## Mathematics

The mission of the Mathematics department is to enable all students to develop skills in analysis and creativity, as well as critical thinking, while they acquire the requisite technical knowledge of mathematics. Our students learn to understand that mathematics is not a series of disjointed facts, procedures and processes, but a continuous discipline with a common foundation. As students are guided along their journey, we recognize there are multiple means to achieving successful ends and therefore eschew a ‘one size fits all’ solution approach.

CBA’s mathematics curriculum offers standard, honors and accelerated courses from Algebra I through Differential Equations, as well as all College Board sanctioned advanced placement courses (i.e. Calculus AB, BC, and Statistics). Progression through the mathematics curriculum is based upon demonstrated ability via meritorious performance and is not defined by grade level.

### MATHEMATICS DEPARTMENT

#### (210S) Algebra I

The first in the series of algebra courses sets the foundation upon which higher level mathematics courses are constructed.  Topics studied include but are not limited to the real numbers system, identifying patterns, use of variables, data organization, graphic display of data, linear equations,  polynomials, factoring, rational expressions, rational equations, systems of linear equations, an introduction to functions, an introduction to matrices, radicals, linear inequalities, quadratic equations, and application problems. (5 credits)

#### (210H) Algebra I - Honors

The first in a series of algebra courses sets the foundation upon which higher level mathematics are constructed.  Topics studied include but are not limited to the real numbers system, identifying patterns, use of variables, data organization, graphic display of data, linear equations, polynomials, factoring, rational expressions, rational equations, systems of linear equations, an introduction to functions, an introduction to matrices, radicals, linear equalities, quadratic equations, inverse matrix applications, Cramer’s rule, probability and odds, completing the square, trigonometric ratios, and application problems.  (5 credits)

#### (220S) Geometry

The course presents geometric concepts both synthetically (without coordinates) and analytically (with coordinates).  Topics studied include but are not limited to logic and reasoning, angle relationships, parallel and perpendicular lines, congruence and similarity in geometric figures (particularly congruent triangles), circles and their arcs and right triangles. An introduction to three-dimensional geometry will include a discussion of surface area and volume. The basic three trigonometric ratios will be introduced, as well as applications of trigonometry. Supplementary topics include set operations, number systems, probability, and an introduction to basic statistics. (5 credits)

#### (220H) Geometry - Honors

The course presents geometric concepts both synthetically (without coordinates) and analytically (with coordinates).  Topics studied include but are not limited to logic and reasoning, angle relationships, parallel and perpendicular lines, congruence and similarity in geometric figures (particularly congruent triangles), circles and their arcs and right triangles. An introduction to three-dimensional geometry will include a discussion of surface area and volume. The six trigonometric ratios will be introduced, as well as applications of trigonometry. Supplementary topics include set operations, number systems, probability, an introduction to basic statistics, quadratic equations, completing the square, graphing a parabola, and SAT preparation. (5 credits)

#### (220A) Geometry-Algebra II

An accelerated course combining the content of Honors Geometry and Honors Algebra II (excluding Trigonometry) into a single year.  Trigonometry is covered in the next course of the accelerated sequence, i.e. Trigonometry/Analysis. This course is intended for the strongest students in mathematics. (5 credits)

#### (230S) Algebra II-Trigonometry

The second in the series of algebra courses revisits topics covered in Algebra I and then expands to topics including but not limited to functions and relations, quadratics, matrices, systems of equations and inequalities, linear programming, irrational numbers, conic sections, polynomial, rational, radical, exponential and logarithmic functions, and the six trigonometric functions and their graphs. (5 credits)

#### (230H) Algebra II-Trigonometry- Honors

The second in the series of algebra courses revisits topics covered in Algebra I and then expands to topics including but not limited to functions and relations, quadratics, matrices, systems of equations and inequalities, linear programming, irrational numbers, conic sections, polynomial, rational, radical, exponential and logarithmic functions, graphing rational functions, the six trigonometric functions and their graphs, trigonometric identities, trigonometric equations, Pascal’s triangle, binomial theorem, probability, sequences, series, systems of three equations, and additional matrix topics. (5 credits)

#### (230A) Trigonometry-Analysis

The sequel to Geometry/ Algebra II (220A), this accelerated course combines the trigonometry content of Honors Algebra II/Trigonometry and Pre-Calculus into a single year. This course enables the strongest students to complete three years of mathematics in two years as a preparation for a Calculus course. (5 credits)

#### (240S) Calculus I - Standard

The course focuses on the study of Calculus of a Single Variable.  Topics include but are not limited to a review of polynomials, trigonometric, exponential, and logarithmic functions, followed by a thorough investigation of limits, continuity, the formal definition of a derivative, derivative rules, higher order derivatives, utilizing derivatives to graph functions, applications of differential calculus to a variety of real-world problems, integration rules, indefinite integrals, definite integrals, integration by u-substitution, areas between graphs of functions and volumes of revolution.  Derivatives and integrals of trigonometric functions are also covered.  (5 credits)

#### (240H) Pre-Calculus - Honors

The last in the series of algebra courses prepares students for the study of Calculus. All major areas covered in Algebra II are reinforced in a greater depth with additional applications aided by the use of calculators. Problems are approached from a variety of perspectives, including graphical, numerical, verbal, and algebraic. The topics require students to exhibit critical thinking skills as they analyze a variety of problems, create functions from a problem situation, and solve optimization problems using those functions. Topics studied include but are not limited to functions, solving equations and systems of equations, series, sequences, matrices, complex numbers, conic sections, polar and parametric equations, vectors, trigonometry, the applications of trigonometry, and an introduction to Calculus. Types of functions studied include but are not limited to linear, quadratic, higher order polynomials, radical, absolute value, rational, trigonometric, inverse trigonometric, exponential, and logarithmic. (5 credits)

#### (240A) Advanced Placement Calculus AB

This course consists of a thorough first-year college-level study of Differential and Integral Calculus. Students are prepared to take the College Board Advanced Placement Calculus AB examination. Each student is required to take the AP Exam to satisfy the course requirements. Admission is by special application. (5 credits)

#### (241S) College Algebra

The course is designed to fortify a student’s algebraic skills.  Topics studied include but are not limited to real numbers, linear equations and inequalities in one variable, absolute value equations and inequalities, linear equations and inequalities in two variables, functions, systems of linear equations, exponents, polynomials, factoring, rational expressions, radicals, complex numbers, quadratic equations, quadratic, exponential, logarithmic, and trigonometric functions. (5 credits)

#### (241H) Calculus I - Honors

The course focuses on the study of Calculus of a Single Variable. Topics include but are not limited to a brief review of polynomials, trigonometric, exponential, and logarithmic functions, followed by a thorough investigation of limits, continuity, the formal definition of a derivative, derivative rules, higher order derivatives, utilizing derivatives to graph functions, applications of differential calculus to a variety of real-world problems, integration rules, indefinite integrals, definite integrals, integration by u-substitution, integration by parts, areas between graphs of functions and volumes of revolution.  Derivatives and integrals of trigonometric functions are also covered. (5 credits)

#### (241A) Advanced Placement Calculus BC

Second course of a two-year sequence in Advanced Placement Calculus for those students who have successfully completed AP Calculus AB. Students are prepared to take the Advanced Placement BC Calculus examination. Each student is required to take the AP Exam to satisfy the course requirements. Admission is by special application. (5 credits)

#### (241) Math Team

The Math Team meets once a cycle during which students compete in the New Jersey State League, Monmouth County Shore League, National Catholic League, and/ or the Continental Calculus League.  The CBA Math Team also participates in the American Math Competition and the Association of Math Teachers of NJ Contest.  All of these competitions challenge the students’ creativity and will also help prepare them for the College Board Subject Tests in Math.  Each year, the team organizes and operates the Annual Brother Christian Jones Middle School Math Tournament for 6th-, 7th-, and 8th-grade students in local schools.  The Math Team is recommended for the more talented math students and is taken as a supplement to the regular Mathematics curriculum.  Department approval is required.  (1 credit)

#### (242S) Statistics

This course is an introduction to the two main branches of statistics; i.e. descriptive and inferential. Topics studied include but are not limited to data analysis, Uniform, Normal, Binomial, Geometric, Poisson, Uniform, and Chi-Square distributions, theoretical probability, experimental probability, confidence intervals, and one and two sample hypothesis testing.  Projects completed throughout the course provide students hands-on experience with statistical concepts.  (5 credits)

#### (242H) Calculus II - Honors

This course is the second part of a two-year sequence which completes the study of Calculus of a Single Variable. Important elements from Calculus I are reviewed and explored in greater depth with more challenging problems. Topics in derivative and integral calculus that were covered in the first part of the sequence are expanded upon and used in a greater variety of applications. The course concludes with advanced integration techniques, improper integrals, and sequences and series. (5 credits)

This course is equivalent to a college-level, non-Calculus Statistics class. Topics covered include data analysis, experimental design, simulation of experiments, probability, inference, confidence intervals and hypothesis testing. The Normal, Binomial, Geometric and Chi-Square distributions are discussed. Students will be prepared to take the AP Statistics exam. Each student is required to take the AP Exam to satisfy the course requirements. Admission is by special application. (5 credits)

#### (243S) Pre-Calculus

The last in the series of algebra courses prepares students for the study of Calculus. All major areas covered in Algebra II are reinforced in a greater depth with additional applications aided by the use of calculators. Problems are approached from a variety of perspectives, including graphical, numerical, verbal, and algebraic. The topics require students to exhibit critical thinking skills as they analyze a variety of problems, create functions from a problem situation, and solve optimization problems using those functions. Topics studied include but are not limited to functions, solving equations and systems of equations, series, sequences, matrices, complex numbers, conic sections, trigonometry and applications of trigonometry.  Types of functions studied include but are not limited to linear, quadratic, higher order polynomials, radical, absolute value, rational, trigonometric, inverse trigonometric, exponential, and logarithmic.  (5 credits)

#### (250A) Linear Algebra

This course gives an introductory treatment of linear algebra that is typical for a first or second year undergraduate course. Its aim is to present the fundamentals in a manner consistent with the abilities of a well-qualified high school student. Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices; determinants and permutations; general (real) vector spaces; inner products (dot products), orthogonality, cross products, and their geometric applications; eigenvectors, eigenvalues, matrix diagonalization; linear transformations. Some applications of linear algebra will be discussed as appropriate. Linear Algebra is covered during the first semester and Differential Equations is the second semester. (2.5 credits)

#### (251A) Differential Equations

This course is designed to introduce the students to differential equations with a single unknown function and a single independent variable. First order differential equations are discussed including separable, linear, and exact equations as well as the use of integrating factors and change of variable techniques. Second order differential equations are discussed including homogeneous and nonhomogeneous equations, those with constant coefficients, and the process of variation of parameters. Students will learn how to find general solutions as well as specific solutions for problems from the sciences. (2.5 credits)

#### FACULTY

Ms. Patricia Amato
Mr. Geoffrey Billet
Work Phone: (732) 747-1959 Ext 226
Mr. Anthony Cecilione
Work Phone: (732) 747-1959 Ext 353
Mr. William Frake
Work Phone: (732) 747-1959 Ext 302
Mr. Nicholas Galeotafiore
Mr. Douglas Gimbar
Work Phone: (732) 747-1959 Ext 314
Mr. Joseph Nitti
Work Phone: (732) 747-1959 Ext 317
Mr. Matthew Reagan
Work Phone: (732) 747-1959 Ext 355
Mr. James Speidel
Work Phone: (732) 747-1959 Ext 343