# Mathematics The mathematics curriculum in the Upper School contains many levels of rigor. Students in the Upper School are required to complete courses in Algebra I, Algebra II, and Geometry before electing other options. Several levels of difficulty and challenge are available in each course. Accelerated courses allow students who have a strong interest in and facility for mathematics to pursue mathematical concepts in more depth and at a faster pace. Consultation among previous teachers, the student, and the Department Chair determines a student’s placement in math.

## Algebra I

This course is for students who have studied pre-algebra and are ready to move on to a yearlong algebra course. Topics include variables, equations, algebraic fractions, linear functions and their graphs, quadratic functions and their graphs, systems of equations, and direct and inverse variation. Use of a graphing calculator reinforces and supports skills learned in this course.

## Algebra II

This course presents the concepts of a traditional Algebra II program for students who have successfully completed Algebra I, and it may be taken prior to or after Geometry. Topics studied include linear and quadratic functions, direct and inverse variation, inequalities and absolute value, systems of equations, and simplifying and solving rational and radical expressions and equations. Use of a graphing calculator reinforces and supports skills learned in this course. Prerequisite: Algebra I or equivalent.

## Accelerated Algebra II

This course is for strong math students who have successfully completed an Algebra I course. The class starts out with a look at sequences and series and how these unique topics have connections to both linear and exponential relationships. It also includes other topics traditionally found in a rigorous Algebra II course. Topics include a thorough study of linear and quadratic functions, direct and inverse variation, inequalities and absolute value, systems of equations, and simplifying and solving rational and radical expressions and equations. If time permits, students will also explore exponential and logarithmic functions. Technology is used to support learning and exploration, leading to a deeper connection to the material. Prerequisite: Algebra I or equivalent.

## Geometry

This course covers the topics of traditional Euclidean geometry: points, lines, planes, angles, properties of parallel lines, triangles, quadrilaterals, polygons, circles, area and volume, and congruence and similarity. Throughout this course, students work with the program Geometer’s Sketchpad in order to gain insight into informal proofs and promote self-discovery. Additional topics may be included as time permits. Some study of formal proofs is included. Prerequisite: Algebra I or equivalent.

## Accelerated Geometry and Trigonometry

In this course, students study all that is covered in the previous geometry course listing, but at a faster pace and in greater depth. This course also places a stronger emphasis on formal proofs and includes an introduction to the study of trigonometry. Throughout this course, students work with the program Geometer’s Sketchpad in order to gain insight into informal and formal proofs and to promote self-discovery. Prerequisite: Algebra I or equivalent.

## Functions, Statistics, and Trigonometry

This course is designed for students who have completed Algebra II and are not yet recommended by the Department to take precalculus. It includes an introduction to statistical representation and measurement, as well as a thorough consideration of linear, exponential, logarithmic, polynomial, and trigonometric functions and their corresponding inverses. Included in the study of trigonometric functions are the unit circle, the six basic functions, basic trigonometric identities, trigonometric equations, the law of sines, and the law of cosines. Students who have successfully completed this course will be ready for Precalculus or Advanced Statistics in the following year. Prerequisites: Algebra II or equivalent and Geometry.

## Precalculus

This course focuses on functions and begins with general function characteristics, including notation, domain and range, operations on functions, composition, symmetry, inverse relationships, and transformations. Students review linear and quadratic functions before exploring polynomial, rational, exponential, and logarithmic functions. The second part of the course includes a study of trigonometry, both application of the unit circle and analytical trigonometry, and the laws of cosine and sine. If time allows, probability and some elementary limits will be studied. Graphing calculators are used to reinforce and support learning, and real-life applications are emphasized. Prerequisites: Algebra II or equivalent and Geometry.

## Accelerated Precalculus

This course focuses on functions and begins with general function characteristics such as notation, domain and range, operations on functions, composition, symmetry, inverse relationships, and transformations. Students then engage in a detailed study of polynomial, rational, exponential, and logarithmic functions. The second part of the course consists of a detailed study of trigonometry and some elementary limits. Graphing calculators are used to reinforce and support learning. Real-life applications are emphasized. Prerequisites: Algebra II or equivalent and Geometry.

## Calculus I

This course starts by reviewing material from Precalculus that will support the study of calculus topics. Students study limits of functions; the derivatives of functions, including logarithmic and exponential functions; and applications of derivatives, which include related rate problems, maxima and minima problems, and curve sketching. The second half of the course focuses on integral calculus, including applications involving the area between two curves and volumes of solids. Upon completion of this course, students have a solid grasp of calculus topics to support further study in this field. Prerequisite: Precalculus.

## Accelerated Calculus I

In this course, students study the limits of functions; the derivatives of functions, including logarithmic and exponential functions; and applications of derivatives, including related rate problems, maxima and minima problems, and curve sketching. The second half of the course focuses mainly on integral calculus, including applications involving the area between two curves. Volumes of solids of revolution, logarithmic and exponential functions, and trigonometric functions and differential equations are also studied. Upon successful completion of this course, students will be prepared to take the Advanced Placement Calculus AB Exam. Prerequisite: Precalculus.

## Calculus II

This course offers a thorough review of the techniques of differentiation and integration. Students will study applications involving surface area, length of a curve, and parametric equations. Other topics include different techniques of integration, sequences, and series (including Taylor polynomials and Taylor series). Upon successful completion of this course, students will be prepared to take the BC Advanced Placement exam. Prerequisite: Accelerated Calculus I.