Mathematics

Mathematics

Teaching Staff:

Ms. Melucci,  Department Supervisor

Ms. Alfano

Ms. Bzdelik

Mrs. Blood

Mrs. Krause

Mrs. Pasquale

Mr. Ayhan

Mr. Petrucelli

Mrs. Harrington

Department Mission

The Mathematics Department at Mountain Lakes High School strives to create an environment where all students can maximize their potential, to address any fears or misconceptions they may have, and to provide them with an experience that will enable them to think critically and become better problem-solvers. Teachers seek to use examples in class that will provide a concrete and conceptual understanding of the material and to engage students by using current technology. All students benefit by having the opportunity to use what they have learned in ways that will impact their world beyond the classroom walls.

The department offers a variety of courses that essentially fall into two levels:

  • College Prep Enriched
  • College Prep Honors

Each level is designed to maximize a student's potential, satisfy personal interest, and provide a foundation to meet future goals. All courses provide an arena where students are be required to think critically, reason logically, and develop a sense about the relation and application of the mathematics to other courses, disciplines, and the real world. The honors courses constitute the most rigorous level and require that the student have the ability to think critically, reason logically, and deal with concepts, which require more abstract reasoning than is necessary in the enriched level. The mathematics staff recommends students to that level which they believe will best serve the needs and the ability level of the student.

MATHEMATICS CURRICULUM

College Preparatory Algebra Enriched
Grade Level: 9
5 Credits - Full Year

This first year course in elementary algebra develops the basic concepts of algebraic skills through three key ideas: the equation and inequality, data analysis, graphs, and translation of verbal situations into algebraic symbols. Extensive use of the scientific calculator enhances the development. Geometric concepts, probability, and graph interpretation allow for the application of the algebraic skills. Formulas, function notation, graphing, the laws of exponents and radicals, operations with polynomials, factoring, and solving quadratic equations by factoring, writing equations of lines, proportions and the quadratic formula are some of the topics presented.

College Preparatory Geometry Honors
Prerequisite: CP Algebra Enriched
Grade Level: 9 or 10
5 Credits - Full Year

This is a course in geometry covering the basic concepts of plane, solid, coordinate, and some analytic geometry stressing deductive proof and reasoning. Throughout the year the properties learned in algebra are re-introduced into this course. The aims and objectives of the course are to develop and show the value of the logic of deductive reasoning and to improve and increase the understanding and application of the terminology, the symbolism, and the structure of mathematics. The problems explored involve intense analytical thought and require strong algebraic skills. Non-Euclidean geometries such as fractal geometry and the Lenart sphere are investigated. Some student projects will involve the use of computer technology.

College Preparatory Geometry Enriched
Prerequisite: CP Algebra Enriched
Grade Level: 9 or 10
5 Credits - Full Year

This is a course in geometry covering the basic concepts of plane, solid, coordinate, and some analytic geometry stressing deductive proof and reasoning. Throughout the year the properties learned in algebra are re-introduced into this course. The aims and objectives of the course are to develop and show the value of the logic of deductive reasoning and to improve and increase the understanding and application of the terminology, the symbolism, and the structure of mathematics.

College Preparatory Algebra II Honors
Prerequisite: CP Geometry Honors
Grade Level 10 or 11
5 Credits - Full Year

This course presents a rigorous and enhanced study of the algebraic concepts introduced in the Algebra I course. These concepts are extensively augmented by the usage of the graphing calculators. The functions - namely the linear, quadratic, absolute value, exponential, and logarithmic - are examined both algebraically and graphically. Because of the emphasis on the graphs of the above-mentioned functions, the graphing calculator is an integral part of this course. Additional topics include the study of the higher-order inequalities, the polynomial and rational functions, the applications of linear and quadratic equations, systems of equations and inequalities, matrix algebra, advanced techniques for graphing functions, and probability.

College Preparatory Algebra II Enriched
Prerequisite: CP Geometry Enriched
Grade Level: 10-12
5 Credits - Full Year

The second course in algebra enhances the topics begun in the Algebra I course. The operations with polynomials include advanced factoring skills, working with negative and rational exponents, complex numbers, absolute value, the quadratic formula, graphing lines and parabolas and deriving their equations. Systems of linear equations, inequalities and applications of linear programming are included. In depth discussions of the linear, quadratic, polynomial, exponential and logarithmic functions are visited. Probability, data analysis and statistics are also covered. Operations and applications using matrices may be investigated with the graphing calculator used extensively as a tool. Synthetic division, arithmetic and geometric sequences round out the course.

College Preparatory Algebra II Core
Prerequisite: CP Geometry Core or CP Geometry Enriched
Grade Level: 11
5 Credits - Full Year

This is the third course of a sequence of a mathematics program. This course provides a general review of the fundamental algebra skills and concepts, and introduces functions and relations. Linear equations and inequalities, quadratic systems of equations, and polynomial and rational expressions are studied in detail. Topics in trigonometry, probability, and statistics are explored. Applications with an algebraic perspective are emphasized. This course would provide qualified students with a third year of college preparatory mathematics.

Discrete Mathematics with Financial Literacy
Prerequisites: CP Algebra II Enriched, CP Algebra II Core, CP
Geometry Enriched
Grade Level: 12
5 Credits - Full Year

The course begins with a review of topics from Trigonometry, followed by a survey of Statistics and Discrete Mathematics, and culminates with a thorough study of Financial Literacy and Economics. All topics lend themselves to a student's development of problem solving, communication, reasoning, and modeling skills. By modeling real world events, students will view mathematics as a useful tool in human decision-making. Successful completion of the course fulfills the graduation requirements of financial literacy.

Pre-Calculus (Honors)
Prerequisite: CP Algebra II Honors
Grade Level: 11 or 12
5 Credits - Full Year

This Pre-Calculus Honors course is somewhat similar in content to the Pre-Calculus course, although more emphasis is given to the development of mathematical concepts and is considerably more abstract and rigorous in approach. In addition, more work is undertaken on the study of vector algebra and the vector equations, parametric equations, and rectangular equations of lines and planes. Topics in advanced algebra are studied including the binomial theorem, mathematical induction, parametric equations, and polar coordinates. Some emphasis is placed on the study of limits in order to provide sufficient background for the next course in calculus.

Pre-Calculus
Prerequisite: CP Algebra II Enriched, CP Algebra II Honors
Grade Level: 10-12
5 Credits - Full Year

This course is essentially the study of elementary functions and their graphs. The graphing calculator is used extensively. Much time is given to the study of analytic geometry, advanced algebra, and trigonometry. A student who successfully completes this course is prepared to study calculus.

Pre-College Math
Prerequisite: CP Algebra II Enriched
Grade Level: 11-12
5 Credits - Full Year

This course is essentially the study of elementary functions and their graphs. The graphing calculator is used extensively. Much time is given to the study of analytic geometry, advanced algebra, and trigonometry. This course is recommended for students who have demonstrated difficulty in College Preparatory Algebra II Enriched. The pace of this course will be determined by the abilities of the class. A student who successfully completes this course is recommended to take Discrete Mathematics. Students who have already taken and passed Pre-calculus cannot enroll in this course as the concepts have already been covered.

Calculus
Prerequisite: Pre-calculus or Honors Pre-calculus
Grade Level: 12
5 Credits - Full Year

The Calculus course presented at the high school level is intended to serve those students who have successfully competed Pre-Calculus or Pre-Calculus Honors. The purpose of this course is to serve as the first study of differential and integral calculus. Much attention is given to the central ideas of the calculus such as limit the slope of the tangent line, the rate of change, and the area under a curve. At the same time, students will deepen their knowledge and understanding of a function and its utility in representing and answering questions about real-world phenomena. The course differs with AP Calculus significantly in both the depths of similar topics, as well as in the range of the topics considered.
In summary, Calculus will enable and provide students with the opportunity to explore the central topics and methods of calculus while developing an awareness of, and appreciation for, the historical origins and the cultural contributions of the calculus.

Advanced Placement Statistics
Prerequisite: Pre-Calculus or CP Algebra II Honors
Co-requisite: Honors Pre-Calculus
Grade Level: 11 or 12
6 Credits - Full Year

The AP Statistics program is built around four essential topics: exploring data, planning a study, probability as it relates to distributions of data, and inferential reasoning. Exploratory analysis of data will make use of graphical and numerical techniques in order to study patterns and departures from patterns. The collection of data will be done according to a well-developed plan in an effort to obtain valid inferences. Probability is the tool used for anticipating what the distribution of data should look like under a given model. Finally, statistical inference will guide the selection of appropriate models. Students who successfully complete this course are expected to take the AP Statistics exam.

Advanced Placement Calculus - AB Level
Prerequisite: Honors Pre-Calculus
Grade Level: 12
6 Credits - Full Year

Advanced Placement Calculus is a college-level course offered to those who successfully complete Honors Pre-calculus and are recommended for further study. The course concerns itself with the material of the calculus of the single variable, as outlined for an AB level curriculum in the College Board's Course Description. Students who successfully complete this course are expected to take the AP Calculus AB exam. Based on the results of this exam, colleges offer advanced placement and/or credit.

Advanced Placement Calculus - BC Level
Prerequisite: Honors Pre-Calculus
Grade Level: 12
6 Credits - Full Year

Advanced Placement Calculus BC is a college-level course offered to those who successfully complete Honors Pre-calculus and are recommended for further study. The topic outline includes all of the AB topics as well as additional topics required for the AP Exam. The course concerns itself with a rigorous treatment of the calculus of a single variable, as outlined for a BC level curriculum in the College Board's Course Description. Examples of additional topics include Taylor series, parametric, polar, and vector functions, and the various applications of integrals. Students who successfully complete this course are expected to take the AP Calculus BC exam. Based on the results of this exam, colleges offer advanced placement and/or credit. Permission of instructor required for admittance into this course. Students may not waive into this course.

Honors Multivariable Calculus
Prerequisite: Calculus
Grade Level: 12
5 Credits - Full Year

Multivariable calculus is a course designed to study the topics from regular calculus extended into three or more dimensions. The class will prove very beneficial for those students interested in advancing their studies in physics, engineering, or applied mathematics at the university level.
The course begins with Euclidean geometry in three dimensions. Topics to be studied include points, lines, and planes, as well as dot and cross product. Functions of two variables will be plotted and analyzed. Contour plots and level curves in various dimensions will be analyzed as well. Part of the course will cover differentiation in multiple dimensions, including the analysis of partial derivatives and tangent planes. Topics such as the chain rule will be extended into n-dimensions. The remainder of the course will also be devoted to the analysis of multiple integrals and how to physically interpret them. The relation to volume will be studied. Physical interpretations of these concepts - like center of mass - will be thoroughly developed. A strong relation to physics concepts will be fostered.