# Math

## Yearlong Courses

- Algebra I
- Geometry
- Geometry Advanced
- Algebra II with Statistics
- Algebra II
- Algebra II / Precalculus Advanced (APA)
- Conceptual Precalculus
- Discrete Math with Applications
- Precalculus
- Calculus
- AP Calculus AB
- AP Calculus BC
- AP Statistics

## Algebra I

This course covers the concept of using variables to represent numbers and arithmetic equations. Students spend time developing arithmetic and problem-solving skills while covering the following topics: properties of real numbers, basic operations, writing and solving algebraic equations and inequalities with one and two variables, polynomials and factoring, first- and second-degree functions and their graphs, quadratic equations, and radical expressions. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [One credit.]

## Geometry

This standard course in geometry covers concepts of Euclidean geometry including definitions, postulates, and theorems. Areas of study include angles, parallel lines, congruent and similar triangles, polygons, the Pythagorean Theorem, trigonometry, circles, area and volume. The content is also explored through analytical geometry, and the students work to improve their algebraic skills. Additionally, the course includes a proof component. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisite: Algebra I.** One credit.**]**

## Geometry Advanced

This advanced course in geometry covers concepts of Euclidean geometry including definitions, postulates, and theorems. Areas of study include angles, parallel lines, congruent and similar triangles, polygons, points of concurrence, the Pythagorean Theorem, vectors and orthogonality, trigonometry, circles, area and volume. The standard content is explored with greater depth than the regular Geometry course with a more of an emphasis on proofs and algebraic skills. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisites: Algebra I and departmental approv****al.** One credit.**]**

## Algebra II with Statistics

This course covers graphing relationships and solving equations through the exploration of data. Students will collect and analyze data with statistical techniques and then learn the algebraic ideas necessary to explore the relationships in greater depth. Data collection will be done with a number of techniques including use of our mathematics laboratory. Statistical topics covered include: data collection techniques, organizing and displaying data through graphical and numerical analysis, probability, and statistical inference. Algebra topics covered include: solving and graphing linear, quadratic, radical, rational, polynomial, exponential, logarithmic and piecewise functions, as well as solving systems of equations. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisite: Geometry.** One credit.]

## Algebra II

This course looks at topics both symbolically and graphically. Major topics include polynomials (linear, quadratic, and higher degree), rational functions, powers and roots, exponentials, logarithms, and trigonometry. Within these areas, transformations, systems of equations, inequalities, applications, and modeling are addressed. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisite: Algebra I**. One credit.]

## Algebra II / Precalculus Advanced (APA)

This course covers topics from Algebra II and Precalculus in a single year. Topics include inequalities, quadratic and polynomial functions, rational functions, exponents and logarithms, matrices, conic sections, sequences and series, polar coordinates, and trigonometry (including analytical trigonometry). This course is recommended for students who have demonstrated excellent analytical and mathematical skills in prior courses and the ability to understand and apply new concepts quickly. The course will meet 7 periods per cycle, and students will need to devote significant time for daily homework and preparation. The course prepares students for placement in AP Calculus. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. This course is recommended for students who have earned an A- or higher in their previous math class. [**Prerequisites: Geometry and departmental approval. **One credit.]

## Conceptual Precalculus

This course covers the topics listed in the Precalculus course description though at a pace and level less demanding than Precalculus. These topics include: linear, quadratic and polynomial functions, rational functions, logarithmic and exponential functions, and trigonometry. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. Upon successful completion of the course, students are prepared for Discrete Math, AP Statistics, or Calculus. [**Prerequisites: Algebra II or Algebra II with Statistics**. One credit.]

## Discrete Math with Applications

This course is a college-preparatory course for seniors that will use sophisticated mathematics to give students the tools to become financially responsible young adults. The course employs algebra, precalculus, probability and statistics, and geometry to solve financial problems that occur in everyday life. Real-world problems in investing, credit, banking, auto insurance, mortgages, employment, income taxes, budgeting, and planning for retirement are solved by applying the relevant mathematics. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisite: Algebra II. **One credit.]

## Precalculus

This course covers a variety of topics: linear, quadratic, and polynomial functions, rational functions, logarithmic and exponential functions, trigonometry, vectors, systems of equations, sequences and series, and conic sections. This course prepares students for placement in AP Calculus. This course uses a web-based, artificially intelligent assessment and learning system (ALEKS) to help quickly and accurately determine each student’s level of comprehension. It then allows for practice and assessment of areas of known weakness. Also, a mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisites: ****Algebra II and departmental approval**. One credit.]

## Calculus

This course studies rates of change and their application to many physical and social phenomena, such as the velocity of a satellite or the profits of a corporation. This course also covers such topics as functions, limits, differentiation and basic integration, and emphasizes practical applications of calculus in business, economics, science and engineering. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisites: Precalculus, Conceptual Precalculus or Algebra II/Precalculus Advanced. **One credit.]

## AP Calculus AB

This course examines such topics as limits, differentiation, applied maximum/minimum problems, related rates, transcendental functions, and techniques of integration. This course, which follows the AP syllabus, is designed to be roughly equivalent to a semester and a half of a college calculus course. This course is recommended for students who have demonstrated excellent analytical and mathematical skills in prior courses, and the ability to understand and apply new concepts quickly. Students will need to devote significant time for daily homework and preparation, and they commit to taking the AP examination. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. This course is recommended for students who have earned a B or higher in their previous math class. [**Prerequisites: Precalculus or Algebra II/Precalculus Advanced and departmental approval. **One credit.]

## AP Calculus BC

This course includes all topics covered in AB Calculus as well as infinite series, vectors, and polar and parametric functions. This course, which follows the AP syllabus, is designed to be equivalent to two semesters of a college calculus course. This course is recommended for students who have demonstrated excellent analytical and mathematical skills in prior courses, and the ability to understand and apply new concepts quickly. Students will need to devote significant time for daily homework and preparation. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. This course is recommended for students who have earned an A- or higher in their previous math class. [**Prerequisites: Precalculus or Algebra II/Precalculus Advanced and departmental approval**. One credit.]

## AP Statistics

This course introduces the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students learn four broad conceptual themes: exploring data, planning a study, anticipating patterns, and statistical inference. Students enrolled in this course, which follows the AP syllabus, commit to taking the AP examination. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisite: Algebra II**. One credit.]

## Fall Semester Courses

## Formal Logic

This course is an introductory course in the field of Abstract Mathematics, and through this course the students learn how to write and read formal proofs. The units include concepts related to the basics of sets and logic as well as truth tables, Venn diagrams, and Cartesian products. These ideas are used when studying the five types of proofs: direct proof, proof by contrapositive, proof by contradiction, existence proofs and mathematical induction. There is a Mathematics laboratory component implemented to allow students to have actual hands-on experience with technology and real-world mathematical modeling.** **[**Prerequisites: Calculus and AP Statistics (including concurrent enrollment) or department approval**. Half credit.]

## Spring Semester Courses

## Multivariable Calculus

This course reviews limits, derivatives, and integrals from single-variable calculus and extends the concepts to functions of two or more variables. Topics of study include partial derivatives, directional derivatives and gradients, tangent planes and normal lines, extreme of functions of two variables, iterated integrals, double and triple integrals and applications. The course focuses on the understanding of these topics from analytical, numerical and graphical perspectives. A mathematics laboratory is utilized to allow students to have actual hands-on experience with technology and real-world mathematical modeling. [**Prerequisites: Calculus and AP Statistics (including concurrent enrollment) or department approval**. Half credit.]