Mathematics

This course is designed to improve basic math skills while simultaneously progressing with algebra skills. The course centers around various topics such as the concepts of variables, equation solving, polynomials, linear equations in two variables, and graphing on the coordinate plane. The basic skills involving the order of operations are continuously practiced. Probability and statistics will also be examined. The graphing calculator will be used throughout the course. Generally students in this class have struggled with math or have had weaker backgrounds in math. This course intends to help them move back into a more full stream math sequence. Full year course. Grade: 9. Prerequisites: none

This course is for students who have demonstrated strong aptitude in their pre-algebra course. It is a fast-paced course centered on the abstract concept of variables, equation solving, and the study of linear equations in two variables. Probability and statistics will also be examined. These students will master factoring and be introduced to the quadratic equation. The graphing calculator will be used throughout the course. Both the depth and the pace of the course are significantly greater than encountered in Algebra 1, and the expectations of students are much higher. Full year course. Grade: 9. Prerequisites: strong Pre-Algebra work. 

Geometry follows Algebra 1 in the McCallie sequence of math. The topic areas covered in the first semester will be Euclidean Geometry, including parallel and perpendicular lines, equations of lines, angles and triangles. The second semester topics include proportionality, similarity of polygons, special right triangles, quadrilaterals, circles, and areas and volumes. Students will explore these topics by means of constructions, two column and paragraph proofs, using the geometric concepts to set up and solve algebraic equations, presentations of problems and concepts to the class, and writing assignments that demonstrate their mastery of the vocabulary and concepts. Methods of assessment will be homework, daily classroom participation, announced and unannounced quizzes, extended writing assignments describing solutions to problems, tests, and semester exams. Full year course. Grade: 9-10. Prerequisites: Algebra 1

This course is designed to continue to improve basic math and algebraic skills while simultaneously progressing with geometry skills. The course reviews the concepts of variables, equation solving, polynomials, linear equations in two variables, and graphing on the coordinate plane, but then expands into angles, triangles, congruences, and circles. Generally students in this class have struggled some with algebra and need some extra review bfore moving onto geometry. Full year course. Grade: 9-10. Prerequisites: none

Geometry Honors aims to formalize and extend the geometry that students have learned in previous courses. It does this by focusing on establishing triangle congruence criteria using rigid motions and formal constructions and building a formal understanding of similarity based on dilations and proportional reasoning. This course also helps students develop the concepts of formal proof, explore the properties of two- and three-dimensional objects, work within the rectangular coordinate system to verify geometric relationships and prove basic theorems about circles. On a daily basis, students in Geometry Honors use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas. Full year course. Grade: 9-10. Prerequisites: Strong grades in Algebra 1. See AP/Honors Course Prerequisites

Algebra 2 builds on skills learned in Algebra 1 (a some in Geometry.) During the first semester, students will: a) Simplify and evaluate algebraic expressions b) Classify properties of real numbers c) Solve and graph different types of equations and inequalities. d) Analyze relations and functions e) Write Linear equations f) Find and use slope of a line g) Solve systems of equations by different methods h) Add, subtract, multiply, and divide polynomials i) Perform operations with complex numbers and j) Solve equations involving roots, radicals, and rational exponents. The second semester student will a) Solve Quadratic functions b) Manipulate the quadratic formula and the discriminant c) Analyze graphs of quadratic functions d) Solve and graph quadratic inequalities e) Use remainder and factor theorems f) Graph inverse functions and relations g) Manipulate conic sections h) Study exponential and logarithmic relations and i) Manipulate trigonometric functions. The course moves methodically and carfeully, with regular nightly homework to help develp skills. Full year course. Grade: 9-11. Prerequisites: Completion of Algebra 1 and Geometry.

This course is for students who have completed Algebra 1 and Geometry, but who may have some gaps in their understanding of the previous material. The pace in this course is slower and is more strongly rooted in fundamental pre-Algebra and Algebra 1 skills to create a stronger foundation for students. The goal of the course is to strengthen the former skills while more slowly introducing the more advanced Algebra 2 topics. Course topics include linear equations, relations and functions, quadratic functions, polynomials and polynomial functions, inverses, and other types of functions as time allows. Students who work hard and do well in this course should develop more confidence in their own mathematical skills, and they may move forward to take more advanced math courses. Full year course. Grade: 10-11. Prerequisites: Completion of Algebra 1 and Geometry.

Algebra II Accelerated is a faster-paced course for students who have demonstrated strong facility, consistent work ethic, and a love of mathematics in previous math courses. The study includes what is covered in Algebra 2: quadratic, radical, exponential, logarithmic, rational, and trigonometric functions. Systems of equations, linear programming, sequences and series, and conics are also covered. Both the depth and the pace of the course are greater than encountered in Algebra II. This course prepares students for Pre-Calculus Accelerated and later for AP Calculus AB. Full year course. Grade: 10-11. Prerequisites: Strong grades in Algebra 1 and Geometry. See AP/Honors Course Prerequisites

Algebra II Honors is a lightning fast course for students who have demonstrated exceptional facility, unwavering work ethic, and a deep love of mathematics in previous math courses. The study includes what is covered in Algegra 2 Accelerated: quadratic, radical, exponential, logarithmic, rational, and trigonometric functions. Systems of equations, linear programming, sequences and series, and conics are also covered. The depth and the pace of this course far exceeds the other two Algebra 2 levels as it is preparing students to take Pre-Calculus Honors and later for AP Calculus BC. Full year course. Grade: 9-11. Prerequisites: Exception grades in Algebra 1 and Geometry. See AP/Honors Course Prerequisites

This course is available to seniors who have completed the three years of required high school math and who desire to continue their study of math to prepare for college level courses. Typically students in the course have found PreCalculus to be a challenge. The course includes an introduction to statistics and probability, with data analysis, and study of college algebra through the investigation of functions from a graphing calculator point of view. The first semester will be the introduction to Statistics and Probability. We will cover organizing and graphing data, numerical descriptive data, probability and discrete random variables and their probability distribution. During the second semester, the class will cover College Algebra with rates of change. We will specifically study linear, quadratic and power functions and rates of change from real work examples. Full year course. Grade: 10-12. Prerequisites: Completion of PreCalculus.

Statistics is a post-precalculus class designed for Upper-Classman as an alternative path to Calculus. While this course is not as formulaically heavy, it does require a diligent effort for vocabulary memorization. Through written notes, experiments, and calculator labs, students will get invaluable hands-on experience for describing the statistics gathered in samples of data. We will be comparing multiple variables both quantitative and categorical in nature. The students will learn how to design their own observational and experimental studies. Furthermore, we will look at how the laws of randomness (probability) will play a role through the many different distributions we will look through, including: Binomial, Geometric, Normal, and Chi-Squared. We will culminate these ideas with quality assurance protocols and the study of sampling distributions. These topics will lay an exceedingly solid foundation for further study of statistical analysis in college. Full year course. Grade: 11-12. Prerequisite: PreCalculus

Regular Pre-calculus is focused on mastering use of the functions and formulas of Algebra II and Trigonometry to finalize the foundation needed to do calculus. Students will leave prepared to take a rigorous, college-level pre-calculus course or introductory calculus course. As the saying goes, "The Calculus isn't hard, it's the mastering of the first 11 years leading up to it." The course starts developing a deep understanding of the properties and language of functions and why they are useful in the real world. We then cover polynomials and rational functions, exponential functions and their real world applications like finance. Next is logarithmic functions, and then we transition to trigonometry- focusing on solving triangles, understanding the unit circle, graphs of trigonometric functions, and solving problems with identities. The push of the class is focused on developing conceptual understanding through progressively more complex problem solving. Students learn the "why" of functions by applying their skills to projects and application problems. Full year course. Grade: 10-12. Prerequisites: Completion of Algebra 2.

Precalculus Accelerated covers the concepts of functions, trigonometry, logarithms, exponents, conic sections, and limits. Students will learn to solve multi-step problems requiring the application of two or more concepts. Additionally, students will learn to create the graph of a function using its equation, and observe the behavior of a function by analyzing its graph. Finally, students will learn how each of the concepts covered directly apply to their engagement with science, economics, physics, and the world at large. Precalculus Accelerated moves more quickly and goes into more depth that Pre-Calculus, and will fully prepare students to take AP Calculus AB. Full year course. Grade: 10-11. Prerequisites: Completion of Algebra 2 Accelerated.

Precalculus Honors is a blazing fast courses covering the concepts of functions, trigonometry, logarithms, exponents, conic sections, and limits. Students will learn to solve multi-step problems requiring the application of two or more concepts. Additionally, students will learn to create the graph of a function using its equation, and observe the behavior of a function by analyzing its graph. Finally, students will learn how each of the concepts covered directly apply to their engagement with science, economics, physics, and the world at large. Precalculus Honors moves even more quickly and goes into more depth than Pre-Calculus Accelerated, and will fully prepare students to take AP Calculus BC. Full year course. Grade: 9-11. Prerequisites: Exceptional success in Algebra 2 Honors. See AP/Honors Course Prerequisites

This course is the choice for students who have successfully completed Pre-Calculus or may have struggled a little in Pre-Calculus Accelerated, or who are new to McCallie with a Pre-Calculus credit from another school. It is designed as an introduction to college level Calculus.The course has three components:(1) a thorough review of pre-calculus skills that are crucial to calculus, (2) finding and using the derivative (differential calculus), and (3) an introduction to integrals (integral calculus). The pace of the course is such that students will NOT be prepared to take the Advanced Placement Calculus Exam in May. Full year course. Grade: 11-12. Prerequisites: Completion of PreCalculus.

This challenging course is the choice for students who have excelled in Pre-Calculus Accelerated or successfully completed Pre-Calculus Honors at McCallie, or who are new to McCallie with a rigorous Pre-Calculus credit from another school. It includes all of the topics of a one-semester college calculus course including limits, derivatives with applications, and the definite integral with applications. Students will frequently practice multiple choice and free-response questions similar to those that appear on the AP exam. Full year course. Grade: 10-12. Prerequisites: Strong grades in PreCalculus Accelerated or Calculus. See AP/Honors Course Prerequisites

This challenging course is the choice for students who have successfully completed Pre-Calculus Honors at McCallie, or who are new to McCallie with a rigorous Pre-Calculus credit from another school. It includes all the topics of a full year college Calculus course including limits, derivatives with applications, the definite integral with applications, advanced integration techniques, parametric and polar equations, and sequences and series. Students will frequently practice multiple choice and free-response questions similar to those that appear on the AP exam. All students will be expected to take the BC Advanced Placement exam in May. Full year course. Grade: 10-12. Prerequisites: Exceptional grades in PreCalculus Honors. See AP/Honors Course Prerequisites

This course is for students who took AP Calculus AB and want the next step in calculus. It will add advanced integration techniques, parametric and polar equations, and sequences and series. Semester Course. Grade: 11-12. Strong grades in AP Calculus AB. See AP/Honors Course Prerequisites

AP Statistics is a challenging course designed as an elective for those students who have completed or are currently in a Calculus course. This course will introduce students to the major tools for collecting, analyzing, and drawing conclusions from data. Topics will include graphical and numerical techniques to study patterns and departures from patterns, planning and conducting a study using statstical analysis, exploring random phenomena using probability and simulation, and estimating population parameters and testing hypotheses. Students will be prepared to take the AP Statistics exam. Full year course. Grade: 11-12. Prerequisites: Concurrent or previous completion of Calculus. See AP/Honors Course Prerequisites

This course is for the exceptional math student who has completed Advanced Placement BC Calculus. Topics include vectors and surfaces, vector valued functions, partial differential equations and multiple integrals, and vector calculus. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC.

This course is for the exceptional math student who has completed Advanced Placement BC Calculus. Topics include first order differential equations, second order linear equations, and higher order linear equations. Additional topics may include series solutions of second order linear equations, the Laplace transform, or systems of first order linear equations. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC.

This course presents the fundamentals of linear algebra through the clearest possible way, through examples, and then to move on to the abstract set of axioms. Topics will include systems of linear equation with matrix solutions, determinates, two and three space vectors, n-dimensional Euclidean spaces, abstract vector spaces, inner product spaces, eigenvalues and eigenvectors, and linear transformations. The course will be conducted in a seminar format with the write up of problems, take-home problem sets, and verbal presentation of problems as a major component to the students' evaluation. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC.

Advanced Proofs will take a look at the formal rules and naming of proofs. We will learn the different methods by which proofs are formatted, as well as the different subjects in which these methods can be used. A lot of these proofs will overlap in subjects with other major mathematical theorems and identities. Advanced Proofs will be taught seminar style, with a majority of the grade coming from the quality of notes taken, and work shown throughout the semester. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC

Graph Theory will look at the almost infinite uses of points and connections. Known as vertices and edges, we will look at how to construct these graphical models and the uses they can present us in the real world. The course will be conducted in a seminar format with the write up of problems and verbal presentation of problems as a major component to the students' evaluation. Students will be expected to research topics and present the concepts to the class. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC.

Combinatorics will study and break down the rules of probability. We will start in finite math and move to the infinite setting. Our studies will bring us into contact with many different types of probability distributions from the discrete and continuous nature. This course will be taught in a seminar style setting, with a majority of the grade coming from the quality of notes taken and work shown throughout the semester. Semester course. Grade: 11-12. Prerequisites: Exceptional success in AP Calculus BC.