# Mathematics

Math is the basic language of science and technology. It influences banking, space travel, construction of automobiles and buildings, sports, and the computer industry. Math is a creative, dynamic system that we use to model and understand our environment. The Mathematics department’s mission is to teach students math literacy and competency and to refine organized thinking. Using logical, analytical, and critical thinking, students will develop mathematical habits and skills to help them to think, process, and problem solve in all areas of learning. Self-discipline and consistent effort, along with asking for help when needed, is necessary for success. The math department provides a rigorous curriculum that serves the needs of a broad spectrum of aptitudes and goals and includes the study of great mathematicians and movements in math. Many students fulfill the three-year math requirement by taking Algebra I, Geometry, and Algebra II (and even Pre-Calculus). The serious math student takes a sequence that culminates in AP Calculus AB or BC or Multivariable Calculus.

## Required Course Offerings

## Algebra I

**Algebra I with Lab** - This course delves into the basic concept of function and it reinforces algebraic thinking. Topics covered include slope, graphs, linear and quadratic equations, exponential functions, polynomials, rational expressions, and radicals. The course meets one additional meeting time per cycle for additional instructional support.

**Algebra I - **This first year of algebra delves into the basic concept of function and it reinforces algebraic thinking. Much of the class is spent solving linear, fractional, and quadratic equations and inequalities. There is also a focus on operations with polynomials, radicals, and fractional expressions. Other topics include factoring polynomials, and graphing linear and quadratic equations.

## Geometry or Geometry Honors

**Geometry** - Students in this course will concentrate on solving problems through algebraic and spatial thinking. This traditional course in plane and spatial geometry includes the following areas of study: reasoning/logic, proofs, ratio and proportion, properties of triangles, quadrilaterals, area, volume, transformations, circles, polygons, coordinate geometry, and right angle trigonometry. Students will demonstrate their learning in words as well as numerically.

**Geometry Honors** - In addition to the topics covered in Geometry, students will develop an axiomatic foundation for plane geometry. They will also study transformational and analytic geometry. The course will include a survey of triangle-based trigonometry and a research paper on a selected topic. Applications of geometry within AP Calculus will be discussed.

## Algebra II or Algebra II Honors

**Algebra II** - The second year of algebra develops mastery of algebraic skills required for further progress in mathematics and for number literacy in society. After reviewing and further developing topics from Algebra I, the course will study polynomial equations of higher degree, conic sections, exponential and logarithmic equations, triangle and circular trigonometry, and probability.

**Algebra II Honors** - In addition to the topics covered in Algebra II, through an accelerated pace, this course is designed to take students through the beginnings of the Pre-Calculus curriculum so that students are prepared to take Honors Pre-Calculus. The course emphasizes more advanced problem solving, and abstract thinking. Throughout the text, the students will always attempt “challenge problems” that the regular class will not attempt.

## Additional Course Offerings

## Functions, Statistics, and Trigonometry

Functions, Statistics, and Trigonometry serves as a link from Algebra II to Pre-Calculus or AP Statistics. Students will explore and model linear, quadratic, exponential, logarithmic, polynomial, trigonometric, circular and other special functions both for their abstract properties and for modeling real-world situations. Statistics is a strong component of this course and will introduce data exploration and modeling, describing relationships of two variables, designing studies and experimental design, probability, simulation, and binomial and normal distributions. The TI-Nspire calculator is used as a learning tool and is required for the course.

## Pre-Calculus or Pre-Calculus Honors

**Pre-Calculus** - Pre-Calculus is designed to prepare the serious student of mathematics for Calculus. Topics covered include a review of basic algebraic concepts; analysis of functions and techniques for graphing polynomial, rational, algebraic, exponential, logarithmic and trigonometric functions; identities; probability and statistics; the formation of algebraic proofs; conics; polar coordinates; vectors; limits and derivatives.

**Pre-Calculus Honors** - In addition to the topics covered in Pre-Calculus, and besides going at an advanced pace and greater depth, this course will explore introductory topics of differential calculus including differentiation, limits and solve-related problems.

## Calculus

Calculus is designed for the student who has successfully completed a pre-calculus course but is not ready to advance to AP Calculus. The course will begin with a review of functions and limits. The theory and techniques of differentiation and integration of polynomial and basic trigonometric functions are the primary topics of this course along with applications for both differentiation and integration. This course will provide a strong foundation that will give students the tools to succeed in future mathematics courses. The TI-84+ and/or TI-Nspire calculator is used as a learning tool and is required for the course.

## Advanced Placement Offerings

## AP Calculus AB

AP Calculus AB is equivalent to the first semester of college calculus, with a short review of pre-calculus topics. The serious student will be prepared to take the Advanced Placement test in AB Calculus. The course reviews analytic geometry and limits. The theory and techniques of differentiation and integration of polynomial, trigonometric and transcendental functions are covered, and applications are included for both integration and differentiation. The TI-83+ calculator is required.

## AP Calculus BC

AP Calculus BC is equivalent to the first and second semesters of college calculus. The serious student will be prepared to take the Advanced Placement test in BC Calculus. The theory and techniques of differentiation and integration of polynomial, trigonometric, and transcendental functions are covered, and applications are included for both integration and differentiation. In addition, differential equations, infinite series, and power series are covered. A graphing calculator (TI-83+ is recommended) is required, as the student will be taught to use the calculator as a support for analysis, and graphing calculators are required by the College Board for the AP Calculus BC test.

## Multivariable Calculus

Multivariable Calculus is for students who have successfully finished AP Calculus BC or have received special consideration from the instructor. Students will explore vector-valued functions, including their differentiation and integration and applications such as velocity, acceleration and as a position function. Differentiating and integrating functions of several variables including partial derivatives and differentials will be covered. Examining area and volume and surface area with multiple integrals will be stressed. The course finishes with vector fields, Green’s Theorem, parametric surfaces, the divergence theorem and Stokes’s Theorem. After finishing the course, we will study Linear Algebra and Probability. The TI-Nspire CX calculator is used as a learning tool and is required for the course.

## AP Statistics

AP Statistics is equivalent to one-semester of introductory, non-calculus, college-based statistics course. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

**Exploring Data** - Observing patterns and departures from patterns**Planning a Study **- Deciding what and how to measure**Anticipating Patterns** - Producing models using probability theory and simulation**Statistical Interference** - Confirming models