Upper School

# Upper School Mathematics

The goals of the mathematics program at Nichols are for students to master algebraic skills, understand algebraic methods, reason graphically and analytically, and use mathematics in solving everyday problems. For each course, the students are divided into levels based on their backgrounds and abilities. Courses at all levels make use of graphing calculators and appropriate computer software.

Algebra II develops computational proficiency while studying absolute value, linear and quadratic equations and expressions, systems of equations and inequalities. Function notation is introduced. Utilizing equations to model real world applications is emphasized.

The Honors and Advanced sections study additional topics including polynomial, rational, power and root equations.

Geometry explores congruency, similarity, transformations, convex polygons, area, and volume. Students are also introduced to the presentation of ideas in the format of formal and informal proof. In order to cement skills studied in Algebra I, the course utilizes the coordinate plane and algebraic descriptions of geometric properties. At all levels, the course employs exploration and discovery in addition to traditional lecture.

The Honors and Advanced sections presume greater proficiency with elementary algebra. These sections study vectors and transformations with greater depth and rigor.

This course utilizes the fundamental concepts and mechanical algebraic skills developed in Algebra II to study Analytic Trigonometry and advanced algebraic concepts. Topics 30 include polynomial, rational, trigonometric, exponential, and logarithmic functions. As time permits, additional topics of study include matrices, polar coordinates, parametric equations, vectors, sequences, series, probability, and analytic geometry.

• ## Algebra II

Algebra II develops computational proficiency while studying absolute value, linear and quadratic equations and expressions, systems of equations and inequalities. Function notation is introduced. Utilizing equations to model real world applications is emphasized.
• ## AP Calculus AB

AP Calculus AB covers all the material presented in Calculus, however it is studied in greater depth and with more emphasis on theory as opposed to computation. Additional topics covered include Mean Value Theorem, volumes by known cross-section, slope fields and differential equations.

Prerequisites: Completion of Honors Precalculus and permission of the Department. The AP exam is a requirement of the course.
• ## AP Computer Science

This second course in computer programming is intended for students who have successfully completed the Introduction to Computer Programming course and wish to continue their studies. The language focus for the second year course is Java. At the completion of the course, students have sufficient programming experience in Java and computer science knowledge to take the Advanced Placement A examination in Computer Science.

Prerequisite: Introduction to Computer Programming. The AP exam is a requirement of the course.

• ## AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: i) Exploring data: Observing patterns and departures from patterns ii) Planning a Study: Deciding what and how to measure iii) Anticipating patterns: Producing models using probability theory and simulation, and iv) Statistical Inference: Confirming models.

Prerequisites: Completion of Algebra II with a Grade of C+ or better and permission from the department.
• ## Data Structures and Topics

Mathematics Elective for Grades 11 and 12

This third course is a continuation of study in computer science. The intention of the course is not only to study certain data structures and their associated algorithms, but also to study topics that are of student interest, such as GUI and applets.

Prerequisite: AP Computer Science A.
• ## Differential Calculus

Differential Calculus
While promoting a deeper understanding of the abstract notion of Function, this course concurrently introduces the fundamentals of Differential Calculus including Limits, the Difference quotient, the Derivative and its applications. The course is organized around families of function with particular attention to polynomial, exponential, logarithmic and trigonometric functions.

Prerequisites: Completion of Precalculus, or completion of Integrated Algebra II and Trigonometry with additional summer work, and permission of the department
• ## Geometry

Geometry explores congruency, similarity, transformations, convex polygons, area, and volume. Students are also introduced to the presentation of ideas in the format of formal and informal proof. In order to cement skills studied in Algebra I, the course utilizes the coordinate plane and algebraic descriptions of geometric properties. At all levels, the course employs exploration and discovery in addition to traditional lecture.
• ## Honors Algebra II

Algebra II develops computational proficiency while studying absolute value, linear and quadratic equations and expressions, systems of equations and inequalities. Function notation is introduced. Utilizing equations to model real world applications is emphasized.

The Honors and Advanced sections study additional topics including polynomial, rational, power and root equations.

• ## Honors Differential and Integral Calculus

This full year course introduces qualified students to the fundamentals of calculus. Topics from differential calculus include slopes of secant and tangent lines, the definition and interpretation of the derivative, applications of the derivative including related rates, optimization and linearization. Topics from the integral calculus include techniques of integration and utilizing integration to find area, distance, and volume.

Prerequisites: Completion of Honors Precalculus and permission of the department.
• ## Honors Geometry

Geometry explores congruency, similarity, transformations, convex polygons, area, and volume. Students are also introduced to the presentation of ideas in the format of formal and informal proof. In order to cement skills studied in Algebra I, the course utilizes the coordinate plane and algebraic descriptions of geometric properties. At all levels, the course employs exploration and discovery in addition to traditional lecture.

The Honors and Advanced sections presume greater proficiency with elementary algebra. These sections study vectors and transformations with greater depth and rigor.

• ## Honors Precalculus

This course utilizes the fundamental concepts and mechanical algebraic skills developed in Algebra II to study Analytic Trigonometry and advanced algebraic concepts. Topics 30 include polynomial, rational, trigonometric, exponential, and logarithmic functions. As time permits, additional topics of study include matrices, polar coordinates, parametric equations, vectors, sequences, series, probability, and analytic geometry.

• ## Integrated Geometry and Algebra

This full-year course provides an introductory geometry course integrated with an intensive review of elementary algebra. Intended for students whose background in algebra needs additional support, this course covers many of the concepts of a traditional geometry course; however, it places less emphasis on formal proof in favor of algebraic computation and manipulation.
• ## Integrated Geometry and Algebra II

Integrated Geometry and Algebra II continues the exploration of the principles of plane and solid geometry through the lens of algebraic problem solving. The course gives students the opportunity to cement fundamentals from an introductory algebra course while advancing their command of geometric reasoning. The course also introduces several algebraic techniques typically studied in a second-year algebra course.
• ## Introduction to Computer Programming

A computer program is a set of instructions that tells a computer how to accomplish a given task. Computer programming is the art and science of planning and implementing computer programs. This course is designed as an introduction to both hardware and software programming. The course begins with basic components of a computer, machine representation of data, number systems, and an introduction to digital electronics through logic gates. The course also introduces the syntax and style of a high level programming language such as C++ or Java. The course stresses the nature and design of algorithms, top-down and object-oriented design, and coding and debugging skills.

Topics include data types, file and screen input and output, conditional statements, iterations, recursion, subroutines, arrays, and if time permits pointers and data structures. Students who do well in mathematics and have a possible interest in pursuing careers in any math or science area should consider taking this course.

Prerequisite: An interest in computers, logic, and digital electronics with completion of Geometry with a Grade of C or better, and permission from the department.
• ## Multivariable Calculus

This introductory course in multivariable calculus focuses on functions of two and three variables. Students apply techniques of calculus to analyze the geometry of curves and surfaces in three-dimensional space. Topics include parametric equations and polar coordinates, vector functions, vectors in two and three dimensions, partial derivatives, and multiple integrals.

Prerequisite: Successful completion of AP Calculus AB and permission of the department.