Math

The mathematics curriculum described in the following course offerings is intended to prepare each girl for college level work in mathematics. Students are encouraged to take full advantage of the mathematics courses each year so that they can thoroughly develop their mathematical skills. At the

end of each year, math teachers will recommend a course for each of their students based on the

student’s performance during the past year, her maturity, study skills, and her ability to handle the

abstract concepts required in the secondary curriculum. Any girl entering an honors course after the 7th

grade year must complete a study of additional topics in the summer and show mastery of the topics on a test before entering the honors course. Summer work may be required for any student moving up a level from their present course, regardless of a transition to honors. All courses are full year and worth 1 credit in math unless otherwise noted.

Calculator requirements for GPS math classes in grades 7-12:
The TI-84+CE is required for all GPS math classes.
(unless a TI-84+ has been previously purchased).

Algebra I

2 Semesters (1 Credit)

Grade Levels: 9

Prerequisite: None

Algebra I emphasizes both the structure of algebra and the development of logical problem-solving skills. Students study in detail linear equations and inequalities, as well as quadratic equations. The study of polynomials and factoring, rational expressions, and radical expressions complete the year. Practical applications and critical thinking are woven throughout the course as students experience the relevance of various topics in the real world.
Geometry

2 Semesters (1 Credit)

Grade Levels: 9, 10

Prerequisite: Algebra I

The Geometry course offers a formal deductive and inductive approach to the study of Euclidean geometry. Students will discover and learn postulates and theorems; develop formal proofs; solve problems about segments, angles, and polygons; explore similarity and congruence in polygons; explore properties of special right triangles and quadrilaterals, slopes of parallel and perpendicular lines, and distance; explore transformations; and develop concepts of spatial relationship in two and three dimensions through calculations of perimeter, area, and volume. Algebra is strongly integrated throughout the year.
Honors Geometry

2 Semesters (1 Credit)

Grade Levels: 9

Prerequisite: Honors Algebra I, or Algebra I with summer work

Honors Geometry offers a formal deductive and inductive approach to the study of Euclidean geometry. Students develop skills in thinking logically, reading with understanding, writing proofs, and developing concepts of spatial relationships in two and three dimensions. Complex algebra is strongly integrated in all problem solving; a strong mastery of Algebra I is expected.
Algebra II

2 Semesters (1 Credit)

Grade Levels: 10, 11

Prerequisite: Geometry, Accelerated Geometry, or Honors Geometry

Algebra II offers an extension of past algebra and geometry concepts by deepening students’ understanding of function behavior and problem-solving skills. Students investigate systems of equations, higher degree polynomials, and sequences and series using a numerical, graphical, and algebraic approach. Real-world applications, the graphing calculator, and segues to higher-level mathematical topics are integrated throughout the year.
Accelerated Algebra II & Trigonometry

2 Semesters (1 Credit)

Grade Levels: 10, 11

Prerequisite: Geometry, Accelerated Geometry, or Honors Geometry

Accelerated Algebra II and Trigonometry offers an extension of past algebra and geometry concepts and prepares students for the study of Precalculus. Investigations into geometry and trigonometric concepts, families of functions and their encompassed behaviors, an introduction to limits and end behavior, as well as the application of the graphing calculator and computer software are integrated throughout the year. Accelerated Algebra II is considered a Pre-AP course as this curriculum is geared toward preparing students for the eventuality of AP AB Calculus. With this plan in mind, the course often offers segues to higher-level mathematical topics to broaden understanding and applicability, as well as connections to future areas of study.
Honors Algebra II & Trigonometry

2 Semesters (1 Credit)

Grade Levels: 9, 10, 11

Prerequisite: Honors Geometry; Geometry or Accelerated Geometry with summer work

Honors Algebra II and Trigonometry offers an extension of past algebra and geometry concepts. Topics of increased sophistication are introduced to complete the student’s preparation for the study of Precalculus. Investigations into geometry and trigonometric concepts, families of functions and their encompassed behaviors, an introduction to limits and end behavior, as well as the application of the graphing calculator and computer software are integrated throughout the year. Honors Algebra II is considered a Pre-AP course as this curriculum is geared toward preparing students for the eventuality of AP Calculus BC. With this trajectory in mind, the course often offers segues to higher-level mathematical topics to broaden understanding and applicability, as well as connections to future areas of study.
Precalculus

2 Semesters (1 Credit)

Grade Levels: 11, 12

Prerequisite: Algebra II, Accelerated Algebra II and Trigonometry, or Honors Algebra II and Trigonometry

The topics studied in Precalculus will provide a deeper understanding of functions and trigonometry. Limit theory will be introduced along with some extensions of discrete math. A student completing this course will be ready for math in the college world. Extensive use of the graphing calculator brings an added dimension to the study of a wide variety of functions in Precalculus. The emphasis is on the utilization of patterns and relationships as connections between algebraic and geometric interpretations are strengthened. Trigonometry is extended and developed in detail in this course, and a brief study of discrete math topics is also included. The purpose of Precalculus is to develop not only essential ideas and facts but also the kinds of mathematical thinking necessary for success in college math classes.
Accelerated Precalculus

2 Semesters (1 Credit)

Grade Levels: 11, 12

Prerequisite: Accelerated Algebra II and Trigonometry, or Honors Algebra II and Trigonometry

The topics studied in Accelerated Precalculus will provide a deeper understanding of functions and trigonometry. Limit theory will be introduced, along with some extensions of discrete math. The purpose of Precalculus is to develop not only essential ideas and facts but also the kinds of mathematical thinking necessary for success in calculus. Extensive use of the graphing calculator brings an added dimension to the study of a wide variety of functions. The emphasis is on student discovery and utilization of patterns and relationships as connections between algebraic and geometric interpretations are strengthened. Accelerated Precalculus is considered a Pre-AP course as this curriculum is geared toward preparing students for the eventuality of AP Calculus AB (Calculus I at the university level). With this plan in mind, the course often offers segues to higher-level mathematical topics to broaden understanding and applicability, as well as connections to future areas of study.
Honors Precalculus

2 Semesters (1 Credit)

Grade Levels: 10, 11, 12

Prerequisite: Honors Algebra II and Trigonometry; Accelerated Algebra II and Trigonometry with summer work

The topics studied in Honors Precalculus will provide a deeper understanding of functions and trigonometry. Limit theory will be introduced, along with some extensions of discrete math. A student completing this course will be ready for math in the college world. At the Honors level, extensive use of the graphing calculator brings an added dimension to the study of a wide variety of functions in Precalculus. The emphasis is on student discovery and utilization of patterns and relationships as connections between algebraic and geometric interpretations are strengthened. Trigonometry is extended and developed in detail in this course, and a brief study of discrete math topics is also included. Application problems from science abound. The purpose of Precalculus is to develop not only essential ideas and facts but also the kinds of mathematical thinking necessary for success in calculus. In fact, the latter portion of this course delves deeply into the introductory units of Calculus I including limits and derivatives.

Honors Precalculus is considered a Pre-AP course as this curriculum is geared toward preparing students for the eventuality of AP Calculus BC (Calculus I & II at the university level). With this plan in mind, the course often offers segues to higher-level mathematical topics to broaden understanding and applicability, as well as connections to future areas of study. Specifically, the students in Honors Precalculus will officially transition into their introductory studies of calculus during the post-Winterim phase of the school year. These investigations in the spring will assist in the curriculum management demands associated with the AP Calculus BC curriculum that will be completed May of the following year prior to the AP Exam.
Calculus

2 Semesters (1 Credit)

Grade Levels: 12

Prerequisite: Precalculus, Accelerated Precalculus, or Honors Precalculus

The Calculus course covers several topics in a typical Calculus I college course. Students use computers and their graphing calculators daily for class work and homework assignments. After an introductory study of functions, limits, and analytic geometry, the course centers on the differentiation of algebraic functions and application of derivatives to curve sketching and related rates of change. Also included are the topics of differentiation of trigonometric functions, Newton's method, and elementary techniques of integration.
AP Calculus AB

2 Semesters (1 Credit)

Grade Levels: 11, 12

Prerequisite: Accelerated Precalculus, Honors Precalculus; Precalculus with additional summer work

Advanced Placement Calculus AB (Calculus I) is a full-year course that covers all topics in a typical college-level calculus course. After an introductory study of functions, limits, and analytic geometry, the course centers on the differentiation of algebraic functions and application of derivatives to curve sketching and related rates of change. Also included are the topics of differentiation of trigonometric functions, elementary techniques of integration applied to find areas between curves and volumes of solids of revolution, the study of the calculus applied to exponential and logarithmic functions, and L’Hopital’s rule.
AP Calculus BC

2 Semesters (1 Credit)

Grade Levels: 11, 12

Prerequisite: Honors Precalculus

The AP Calculus BC course is a full-year course in calculus, covering topics typically studied in both Calculus I and Calculus II. Whereas AP Calculus AB begins with an introductory study of functions, limits, and analytic geometry, and centers on the differentiation of algebraic functions and application of derivatives to curve sketching and related rates of change, AP Calculus BC topics include vector functions and parametrically defined functions, graphs in polar coordinates, sequences and series of functions, Taylor series, and elementary differential equations.
Advanced Financial Algebra and Statistics

2 Semesters (1 Credit)

Grade Levels: 12 (11 as second math)

Prerequisite: Algebra II

Advanced Financial Algebra and Statistics is a fourth-year mathematics course designed for students who have successfully completed Algebra II. The course extends and deepens student understanding of algebra, statistics, and research design while introducing students to relevant financial and business applications. Students will create, apply, and interpret a wide variety of algebraic function-models to aid in real-world decision making. Statistical research and analysis will be utilized to determine the efficacy of model applications and further assist in exploring scenarios with financial implications. Financial contexts for these mathematical concepts will include business operations and optimization, tax considerations, insurance and risk management, banking services, budget creation, loan and credit analysis, investment strategies and retirement plans, stock market performance, real estate fundamentals, and automobile ownership. Instruction and assessment will include the appropriate use of manipulatives and technology. Topics will be represented in multiple ways, such as concrete/pictorial, verbal/written, numeric/data-based, graphical, and symbolic.
AP Statistics

2 Semesters (1 Credit)

Grade Levels: 10-12

Prerequisite or Corequisite: Honors Algebra II or Precalculus

Reasoning based on probability and statistics gives modern society the ability to cope with uncertainty with astonishing power to improve decision-making accuracy and test new ideas. It’s a key analytical tool used in education, the social sciences, and business administration and is often a required college subject for majors in those areas. Statistics is frequently used for data analysis in the sciences and forms the mathematical basis for quality control in manufacturing. AP Statistics is a college-level class—a fun and exciting activity-based course that exposes students to the following themes: exploring data (i.e. describing patterns and departures from patterns), sampling and experimentation (i.e. planning and conducting a study), anticipating patterns (i.e. exploring random phenomena using probability and simulation), and statistical inference (i.e. estimating population parameters and testing hypotheses). Since most statistical analysis is done on calculators or computers, students will learn how to perform statistical analysis on TI-84 calculators as well as more traditional techniques.
Honors Multivariable Calculus

1 Semester (0.5 Credit) - Fall

Grade Levels: 12

Prerequisite: AP Calculus BC

Multivariable Calculus (also known as Multivariate Calculus or Calculus III) examines the differentiation and integration of functions involving several variables. Emphasis is placed on multivariable functions, partial derivatives, multiple integration, solid analytical geometry, vector valued functions, and line and surface integrals. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics, and computer graphics.
Honors Differential Equations

1 Semester (0.5 Credit) - Spring

Grade Levels: 12

Prerequisite: AP Calculus BC

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations and how to solve those equations and interpret the solutions. In application, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines. 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.