Math

This course presupposes a working knowledge of the skills necessary to begin algebra, along with a willingness to strengthen those skills while learning the fundamentals of algebra. Course content includes operations with algebraic expressions, linear equations and inequalities, polynomials, quadratic equations, and an introduction to the notion of functions.

Geometry aims to advance the ability to think logically and analytically. Properties of plane and solid geometric objects are discovered and verified or deduced. Students learn to supply formal proof of valid propositions and recognize invalid ones. Algebra skill development continues and coordinate geometry is introduced. Computer software aids discovery and visualization. Honors Geometry provides an intensive pace, greater depth, and greater breadth. Prerequisite: Algebra I.

Like Algebra I, this course stresses basic skills. Essential facts and techniques from Algebra I are reviewed, and the student’s command of skills is strengthened. Manipulation of algebraic expressions, equation solving, functions and their graphs, complex numbers, exponents, logarithms, trigonometry, radian measure, sequences and series, and probability are studied. Honors Algebra 2 & Trigonometry provides an intensive pace, greater depth, and greater breadth. Prerequisite: Algebra I and Geometry.

Combining topics from Honors Algebra 2 & Trigonometry and Honors Precalculus, this course prepares students for Accelerated Introduction to Calculus. It is a fast-paced, rigorous course that emphasizes intuitive understanding in addition to skill development. Non-routine problems are an integral part of the course. Prerequisite: strong performance in Honors Geometry & Trigonometry.

Precalculus is a year-long course that extends algebra knowledge and problem-solving skills while introducing key topics from precalculus. Included are such subjects as measures of central tendency and dispersion, best-fit lines, the behavior of polynomials, exponential and logarithmic functions, complex numbers, and the binomial theorem. Honors Precalculus provides an intensive pace, greater depth, and greater breadth. Prerequisite: Algebra 2 & Trigonometry.

The term-contained version of Precalculus is offered only to the sixth form. Other students should see the description for the year-long Precalculus above. Prerequisite: Algebra 2 & Trigonometry is the prerequisite for Precalculus while Precalculus 1 is the prerequisite for Precalculus 2.

Aimed at providing solid preparation for a general calculus course, Introduction to Calculus stresses the behavioral characteristics of elementary functions and those derived from them by addition, multiplication, composition, and inverse. Much attention is paid to inferring, from the equations that define them, the attributes of graphs, such as symmetry, asymptotes, periodicity, continuity, and end behavior. Calculus language and logic are introduced and the course is highlighted by an introduction to calculus topics. Honors Introduction to Calculus provides an intensive pace, greater depth, and greater breadth. Prerequisite: Precalculus.

The term-contained version of Introduction to Calculus is offered only to the sixth form for the fall and winter Terms. Other students, including sixth formers who wish to take the course for the full year, should see the description for the year-long Introduction to Calculus above. Prerequisite: Precalculus is the prerequisite for Introduction to Calculus 1 while Introduction to Calculus 1 is the prerequisite for Introduction to Calculus 2.

This is a fast-paced, rigorous course that emphasizes intuitive understanding in addition to skill development. It includes topics from Honors Introduction to Calculus, as well as mathematical induction, De Moivre’s theorem, polar coordinates, partial fractions, and an introduction to calculus topics. Non-routine problems are an integral part of the course. Prerequisite: strong performance in Accelerated Algebra 2 & Trigonometry or Honors Precalculus.

Calculus includes topics such as limits, continuity, derivatives, and mean value theorem. Students learn graphical, numerical, verbal, and modeling approaches to elementary functions. The emphasis is on the interplay between geometric and analytic information and the use of calculus both to predict and to explain the observed local and global behavior of a function. The course covers the derivatives of all elementary functions as well as the rules for differentiating, products, quotients, and composite functions, and the concept of a differential equation. Prerequisite: Introduction to Calculus.

Honors Calculus includes topics such as differential and integral calculus which are studied both intuitively and formally. Topics include the chain rule, the mean value theorem, Riemann sums, numerical methods for approximating derivatives and definite integrals, and areas of curves and real-world applications. Prerequisite: Honors Introduction to Calculus.

Advanced Studies in Calculus topics include sequences and their limits, differential and integral calculus, infinite series and their convergence, and basic differential equations. All topics are represented in rectangular, polar, and parametric representations. Prerequisite: Accelerated Introduction to Calculus.

These independent, term-contained courses survey substantive topics at a level commensurate with collegiate mathematics. Topics are selected with the backgrounds of the students in mind. Recent studies include multivariate calculus, statistics, linear algebra, number theory, and the mathematics of chaos. Investigations using specialized computer software are a common feature of the course. A student may take these courses more than once as topics vary from year to year. Prerequisite: completion of or concurrent enrollment in Advanced Studies in Calculus AB or BC.

Statistics topics discussed include displaying and describing data, the normal curve, regression, probability, statistical inference, confidence intervals, and hypothesis tests with applications in the real world. Students also have the opportunity to analyze data sets using technology. Prerequisite: Precalculus or Introduction to Calculus.

Features of this course are selection and analysis of data, developing probability models, and using statistical inference. Topics include regression and correlation, sample and experimental design, discrete and continuous random variables, normal, geometric, and binomial distributions, significance testing, and the chi-square test. Prerequisite: strong performance in Honors Precalculus or Honors Introduction to Calculus.