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The courses offered in the Mathematics Department fall basically into three levels: honors, college preparatory, and core levels. Each level has been designed to challenge the students' levels of ability, satisfy personal interest and meet future goals. 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 courses of the other two levels. The mathematics staff recommends students to that level which they believe will best serve the needs and the ability level of the student.

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.

This is the first course in a three-year college preparatory mathematics program, which presents material generally included in Algebra I. This course is designed for the student who has experienced difficulty with mathematics in the seventh and eighth grades.

The objectives of the course are twofold: primarily, to improve the basic computational skills of addition, subtraction, multiplication and division of whole numbers, decimals and fractions; secondarily, to introduce the principles of algebra and develop a familiarity with monomial and polynomial manipulations, including factoring, and the solution of first degree equations.

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.

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.

Grade Level: 10

5 Credits - Full Year

This is the second year of a three-year math sequence. Plane geometry as well as coordinate and 3-dimensional geometry are studied. Parallelism, polygons and their properties, similarity, the application of the Pythagorean Theorem, circles, areas, and volumes are the topics of consideration. Throughout the year the algebraic skills are continually applied and reinforced. In all areas a logical verification of the concepts is presented.

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 graphic functions, and probability.

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 are investigated with the graphing calculator used extensively as a tool. Synthetic division, arithmetic and geometric sequences round out the course.

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.

5 Credits - Full Year

Discrete Mathematics involves counting, measuring, and modeling finite systems which apply to liberal arts fields as well as to the natural, physical, and computer sciences and contemporary mathematics. Discrete mathematics topics lend themselves well to students’ development of problem solving, communication, reasoning, and modeling skills. By modeling real world events, some related to social choice issues, mathematics is viewed as a useful tool in human decision making. This course will include such topics as voting, apportionment and fair division, graph theory and coloring, coding theory, combinations, matrices, algorithms, numbers sequences and recursion.

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.

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.

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.

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.

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.

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 Acorn booklet. Students who successfully complete this course are urged to take the AP exam. Based on the results of this exam, colleges offer advanced placement and/or credit.

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 Acorn booklet. 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 urged to take the AP 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.

Grade Level: 9-12

REALbasic – Computer Programming I is a programming course focusing on “Object-oriented Programming (OOP” using REALbasic. This course is designed for students who wish to further their study of programming and is a prerequisite for Introduction to Java – Computer Programming 2 and AP Computer Science. REALbasic uses a modern version of the BASIC programming language and object-oriented structure. Students will create their own stand-alone software/applications. Enrollment of freshmen requires a recommendation from their Eighth Grade computer instructor.

Grade Level: 9-12

2 1/2 Credits – 1/2 year

Introduction to Java – Computer Programming II introduces students to Object-oriented programming concepts, teaches them the fundamentals of the Java language and syntax, introduces them to the major class libraries in Java, and prepares them to begin development of applications in Java. Students familiar with object-oriented concepts can learn how to develop Java applications.

Grade Level: 10-12

Full Year – 5 Credits

AP Computer Science is an advanced course in computer programming and problem solving. Students will study standard computer algorithms, data structures, computer systems, and file types using the Java programming language. This fast-paced course follows the curriculum set up by the College Board for the AP Computer Science course. The topic outline for this course is as follows:

2. Program Implementation

3. Program Analysis

4. Standard Data Structures

5. Standard Algorithms

6. Computer Systems

Although students will be using the Java programming language, programming skills are the focus of this course. All students enrolled in this course are encouraged to take one of the two levels of the AP Computer Science tests in the spring. Computers Programming I – REALbasic and Computer Programming 2 – Introduction to Java are prerequisites for Advanced Placement Computer Science.

Grade Level: 11,12

Full Year – 5 Credits

Honors Advanced Data Structures is the continuation of AP Computer Science A. This course covers advanced data structures such as two dimensional arrays, Linked Lists, Sets, Maps, Stacks, Queues, Binary Trees, and hashing. Algorithms to traverse, insert, delete, search and sort using each of these data structures will be analyzed for average efficiency. Students will also work with case studies to gain experience with large programs comprised of several classes. AP Computer Science A is a prerequisite for Honors Advanced Data Structures.

Students whose Individualized Educational Plans require an individualized approach to math instruction will enroll in the General Math program. A developmental sequence of skills forms the outline of topics to be covered:

2. Pre-Algebra

3. Algebra

4. Geometry

5. Business Mathematics

6. Standardized Test Preparation

This course must be recommended by the Child Study Team.

Remediation of those students found deficient by standardized test scores. This class is individualized according to the needs of students.

96 Powerville Road

Mountain Lakes, NJ 07046

Mountain Lakes, NJ 07046

Phone: 973-334-8400

Fax: 973-334-3550

Fax: 973-334-3550

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