# Mathematics Course Descriptions

## Algebra 1

Algebra 1 is the foundation for all subsequent mathematics courses and provides for students the underpinning of all future problem solving. Students will learn the language of algebra that will be utilized throughout their formal study of mathematics. Concepts to be studied will include number systems, properties, equations and inequalities, simplifying and factoring polynomials, simplifying rational expressions, and graphing both linear and quadratic functions. Students will continually be involved with solving problems requiring analysis and modeling of real world data.

## Geometry

*Successful completion of Algebra 1 required*

The underlying theme of the course is to introduce the concepts of geometry to the students, while reinforcing the concepts learned in Algebra I. Furthermore, the basic concepts of coordinate geometry are interwoven throughout the course. Students are expected to use inductive and deductive thinking skills to solve geometric problems, and they are expected to describe how they arrived at the solutions. This course is also designed with a wider scope to reach pupils of different learning abilities through use of hands-on activities, small-group work, projects, and problems related to real-life applications.

### Honors Geometry

*Successful completion of Algebra 1 requiredDepartmental recommendation required*

Students begin the course with the study of inductive reasoning and subsequently learn geometry by identifying patterns and relationships that can be generalized into the theorems of geometry. Often work is done in small groups during class time with the teacher acting as mentor rather than lecturer. The class as a whole discusses its findings, checks homework answers, and asks questions about the work. The content of the course includes line and angle properties; constructions; triangle and quadrilateral properties; characteristics of all polygons and circles; surface area and volume of solids; basic triangle trigonometry; and proofs using the geometric relationships which have been discovered. Throughout the year students gain experience in reading a math textbook, cooperative learning, writing about mathematics, and oral explanation of concepts.

## Algebra 2

A continuation and extension of the skills developed in Algebra 1 and taken after Geometry, Algebra 2 builds a broader base of concepts with a deeper understanding of algebraic ideas. Topics emphasized will include linear, quadratic, exponential and logarithmic equations, functions, and their graphs; systems of equations and inequalities; matrices; polynomial and rational expressions, equations, and their graphs; and sequences and series. The year will also provide a brief introduction to topics in conic sections, probability, and trigonometry.

## Honors Algebra 2

*Successful completion of Geometry or Honors Geometry required**Departmental recommendation required*

Honors Algebra 2 moves quickly through linear algebra and graphing to focus first semester on matrices, quadratic functions, and polynomial functions. Second semester topics include rational exponents, radical functions, exponential and logarithmic functions, rational functions, conic sections, counting methods and probability, and lastly sequences and series. Students are expected to display their understanding of concepts using appropriate mathematical language both verbally and in writing. Along with their studies, students are introduced to the graphing calculator and taught to use it in conjunction with paper and pencil methods. This course highly recommended for students who plan to take Honors Precalculus.

## Precalculus

Students will study and graph polynomial, rational, exponential, logarithmic, as well as trigonometric functions. Then using the graphing calculator and data lists from real situations, the student finds the linear, quadratic, cubic or exponential curve of best fit to find the equation that best describes the data presented. A great deal of time is spent on interpreting the equations, relating them to the graph, and finally the applications of the material. Much time and emphasis is devoted to the study of Trigonometry. The unit circle is used to define the six trigonometric functions, to find the value of the functions for specific angles, and to draw the graph of each of the six functions. The trigonometric properties are derived and used to prove trigonometric identities. The trigonometric functions are used to solve applied problems involving right triangles and oblique triangles. The course is completed with a brief study of sequences, inductions, counting and probability.

## Honors Precalculus

*Successful completion of Algebra 2 or Honors Algebra 2 required**Departmental recommendation required*

Honors Precalculus is a preparation for one of the calculus courses, typically AP Calculus AB. Principally, it is a study of functions from both algebraic and geometric viewpoints, with a focus on applications. Beginning with the study of linear data analysis, students practice modeling real data and explore the usefulness and accuracy of different models. Building on their knowledge of a variety of basic functions, students discover how to express complex mathematical relationships through transformations and compositions. Students are then able to explore non-linear data analysis in order to deal with more complex data sets. A significant amount of time is spent developing the foundations for and understanding the intricacies of trigonometric functions. A study of the concept of limits and instantaneous rates of change facilitates a smooth transition into the subsequent calculus course.

## Mathematics of Finance

*Spring semester only; Open to seniors*

The course covers many financial topics such as banking, college costs, car loans, mortgage loans, insurance, credit cards, credit scores, budgets, taxes, retirement planning, financial goals, personal goals, and career choices so that students will be more educated in making wise financial decisions and choices. The course also includes a study of sequences and series (including Fibonacci and Golden Ratio) and probability, concepts that are tested on the ACT and SAT in addition to general standardized test review.

## Statistics

*One-semester elective**Successful completion of Algebra 2 or Precalculus required*

The course content focuses on data exploration, experimental design, simulation procedures, and the examination of surveys and information from samples. Real data is used for all statistics lessons. Students learn to select appropriate graphs and plots for a given set of data and to use technology to create graphs. They will learn to examine graphs and plots in order to describe the data, detect patterns in the facts, and make conjectures about them. Analysis of the data in natural context is stressed in addition to the importance of clear, written communication of findings and conclusions. Students are also coached in techniques for the analysis of data found in the media or chosen fields of study. Students will be involved in hands-on experiments revealing the concepts of the course. Students will generate their own data, surveys, and simulation results through individual and group projects.

## AP Statistics

*Successful completion of Precalculus or Honors Precalculus**Departmental recommendation required*

AP Statistics is a year-long course equivalent to a one-semester, non-calculus based college course in statistics. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from real data. The four main areas of study are exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Statistics, more than any other mathematics course, is ideally suited for hands-on, small group activities, therefore it functions as a lab-oriented course. In addition to student generated data and real world data available from a variety of sources, technology plays an important role in the course. Each student will be required to have a TI-83+ graphing calculator, and the computer program Minitab is used. While the calculator may be used on the AP exam, students will not be required to use computers. However, students will be required to read output from standard statistical packages. The AP Exam is a requirement of the course.

## Calculus

*Successful completion of Precalculus or Honors Precalculus required**Departmental recommendation required*

Calculus is the study of the interplay between changing quantities. This course covers topics from both differential and integral calculus. Through the study of infinite processes involving the infinitely small (i.e., limits), students explore the concept of instantaneous rates of change (i.e., the derivative) and learn a variety of techniques for differentiation. Derivatives are then employed in the study of applications including optimization, curve-sketching, rectilinear motion, and related rates. After developing the concept of the antiderivative and learning a variety of techniques for antidifferentiation, students investigate applications including rectilinear motion and differential equations. Another instance of infinite processes involving the infinitely small (this time Riemann sums) leads students into the study of the definite integral and its applications including area, volume, and average value. Aided by digital technology where appropriate, students learn to explore and solve problems numerically, graphically, and analytically as well as to improve their abilities in both the verbal and written discussion of mathematical topics. The emphasis throughout the course is on the deepening of conceptual understanding rather then the memorization of problem types.

## Mathematical Modeling

*Successful completion of Algebra 2 or Honors Algebra 2 required*

Mathematical modeling is the application of mathematical concepts, structures, and techniques to describe and predict the behavior of real-world systems. This course focuses on crafting models by reducing complex systems from the world around us into mathematical language, using mathematical techniques to analyze these models, and then interpreting those results in the context of our original real-world problems. The mathematical structures and techniques employed include recursive and iterative functions, Euler’s method and nonlinear differential equations, and probability and agent-based modeling. Topics covered include population growth, finance, epidemiology, predator-prey scenarios, and error approximation. Advanced features of Excel, basic computer programming with Python, and agent-based modeling with NetLogo are introduced. No programming experience is necessary.

## Mathematics and Society

*Fall semester elective; Open to seniors*

This course will provide students an opportunity to explore and appreciate the role mathematics has played in the history of mankind. Students will see how different cultures and people have contributed to the development of mathematics and they will explore the relationship between important mathematical discoveries, the arts, fashion, technological advances, and historical events.

## AP Calculus AB

*Successful completion of Honors Precalculus with departmental recommendation OR successful completion of Precalculus with departmental recommendation and the successful completion of summer work assigned by Department Chair required*

AP Calculus AB covers all topics in the AB curriculum, broadly limits, derivatives, and integrals. Applications of derivatives include behavior of graphs, related rates, optimization, and rectilinear motion. Applications of integrals include finding area, solving differential equations, and calculating volume by disks, washers, and shells. Functions are explored algebraically, numerically, and graphically. Students are expected to convey clear understanding of concepts verbally and in writing as well as being able to work problems mathematically. Group projects enhance understanding of major concepts. Students use a graphing calculator and are required to take the AP exam.

## AP Calculus BC

*Successful completion of Honors Precalculus required**Departmental recommendation required*

AP Calculus BC covers all topics in AP Calculus AB. Additionally, students study arc length, area of surface of revolution, logistic equations, partial fractions, improper integrals, integration by parts, infinite series, Euler’s Method, L’Hospital’s Rule, Taylor and Maclaurin polynomials, polar coordinates, vector-valued functions, and parametric equations. Students use a graphing calculator and are expected to take the AP exam.

## MSON Multivariable Calculus

*Successful Completion of AP Calculus BC required*

The mathematics of three dimensions is the emphasis of this college-level course. Multivariable Calculus will explore the geometry of three-dimensional space, including vector arithmetic. It will also explore three-dimensional surfaces, using the tools of derivatives and integrals expanded into multiple dimensions. A robust unit on differential equations will allow students to review the topics of single-variable calculus. The emphasis throughout the course will be on problem-solving and on real-world applications of the tools students learn in fields such as economics, astronomy, physics, engineering, and medicine.

## MSON Advanced Math Topics: Personal Finance

*Fall semester elective; Open to juniors and seniors*

This course is a one semester course for those interested in learning topics related to mathematics that are outside the standard mathematics curriculum or explore topics already within the curriculum but at a deeper level. MSON is hoping to augment the mathematical selections with a course in Personal Finance. Students will choose from a list of suggested topics related to personal finance that they would like to explore. The remainder of the course focuses on topics chosen by the teacher with student input. Examples may include topics such as goal setting, saving and investing, borrowing and credit, budgeting and financial risk. Students should be willing to explore unfamiliar mathematics, exhibit an interest in mathematical reasoning,, and display a hefty dose of mathematical curiosity.

## MSON Advanced Abstract Math

*Fall semester elective; Open to juniors and seniors*

This student-driven course is for those interested in learning topics outside the standard mathematics curriculum, as well as learning topics already within the curriculum at a deeper level. At the beginning of the course, there will be a brief unit on proof techniques. After a short time, students will be expected to turn in a list of several mathematical topics about which they would like to learn more. The TEACHER will then choose from these topics to form a cohesive unit and collect input from as many students as possible. Topics from previous semesters include fractal geometry and dimension, Cantor’s set theory, number theory, cryptography, power series, and Fibonacci numbers, to name a few. Students share solutions, which will be evaluated in terms of accuracy both in writing and in spoken communication, as both of these skills are of paramount importance to the budding scientist or mathematician.