# Mathematics

The mathematics department focuses on developing **a student’s ability to solve problems, both independently and in collaboration, and to embrace the complexity** they present. Our extensive course offerings and varied methods of instruction are uniquely designed to challenge and stimulate students, who practice **core skills while exploring the applications of their work to life outside the classroom.**

On a daily basis, students **solve problems on the board, create their own math problems, debate solutions with their classmates, design inventive projects, analyze mistakes, and receive individualized feedback **sfrom teachers. In striving toward mastery of the material covered in each course, students prepare themselves for future studies while also developing an enjoyment for mathematics as a whole.

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### Course of Study

## Algebra 1

Algebra I is an introductory course in which you will engage the language of algebra and functions, with emphasis on reading, writing, and evaluating algebraic expressions. In addition, the course deals with the fundamental operations of polynomials, linear equations, linear inequalities, quadratic equations, factoring, fractional equations, radicals, and radical equations. All of our studies are supplemented by word problems taken from the wider world.

## Geometry

*Prerequisite: Completion of Algebra I, up through the study of quadratic equations*

Geometry promotes deductive reasoning through the application of logic to geometric figures. The framework for this study consists of proofs, both formal and informal. The course begins with an introduction to the terminology and concepts of geometry, which are developed through the examination of increasingly complex figures, largely in two dimensions. As the year progresses, a third dimension is introduced, and the concepts of surface area and volume are fleshed out. Expect this course to develop your problem-solving, organizational, and communication skills, as you develop a more concrete understanding of the mathematics of shapes.

## Applied Algebra II

*Prerequisite: Completion of Algebra I and Geometry*.

Applied Algebra II allows you to review and build upon your understanding of the algebraic concepts covered in Algebra I. We begin by solving linear equations and inequalities, eventually progressing to manipulate and graph linear, quadratic, polynomial, logarithmic, and exponential functions and equations. The basics of trigonometry are also explored. This course includes more Algebra I review and more projects than the other Algebra II offering in order to develop your base of mathematical knowledge, your problem-solving abilities, and your understanding of the application of algebraic concepts. A Ti-84 Plus and computer or iPad are used extensively in this course.

## Theoretical Algebra II

*Prerequisite: Completion of Algebra I and Geometry.*

This course covers all of the same concepts that are covered in Applied Algebra I but more deeply and at a quicker pace. The course also covers matrices, sequences, and series. We conclude with an extensive study of trigonometry. In this course you can expect to develop a strong understanding for the complexities of algebraic concepts and strengthen your ability to solve problems independently and collaboratively. A Ti-84 Plus calculator and a computer or IPad are used extensively in this course.

## Precalculus

*Prerequisite: Completion of Algebra II*

Precalculus furthers the study of algebraic technique and is designed for students with substantial ambition in mathematics, science, engineering and related fields. Logarithms, exponentials, and trigonometry, introduced in Algebra II, are studied in greater depth and with particular regard to their applications. Basic familiarity with those topics is assumed in this class. These topics are developed through a cooperative approach, where students work in teacher-supported groups to solve increasingly complex problems. The course leads up to an introduction to the conceptual aspects of limits as applied to finding slopes, the central concept of differential calculus. Successful completion of this course will prepare students to advance to AP Calculus.

## Advanced Placement Calculus

*Prerequisite: Completion of Precalculus.*

Advanced Placement Calculus is designed to offer a thorough introduction to the differential and integral calculus of a single variable. The course uses a variety of methods, numerical, graphical and analytical, to explore elementary functions. This is a demanding course, offering the possibility of college credit through the College Board’s AP program, and as such requires your considerable commitment. It is expected that, before enrolling, you will have had a thorough mathematical background, such as you may gain in our Precalculus offering. The AP exam in the spring is an integral part of the course.

## Statistics

*Prerequisite: Completion of Applied Algebra II or Theoretical Algebra II/Trigonometry*

The goal of this course is that you become informed decision-makers when presented with statistics in your educational, professional, and personal lives. Along the way, you will be introduced to the fundamentals of statistics, which include tactics for collecting data and designing experiments, randomness in data, confidence intervals, tests of significance, correlations, and regressions. Using these foundational understandings, you will analyze, interpret, and critique a diverse set of real-world data. Throughout, expect to write, think, struggle, collect, create, question, and collaborate in the process of building your statistical skills.

## Advanced Topics in Mathematics

*Prerequisite: Completion of Advanced Placement Calculus*

This course, whose content varies year to year, is designed for those students who have completed the usual high-school mathematics curriculum. Typically, the fall term is spent with problem sets developed at Exeter Academy that serve to broaden your mathematical horizons while deepening your familiarity with computational basics. In the winter we return to the Calculus textbook, covering the additional material needed for success on the BC Calculus exam, which is given in May. The spring is spent on a broad review of Calculus and other concepts helpful for success at the college level. A TI 83-84 series calculator is required for this course and will be used extensively.

Other advanced topics in mathematics that have been offered at Dublin include: AP Microeconomics, AP Macroeconomics, and AP Statistics. For a course of study of Set Theory, Number Theory, Abstract Mappings, Advanced Topics in Calculus of One and Several Variables, Infinite Sequence and Series, and Vector Space Geometry, a score of a three or higher on the AP Calculus exam is a prerequisite.