Mathematics

ALGEBRA 1 - COLLEGE PREP (210S)                                                                   5 Credits – Grade 9
Course Overview: Algebra I, the first in a series of algebra courses, sets the foundation upon which higher-level mathematics courses are constructed. As such, our mission is to help students develop the skills necessary to analyze situations from a verbal, numerical, graphical, as well as symbolic perspective in order to be able to recognize and develop patterns. 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.

ALGEBRA 1 - HONORS (210H)                                                                               5 Credits – Grade 9
Course Overview: Algebra I, the first in a series of algebra courses, sets the foundation upon which higher-level mathematics courses are constructed. As such, our mission is to help students develop the skills necessary to analyze situations from a verbal, numerical, graphical, as well as symbolic perspective in order to be able to recognize and develop patterns. 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. This course carries a 5% weight.

GEOMETRY - COLLEGE PREP (220S)                                                          5 Credits – Grades 9, 10
Course Overview: By analyzing two and three-dimensional objects via spatial, inductive, and deductive reasoning, our mission is to help students develop and practice complex problem-solving skills to use not only for testing and proving conjectures about geometric shapes but also for logically defending positions and effectively critiquing arguments made by others on topics outside of mathematics. 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.

GEOMETRY - HONORS (220H)                                                                       5 Credits – Grades 9, 10
Course Overview: By analyzing two and three-dimensional objects via spatial, inductive, and deductive reasoning, our mission is to help students develop and practice complex problem-solving skills to use not only for testing and proving conjectures about geometric shapes but also for logically defending positions and effectively critiquing arguments made by others on topics outside of mathematics. 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. This course carries a 5% weight

ACCELERATED GEOMETRY / ALGEBRA II (220A)                                  5 Credits – Grades 9, 10
Course Overview: Geometry/Algebra II is an accelerated course that covers both courses in a single school years. The goal of this course is to accomplish the mission stated for Geometry in the first semester and the majority of the mission (excluding the Trigonometry aspect) stated for Algebra II / Trigonometry in the second semester of an academic year. This course carries a 10% weight.

ALGEBRA II / TRIGONOMETRY – COLLEGE PREP (230S)                  5 Credits – Grades 9, 10, 11
Course Overview: Algebra II, the second in a series of algebra courses, builds upon the foundation established in Algebra I and, to a lesser extent Geometry. As such, our mission is to help students develop the skills necessary to analyze complex situations from a verbal, numerical, graphical, as well as symbolic perspective to recognize, develop, and apply patterns when solving algebraic and trigonometric problems. Algebra II/Trig covers 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.

ALGEBRA II / TRIGONOMETRY – HONORS (230H)                               5 Credits – Grades 9, 10, 11

Course Overview: Algebra II, the second in a series of algebra courses, builds upon the foundation established in Algebra I and, to a lesser extent Geometry. As such, our mission is to help students further develop the skills necessary to analyze complex situations from a verbal, numerical, graphical, as well as symbolic perspective to recognize, develop, and apply patterns when solving algebraic and trigonometric problems. Algebra II/Trig covers 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. This course carries a 5% weight.

TRIGONOMETRY / ANALYSIS (230A)                                                        5 Credits – Grades 10, 11
Course Overview: Trigonometry / Analysis, the second in the series of accelerated courses, builds upon the foundation established in Accelerated Geometry / Algebra II. As such, our mission is to satisfy the trigonometric aspects of the stated mission for Algebra II / Trigonometry as well as the stated mission for Precalculus. This course enables the strongest students to complete three years of mathematics in two years as preparation for a Calculus course. This course carries a 10% weight. 

PRECALCULUS - COLLEGE PREP (243S)                                                  5 Credits – Grades 11, 12
Course Overview: Building upon students’ prerequisite knowledge of algebra and geometry with continued theoretical instruction and demonstration of analytical techniques, our mission is to strengthen students’ mathematical proficiency through problem solving, inquiry, and discovery with an emphasis on modeling and reasoning so that informed decisions can be made as a result of applying mathematics. 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 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.

PRECALCULUS - HONORS (240H)                                                               5 Credits – Grades 11, 12
Course Overview: Building upon students’ prerequisite knowledge of algebra and geometry with continued theoretical instruction and demonstration of analytical techniques, our mission is to strengthen students’ mathematical proficiency through problem solving, inquiry, and discovery with an emphasis on modeling and reasoning so that informed decisions can be made as a result of applying mathematics. 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 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. This course carries a 5% weight.

CALCULUS I – COLLEGE PREP (240S)                                                       5 Credits – Grades 11, 12
Course Overview: Through the graphical, analytical, numerical, and verbal investigation of limits, differentiation as well as integration techniques and applications, our mission is to introduce students to the aforementioned calculus concepts in order to prepare them for their first semester of college Calculus. 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.

CALCULUS I – HONORS (241H)                                                                    5 Credits – Grades 11, 12
Course Overview: Through the graphical, analytical, numerical, and verbal investigation of limits, differentiation as well as integration techniques and applications, our mission is to introduce students to the aforementioned calculus concepts in order to prepare them for their first semester of college Calculus or Honors Calculus II at CBA. 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. This course carries a 5% weight.

CALCULUS II - HONORS (242H)                                                                           5 Credits – Grade 12
Course Overview: Honors Calculus II is a continuation of the Honors Calculus I course, which completes the study of Calculus of a Single Variable. Consequently, our mission is to review introductory material to reinforce student understanding of differential and integral calculus as well as expand their abilities in the aforementioned by covering each in more depth and by introducing more advanced applications. 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. This course carries a 5% weight. 

AP CALCULUS AB (240A)                                                                      5 Credits – Grades 11, 12
Course Overview: This course consists of a thorough first-year college-level study of Differential and Integral Calculus. Through the graphical, analytical, numerical and verbal investigation of limits, differentiation as well as integration techniques and applications, our mission is to develop students’ understanding of the aforementioned calculus concepts while preparing them to successfully execute the AP Calculus AB examination.

Each student is required to take the AP Exam to satisfy the course requirements. This course carries a 10% weight

AP CALCULUS BC (241A)                                                                               5 Credits – Grades 11, 12
Course Overview: This is the second course in a two-year sequence in AP Calculus for those students who have successfully completed AP Calculus AB. In addition to the graphical, analytical, numerical, and verbal investigation of all topics covered in AP Calculus AB, the study of parametric, polar, and vector functions, as well as series, is pursued to fulfill our mission of further developing students’ understanding of calculus concepts while preparing them to successfully execute the AP Calculus BC examination.

Each student is required to take the AP Exam to satisfy the course requirements. This course carries a 10% weight. 

AP STATISTICS (242A)                                                                                            5 Credits – Grade 12
Course Overview: Through the investigation of the major concepts and tools for collecting, analyzing, and drawing conclusions from data, our mission is to help students build a conceptual and practical understanding of four major themes: i.e. exploring data, sampling and experimentation, anticipating patterns, and statistical inference, while preparing them to successfully execute the AP Statistics examination. 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.

Each student is required to take the AP Exam to satisfy the course requirements. This course carries a 10% weight.

STATISTICS COLLEGE PREP                                                                            5 Credits - Grade 12

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 with hands-on experience with statistical concepts.

COLLEGE ALGEBRA (241S)                                                                                  5 Credits – Grade 12
Course Overview: Through the reinforcement of previously taught concepts, processes and skills, our mission is to strengthen students’ understanding of numerical, analytic and graphical approaches to solving algebraic problems. 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. 

LINEAR ALGEBRA / DIFFERENTIAL EQUATIONS (250A / 251A)                                      2.5 Credits Each– Grade 12
Course Overview: The course engages the most advanced mathematics students with the gateway to college-level, abstract mathematics courses. Our mission is to present the fundamentals of both courses in a manner consistent with the abilities of a well-qualified high school student. There is a strong emphasis on advanced mathematical proof and rigor while introducing some of the applications of linear algebra and differential equations.  Linear Algebra is covered during the first semester and Differential Equations is the second semester.

The Linear Algebra 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. This course carries a 10% weight. 

The Differential Equations 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. This course carries a 10% weight

DISCRETE MATHEMATICS                                               2.5 Credits - Grade 12

This course gives an introductory treatment of discrete mathematics that is typical of a first or second semester undergraduate course. Its aim is to present fundamentals in a manner consistent with the abilities of a well-qualified high school student. Topics include: logic of compound and quantified statements, number theory and methods of proof, as well as sequences and mathematical induction. This course carries a 10% weight.

MATH TEAM 1 Credit - Grades 9, 10, 11, & 12

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.