Mathematics

Prerequisites: None

Algebra I, the introduction to mathematics at VES, is a vast world of functions, graphs and the fascinating exploration of numbers and their invaluable uses and qualities. The course seeks to develop a facility in working with numbers, variables, graphs, inequalities, tables and various equations. Particular emphasis is placed on solving word problems and reading questions carefully. This process helps build algebraic skills and strengthens the understanding of needing to solve problems in a context, rather than from drill and practice alone. Topics include the study of equations and graphs (linear and quadratic), linear data versus nonlinear data, exponents, inequalities, radicals, solving fractional equations, special products and factoring.

Prerequisite: Algebra I or permission of the Department Chair

This course is designed to integrate algebra with the foundations of geometry. Topics include, but are not limited to angles, triangle congruences, parallel lines, polygons and polyhedrons, area, volume, circles and spheres, similarity, right triangle trigonometry and transformations. Independent thinking and discovery are encouraged throughout the course, as well as the study of and defending geometric proofs. This course seeks to demonstrate math’s usefulness and encourages students to see connections to real-world problems. Problem solving, logical reasoning and critical thinking skills will be emphasized through the use of cooperative learning, manipulatives and technology.

Prerequisite: Algebra I or permission of the Department Chair

The study of Honors Geometry encompasses far more than its definitions, postulates, and theorems. Students will consistently be challenged to reason analytically. The process of formal proof is emphasized early in the course, and direct proofs are investigated extensively. Proofs include parallel and perpendicular lines, congruent triangles, parallelograms, and geometric inequalities. Emphasis is also placed on applications. Topics include circles, right triangle trigonometry, coordinate geometry, areas, and volumes. Technology is used to model and explore the geometry presented within the course.

Prerequisite: Algebra I and Geometry or permission of the Department Chair

This course provides an extension of the basic algebraic concepts from Algebra I and Geometry. Students discuss, represent, and solve increasingly sophisticated problems using more advanced algebraic techniques, bringing opportunities for doing mathematics into focus. Incorporating appropriate technology, they study the properties and algebra of quadratic, exponential, logarithmic, and rational functions, systems of equations, and inequalities, and applied right triangle trigonometry. This course provides a sound understanding of basic linear, polynomial, and trigonometric functions.

Prerequisite: Honors Geometry or permission of the Department Chair

The main topics of Honors Algebra II / Trigonometry are basic number theory, algebraic properties and proofs, formal notation, word problems, and applying the algorithms used to solve them. As the course progresses, students solve higher-order equations, polynomial, logarithmic, and exponential functions and work with more extensive word problem applications. The trigonometry section of the course focuses on radian and degree trigonometric concepts including basic right triangle trigonometry, the unit circle, graphs of trigonometric functions, and word problems and applications.

Prerequisite: Algebra II / Trigonometry

Math Analysis helps students understand the fundamental concepts of algebra, trigonometry, and analytic geometry. Topics covered in this course are the study of functions (polynomial, rational, trigonometric, exponential, and logarithmic), systems of equations and inequalities, and solving triangles in anticipation of the student continuing to AP Statistics, Calculus, or a post-secondary mathematics course. A balance is maintained among the algebraic, numerical, graphical, and verbal methods of representing problems and solutions. Students use technology to visualize topics from numerical and graphical representations.

Prerequisite: Honors Algebra II / Trigonometry or permission of the Department Chair

The mathematical spectrum heightens as enter students into the world of honors analysis. This course is aimed at those who have demonstrated mathematical ability in their previous coursework to prepare them for Advanced Placement Calculus or college mathematics the following year. The first term begins with an emphasis on mathematical reasoning with a specific focus on general functions and their properties. After a guided tour of the functions, students begin to explore the concepts of complex numbers, exponential and logarithmic functions, polynomial and trigonometric functions, and as time permits, sequences and series.

Prerequisite: Algebra II / Trigonometry or permission of the Department Chair

The course concentrates on application rather than formal theory. Students learn to formulate questions that can be addressed with data, and to collect, organize and display relevant data to answer them. They learn to select and use appropriate statistical methods. Students develop and evaluate inferences and predictions, and apply basic concepts of probability.

Prerequisites:  
Students Must Have:

1. An interest in pursuing higher-level mathematics
2. Completed Algebra II/Trigonometry with an average of 85 or better
3. The support of the department and the recommendation of their current teacher
4. PSAT Critical Reading score of 500 or better (or an equivalent score on the SAT, Pre-ACT or ACT)

Course Description:
Statistics is the most widely applicable branch of mathematics, used by more people than any other kind of math both in the workplace and by consumers. Students study lists of raw data, graphical displays and charts, rates, probabilities, percentages, averages, forecasts and trend lines. Advanced Placement Statistics provides the opportunity for students to acquire statistical literacy. This course is designed to be the equivalent of an introductory college-level Statistics course. The syllabus has been constructed under the guidelines of the College Board and will prepare the student to take the Advanced Placement examination in the spring.

Underclassmen are required to take the AP exam. Seniors are required to take the exam, although an exemption may be obtained from the College Counseling Office. (Aside from potentially receiving college credit, exam scores can provide useful information for selection and placement in post-VES math courses.)

Prerequisite: Math Analysis or permission of the Department Chair

Students learn the mechanics behind solving derivatives and integrals both by hand and using a graphing calculator. Interspersed among the lessons throughout the year are applications of the course material in the form of physical motion, product package design, architecture, finance, flowing water, medication, populations, swings, springs, see-saws, police radars, wrecking balls, balloons, ballistics, bacteria and rocket science, to name a few. This is not a class about theorems or mathematical rigor as is the AP Calculus class, but is an excellent basis for college calculus.

Prerequisite:
Students must have:

1. A grade of 90 or better in Honors Analysis
2. The support of the department and the recommendation of their current teacher
3. PSAT Math score of 550 or better (or an equivalent score on the SAT, Pre-ACT or ACT)

Course Description:
This is a rigorous course aimed at building a strong foundation in differential and integral calculus along with its various applications. Topics include the study of limits and continuity, differentiation and integration of polynomial, logarithmic, exponential, and trigonometric functions. Various applications of these topics are studied, including position, velocity, acceleration, optimization, related rates, accumulation, slope fields, exponential growth and decay, and area and volume. Techniques of integration also are studied with a particular emphasis placed on the fundamental theorem of calculus and its applications. The course prepares students for the College Board AP examination and their continued study of mathematics in AP Calculus BC, or a course at college and provides the potential for students to begin their college mathematics at a more advanced level of calculus.

Underclassmen are required to take the AP exam. Seniors are required to take the exam, although an exemption may be obtained from the College Counseling Office. (Aside from potentially receiving college credit, exam scores can provide useful information for selection and placement in post-VES math courses.)

Prerequisites:
Students must have:

1. Successfully completed the AP Calculus AB course by scoring > 3 on that exam
2. The support of the department and the recommendation of their current teacher

Course Description:
This course is highly rigorous and aimed at building a strong foundation in differential and integral calculus, along with its various applications. The curriculum includes all of the material covered in the AP Calculus AB course, with more emphasis on the underlying proofs. Additional topics include the study of Euler’s method, logistical growth models, integration by parts, partial fractions, volumes by cylindrical shells, arc length and indeterminate forms. Focus is put upon polynomial approximations and series (Taylor and Maclaurin), as well as polar, parametric and vector functions and the analysis of planar curves. Students prepare for the College Board AP examination, and have the potential to begin their college mathematics at a significantly more advanced level of calculus.

Underclassmen are required to take the AP exam. Seniors are required to take the exam, although an exemption may be obtained from the College Counseling Office. (Aside from potentially receiving college credit, exam scores can provide useful information for selection and placement in post-VES math courses.)

Prerequisite: AP Calculus BC with a score of 3 or higher on the AP Calculus exam and permission of the Department Chair.

The course begins with a thorough review of analytic geometry, polar coordinates and parametric equations, then proceeds to vectors in both 2-space and 3-space. The topics include tangent and normal vectors, curvature, dot product, cross product, curves and planes in 3-space and quadric surfaces. Further topics include the analysis of cylindrical and spherical coordinates, partial derivatives, gradients, directional derivatives, and double and triple integrals. Stokes’ and Green’s theorems as well as the related underpinnings of vector theory will be discussed and studied as time permits.

Prerequisite: Multivariable Calculus, AP Calculus BC with a score of 3 or higher on the AP Calculus exam, and permission of the Department Chair.

The course will focus on extending the concepts of Multivariable Calculus and cover topics including vector functions, multivariate functions, multiple integrals, introduction to vector calculus, differential equations, and linear algebra. (A detailed bulleted list of course objectives is attached as an addendum). Assessments will be quizzes, tests, and when possible, projects depending on the Unit. Differential Equations & Linear Algebra will present interesting and challenging material for the student who has completed the Calculus curriculum and desires even more advanced mathematical coursework at VES.

Prerequisite: Open to a limited number of seniors who have completed and excelled in at least one AP Science and/or AP Mathematics course. Tests scores (standardized and AP), grades, interview, essay, teacher recommendations and transcript rigor are all factors in the application process.

Course Description:
A year-long core academic class that seeks to provide rigorous interdisciplinary study in a collaborative and project-based setting, this class quickly becomes a student-driven format with significant critical thinking applied throughout the course.

First semester topics include Team Building, Effective Collaboration, Learning Styles, Analysis, Methodology, Innovation and Design Thinking as well as day-long mini projects and three team-based collaborative projects with presentations. Second semester is designed around a thesis project that is significant in scale, interdisciplinary in nature, and collaborative in format. Teams work toward creating a significant document and large-scale presentation that will be delivered to both small and large panels. Teams build a website to track and display their project and a physical design model or equivalent display (ex., a piece of music, a computer program, etc.) depending on each individual project’s aim and components. Clearly defined individual roles will be identified in all facets of the project, while ensuring a collaborative approach among the team throughout the venture.