# Mathematics 2014-2015

**Shannon Lambert**, Department Head

The Mathematics Department espouses the standards set forth by the National Council of Teachers of Mathematics. Each course seeks to help the student learn to value mathematics, become confident in her ability to do mathematics, become a mathematical problem-solver, and learn to communicate and reason mathematically. The student is expected to be actively involved in doing mathematics through exploration, modeling, conjecture making, researching, decision-making, and problem solving.

**Department Requirements**

Successful completion of three years of mathematics which must include two years of Algebra and one year of Geometry. A fourth (full) year of mathematics is strongly recommended

**Course Descriptions**

**Algebra 1**

Algebraic thinking involves discovering patterns, making generalizations about numbers and using symbols to represent relationships. This course is the foundation of the language of mathematics. Students will study the properties of real numbers, solve equations and inequalities, combine rational expressions and problem solve. They will practice incorporating real world data into applications of Algebra through the use of IPad applications and TI-84 series graphing calculators.

**Prerequisite:** none

**Algebra 2**

This rigorous course thoroughly reviews and extends the concepts of Algebra 1 through the study of quadratic equations and inequalities, complex numbers, roots and radicals, functions, systems of equations, graphing and advanced problem-solving. Students will be expected to use TI-84 series graphing calculators to confirm solutions and support critical thinking skills.

**Prerequisite:** Algebra 1; recommendation of the department is necessary for Honors

**Geometry**

This course covers geometric construction (via compass and straightedge), the properties of plane and solid figures, perimeter, area, volume and the Pythagorean Theorem. Concepts are explored using both inductive and deductive reasoning. Students are encouraged to think for themselves about what might be true, explore their ideas through hands-on or computer-based investigations and then confirm their results through rigorous proof.

**Prerequisite:** Algebra 1; recommendation of the department is necessary for Honors

**Advanced Geometry**

This course is designed to provide advanced work in geometry for students who have completed a full year course in Euclidean geometry. Prior study of trigonometry is strongly recommended. Topics vary each year depending on student interest. Topics include in-depth work in sequences and patterns, symmetry, non-Euclidean geometry (spherical and hyperbolic surfaces), dissection of planar and solid figures, biomechanics and minimal surfaces via soap films. Most topics are explored using hands-on or computer-based activities, and are assessed through student projects. Students will have the opportunity to do independent exploration of topics that particularly interest them. This course is appropriate for serious math students and students whose interests lie in the arts.

**Prerequisite:** Geometry (required), Algebra 2 (required)

**Intro to Precalculus**

This year-long course focuses on strengthening and expanding intermediate and advanced algebra skills and applications of mathematics. An in-depth study of linear, trigonometric, and circular functions is included. The conic sections are introduced as special quadratic relations.

**Prerequisite:** successful completion of two years of Algebra and Geometry

**Precalculus**

Our goal for Precalculus is to help students learn the skills and concepts needed to understand Calculus. Precalculus is a combination of elements from Algebra, Trigonometry and Geometry. This year-long course includes algebraic, exponential, logarithmic, and trigonometric functions and their graphs as well as an introduction to sequences, summation notation, and analytic geometry. Some SAT and ACT preparation is included in this course. The TI-84 series graphing calculator is required for this course.

**Prerequisite:** successful completion of two years of Algebra and Geometry; recommendation of the department is necessary for Honors

**Calculus**

This year-long course begins with the study of sequences and summation, conic sections, mathematical induction, matrices and vectors. The concept of limit will be introduced from both an intuitive and formal approach. The definition of and techniques for finding the derivative will lead to curve sketching and practical applications. The concept of integral along with the techniques for finding the integral and its basic application will also be covered. The TI-84 calculator is used extensively throughout this course.

**Prerequisite:** successful completion of Precalculus or Precalculus Honors

**AP Statistics**

The AP course in Statistics provides motivated and capable math students with an introduction to statistics and statistical analysis, in preparation for the AP exam in May. Students learn methods for designing experiments, taking an appropriate sample of a population, discussing a set of data and making decisions about results based on data and their summary statistics. Reading and critical thinking are important parts of this course, and answers will often require interpretation rather than simply being taught "right" or "wrong." The skills taught in Statistics are discussed in their real-world applications, and lively debates often erupt on the subject of opinion polling, healthcare and criminal justice. A TI-84 series graphing calculator will be required for many of the calculations and procedures taught in this course.

**Prerequisite: **strong background in Algebra or some level of Precalculus and the recommendation of the department based on demonstrated skills and motivation

**Personal Finance**

*year-long course that meets twice a week*** **

Planning your financial future is one of the most important things you may do in your life. This seminar course teaches financial literacy and is designed to provide students with the information and tools they need to meet financial challenges they will face in the real world. The major topics covered include planning a budget, banking and credit, investing in stocks, bonds and mutual funds, tax strategies, real estate investments, insurance and retirement planning, preparing for an interview.

TI-84 graphing calculator required. Senior elective. This course does not meet the full-year senior mathematics recommendation.

**Prerequisite:** none

**AP Calculus AB and BC**

Calculus allows us to study how some quantities change and accumulate in relation to others. The AP Calculus curriculum, as designed by the College Board, is divided into two courses, each of which is offered on a year-long basis at Lincoln. AP Calculus courses teach students not only how to solve particular problems, but how to think creatively about the skills they are gaining and to express their thinking graphically, analytically, numerically and verbally. Each course prepares students for the corresponding AP exam in May.

AP Calculus AB allows motivated students with strong skills the opportunity to build on work done in Precalculus Honors and learn calculus topics as applied to various types of functions, including trigonometric, logarithmic and exponential functions. The course begins by taking a new look at graphs of functions with an eye to limits and continuity. The central concept of the derivative, along with its many applications in the real world and in other mathematical topics, is the focus of the middle portion of the year. The AB course wraps up with a study of integration methods and their various applications.

AP Calculus BC is offered to exceptional students who complete Calculus AB by the end of their junior year. Topics from Calculus BC are reviewed throughout the year as the basis for extended applications and material. Familiar concepts of differentiation and integration are applied in new graphing situations such as the polar plane, parameterized curves and vector-valued functions. New applications and methods for integration are explored, and the year finishes with a thorough investigation of infinite sequences and series.

**Prerequisite:** successful completion of Precalculus Honors and the recommendation of the department based on demonstrated skills and motivation.

**Discrete Math**

*year-long course that meets four times a week *

Discrete Math is the study of structures that are discrete by nature rather than continuous. Discrete Math encompasses several topics. Topics related to graph theory, logic, combinatorics, probability, number theory, and game theory will be explored.** **It is our goal that students will be challenged daily to inquire, process and think critically, reflect and report data.

This year-long course requires a TI-84 graphing calculator. Senior elective.

**Prerequisite**: Completion of Algebra I, II and Geometry