Upper School (Grades 9 - 12)

# Math

The Upper School Mathematics program provides students with a strong foundation by teaching critical thinking skills, challenging students to achieve proficiency with analytical and computational techniques and to apply logical thinking towards advanced problem solving. Students develop mathematics vocabulary and use mathematical modeling in all fields of study. Students study Geometry and Algebra 2/Pre-Calculus and then determine together with the Math Department whether to pursue a track that leads to a conceptual/analytical approach via the exploration of real-world math and decision-making or the rigor of higher math education via Probability, Statistics, and AP Calculus.

### List of 6 items.

• #### Geometry

Students will explore important ideas in geometry and trigonometry, and apply skills with functions and algebra. The first unit explores similarity by thinking of shadows and reflections.  In the second unit, students use the ancient tools of straightedge and compass to construct figures. Using logic and Euclid’s postulates, students will be introduced to the ideas of mathematical proof as well as transformational geometry. Coordinate geometry is explored in order to better analyze figures. Concepts such as area, surface area, and volume will be connected to trigonometry in the solving of complex problems.
• #### Algebra 2

The ideas of advanced algebra are explored by investigating several large problems. In the first unit, students will investigate population growth by fitting a function to a set of data. They will consider the nature of various mathematical descriptions of growth, including linear and exponential functions, slope, and derivatives. Students also learn about common and natural logarithms. In the second unit, students will explore the key ideas of probability and strategic thinking. Students will continue to develop their abilities to tackle substantial problems, to reason mathematically, and to communicate their thinking—that is, their understanding of what it means to do mathematics. The third unit further develops the ideas of trigonometry by investigating motion on a Ferris wheel. Students also explore projectile motion and how these physics principles connect to ideas of functions. The last unit focuses on functions and their properties. Students will explore polynomials, rational functions, and many others.
• #### Pre-Calculus

This class introduces mathematical foundations necessary for the study of calculus. Pre-Calculus is an introduction to analytic geometry and the elementary functions of analysis, including algebraic, trigonometric, logarithmic, and exponential functions. The use of the graphing calculator will be included. Students will come to understand the definitions, graphs, properties, and applications of the functions that will be of importance during the study of calculus, as well as to learn to read, analyze, and solve situational problems in which mathematics is applicable.
• #### AP Calculus

In this Advanced Placement course, students are expected to engage with the mathematics of calculus—experimenting and exploring, not just with a pencil and paper but with graphing calculators, computers, and most importantly with fellow students. Students are expected to work closely with the other students in their class on a variety of group projects, spending a lot of their time discussing and explaining their reasoning both verbally and in writing. This course requires engagement with material that is real and current and connected to students’ lives in a very real way, teaching them that they can find calculus in the newspaper and in television shows, and in sporting events and their favorite foods. As a result of this class’s rigorous preparation, students will be well equipped to take the Advanced Placement exam.
• #### Probability and Statistics

In this course, students will learn the basics of conducting and analyzing experiments. Students will learn how mathematicians use probability to calculate real world experiments. Furthermore, students will conduct their own experiments based on what they learned. Students will study the key concepts of random sampling, modeling, simulation, and randomized experiments. In addition, they examine conditional probability, permutation, types of events, random variables, expected values, and probability concepts in problem solving. In the Statistics portion of the course, students will analyze data from given articles or experiments. Some key concepts will be quantitative data, data sets and dot plots, bivariate data, scatter plots, residuals and linear regression, categorical data, bar graphs, pie charts, and frequency.
• #### Analytics: The Mathematics of Decision Making

Analytics is the study of complex systems for the purpose of improving decision-making. In this course, students will learn to use spreadsheets to organize and analyze data. They will apply the processes they learn to the decisions that they have to make in their lives. Students will use Multi Criterion Decision Making (MCDM) to analyze their college lists, helping them decide which colleges to apply to, and then later in the year use linear optimization methods to help decide which college they may want to attend. They will analyze career paths and potential jobs, look at optimizing schedules and production plans for companies, and learn to question their findings and try to improve the results. The skills and procedures learned in this course are directly applicable to business and to life.

## The Kew-Forest School

119-17 Union Turnpike
Forest Hills, NY 11375
(718) 268-4667
The oldest independent school in the borough of Queens, The Kew-Forest School is an independent co-educational, college preparatory school for students in Preschool through Grade 12.