# MATHEMATICS

### COURSE DESCRIPTIONS

#### 141  |   ALGEBRA I HONORS     1.0 credit

The study of equations and graphs is a focal point of this course for students with a strong mathematics background and high ability. Ideally, a student will understand and be able to solve problems in factoring, equation solving, the quadratic formula and graphing of equations and inequalities, systems of equations, exponents, quadratic equations, factoring, radicals and functions. Students will be able to solve problems in linear and quadratic equations as well as systems of equations in two and three variables. The study of applications and problem solving will also be stressed.

#### 142  |   ALGEBRA 1      1.0 credit

Designed for students with more individual needs, this course gives a good background for students to complete a four-year mathematics program. Standard algebraic skills and concepts are taught. Ideally students will be able to solve problems in factoring, equation solving, the quadratic formula and graphing of equations and inequalities, systems of equations, exponents, quadratic equations, factoring, radicals and functions.

#### 144  |   ALGEBRA I      1.0 credit

This course gives a good background for students who intend to take a standard three or four-year mathematics program. Standard algebraic skills and concepts are taught. Ideally, a student will understand and be able to solve problems in factoring, equation solving, the quadratic formula and graphing of equations and inequalities, systems of equations, exponents, quadratic equations, factoring, radicals and functions.

#### 145  |   ALGEBRA II HONORS     1.0 credit

Prerequisites: 85% in Algebra I Honors (or 93% in Algebra I).

In this course, students with a strong Algebra I background will continue the study of algebraic structure. Functions and relations will be covered. Ideally, the student will understand and be able to do equation solving: linear – one and two variable, quadratic, exponential and logarithmic; sequences; series; matrices; determinants and probability and basic statistics. Taken as a freshman, this course will lead to the study of Calculus as a senior.

#### 243  |   ALGEBRA 2     1.0 credit

Prerequisites: Successful completion of Algebra 1 or Algebra 1b or Geometry.

This course is designed for students with more individualized needs in mathematics. It will take the standard Algebra II curriculum and present the major topics. In this course, algebraic structure is stressed. Ideally, the student will understand and be able to solve problems dealing with functions and relations including linear (one and two variable), quadratic, exponential and logarithmic.

#### 244  |   ALGEBRA II      1.0 credit

Prerequisite: Successful completion of Algebra I.

In this course, algebraic structure is stressed. Ideally, the student will understand and be able to solve problems dealing with functions and relations including linear (one and two variable), quadratic, exponential and logarithmic. The student will also be exposed to the following topics: sequences, series, matrices, determinants and probability.

#### 245  |   GEOMETRY WITH TRIGONOMETRY HONORS     1.0 credit

Prerequisites: 85% in Algebra II Honors (or 93% in Algebra II).

This course introduces the student to geometric terms, theorems, logic, formal and informal proofs. Ideally, a student will understand and be able to work with congruent triangles, parallelograms, circles and polygons. He will receive periodic reviews of algebra during this course of study. The student will receive an introduction to trigonometric and circular functions including the Law of Sines, Law of Cosines, trigonometric identities, trigonometric graphs, trigonometric inverses  solutions of triangles, and the unit circle. This course is designed for the student who has a strong mathematics background.

#### 340  |   AP STATISTICS     1.0 credit

Prerequisites: 80% in Algebra II Honors.

This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course:  exploring data, sampling and experimentation, anticipating patterns, and statistical inference.

»  A fee is charged for the AP exam.

#### 341  |   PRE-CALCULUS HONORS     1.0 credit

Prerequisites: 85% in Algebra II Honors (or 93% in Algebra II) AND 85% Geometry with Trigonometry Honors (or 93% Geometry with Trigonometry).

This course is intended to prepare students with strong math skills for Calculus in their senior year of high school or first year of college. The major areas of study will be polynomial, rational, exponential, logarithmic, and trigonometric functions, sequences and series, analytic trigonometry, parametric and polar equations, limits, the concept of a derivative, and calculation of basic derivatives. Students will understand and solve problems from multiple perspectives using algebraic representations, graphs, and numerical methods. They will also develop their ability to exploit the utility of a graphing calculator in the solution of problems.

#### 343  |   GEOMETRY      1.0 credit

Prerequisites: Teacher recommendation.

This course introduces the student to geometric terms, theorems, logic, formal and informal proofs. Ideally, a student will understand and be able to work with congruent triangles, parallelograms, circles and polygons and complete periodic reviews of Algebra. Students will receive an exposure to right triangle trigonometry. This course is designed for the student who has more individualized needs.

#### 344  |   GEOMETRY WITH TRIGONOMETRY     1.0 credit

Prerequisite: Successful completion of Algebra II.

This course introduces the student to geometric terms, theorems, logic, formal and informal proofs. Ideally, a student will understand and be able to work with congruent triangles, parallelograms, circles and polygons and complete periodic reviews of Algebra. The student will receive an introduction to trigonometric and circular functions including the Law of Sines, the Law of Cosines, trigonometric identities, graphs, inverses, solutions of triangles, and the unit circle.

#### 440  |   AP PRE-CALCULUS     1.0 credit

Prerequisites: 85% in Algebra II Honors (or 93% in Algebra II) AND 85% Geometry with Trigonometry Honors (or 93% Geometry with Trigonometry).

In AP Precalculus, students explore everyday situations and phenomena using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, an important practice for thriving in an ever-changing world. AP Precalculus prepares students for other college-level mathematics and science courses. The framework delineates content and skills common to college precalculus courses that are foundational for careers in mathematics, physics, biology, health science, social science, and data science.

»  A fee is charged for the AP exam.

#### 441  |   AP CALCULUS  — AB      1.0 credit

Prerequisite: 90% in Pre-Calculus Honors.

This course covers all of the topics set forth by the College Board Advanced Placement Program in Calculus AB. Ideally, the student will understand and be able to work with the concepts of functions, graphs, and limits, along with their derivatives and applications of the derivative. Integral calculus and its applications will also be studied. This course is fast paced and designed for highly motivated and talented students.

»  A fee is charged for the AP exam.

#### 442  |   Calculus     1.0  Credit

Prerequisites:  Pre-Calculus.

This course is designed to give students an overview of Calculus topics such as limits and continuity, derivatives, anti-derivatives, integrals and differential equations. While this course covers many of the same concepts found in Advanced Placement Calculus, it is not bound by the pace and rigor necessary for success on the AP Calculus exam.  Course Topics will include: Functions, Limits, Continuity, Derivatives, Applications of Derivatives, Integration, Applications of Definite Integrals, and Integration Techniques.

#### 444  |   PRE-CALCULUS     1.0 credit

Prerequisite: Successful completion of Algebra II and Geometry with Trigonometry.

This course is designed to be a strong fourth year math course with emphasis on applications and analysis of a variety of mathematical concepts. Ideally, a student will understand and be able to solve problems in major areas of study. These areas are: functions, vectors and trigonometry, inequalities, exponents and logarithms, analytic geometry. The student will also have knowledge of polar coordinates, parametric equations, and matrices. Admission to this course is ordinarily limited to seniors.

#### 445  |   PROBABILITY/STATISTICS & COLLEGE ALGEBRA WITH TRIGONOMETRY     1.0 credit

Prerequisite: Successful completion of Algebra 2.

This course is designed for students who plan to enter fields such as economics, business, education, biology, medicine, and many others.  Ideally, a student will understand and be able to work with the concepts of random variables, probability functions, and binomial and normal distributions. College Algebra with Trigonometry is an effective mathematical tool to prepare a student for college algebra or precalculus. Ideally, a student will understand and be able to work with the concepts of linear, quadratic, exponential, logarithmic, and systems of functions, as well as their graphs, solutions and applications. The student will receive an introduction to trigonometric and circular functions including the Laws of Sines and Cosines, trigonometric identities, graphs, inverses, and the Unit Circle.

#### 449  |   AP CALCULUS — BC     1.0 credit

Prerequisites: 93% in Pre-Calculus Honors with teacher recommendation.

This course is a first and second course of study in elementary calculus. Students will prepare for the Advanced Placement Calculus BC exam which could lead to an additional semester of college math credit beyond the Advanced Placement Calculus AB credit. In addition to the AB topics, students will study vector and parametric functions, their derivatives and applications, polar curves, additional methods of integration, sequence and series and convergence.

»  A fee is charged for the AP exam.

### FLOWCHART ### MATHEMATICS DEPARTMENT DIRECTORY

Steve Naumann, Chair- Ex. 2249

Kyle Galli ’10 – Ex. 2247

Joe Kalczynski ’96 – Ex. 2292

Christina Jamil – Ex. 2248

James Higdon ’10 – Ex. 2291

Carolyn Popp – Ex. 2245

Kevin Krysiak – Ex. 2246

Daniel Kuptz – Ex. 2244

Noelle Ochoa – Ex. 2238 