Mathematics
A significant number of students at BHS elect to take four years of mathematics even though there is only a three-year requirement for graduation. The multitude of math electives offered provides students the opportunity for a complete and thorough mathematics experience. For students seeking a rigorous mathematics program, AP Calculus AB, AP Calculus BC, and AP Statistics are offered. Because of the personal and professional challenges that will face the BHS graduates, the Mathematics Department encourages all students to keep mathematics in their high school program all four years. Students are strongly encouraged to bring their own graphing calculators to all high school math courses. Students in mathematics courses will be encouraged to participate in local, state and national mathematics competitions.
The academic level categories are as follows:
Academic: Courses with the core academic curriculum for all levels.Accelerated (A): College preparatory courses that have a high academic demand and requirements. This course of study will challenge students and prepare them well as they pursue a post-secondary education.Honors (H): Honors courses require a high level of academic maturity, interest, ability, intellectual curiosity, and the ability to study and work independently. The pace is rigorous and enrollment is selective.Advanced Placement (AP): Advanced Placement is the most academically demanding course level possible. Successful completion of the course may lead to college credit. Enrollment is highly selective and honors credit is earned. Students are strongly encouraged and expected to take the AP exams in May.Algebra I (03436)
Full-Year Course; Level - Academic; Grade 9-12
Credit Value: 5.0
Prerequisite: None
This course is designed as a first-year high school algebra course. The topics are derived from the New Jersey Student Learning Standards and include the real number system, algebraic expressions, equations and inequalities, linear functions, graphing functions, systems of equations and inequalities, exponents, and polynomials. This course will cover essential topics of algebra at an appropriate pace and level of difficulty. The approach to algebra in this course is characterized by visualization of problems, logical reasoning, applying the principles taught in class, completing projects, and employing technology such as graphing calculators and online resources.
Algebra I (A) (03422)
Full-Year Course; Level - Accelerated; Grade 9-12
Credit Value: 5.0
Prerequisite: None
This course is designed as a first-year high school algebra course. The topics are derived from the New Jersey Student Learning Standards and include the real number system, algebraic expressions, equations and inequalities, linear functions, quadratic functions, polynomial functions, exponential functions, radical functions, systems of equations and inequalities, and probability and statistics. Students will represent quantitative relationships in various ways, distinguish linear, quadratic, and exponential relations, and choose a model to best fit any given data among those relations. The approach to algebra in this course is characterized by utilizing the textbook, extending the lesson, applying the principles taught in class, employing technology such as graphing calculators and online resources, and drawing conclusions based on logical and mathematical reasoning.
Geometry (03425)
Full-Year Course; Level - Academic; Grade 9-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra I (any level)
The course commences with an overview of geometry by using the New Jersey Student Learning Standards and through elementary concepts and terminology. Emphasis is placed upon the logical structure of the course by introducing various methods of reasoning. Students develop their reasoning powers through the construction of informal proofs dealing with geometric shapes and with hands-on learning opportunities. Transformations will be presented as they apply to translations, reflections, rotations, and glide reflections. Other concepts covered will include similarity, congruence, properties of polygons, the Pythagorean Theorem, properties of circles, perimeter, area, surface area and volume of geometric shapes, basic rules of logic and reasoning, coordinate geometry, units of measurement, and constructions by hand and with the computer.
Geometry (A) (03432)
Full-Year Course; Level - Accelerated; Grade 9-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra I (any level)
The course commences with an overview of geometry by using the New Jersey Student Learning Standards and through elementary concepts and terminology. Emphasis is placed upon the logical structure of the course by introducing various methods of reasoning. Students develop their reasoning powers through the construction of informal proofs dealing with geometric shapes and with hands-on learning opportunities. Transformations will be presented as they apply to translations, reflections, rotations, and glide reflections. Other concepts covered will include similarity, congruence, properties of polygons, the Pythagorean Theorem, properties of circles, perimeter, area, surface area and volume of geometric shapes, basic rules of logic and reasoning, coordinate geometry, units of measurement, and constructions by hand and with the computer.
Geometry (H) (03433)
Full-Year Course; Level - Honors; Grade 9-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra I (any level)
The power and practice of deductive reasoning is stressed in this course. The analytical approach to problem solving and the importance of technique and structure will undergird all the work to be mastered by students who possess an excellent foundation in algebra. The course content is similar to the content listed for the Geometry (A) course but the pace and level of the work will be accelerated and extremely challenging. More time is dedicated to proofs, advanced problem solving, using Geometer's Sketchpad in the computer lab and basic trigonometric relationships to solve right triangle problems.
Algebra II (03428)
Full-Year Course; Level - Academic; Grade 9-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra I (any level)
This course is a natural extension and enrichment of the Algebra I curriculum. Topics in this course are derived from the New Jersey Student Learning Standards and include absolute value and polynomial functions, the complex number system, exponential and logarithmic functions, rational functions, arithmetic and geometric sequences and series, probability and statistics, data analysis, interpretation and conclusions, factoring, inverse functions, trigonometric functions as applied to right triangles and their graphs, radian measure, and the unit circle. Students will be encouraged to solve problems, communicate mathematically, make connections, reason, represent ideas and use technology.
Algebra II (A) (03442)
Full-Year Course; Level - Accelerated; Grade 9-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra I (any level)
This course is a natural extension and enrichment of the Algebra I curriculum. Topics in this course are derived from the New Jersey Student Learning Standards and include absolute value and polynomial functions, the complex number system, exponential and logarithmic functions, rational functions, arithmetic and geometric sequences and series, probability and statistics, data analysis, interpretation and conclusions, factoring, inverse functions, trigonometric functions as applied to right triangles and their graphs, radian measure, and the unit circle. Students will be encouraged to solve problems, communicate mathematically, make connections, reason, represent ideas and use technology.
Algebra II (H) (03443)
Full-Year Course; Level - Honors; Grade 10-12
Credit Value: 5.0
Prerequisite: Successful completion of Geometry (A/H)
This course is a natural extension and enrichment of the Algebra I curriculum. Topics in this course are derived from the New Jersey Student Learning Standards and include absolute value and polynomial functions, the complex number system, exponential and logarithmic functions, rational functions, arithmetic and geometric sequences and series, probability and statistics, data analysis, interpretation and conclusions, factoring, inverse functions, trigonometric functions as applied to right triangles and their graphs, radian measure, and the unit circle. Although the course content is similar in nature to the Algebra II (A) course, the pace of the class is accelerated, the degree of difficulty of the work assigned is heightened, and the concepts and skills are investigated more in depth to provide a challenge to the honors student. Students will be encouraged to solve problems, communicate mathematically, make connections, reason, represent ideas and use technology.
Probability And Statistics (A) (03453)
Full-Year Course; Level - Accelerated; Grade 11-12
Credit Value: 5.0
Prerequisite: Algebra II (A) OR Algebra II and departmental permission
This course will introduce students to the major concepts and tools of probability and statistics. It will allow students to explore the basic constructs of probability, including permutations and combinations, experimental versus theoretical probability, dependent and independent events, simple and conditional probability. Normal distributions, binomial distributions and z-scores will be created, analyzed and interpreted. Methods of collecting, organizing, displaying, describing and analyzing data will be investigated. Statistical computational skills such as mean, mode, quartiles, outliers, variance, range, median, and standard deviation will be learned, analyzed, interpreted and applied. Regressions of many types will be used to understand data and those regression equations will be used to make predictions of events not measured. Experiments and observational studies will be used to allow students to use critical thinking and analytic skills based on numeric evidence. Experiments and observational studies will be used to allow students to use critical thinking and analytic skills based on numeric evidence. Assessments in this course will include traditional tests and quizzes as well as labs, group projects, experiments, and/or class activities.
Math Concepts (03437)
Full-Year Course; Level - Academic; Grade 12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra II (any level)
Math Concepts is designed to build confidence and encourage an appreciation of mathematics. Students will see every day uses and practical applications of the mathematics they are studying and appreciate the universality of mathematics. This course enables students to broaden their understanding of mathematics as it is applied in the workplace, in post-secondary education, and in daily life. Students will investigate questions involving the use of statistics, explore personal finances, apply geometric concepts for practical design purposes, and/or develop problem solving strategies. Students will synthesize their mathematical skills as they solve problems and communicate their thinking. The objective for the course is to introduce students to additional interesting and practical math topics, promote clear and precise thinking, and better prepare the student for the future through math content and technology. This course does not fulfill mathematics graduation requirements.
PreCalculus (03468)
Full-Year Course; Level - Academic; Grade 11-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra II (any level)
PreCalculus will provide students an opportunity to enhance and extend in-depth knowledge and skills with formal algebra concepts, study more advanced math topics and explore additional areas in trigonometry. Function analysis for polynomial, exponential, logarithmic, and rational functions will be emphasized and include mapping, domain, range, zeros, composition, inverses, piece-wise definitions, translations, solutions, and graphs. Additional topics in trigonometry will include the unit circle, evaluation and graphing of the six basic trigonometric functions, and applications. Throughout the course, students will be encouraged to solve problems, communicate mathematically, make connections, reason, represent ideas, and use technology.
PreCalculus (A) (03463)
Full-Year Course; Level - Accelerated; Grade 11-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra II (A)
Students will review related algebraic concepts while studying advanced math topics. Functions will be emphasized and will include mapping, domain, range, zeroes, composition, inverses, piece-wise definitions, translations, solutions, graphs and applications. Polynomial, exponential, logarithmic, and rational functions will be addressed in each of these areas. Trigonometry will be approached via circular functions, and then related to the acute angles of the right triangle. The six basic trigonometric functions, inverses and graphs will be developed, including amplitude, period, phase shifts and reflections. The Law of Sines and Law of Cosines as well as applications will be explored. Trigonometric identities will be verified and trigonometric equations will be solved. Conic sections will be addressed in this course and will include a study of circles, ellipses, hyperbolas and parabolas.
PreCalculus (H) (03465)
Full-Year Course; Level - Honors; Grade 11-12
Credit Value: 5.0
Prerequisite: Successful completion of Algebra II (H)
The course content is similar in nature to Pre-Calculus (A) course but the entire course content is treated in greater detail. DeMoivre's theorem, conic sections, parametric and polar equations, the binomial expansion theorem, logistic functions, vectors, conversions among number bases, limits and the definition of a derivative, and conversions between rectangular, polar and trigonometric coordinates are also included in this course. The pace and level of the work in this honors level course will be accelerated and extremely challenging. More time is dedicated to graphing, advanced problem solving and more complex graphing skills. Students are exposed to transcendental functions, curve sketching, and other topics that will prove to be a worthwhile challenge and appropriate preparation for the next levels of mathematics.
Calculus (H) (03469)
Full-Year Course; Level - Honors; Grade 12
Credit Value: 5.0
Prerequisite: Successful completion of PreCalculus (A/H)
The course starts with a thorough presentation of limits and continuity. The differential branch of Calculus is developed and applied to polynomial, rational, exponential, logarithmic, and circular functions with applications that include related rates, position, velocity, acceleration, finding maximum and minimum points and the concavity of graphs. Definite and indefinite integrals are studied as the inverse operation of the derivative. Applications to model physical, biological or economic situations also serve to broaden the calculus experience. Techniques to find areas and volumes of various shapes are studied and applied.
AP Calculus (AB) (03483)
Full-Year Course; Level - AP; Grade 12
Credit Value: 5.0
Prerequisite: Successful completion of PreCalculus (A/H)
The course starts with a thorough presentation of limits and continuity. The differential branch of Calculus is developed and applied to polynomial, rational, exponential, logarithmic, logistic, and circular functions with applications that include related rates, position, velocity, acceleration, finding maximum and minimum points and the concavity of graphs. Definite and indefinite integrals are studied as the inverse operation of the derivative. Techniques to find areas and volumes of various shapes are studied and applied. Applications to model physical, biological or economic situations also serve to broaden the calculus experience. The AP Curriculum will be followed in this course, and students are encouraged to take the AP exam in May.
AP Calculus (BC) (03488)
Full-Year Course; Level - AP; Grade 12
Credit Value: 5.0
Prerequisite: Successful completion of AP Calculus (AB); or final grade of A or above in PreCalculus (H)
The AP Calculus BC course contains all of the topics taught in the AB curriculum with an intensive focus on theory and applications. Additional topics covered are indeterminate form, improper integrals, Euler's Method, lengths of curves, integration with partial fractions, polar and parametric equations and graphs and the calculus applications of these equations, convergence and divergence, infinite series, power series, Taylor polynomials and series, LaGrange error, slope fields and vector functions. The AP BC curriculum will be followed in this course, and students are encouraged to take the AP exam in May.
AP Statistics (03497)
Full-Year Course; Level - AP; Grade 10-12
Credit Value: 5.0
Prerequisite: Final grade of B+ or better in Algebra II (H) OR final grade of A or better in Algebra II (A) OR successful completion of PreCalculus (A)
The four conceptual themes of this course are exploring data, observing patterns and departures from patterns; planning a study, deciding what to measure and how to measure it; anticipating patterns, introducing probability and simulation; and inferring from the sample data, confirming models for explanations of patterns. A few important skills for success in this course include good reading comprehension, clear written communication, quantitative reasoning, and technology (graphing calculator and statistical software) skills. The AP Statistics curriculum will be followed in this course, and all students enrolled in this course are expected to take the AP exam in May.
AP Computer Principles (03391)
Full-Year Course; Level - AP; Grade 10-12
Credit Value: 5.0
Prerequisite: Final grade of “B” or better in Algebra I (A)
Students in AP Computer Science Principles will be introduced to the central ideas of computer science, instilling the ideas and practices of computer thinking and inviting students to understand how computer changes the world. The course will engage students in deep learning of computational content, develop computer thinking skills, and explore creative aspects of the field. The course will focus on fostering students to be creative. Students will apply creative processes when developing computational artifacts, and think creatively while using simulations to explore questions that interest them. The course will introduce programming as a means to solve computational problems and create exciting and personally relevant projects. In addition to programming there are six other major themes which include creativity, abstraction, data and information, algorithms, internet and global impact. Students will design and implement innovative solutions using an iterative process similar to what artists, writers, computer scientists, and engineers use to bring ideas to life. This course does not fulfill mathematics graduation requirements.
AP Computer Science (03489)
Full-Year Course; Level - AP; Grade 11-12
Credit Value: 5.0
Prerequisite: Final grade of B or better in Algebra II (A)
Students will review and continue the studies of concepts learned in the Introduction to Computer Programming Course in far greater depth, including object relationships in object-oriented programming, polymorphism, inheritance, and abstraction. Students will extend the idea of arrays to lists and learn the different sorting methods and of arrays as well as their efficiency, including the Big notation. Students will also develop preliminary ideas of data structures design, problem solving, and abstraction. As part of the AP subset, students will be exposed to a large data study, Gridworld, and revise and edit the programs in that study. Goals of this course will be to have students not only comprehend the Java programming language itself but also to apply newly found algorithm and problem solving skills towards other programming languages as well. Students will be prepared and encouraged to take the AP Computer Science A exam in May. This course does not fulfill mathematics graduation requirements.
Math Test Preparation
Semester Course; Level - Academic; Grade 10-12
Credit Value: 2.5
Prerequisite: Recommendation of guidance and/or special services
This elective course is for students who have exhibited a need for remediation in state-mandated Algebra 1 mathematical skills as required in part through the State Assessment Program (PARCC/NJSLA). Topics include functions, reasoning and modeling, statistics and probability and continued development of algebraic thinking skills. Students who received a Level 3 or below on the Algebra 1 state-mandated testing could enroll in this course for at least one semester. This course does not fulfill mathematics graduation requirements.