Curriculum Detail

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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. 
  • Advanced 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 reinforced. Utilizing equations to model real world applications is emphasized. Additional topics in the Advanced Algebra II course include polynomial, rational, exponential and logarithmic functions as well as an introduction to trigonometric functions. The Advanced Algebra II course moves at an accelerated pace and at a greater depth of inquiry. Placement in Advanced Algebra II is determined by the Mathematical Sciences department.
  • Advanced Geometry

    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. The course includes an introduction to statistics. This course is built upon the Pre-AP Geometry with Statistics framework. The Advanced Geometry section presumes greater proficiency with elementary algebra; these sections study vectors and transformations with greater depth and rigor. The Advanced Geometry course moves at an accelerated pace. Placement in Advanced Geometry is determined by the Mathematical Sciences department.
  • Advanced Precalculus


    For Grades 11 and 12


    For Grades 11 and 12

    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. 

    The Honors and Advanced sections signify additional course work. 
        
  • 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 reinforced. 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. Placement is determined by the Mathematical Sciences department.
  • AP Computer Science

    This second course in computer programming is intended for students who wish to continue their studies after having completed the first-year course. In addition to the topics listed in the College Board’s course description, the course covers computer science topics included in the ACSL contests including assembly language, FSA’s, and graph theory. Prerequisite: Introduction to Computer Programming. Placement is determined by the Mathematical Sciences department.
  • AP Precalculus

    “In AP Precalculus, students explore everyday situations using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, an important practice for thriving in an ever-changing world” (AP Central). Placement in AP Precalculus is determined by the Mathematical Sciences department.
  • 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. Placement is determined by the Mathematical Sciences 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


    Mathematics Elective for Grade 12

    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. The course includes an introduction to statistics. This course is built upon the Pre-AP Geometry with Statistics framework.
  • 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 reinforced. Utilizing equations to model real world applications is emphasized. The Honors Algebra II course moves at an accelerated pace and covers additional topics. Placement in Honors Algebra II is determined by the Mathematical Sciences department.
  • 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. Placement is determined by the Mathematical Sciences department.
  • Honors Geometry


    For Grade 9 

    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


    For Grades 11 and 12

    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.

    The Honors and Advanced sections signify additional course work. 
        
  • Integrated Geometry and Algebra


    For Grade 9

    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


    For Grade 10
     
    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. Students are introduced to hardware and software programming through number systems, Boolean algebra, digital electronics and Java. With an object’s first approach, the course stresses debugging skills, problem solving techniques, teamwork and efficiency. Prerequisite: Geometry. Placement is determined by the Mathematical Sciences 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 BC. Placement is determined by the Mathematical Sciences department.
  • Precalculus

    This course utilizes the fundamental concepts and mechanical algebraic skills developed in Algebra II to study Analytic Trigonometry and advanced algebraic concepts. Topics 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. Available for dual enrollment.

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