Noble and Greenough School Course Catalog

This course covers the most fundamental and, therefore, most important skills in secondary school mathematics. Included in the course are a study of the rational and irrational numbers, extensive work with equations and inequalities, graphing of linear and quadratic functions, solving systems of equations, polynomial algebra, rational expressions and equations, and a variety of word problems. Use of the TI-84 graphing calculator will begin with the study of linear functions, and therefore is a required tool for the course.

This year-long course has three main objectives: first, to impart an understanding and mastery of basic Euclidean geometric facts; second, to improve the student's ability to perceive problems visually and to improve the student’s use of perception, intuition, and pattern-recognition in problem-solving; and third, to introduce the student to a basic formal deductive mathematical system in which definitions and postulates lead to the discovery and proof of theorems. The year will be devoted to topics traditionally included in a high school geometry course: points, lines, planes, triangles, quadrilaterals, circles, parallelism, congruence, similarity, area, general polygons, and surface area and volume of solids.

This course will solidify concepts from Algebra I and provide applications of geometric theorems and ideas. Students will study algebraic topics such as equations/inequalities, functions/graphs, linear functions, systems of equations, quadratics, and rational expressions/equations. Among the geometric topics studied are points, lines, and planes; triangles, polygons, and circles; angles; parallel and perpendicular lines; and congruence and similarity. Students will also study the surface area and volume of solids. Mathematical communication and organization will be central to all concepts.

While covering essentially the same syllabus as the regular geometry course, students in Honors Geometry will move at a faster pace, cover topics in greater depth, and be required to do significantly more formal proof-writing. A student must demonstrate strong interest and background in mathematics and high achievement in a comprehensive Algebra I course to earn consideration from the Department for honors placement.

This year-long course builds on the foundations studied in Algebra I, and it will examine and analyze algebraic concepts at a pace that allows additional time for mastery. It is a course designed to improve skills and confidence as well as to study the traditional topics of Algebra II: factoring techniques; properties of exponents and logarithms; functions (polynomial, logarithmic, and exponential).

This year-long course builds on the foundations studied in Algebra I. Specifically, it includes coverage of: polynomial functions, equations, and inequalities; the complex number system; advanced factoring techniques and binomial expansion; elementary trigonometry; properties of exponents and an introduction to logarithms.

Honors Algebra II covers the underlying theory and unifying connections between topics more deeply than the regular and accelerated sections of Algebra II, where more emphasis is given to exposure than to depth. It includes coverage of: polynomial functions, equations, and inequalities; the complex number system; advanced factoring techniques and binomial expansion; rational functions; trigonometry; properties of exponents and logarithms.

This course includes the collection, evaluation and organization of data, probability distributions, sampling, hypothesis testing, correlation, and linear regression. The emphasis is on developing a working knowledge of these tools rather than mastering the complete theory behind the methods.

How did statisticians figure out how many German tanks were produced in WW2 without stepping foot on the battlefield? How do medical professionals conduct a clinical trial for a vaccine? What variables best predict SAT scores? How are election polls carried out? How might a company determine whether it has a gender-bias in its hiring process? These are all questions that we will attempt to answer in AP Statistics. We will explore descriptive statistics, distributions of data, linear regression, the design of observational studies and experiments, probability and random variables, and then develop skills to conduct a wide range of inferential procedures such as confidence intervals and significance tests. Each quarter typically includes at least one project-based assignment. AP Statistics welcomes both poets and quants: all that is required to succeed is hard work, a sharp eye for detail, critical thinking skills, and a desire to investigate problems and puzzles facing our society and community. This full-year course is equivalent to a one-semester introductory college statistics course and is recommended for Classes I and II.

This year-long Precalculus course revisits many topics learned in an Algebra II course; polynomial, exponential, logarithmic, and trigonometric functions. This course places greater emphasis on solving advanced equations and analysis. Functions will be examined graphically, numerically, algebraically, and verbally to give students the benefit of alternate presentations.

This semester long Precalculus course revisits many of the topics studied in Algebra II but places more emphasis on abstract thinking. Students are asked to apply concepts more generally and to make more connections between topics. As its name suggests, this course prepares the student for the eventual study of calculus. Topics to be covered include: formal definitions of function, domain, and range; composition and inversion of functions; techniques of graphing; triangle and circle trigonometry; sequences and series; exponential and logarithmic functions.

This course covers all of the topics of Precalculus plus complex numbers, vectors, induction, matrices, followed by BC Calculus topics, specifically the theory of limits, the derivative, techniques of differentiation, and applications of derivatives. The pace of this course is rapid and therefore the course is open by invitation only to those students who, in the opinion of the math department, have demonstrated strong interest and performed at a consistently high level in their previous mathematics courses.

This year-long course provides an introduction to calculus, but is not intended to prepare the student for either the AB or the BC Advanced Placement examination. The first semester deals primarily with the properties of limits and differential calculus and the second semester with those of integral calculus.

This is a two-semester Advanced Placement sequence in calculus, which gives a thorough introduction to the fundamentals of differential and integral calculus. The fall semester is primarily devoted to the development of differential calculus and covers limits, the derivative, methods of differentiation, and applications of the derivative. The spring semester begins with the fundamental theorem of integral calculus and studies the integral, its methods and its applications, including a brief introduction to differential equations and slope fields.This course prepares students for the College Board's AP exam in Calculus AB.

BC Calculus is a full-year, AP course that offers the second and third semesters of this three-semester advanced calculus sequence. Topics covered during these two semesters are the integral, its methods and applications, the calculus of transcendental functions, vector functions, polar coordinates, infinite series, and differential equations. This course prepares students for the College Board's AP exam in Calculus BC.

This course is an extension to the principles and techniques of the integration and differentiation learned in single-variable calculus (BC Calculus). Topics include functions of 2 or more variables, vectors, integration with multiple variables, optimization in several variables, partial derivatives and gradient. We will use a 3-D grapher to help visualize these functions.

The Advanced Topics in Mathematics course will explore a variety of topics determined by the mutual interest of the students and the instructor. Such topics might include: additional topics from integral calculus, an introduction to linear algebra, probability theory, combinatorics, famous problems and theorems of mathematics, methods of problem-solving, advanced problems in geometry and algebra, and number theory.