and data to the graphs of trigonometric functions, which they use to model periodic phenomena, interpreting values such as amplittude, frequency and midline given the context of the problem.
Students begin considering compound events as subsets of sample spaces. Students examine situations involving pairs of independent and non-independent events, and they calculate probabilities of compound events in unifrom probability models.
Students extend their understanding of variability in data and of ways to describe variability in data. They calculate and interpret standard deviation. Students use distributions to describe variability, and normal distributions are introduced as a way to model data distributions that are bell-shaped and approximately symmetric. Students calculate and interpret areas under a normal curve and explore reasoning that allows them to draw conclusions based on data from statistical studies. Students use data from a random sample from a population to estimate the values of population characteristics, and they use margin of error to quantify the uncertainty associated with their estimates.