This course is designed to present a logical development from the base established in the Pre-Algebra course.  Mathematical reasoning is interwoven throughout the course as are various problem solving techniques using algebraic expressions and equations.  The students use technology to explore concepts and work with a computerized graphing utility when appropriate.  After completing the course, students  have the ability to better analyze a problem and apply the most efficient and effective problem solving technique.  The students are then prepared to advance to the next level of algebra - Algebra II - the following academic year.

Algebra II is designed to present a logical development from the base established in the Algebra I course.  Algebra II introduces the exponential and logarithmic functions, expands knowledge of analytic geometry, and introduces right triangle trigonometry.  Students manipulate graphs containing conics and parabolas.  Typically, new concepts are introduced through a traditional lecture/demonstration format; however, students use their computers to graph and research math through technology.  After completing the course, the student is prepared to advance to Precalculus after a year of Geometry.

This course prepares students for the AP* Calculus AB exam as well as for future study in mathematics. It presents calculus as the mathematics of change and motion, and demonstrates its usefulness through a variety of applications.  Concepts are represented using the rule of four:  numeric, algebraic, geometric, and verbal, particularly as applied to functions.  Students practice problems incorporating all of these four approaches with the expectation that they make connections between approaches.  Every student is required to take the AP Calculus AB exam in May.

The four main sections of this AP Statistics course are exploratory analysis, planning a study, probability, and statistical inference.  Students, usually juniors or seniors, must have completed a course in precalculus prior to enrolling in AP Statistics.  This course includes frequent activities and explorations as the students actively participate in developing their understanding of the material.

This course serves as a capstone for most seniors who are not already taking or have taken Advanced Placement Calculus.  Students are required to apply most of the algebra, geometry, and ideas about functions that they have learned in their previous three years in the Upper School.  The emphasis in the course is on “doing calculus.”  Students learn to differentiate algebraic functions, trigonometric functions, and exponential and logarithmic functions.  The chain rule is developed as the most important technique for differentiation, and implicit differentiation follows as a consequence. Solutions of problems involving related rates, the determination of extreme values of functions, and the analysis of motion on a line are offered as applications of the derivative.  The definite integral is developed and used to compute areas of plane regions and surface areas and volumes in three-dimensional space.

The primary goals of the College Algebra course are to strengthen algebraic skills and to engage in an in-depth study of the function, beginning with the linear function and progressing through the quadratic, cubic, polynomial, and special functions.  Graphing and the meaning of the mathematical symbols that are required in any discussion of the function are emphasized.  Graphing is done both by hand and with the use of a computerized graphing utility, depending upon the objective of the lesson.  Applications of the various function families are studied as well.  Additionally, students learn to appropriately access internet sources when doing research or review.

Discrete Math Topics is a course designed to help students connect Mathematics to the world around them.  Math plays a vital role in our daily life, and this course attempts to illustrate this point through an application-oriented approach to Math concepts.  Emphasis is placed on  applications drawn from the students’ areas of interest and from situations that occur in “the real world”. This course introduces and illustrates varied abstract mathematical concepts through examples drawn from common life experiences.  A major objective of Discrete Math Topics is to illustrate the practical value of mathematics in applied areas, and thus to address the common question “What will I ever use this for?”

Geometry is a course that follows the Euclidean tradition, thereby placing a strong emphasis on deductive reasoning and rigorous proof.  Content includes perpendicularity, congruence and similarity, triangles, quadrilaterals, polygons, and circles.  The second half of the course focuses on area, volume, and analytic geometry and trigonometry in preparation for Precalculus. Information and new ideas are, for the most part, introduced in a traditional lecture-type setting and then reinforced through homework assignments. 

Honors Calculus III is offered on a tutorial basis to students from St. Christopher’s and St. Catherine’s Schools who have completed Honors (AP) Calculus I and II by the end of their junior years.  The course begins in the fall with a reworking of the Advanced Placement Examination of the previous spring.  This reworking serves as a review of the topics covered in Honors (AP) Calculus I and II and as an introduction to the Mathematica software that students use to implement their calculations and graphing throughout the course.  Several topics that do not appear in the Advanced Placement syllabus but do appear in university level courses in the calculus of a single independent variable -- curvature, the conic sections in polar coordinates, and the use of parametric equations with Mathematica in the solution of challenging locus problems---are considered.  Attention is then turned to multivariate calculus, which is the main concern of the course.  Ideas of function, limit, and continuity are extended to the plane and to higher dimensional spaces.  Analytic geometry with vectors in 3-space, vector differentiation, partial derivatives, Newton’s method for the approximate solution of two equations in two independent variables, transformations of coordinate systems, and multiple integrals are studied.    Ample opportunity is offered for both students and their teacher to follow their mathematical interests, and the option of undertaking individual or class projects is always available.

Honors Geometry is offered to 9th and some 10th grade boys with strong ability and interest in mathematics. It is a rigorous course in Euclidean geometry in which proof and the axiomatic, deductive nature of mathematics are emphasized. Analytic methods are introduced early in the course to translate geometrical ideas into an algebraic setting. Calculators may be used for tedious numerical work and for approximations, but students are encouraged to use proper mathematical symbols to provide exact results from their calculations. Elementary set theory and logic, simple counting theory, and problems in probability are developed.  Applications of ideas and results obtained in this course are offered in science and other branches of mathematics. Switching circuits are designed to test arguments and accomplish arithmetic operations. Finally, the course is enriched with stories from the history of mathematics.

The themes of Precalculus Honors are multifold.  It is a survey course on the topics necessary to do well in calculus and therefore places a strong emphasis on the idea of the deterministic function by highlighting the Cartesian relationship between an equation (algebra) and its graph (geometry).  The course also seeks to expose students to complex multi-step problems, voluminous material, and abstract thought patterns in a manner that is quite new to them.  Material is presented in a much more sophisticated manner than in previous courses with stress placed on the “why” rather than the “how” and on application rather than rote memorization.  Major function types studied include linear, quadratic, polynomial, rational, piecewise, exponential, logarithmic, trigonometric, parametric, and polar. Fundamental algebraic concepts such as equation-solving and domain are interwoven with advanced algebraic topics such as matrices and trigonometric inverse functions.  More expansive and mind-bending topics such as infinity and asymptotic behavior are also included in preparation for the rigors and sophistication of AP Calculus and beyond.  A graphing calculator is utilized within this context, often as a tool for computation, analysis, and error-checking.

Precalculus is designed to prepare students for either Calculus or Statistics. The course begins with a review of algebra and analytic geometry that is tailored toward the study of functions. The continuous and smooth transition from review to the study of polynomial, rational, and algebraic functions leads to a definition of exponential and logarithmic functions. The significance of the natural base (e) is noted, but computations with natural exponents and logarithms are not pursued in depth. The trigonometric functions and their inverse functions are studied at length. The properties of the trigonometric functions are derived from the analytic geometry of the unit circle in standard position. Applications of trigonometry follow a study of its functional aspects. 

This course is designed to provide students with a comprehensive introduction to statistical concepts and techniques. Emphasis will be placed on real-world applications, with a focus on projects, spreadsheets, and cross-curricular connections. Students will learn to collect, analyze, and interpret data using a variety of tools and techniques. This class is designed to be challenging, but also engaging and fun, with opportunities to explore the intersection of statistics and other subjects such as psychology and business.