Mathematics

The ability to use and understand mathematics in our world is critical. Whether you are interested in finance, science, computers or even the arts, math is a necessary and invaluable tool. Prep requires all students to complete four years of mathematics during their time on campus. Our classes are offered at varying ability levels, allowing you to explore, discuss, learn and retain concepts at a pace that is appropriate for you. Our four year math curriculum provides a thorough background in Algebra, Geometry and Trigonometry, and prepares you to continue your study of mathematics beyond the high school level. Our classes in Calculus and Statistics provide you to study advanced and applicable concepts at an advanced level. Our teachers stress the importance of exploring topics graphically and using critical thinking and analysis to provide confirmation of new concepts or theorems. We use iPad apps and the TI-84 graphing calculator to provide a variety of ways to learn and practice concepts. We value solutions that are detailed and well organized as this will provide you with an approach that will provide future success in math. We structure our classes so that you are engaged in asking or answering questions; completing problems individually or in small groups.

Our teachers expect you to come to class ready to work each day and to alert them to any difficulties that you may be experiencing trying to learn and do your best. We are always willing to answer questions and to provide you with extra help so that you can reach, and eventualy exceed your expectations.

The Math Department sponsors three extra-curricular activities - Stock Market Club, Trig Star Club and Math Team. The Stock Market Club takes an annual trip to the floor of the New York Stock Exchange. Our Math Team has advanced to regional and state competitions as a result of their success in the Fairfield County Math League. Our Trig Star Club has won the State Championship for the last six years and compete on a national level each year.

The Math Department at Prep gives students a strong foundation to succeed in the math classroom, but also develops critical thinking and reasoning skills that students will use in their lives. Come check us out.

Mrs. Katherine Brennan

Mathematics Department Chair

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Four years of math is required for each student.

Mathematics Courses

Algebra I Level 3

Students learn how to solve problems using variables, work with exponents, factor polynomials and simplify rational and irrational expressions. Students solve linear equations and inequalities as well as radical and quadratic equations. Students learn to graph various types of functions and how to solve word problems using algebra. The Level 3 course provides students with the opportunity to spend more time studying fundamental concepts to ensure success in future math courses.

Algebra I Level 2

Honors Algebra I

Students learn how to solve problems using variables, work with exponents, factor polynomials and simplify rational and irrational expressions. Students solve linear equations and inequalities as well as radical and quadratic equations. Students learn to graph various types of functions and how to solve word problems using algebra. The Honors level course will challenge students with an accelerated pace, in depth study of important concepts, and application to real world situations.

Geometry Level 3

Students study spatial relationships in two and three dimensions and inductive and deductive reasoning. They study theorems involving parallel lines, congruent triangles, similar triangles, and circles. Students learn right triangle trigonometry and area and volume formulas. The Level 3 course provides students with the opportunity to spend more time studying fundamental concepts to ensure success in future math courses.

Geometry Level 2

Honors Geometry

Students study spatial relationships in two and three dimensions and inductive and deductive reasoning. They study theorems involving parallel lines, congruent triangles, similar triangles, and circles. Students learn right triangle trigonometry and area and volume formulas. The Honors level course will challenge students with an accelerated pace, in depth study of important concepts, and application to real world situations.

Algebra II Level 3

Students develop the skills to work in the real and complex number systems. Students study rational and irrational numbers and problem solving with them. Students review linear functions and begin a study of quadratic, exponential and logarithmic functions. Students also study conic sections as well as permutations and combinations. The Level 3 course provides students with the opportunity to spend more time studying fundamental concepts to ensure success in future math courses.

Algebra II Level 2

Honors Algebra II

Students develop the skills to work in the real and complex number systems. Students study rational and irrational numbers and problem solving with them. Students review linear functions and begin a study of quadratic, exponential and logarithmic functions. Students also study conic sections as well as permutations and combinations. The Honors level course will challenge students with an accelerated pace, in depth study of important concepts, and application to real world situations.

Introductory Pre-Calculus With Trigonometry

This course includes the study of many topics found in Pre-Calculus and also addresses topics commonly found in required college courses for non-math majors. The pace will allow for review of key algebra and geometry concepts that are needed for success in this course and beyond. Topics will include linear, polynomial, exponential and logarithmic functions as well as major areas of trigonometry including the Unit Circle, Law of Sines, Law of Cosines and basic identities. Applications to these topics will also be included.

Pre-Calculus

Honors Pre-Calculus

Pre-Calculus is designed to prepare students for a course in Calculus. One third of the course is spent studying trigonometry. In addition, students continue their study of polynomial, rational, exponential, and logarithmic functions. Students also study basic sequences and series, probability and introductory topics in calculus. The Honors level course will challenge students with an accelerated pace, in depth study of important concepts, and application to real world situations.

Honors Pre-Calculus with Introductory Calculus

Students will cover all topics covered in the Pre-Calculus curriculum, including polynomial, rational, exponential and logarithmic functions, and an extensive study of trigonometry. In addition, students will study limits, rates of change, and derivative rules. Students who successfully complete this course can enroll in AP Calculus AB or BC in their senior year. Students will be expected to complete independent assignments throughout the year.

Calculus

Calculus is open to students who have completed Pre-Calculus. This course begins with a brief review of trigonometric functions, natural logarithms and exponential functions. This course includes a study of limits, rates of change, derivatives and an introduction to integrals and selected applications. All topics will be investigated numerically, algebraically and graphically.

AP Calculus AB

AP Calculus BC

AP Calculus BC covers all topics outlined in the syllabus written by the College Board. Students will study all topics from AP Calculus AB. Additionally, students will study parametric, polar and vector function; L’Hopital’s Rule; Euler’s method; applications of integrals; antiderivatives by substitution and parts; improper integrals; Polynomial approximations and series. These topics are investigated numerically, algebraically and graphically. Students will be prepared to take the AP Calculus BC exam in May.

Statistics

AP Statistics

AP Statistics covers all topics outlined in the syllabus written by the College Board. Students will study the major concepts and tools relating to collecting, analyzing, and drawing conclusions from data. Students will be exposed to themes including exploring data, sampling, and experimentation, anticipating patterns and statistical inference. The use of a TI-83/84 calculator is integral for this course. Students will be prepared to take the AP Statistics exam in May.

Arrupe Virtual Learning Institute

Linear Algebra

This course will cover the essentials of linear algebra. Topics covered will include matrix arithmetic, systems of equations, the determinant function, vectors in R2 and R3, general vector spaces, eigenvalues and vectors, and linear transformations. This course is a yearlong course that is offered online through the Arrupe Virtual Learning Institute. This course has a weekly synchronous meeting that is mandatory.

Multivariable Calculus

Special Note: Dual Credit Course with Creighton University

This course will focus on the study of fundamental theorems and applications of multivariable calculus, extending the calculus of one-dimension studied in AP Calculus BC to Euclidean spaces of arbitrary dimension. The course will begin with careful consideration of vectors in Rn and then move on to the theory of partial derivatives and vector fields. Multiple Riemann integrals and their applications will be covered in term 2, as well as important theorems of vector calculus including the theorems of Green, Gauss, and Stokes. In particular, a nontrivial amount of real analysis and point-set topology will be studied to facilitate the development of certain multivariable calculus concepts. This increased sophistication will allow students to see more clearly how multivariable calculus is a beautiful generalization of single-variable calculus. This course is a yearlong course that is offered online through the Arrupe Virtual Learning Institute. This course has a weekly synchronous meeting that is optional.

Statistical Reasoning in Sports

The purpose of this course is to learn the foundational concepts and tools of descriptive and inferential statistical reasoning in a fun way. This is an introductory, non-AP course, that covers most of the concepts in an introductory statistics course by working with data from high school, amateur, and professional sports. In our data-saturated world, citizens must be able to ask thoughtful questions, properly analyze data, and, most importantly, use critical thinking skills to draw appropriate conclusions and recognize inappropriate conclusions made by others. A culminating activity will include applying course concepts by analyzing data from a selected school sport activity, assuming approval from school administration and coaching staff. This course is a spring semester course that is offered online through the Arrupe Virtual Learning Institute. This course has a weekly synchronous meeting that is optional.

Geometry (Summer - Fast Track)

This course includes an in-depth analysis of plane, solid, and coordinate geometry as they relate to both abstract mathematical concepts as well as real-world problem situations. Topics include logic and proof, parallel lines and polygons, perimeter and area analysis, volume and surface area analysis, similarity and congruence, trigonometry, and analytic geometry. Emphasis will be placed on developing critical thinking skills as they relate to logical reasoning and argument. Students will be required to use different technological tools and manipulatives to discover and explain course content.

This is intended for rising sophomore students. The course runs for two months over the summer and has a time commitment of 6 - 8 hours per day. Students must obtain permission from the Mathematics Department Chair to enroll in the course.

Pre Calculus (Summer - Fast Track)

Pre-Calculus is defined to be the study of functions and limits. In this course, the fundamental concepts of functions and limits will lead you to begin understanding the branch of mathematics referred to as Calculus. Our focus will be to discover a wide range of functions that are the building blocks of Calculus. This summer you will use your mathematics in a wide variety of applications. You have often asked, “[w]here am I going to use all this Algebra and Geometry?” In this course, you will begin to find the answer to that question. If you are expecting to review the same material you worked in your last course, this is not the class for you. Get ready for a course that will challenge the best student.

Our Math Faculty