# Mathematics Courses

#### Algebra I

Algebra I is a foundational course for Geometry, Algebra II and Precalculus. The major topics studied are solving linear equations and inequalities, word problems based on linear relationships, working with polynomials to include factoring, solving systems of equations to include word problems, solving quadratic equations to include the quadratic formula, completing the square, and factoring, properties of exponents, working with rational expressions, and working with radical expressions to include the Pythagorean Theorem.

#### Geometry

Geometry provides an introduction to Euclidian Geometry by examining geometric figures in two and three dimensions. Algebraic methods are reviewed and used in geometric applications. First semester topics include points, lines, planes, deductive reasoning, parallel lines and planes, triangles, congruence, polygons, quadrilaterals, and inequalities. We will also introduce the proof process to include two-column and indirect proofs. In the second semester we will consider applications of similarity, Pythagorean theorem, right triangle trigonometry, circles, area, surface area and volume of solids and coordinate geometry.

#### Algebra II

Algebra II builds on the foundations set in Algebra I. Major topics studied are linear and data analysis, systems of equations, matrices, quadratic functions, exponential functions, inverse functions, rational functions, radical functions, conic sections, sequences and series, and probability. Multiple representations of functions are emphasized as are algebraic skills. Real world applications and technology are incorporated throughout the course.

#### Precalculus

Precalculus is a course designed to weave together the material from previous math courses, build problem solving skills, and study new content in preparation for students to take calculus. Topics studied are Linear, Quadratic and Polynomial Functions, Exponential and Logarithmic Functions are revisited, development of e and the natural logarithm; Trigonometry is a major focus of the second semester; Rational function are studied at a deeper level than students encountered in Algebra II; graphical and algebraic limits are studied; probability from Algebra II is built upon and extended. Technology is incorporated throughout the course as are real world applications.

#### Elements of Precalculus

Elements of Precalculus examines all of the major topics as those in Precalculus. Fundamental concepts are reviewed more in depth, and the pace of the course is slower. Elements of Precalculus is recommended for students earning an 80 or below in an Algebra 2 course. Technology is incorporated throughout the course, as are real world applications.

#### Honors Precalculus

Honors Precalculus is designed to to place greater emphasis on more challenging applications of the topics covered, preparing for enrollment in the BC Calculus course. Topics include all those listed in the Precalculus course and will also include more abstract graphing of functions, data analysis, and study of recursion, sequences and series. This course is designed for those students earning grades of A- or better in Algebra II.

#### Precalculus with Human Rights Focus

This unique interdisciplinary course will cover all mathematical topics listed in the traditional Precalculus course, but it will also apply these principles to modern human rights issues. Human Rights topics could include education and literacy, hunger, poverty, health, environmental crises and more. The course will use traditional assessments (e.g., quizzes and tests) as well as alternative assessments based on the social issues discussed in class. These alternative assessments could take the form of class discussions, case study analyses, group presentations or brief position papers. Depending on availability, there may be opportunities to interact with experts in the human rights organizations. The data for these case studies will come from organizations such as the United Nations Sustainable Development Goals or other local, research-based NGOs. This course will be taught at the standard Precalculus level.

#### AP Calculus AB

#### AP Calculus BC

AP Calculus BC covers two college semesters of Calculus. Topics studied are limits and continuity, derivatives and their applications, integrals and their applications, differential equations, sequences and series. This course is recommended for students who have completed Honors Precalculus or earned an A in Precalculus or an A in Precalculus with Human Rights Focus. Students are prepared to take the BC Calculus exam.

#### Calculus C

#### AP Statistics

AP Statistics is an introduction to Statistics. Topics covered are displaying and describing data, gathering data, probability and inference. Much of second semester is spent studying inference: sampling distributions, confidence intervals, significance tests, normal distributions, t distributions, chi square distributions. Concepts are studied through real-world applications, and technology is emphasized. AP Statistics is open to students who have are currently enrolled in or have completed a Precalculus course. Students are prepared to take the AP Statistics exam.

#### Multivariable Calculus

Multivariable Calculus will include partial differentiation and partial differential equations, line integrals, multiple integrals and surface integrals. Lagrange multipliers are typically covered. Emphasis will be placed on problem-solving and the theorems that underlie these branches of mathematics. If time is available, further topics may include systems of differential equations, the calculus of probabilities, or other topics at the discretion of the instructor. A score of 4 or a 5 on the BC Calculus exam is a prerequisite for the course.

#### Non-Euclidean Geometry and the Shape of Space

Geometry, Topology and Shape allows students to investigate and develop elementary theorems in non-Euclidean geometries. Students will complete constructions and proofs in the Euclidean plane as well as in non-Euclidean space. The course also includes an intuitive elementary study of manifolds. Strengthening communicating mathematical findings verbally and in writing emphasized throughout the course.

#### Special Topics in Mathematics I

Mathematics will be utilized to develop techniques of thought that can be used to solve problems, analyze situations and hone the way we look at our world. These strategies will help in dealing with real-life decisions both inside and outside the realm of mathematics. We will study traffic patterns, wildlife management, population growth as well as the beauty, symmetry and order of mathematics. The use of technology will be emphasized.

#### Special Topics in Mathematics II

Mathematics will be utilized to develop techniques of thought that can be used to solve problems, analyze situations and hone the way we look at our world. These strategies will help in dealing with real-life decisions both inside and outside the realm of mathematics. We will study economics, financial literacy, drug testing, statistics in sports, mathematics of voting, population growth and other related topics. The use of technology will be emphasized.

#### Statistics, Probability and Actuarial Science

This one-term, non-AP course introduces students to fundamental concepts in statistics. The course begins with an introduction to presenting and interpreting data. Using case studies from a variety of disciplines, students explore in detail the background, concepts, and tools for studying that data and its variability. The main focus of the course is to discover methods of basic inference using various methods by working with simulations, probability, and real data. Topics include basic probability, basic linear regression, estimators, simulations, experimental design, and statistical inference. The final project of the course will ask students to apply mathematical and statistical methods to assess risk in insurance, finance or some other industry.

#### Finite Mathematics

Finite math is a generic title for a collection of mathematical topics. This course will offer an overview of many applications of mathematics, especially in the social and management sciences. Topics will include: mathematical model building, induction, combinatorics, the binomial theorem, matrix algebra, logic, voting coalitions, and linear programming. Students are expected to be involved in formulating problems, applying the appropriate mathematics to find a solution, and evaluating the solution. Computers and calculators are incorporated as computational and modeling aids.