# Mathematics

In York’s mathematics program, students learn to solve problems in a logical and systematic way, using the efficient and precise techniques and notations developed in the different branches of mathematics. Students learn to value mathematics by relating equations to models of phenomena in the real world. They become creative mathematical problem solvers by analyzing data in groups, communicating mathematically with their peers, and discovering the significance of their answers in real mathematical applications. Strong algebra skills and deductive reasoning are developed throughout the program, as well as a clear understanding of mathematics concepts.

#### Algebra I

Students learn how to solve algebraic equations and strengthen their problem solving skills. Each algebraic equation is related to a particular type of situation, thus giving more meaning to each type of problem solved. While calculators are used to enable the students to solve more ‘real world’ types of work problems, mental math is encouraged.

#### Geometry

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.

#### Algebra II

The goal of this course in advanced algebra is to relate each new idea to the concept of 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.

#### PreCalculus

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. The course prerequisite is successful completion of Algebra II or with consent of the Math/Science Division Head.

#### Honors PreCalculus

This course combines advanced Algebra II skills with trigonometry, data analysis, vectors, and an introduction to Calculus. While strengthening Algebra II skills, students learn to apply concepts to real-world problems through mathematical modeling. Higher order thinking is emphasized, where students are required to solve novel problems by utilizing creative problem-solving strategies. 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 regular Precalculus class, but in greater depth and breadth. Therefore, Honors Precalculus is for students who have a strong interest in and aptitude for math, and who are willing to do the work necessary to tackle challenging problems at an accelerated pace.

#### Calculus

This course introduces students to the basic concepts of differential and integral calculus, and is roughly equivalent to one semester of college calculus. Although this course is not aimed at preparing students for the Advanced Placement Calculus AB exam, the topics covered are very similar. The pacing of this course is slower than in Calculus AB, in part because the material does not need to be finished in early May in time for the AP exam.

#### AP Statistics / 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. Important components of the course include the use of technology (computers and calculators), projects, and laboratories, and cooperative group problem-solving. The course covers 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.

#### 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

This course continues the study of calculus begun in previous courses. An extensive review of earlier topics is combined with an assortment of challenging new topics and techniques. The new topics include those usually covered in the second semester of college calculus. Topics are approached with an increased emphasis on mathematical rigor. 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 also be designed to help prepare the students for this exam.

#### After Calculus BC

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 through Stanford University’s EPGY program during their senior year at York. Please consult with the math/science department head, the college counselor, and the Academic Dean for more information.

#### Extracurricular Activities in Math

- Math Counts
- Math Challenge Teams
- Mathletics
- American Mathematics Contest--AMC 10 and AMC 12