Mathematics

 

College Preparatory Algebra 1
Grade Level 9
5 Credits
Algebra builds upon the skills learned in the expressions and equations strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. In this course, students will model relationships using equations and inequalities in one and two variables.  Models explored will include linear, exponential, and quadratic relationships with an emphasis on domain, range, and function notation.  Students will sketch graphs and use key features to interpret and justify solutions. Students will extend their ability to graph functions using transformations. Students will reveal properties of quadratic equations through the process of factoring and completing the square, and will solve quadratic equations using square roots, the quadratic formula, factoring, and completing the square. This course will also include a unit on data analysis involving the analysis of two-way frequency tables, representing and comparing data using dot plots, histograms, and box plots, fitting models to bi-variate data and analyzing residuals and correlation coefficients to determine appropriateness of fit. A graphing calculator and various other technology will be used throughout this course.

College Preparatory Algebra 1 Enriched
Grade Level 9
5 Credits 
Algebra builds upon the skills learned in the expressions and equations strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. In this course, students will model relationships using equations and inequalities in one and two variables.  Models explored will include linear, exponential, and quadratic relationships with an emphasis on domain, range, and function notation.  Students will sketch graphs and use key features to interpret and justify solutions.  Students will extend their ability to graph functions using transformations. Students will reveal properties of quadratic equations through the process of factoring and completing the square, and will solve quadratic equations using square roots, the quadratic formula, factoring, and completing the square.  This course will also include a unit on data analysis involving the analysis of two-way frequency tables, representing and comparing data using dot plots, histograms, and box plots, fitting models to bi-variate data and analyzing residuals and correlation coefficients to determine appropriateness of fit. A graphing calculator and various other technology will be used throughout this course.


College Preparatory Geometry
Grade Level 10
Prerequisite: CP Algebra 1 or CP Algebra 1 Enriched
5 Credits

Geometry builds upon the skills learned in the geometry strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. In this course, students deepen their understanding of lines, angles, and triangles by performing constructions using a variety of tools and technologies. Students will explore transformations in terms of rigid motions, representing transformations in the plane, and describing transformations as functions. Students will solve problems involving similar geometric figures and will explore proof to deepen their understanding of congruence. Students will learn to compute perimeters and areas of triangles, rectangles, and polygons; and will explore the measurement of circles in two and three dimensions. Students will extend their understanding of geometric measurement by giving informal arguments for various formulas and using volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Students will use geometric shapes, their measures, and their properties to describe objects, apply concepts in modeling situations, and apply geometric methods to solve problems.

College Preparatory Geometry Enriched
Grade Level 9-10
Prerequisite: CP Algebra 1 with Teacher Recommendation or CP Algebra 1 Enriched
5 Credits

Geometry builds upon the skills learned in the geometry strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. In this course, students deepen their understanding of lines, angles, and triangles by performing constructions using a variety of tools and technologies. Students will explore transformations in terms of rigid motions, representing transformations in the plane, and describing transformations as functions. Students will solve problems involving similar geometric figures and will explore proof to deepen their understanding of congruence. Students will learn to compute perimeters and areas of triangles, rectangles, and polygons; and will explore the measurement of circles in two and three dimensions. Students will extend their understanding of geometric measurement by giving informal arguments for various formulas and using volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Students will use geometric shapes, their measures, and their properties to describe objects, apply concepts in modeling situations, and apply geometric methods to solve problems. 

College Preparatory Geometry Advanced
Grade Level 9-10
Prerequisite: CP Algebra 1 Enriched
5 Credits

This course builds upon the skills learned in the geometry strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. The advanced course is taught at a faster pace and challenges students with more rigorous work.  Students will deepen their understanding of lines, angles, and triangles by performing constructions using a variety of tools and technologies. Students will explore transformations in terms of rigid motions, representing transformations in the plane, and describing transformations as functions. Students will solve problems involving similar geometric figures and will explore proof to deepen their understanding of congruence. Students will learn to compute perimeters and areas of triangles, rectangles, and polygons; and will explore the measurement of circles in two and three dimensions.  Students will extend their understanding of geometric measurement by giving informal arguments for various formulas and using volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Students will use geometric shapes, their measures, and their properties to describe objects, apply concepts in modeling situations, and apply geometric methods to solve problems.

College Preparatory Geometry Honors
Grade Level 9-10
Prerequisite: Teacher Recommendation and CP Algebra 1 Enriched
5 Credits

Geometry builds upon the skills learned in the geometry strand of the New Jersey Student Learning Standards for grades 6, 7, and 8. This course is designed for students who have exceeded expectations in the mastery of these standards. The course will present challenging work requiring advanced analytical thought.  Students will deepen their understanding of lines, angles, and triangles by performing constructions using a variety of tools and technologies. Students will explore transformations in terms of rigid motions, representing transformations in the plane, and describing transformations as functions. Students will solve problems involving similar geometric figures and will explore proof to deepen their understanding of congruence. Students will learn to compute perimeters and areas of triangles, rectangles, and polygons; and will explore the measurement of circles in two and three dimensions. Students will extend their understanding of geometric measurement by giving informal arguments for various formulas and using volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Students will use geometric shapes, their measures, and their properties to describe objects, apply concepts in modeling situations, and apply geometric methods to solve problems. 

College Preparatory Algebra 2
Grade Level 11-12
Co/Prerequisite: CP Geometry or CP Geometry Enriched or CP Geometry Honors
5 Credits

Building on the understanding of linear, exponential and quadratic functions from Algebra 1, this course will extend the study of functions to include polynomial, rational, and radical functions. The learning standards in this course continue the work of modeling situations and solving equations. Building on the understanding of trigonometric ratios and circles from Geometry, students will extend trigonometry to model periodic phenomena. Students will explore the effects of transformations on graphs of functions and will learn to identify appropriate models for given situations. The learning standards in this course require development of models more complex than those of previous courses. This course will also relate the data representations and summary statistics learned in prior courses to different types of data and probability distributions. Students will also explore methods of data collection including, samples, surveys, experiments and simulations. A graphing calculator and various other technology will be used throughout this course.
                                                                          
College Preparatory Algebra 2 Enriched
Grade Level 9-11
Co/Prerequisite: CP Geometry Enriched or CP Geometry Honors
5 Credits

Building on the understanding of linear, exponential and quadratic functions from Algebra 1, this course will extend the study of functions to include polynomial, rational, and radical functions. The learning standards in this course continue the work of modeling situations and solving equations. Building on the understanding of trigonometric ratios and circles from Geometry, students will extend trigonometry to model periodic phenomena. Students will explore the effects of transformations on graphs of functions and will learn to identify appropriate models for given situations. The learning standards in this course require development of models more complex than those of previous courses. This course will also relate the data representations and summary statistics learned in prior courses to different types of data and probability distributions. Students will also explore methods of data collection including, samples, surveys, experiments and simulations. A graphing calculator and various other technology will be used throughout this course.

College Preparatory Algebra 2 Advanced
Grade Level 9-11
Co/Prerequisite: CP Geometry Enriched or CP Geometry Honors
5 Credits

This course builds upon the skills learned in a first course in algebra. The advanced course is taught at a faster pace and challenges students with more rigorous work. Building on the understanding of linear, exponential and quadratic functions from Algebra 1, this course will extend the study of functions to include polynomial, rational, and radical functions. The learning standards in this course continue the work of modeling situations and solving equations. Building on the understanding of trigonometric ratios and circles from Geometry, students will extend trigonometry to model periodic phenomena. Students will explore the effects of transformations on graphs of functions and will learn to identify appropriate models for given situations. The learning standards in this course require development of models more complex than those of previous courses. This course will also relate the data representations and summary statistics learned in prior courses to different types of data and probability distributions. Students will also explore methods of data collection including, samples, surveys, experiments and simulations. A graphing calculator and various other technology will be used throughout this course.

College Preparatory Algebra 2 Honors
Grade Level 9-11
Co/Prerequisite: Teacher Recommendation and CP Geometry Enriched or CP Geometry Honors
5 Credits

This course will present challenging work and is geared toward students who grasp mathematical concepts quickly.  Building on the understanding of linear, exponential and quadratic functions skills learned in a first course in algebra, this course will extend the study of functions to include polynomial, rational, and radical functions. This course is designed for students who have exceeded expectations in the mastery of these standards. The learning standards in this course continue the work of modeling situations and solving equations. Building on the understanding of trigonometric ratios and circles from Geometry, students will extend trigonometry to model periodic phenomena.  Students will explore the effects of transformations on graphs of functions and will learn to identify appropriate models for given situations. The learning standards in this course require development of models more complex than those of previous courses. This course will also relate the data representations and summary statistics learned in prior courses to different types of data and probability distributions. Students will also explore methods of data collection including, samples, surveys, experiments and simulations. A graphing calculator and various other technology will be used throughout this course.

Pre-Calculus
Grade Level 10-12
Prerequisite: CP Algebra 2 Enriched or CP Algebra 2 Honors
5 Credits

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, conics, and advanced algebra, and trigonometry. A student who successfully completes this course is prepared to study calculus. 

Pre-Calculus Honors
Grade Level 9-12    
Prerequisite: Teacher Recommendation and CP Algebra 2 Enriched or CP Algebra 2 Honors
5 Credits
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 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-College Math/Trigonometry
Grade Level 11-12
Prerequisite: CP Algebra 2 Enriched
5 Credits

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.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 Applications of Math with Financial Literacy or Probability and Statistics. Students who have already taken and passed Pre-Calculus cannot enroll in this course as the concepts have already been covered.

Probability and Statistics
Grade Level 11-12
Prerequisite:  Pre-Calculus or Pre-College Math
5 credits

The course is presented at the high school level and is intended to serve those students who have successfully completed Pre-Calculus or Pre-College Math. The general aim of the course is to develop the basic topics of probability and statistics, including exploring data, planning a study, the laws of probability, and inferential reasoning. Probability and Statistics will provide a set of tools for collecting, analyzing, and drawing conclusions from data, particularly under the conditions of variability and uncertainty. Available technology will play a role in the course to enhance and deepen their understanding of these concepts and give students the opportunity to learn statistics by actively engaging in activities that teach and reinforce concepts and ideas of statistics. By helping students organize their thinking, statistics allows for more informed decision-making.

Advanced Placement Statistics
Grade Level 11-12
5 Credits
Prerequisite: Teacher Recommendation OR successful completion of Pre-Calculus or CP Algebra 2 Honors
Co-requisite: CP Algebra 2 Honors or Honors Pre-Calculus

Any student not in receipt of a Teacher Recommendation or who does not meet the prerequisite detailed above may complete and submit a Course Placement Application by the required deadline. Submission of a completed form does not guarantee enrollment in the course.

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 enroll in AP Statistics are expected to register for and take the AP Statistics Exam. Students who have already taken and passed Probability and Statistics cannot enroll in this course as the concepts have already been covered.

Calculus
Grade Level 11-12
Prerequisite: Pre-Calculus or Pre-Calculus Honors
5 Credits

The Calculus course presented at the high school level is intended to serve those students who have successfully completed 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 from 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 Calculus - AB Level
Grade Level 10-12
5 Credits
Prerequisite: Teacher Recommendation OR successful completion of Honors Pre-Calculus

Any student not in receipt of a Teacher Recommendation or who does not meet the prerequisite detailed above may complete and submit a Course Placement Application by the required deadline. Submission of a completed form does not guarantee enrollment in the course.
NOTE: Students seeking advanced credit to accelerate into AP Calculus AB through a summer course must fill out a Course Placement Application. Approval must be obtained from the Department Supervisor, the Director of Counseling, and the Principal prior to enrollment, and a Qualifying Exam is required after completion of the course.

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 enroll in AP Calculus AB are expected to register for and take the AP Calculus AB Exam. Students who have already taken and passed Calculus cannot enroll in this course as the concepts have already been covered.
 
Advanced Placement Calculus - BC Level
Grade Level 10-12
5 Credits
Prerequisite: Teacher Recommendation OR successful completion of Honors Pre-Calculus

NOTE: Students seeking advanced credit to accelerate into AP Calculus BC through a summer course must fill out a Course Placement Application. Approval must be obtained from the Department Supervisor, the Director of Counseling, and the Principal prior to enrollment, and a Qualifying Exam is required after completion of the course.

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. Consideration for admission to this course is only given to students who have had strong academic performance on summative assessments in Honors Pre-Calculus. Students who enroll in AP Calculus BC are expected to register for and take the AP Calculus Exam. 

Honors Abstract and Linear Algebra
Grade Level 10-12
Prerequisites: Qualifying Score on Placement Exam
5 Credits

Abstract algebra involves the study of abstract entities such as sets, functions, operations and mathematical spaces that are far more complex than ordinary numbers.  This course will also include the study of matrix theory and linear algebra which address structures that can be described by systems of linear equations.  These concepts are extremely useful in optimization, physics, economics and social sciences, natural sciences, and engineering.

Honors Multivariable Calculus
Grade Level 11-12
Teacher Recommendation Required
5 Credits 
Prerequisite: AP Calculus AB or AP Calculus BC

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.

Applications of Math with Financial Literacy $
Grade Level 12
Prerequisites: CP Algebra 2 Enriched or CP Algebra 2
5 Credits

This course provides a survey of topics in mathematics including statistics, discrete mathematics, and everyday applications of mathematics.  This course culminates in a thorough study of financial literacy.  All topics lend themselves to a student’s development of problem solving, communication, reasoning, and modeling skills.  By modeling real world scenarios, students will embrace mathematics as a useful tool in decision-making.  Successful completion of the course fulfills the graduation requirement for financial literacy.

 

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