# Mathematics

We recognize that mathematics is a language shared by all civilizations and all populations regardless of culture, religion, or gender and our programs are designed to improve every student's quantitative literacy. We aim to foster strong critical thinking and mathematical reasoning in our students, with the goal of teaching them to view the world through a mathematical lens.
• ## Algebra I

Algebra is the base upon which nearly all of mathematics is built; it is a leap from arithmetic to abstract, defining the rules for the study of mathematical symbols and how to manipulate them. Taken seriously, this is every student's first foray into quantitative thinking. Though Algebra may strike you as a dizzying mix of symbols, definitions, and procedures, it all boils down to just two activities—solving for x and working with formulas.
• ## Algebra II

The goal of this course in advanced algebra is to relate each new idea to the concept of a function. Applications are handled by creating mathematical models of a phenomena in the real world. Students frequently work in small groups learning to select a kind of function (quadratic, exponential, etc) that fits a given situation, and deriving an equation that suits the information in the problem. The students then use the equation to make predictions or interpretations about the real world. Although graphing calculators are incorporated to enhance the curriculum, the emphasis remains on the thought process and on understanding mathematical concepts. Computer explorations are utilized throughout the course to assist in the understanding of functions.
• ## AP Calculus AB

Students master the basic topics of differential and integral calculus, equivalent to one semester of college calculus. Besides learning a variety of differentiation and integration techniques, students also gain a deep, conceptual understanding of these topics. Clear mathematical statements demonstrating this conceptual knowledge will be required, as students prepare for the AP Calculus AB exam. All students enrolled in the course are expected to take the AP exam.
• ## AP Calculus BC

Students will continue their understanding of the mathematical contexts and concepts within calculus, namely the three big ideas of limits, derivatives, and integrals, with the addition of a fourth: series. The depth and breadth is equivalent to a second year of college-level calculus. Specifically, this course will focus on drawing connections between verbal, graphical, numerical, and analytic representations of functions. This course is designed to assist students in developing strategies and techniques to solve a diverse set of application problems, and then evaluate the reasonableness of solutions. Students will be required to use proper notation and will be able to communicate effectively with their peers and with the mathematical community. Technology will be used regularly throughout the course, with a special emphasis on graphing calculators, as a way of investigating and analyzing functions to help students draw conclusions that would have been impossible or too time consuming without supporting technology. The course will include all of the concepts and techniques that appear on the AP Calculus BC exam, and all students enrolled in the course will be expected to take this exam in May. Testing throughout the year will be designed to help prepare the students for this exam.
• ## AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Examples are drawn from applications in the natural and social sciences. Students collborate with their classmates to learn statistics by doing statistics via in-class activities and simulations, computer labs, and projects. In AP Statistics, students will master four broad conceptual themes: Exploring Data: Analysis of data through the use of graphical and numerical techniques to study patterns and departures from patterns. Sampling and Experimentation: Planning and conducting a study. Anticipating Patterns: Exploring random phenomena using probability and simulation for anticipating what the distribution of data should look like under a given model. Statistical Inference: Estimating population parameters and testing hypotheses.
• ## Calculus

Calculus is the mathematics of continuous change. To understand calculus requires a command of geometry and algebra, skills equivalent to fluency in a foreign language for many students.
• ## Geometry

Geometry is the study of shape, and draws on the right side of the brain. The subject appeals to visual thinkers who might otherwise cringe at its logic, though many students love geometry precisely because it is so logical. Students learn important definitions, postulates, and theorems connected with Euclidean geometry and apply them to solve geometrical application problems. A balance is sought between an intuitive understanding of what is true, and the need for a thorough, careful, deductive reasoning about one’s perceptions. Students learn how to order their arguments in clear, precise language when writing their proofs of geometry theorems. Students will also develop spatial skills in two and three dimensions, and review their algebra skills throughout the course. Students work on group projects and utilize computer exploration.
• ## Linear Algebra

Students who complete AP Calculus BC junior year or earlier have the option of taking our Statistics course or enrolling on their own in an advanced math class outside of York. Several recent students have taken multivariable calculus at MPC during their senior year at York, or through online programs offered by Stanford University, One Schoolhouse, or Johns Hopkins Center for Talented Youth. Please consult with the Math/Science department head, the college counselor, and the Director of Teaching and Learning for more information.
• ## Math Modeling

The overall goal of this course is to enable students to build mathematical models of real-world systems, analyze them, and make predictions about the behavior of these systems. A variety of modeling techniques will be discussed with examples taken from physics, biology, chemistry, economics, social sciences, and other fields. Mathematical modeling uses graphical, numerical, symbolic, and other techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, on the use of appropriate supporting technology (e.g., Microsoft Excel or Google Sheets, Python, and other software or programming languages), and on the effective communication of quantitative concepts and results through relevant projects and presentations. This course is not intended to be a prerequisite for Calculus, though it will introduce and help students understand the basic topics of differential and integral calculus through application. Likewise, the class can be a math elective for students seeking an additional math class, for those hoping to solidify math concepts through modeling applications, or both.
• ## Multivariable Calculus

Students who complete AP Calculus BC junior year or earlier have the option of taking our Statistics course or enrolling on their own in an advanced math class outside of York. Several recent students have taken multivariable calculus at MPC during their senior year at York, or through online programs offered by Stanford University, One Schoolhouse, or Johns Hopkins Center for Talented Youth. Please consult with the Math/Science department head, the college counselor, and the Director of Teaching and Learning for more information.
• ## Pre-Calculus

This course combines advanced Algebra II skills with trigonometry, data analysis, vectors, and an introduction to Calculus. In addition to strengthening Algebra II skills and problem-solving strategies, students learn to apply concepts to real-world problems through mathematical modeling. While the emphasis is on honing algebraic and graphical analysis skills, the course makes extensive use of the graphing calculator. Many of the same topics will be covered as in the Honors Precalculus class, but not as rigorously and at a different pace.
• ## Pre-Calculus Honors

Honors Precalculus reinforces and expands upon the concepts you encountered in Algebra II in order to prepare you for success in Calculus (and the SAT math 2 subject test). You’ll learn how to describe both new and already familiar functions verbally, algebraically, graphically, and numerically. You’ll also learn how to transform these functions in order to model real-world data. In addition, you’ll become familiar with other coordinate systems and with the use of vectors to model physical quantities. Experience with proofs will strengthen your ability to make conjectures, construct logical arguments, and justify your reasoning. Since math is best learned by doing, you’ll frequently have the opportunity to collaborate with your classmates in small group hands-on activities to explore and learn new concepts and techniques. While our focus is on learning algebraic analysis and problem-solving techniques, you’ll also make extensive use of your calculator to solve problems graphically and numerically. While Honors Precalculus covers Precalculus topics in greater depth, its scope is also much broader and includes numerous abstract and challenging enrichment topics. As a result, Honors Precalculus is intended for students who have a strong interest and aptitude for math, and who are ready, willing, and able to do the work necessary to tackle demanding problems at an accelerated pace.

# Faculty

• Jeff Hanna
Math/Science Department Chair, Physics
• Pam Durkee
• Scot Johnson
Math, Physics
• Kim Kiest
Math, Science, Discipline Committee Chair, Environmental Sustainability Coordinator
• June Trachsel
Math
• Kande Williston