ANALYTICAL PRECALCULUSHow can we move beyond “doing” math to creative problem solving? What skillsand mindsets are needed to pursue math at a higher level? In Analytical Precalculusstudents begin to move from concrete applications to abstract math concepts whilestill emphasizing the value and importance of modeling mathematical phenomena.This pathway is particularly visible in the progression through topics in trigonometry, afoundational concept of the course. A review of right-triangle trigonometry moves tothe introduction of the Unit Circle as a tool. This tool is then adapted in an exploration ofhow trigonometric patterns can be used to model cyclical behavior, followed by a lookat analytic trigonometry where identities and algebra skills are used to manipulate andtransform expressions to verify equivalence. Students use this context to review mathskills such as operations with fractions and factoring, strengthening and applying themto new contexts. Additional units include exponential and logarithmic functions as well asan introduction to limits and the derivative, preparing Analytical Precalculus students withthe material they need to be ready for Single Variable Calculus, the subsequent coursemany will take.Prerequisite: Analytical Algebra II or department chair approvalSTATISTICS AND QUANTITATIVE REASONINGMATHEMATICSHave you ever noticed how data is used to prove points? Have you ever wonderedwho is being represented in surveys that are being referenced to sway you towards aparticular decision or product? Once you start looking for data you will see it everywhere.Statistics is the science of collecting and analyzing data. In this class students explore thecomponents of statistical problem solving: formulate a question; design and implementa plan to collect data; analyze the data by measurement and graphs; andinterpret the results in the context of the original question. Unit topics includepopulation surveys, observational studies, randomized experiments, the NormalDistribution, probability, and introductory hypothesis testing. Through these topics,students work to answer questions with data they have gathered and drawnfrom professional research organizations and popular media. Students stretchto think beyond the traditional math classroom. They will lean into and exploreuncertainty, approach the world with questions rather than answers, and considerthe way data is presented in the media. Students demonstrate their learning bydesigning their own survey or experiment, applying the Normal Distribution to SATand ACT data, and designing a game that relies on probability, in addition to moretraditional assessments. Students rely heavily on Desmos and Google sheets fortheir data analysis. Students apply the skills they develop throughout the yearin the last unit as they construct questions that can be answered quantitatively,conduct hypothesis testing, and craft a report to present their results.Prerequisite: Algebra II with Data and Modeling or Analytical Algebra II
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