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## Course Descriptions

MATHEMATICS

Algebra 1 Enriched
Prerequisite: None

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 technologies will be used throughout this course.

Prerequisite: None

Teacher Recommendation OR Approved Course Placement Application Required for Advanced or Honors
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.  The Advanced course is taught at a faster pace and challenges students with more rigorous work. The Honors course is designed for students who have exceeded expectations in the mastery of previous learning standards and will present challenging work requiring advanced analytical thought.

Prerequisite: Algebra 1 Enriched

Teacher Recommendation OR Approved Course Placement Application Required for Advanced or Honors
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 technologies will be used throughout this course.  The Advanced course is taught at a faster pace and challenges students with more rigorous work. The Honors course is designed for students who have exceeded expectations in the mastery of previous learning standards and will present challenging work requiring advanced analytical thought.

Prerequisite: Algebra 2 (Enriched, Advanced, Honors)
Teacher Recommendation OR Approved Course Placement Application Required for Advanced or Honors

Precalculus extends the study of linear, exponential, quadratic, polynomial, rational and radical functions to trigonometric functions, parametric functions, and conic sections.  Students will learn to verify trigonometric identities and use these identities to solve trigonometric equations.  Students will explore the relationships within the Law of Sines and Law of Cosines, and will be introduced to vectors and basic vector operations. This course also extends the development of data analysis skills, including the study sampling techniques, graphical displays, summary statistics, probability distributions, confidence intervals, and significance testing.  The course will end with an introduction to the study of Calculus through an exploration of the continuity of functions, evaluation of limit values, and the formal definition of a derivative.  The Advanced course is taught at a faster pace and challenges students with more rigorous work. The Honors course is designed for students who have exceeded expectations in the mastery of previous learning standards and will present challenging work requiring advanced analytical thought.

Calculus
Teacher Recommendation OR Approved Course Placement Application Required

The course serves as a high school level introduction to differential and integral calculus.  This course differs from AP Calculus AB and AP Calculus BC in both the range of topics and the depths in which they are studied. The topics of this course focus upon the central ideas of calculus, such as limits, slopes of tangent lines, rates of change, areas under curves. Students will also deepen their knowledge and understanding of functions and how they are used to represent real-world phenomena.

Teacher Recommendation OR Approved Course Placement Application Required

AP Calculus AB is designed to be the equivalent of a first semester college calculus course devoted to topics in differential and integral calculus. The course focuses on students’ understanding of calculus concepts and provides experience with methods and applications. The big ideas of calculus (e.g., modeling change, approximation and limits, analysis of functions) are emphasized and a multi-representational approach is taken to express concepts, results, and problems graphically, numerically, analytically, and verbally. Exploring connections among these representations builds a deep understanding of how calculus applies limits to develop important ideas, definitions, formulas, and theorems to build arguments and justify conclusions. The course maintains an emphasis on clear communication of methods, reasoning, justifications, and conclusions throughout.
Students who have previously earned credit for Calculus cannot enroll in this course.
Students who enroll in AP Calculus AB are expected to complete the AP Exam.

Prerequisite: Precalculus (Honors)
Teacher Recommendation OR Approved Course Placement Application Required

AP Calculus BC is designed to be the equivalent to both first and second semester college calculus courses. The course focuses on students’ understanding of calculus concepts and provides experience with methods and applications. The big ideas of calculus (e.g., modeling change, approximation and limits, analysis of functions) are emphasized and a multi-representational approach is taken to express concepts, results, and problems graphically, numerically, analytically, and verbally. Exploring connections among these representations builds a deep understanding of how calculus applies limits to develop important ideas, definitions, formulas, and theorems to build arguments and justify conclusions. AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.The course maintains an emphasis on clear communication of methods, reasoning, justifications, and conclusions throughout.
Students who have previously earned credit for Calculus cannot enroll in this course.
Students who enroll in AP Calculus BC are expected to complete the AP Exam.

Data Science
Prerequisite: Algebra 2 (Enriched, Advanced, Honors)
Teacher Recommendation OR Approved Course Placement Application Required

The course is centered around the basic topics of probability and statistics, including the exploration of data, experimentation, laws of probability, inferential reasoning, and statistical coding. Students will learn to collect, analyze, and draw conclusions from data, under the conditions of variability and uncertainty. Technology and introductory coding will enhance understanding of these concepts.  Activities in this course will expose students to potential careers in data science.

Prerequisite: Algebra 2 (Enriched, Advanced, Honors)
Teacher Recommendation OR Approved Course Placement Application Required

AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions, and conclusions.
Students who have already earned credit for Probability and Statistics cannot enroll in this course.

Honors Abstract and Linear Algebra
Prerequisite: Algebra 2 (Honors)
Teacher Recommendation OR Approved Course Placement Application Required

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