Curriculum Detail

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Mathematics

The goal of the Mathematics Department is to facilitate for our students the development of those skills necessary for logical thinking and quantitative reasoning. In Algebra and Geometry, all students are grouped homogeneously. The B sections, and particularly the Honors sections, emphasize deeper understanding of the material and expose students to an increasing number of non-routine problems. Students entering Algebra II Honors and B level courses above this level will be expected to own or purchase a graphing calculator. Students should check with the department to find out what type of calculator is being used. Because of the sequential nature of mathematics, students enrolled in year-long courses must pass the second semester of the course in order to gain credit.
  • Algebra I (Honors)

    Algebra I Honors is an accelerated course studying algebra from the basic number properties through the quadratic formula. Topics include inequalities, functions, systems of equations, exponents, radicals, and quadratics. The course emphasizes understanding the ideas of algebra and applying these ideas accurately to a wide range of problems. Problem-solving techniques are applied throughout the course.
    *Department permission required.
  • Algebra IB

    Algebra I is the study of beginning algebra from the basic properties of numbers through the quadratic formula. Topics include inequalities, functions, systems of equations, exponents, radicals, and quadratics. The course emphasizes understanding the ideas of algebra and applying these ideas accurately to a wide variety of problems. Problem-solving techniques are employed throughout the course.
  • Algebra II (Honors)

    This course covers real number concepts and some review of Algebra I. Topics include linear, quadratic, exponential, and logarithmic functions, combinations, sequences and series, analytic geometry, and graphing. The course also works with elementary trigonometric func­tions through identities. Both equation solving techniques and problem solving receive emphasis. A goal is to develop logical thinking through the specific ideas of algebra. Students conclude the course with a research topic of their choice. 
    *Department permission required.
  • Algebra IIB

    This course reviews concepts from Algebra I concepts and Geometry and then expands upon those concepts through the study of a variety of advanced topics. These topics include linear, quadratic, polynomial, rational, exponential, and logarithmic functions. In addition, emphasis will be placed on graphing in the coordinate system, analytical geometry, solving systems of equations and inequalities, and the application of matrices and determinants. Throughout the course, students will explore the utilization of these concepts through modeling and the direct application of the graphing calculator.
  • Algebra IIC

    This course reviews Algebra I concepts and then covers the following topics in Algebra II: linear, quadratic, exponential, and loga­rithmic functions with an emphasis on graphing. Problem solving techniques are emphasized. This course moves at a slightly slower pace than Algebra II–B. The graphing calculator is used to support the concepts.
    *Department permission required.
  • AP Calculus AB

    This course adheres closely to the recom­mendations of the Committee on Mathematics of the Advanced Placement Program. It includes a thorough study of functions, analytic geometry, and limits preliminary to the development of both differential and integral calculus. Students will use a graphing calculator throughout the year to enhance their understanding of the material and to deal with some functions which would otherwise be inaccessible. Students enrolled in this course take the Advanced Placement Examination for Calculus AB. All students are required to take the AP examination, contingent on a pre-examination test in the spring.
    Prerequisite: Pre-­Calculus
    *Department permission required.
  • AP Calculus BC

    This course covers differential and integral calculus, vector functions, graphics in polar coordinates, parametrically defined curves, areas of polar cones and improper integrals. Also included is the study of power series as well as elementary differential equations. Students enrolled in this course take the Advanced Placement Examination for Calculus BC.  All students are required to take the AP examination, contingent on a pre-examination test in the spring.
    Prerequisite: Pre­-Calculus(H)
     *Department permission required.
  • AP Statistics

    This course introduces students to the major concepts of collecting, analyzing, and drawing conclusions from data. These are activities of major importance to contemporary society. The techniques studied in this course are required when pursuing various careers such as psychology, engineering, biology, business, sociology, education, and health sciences. The major emphasis will be on applications. Students will be exposed to four conceptual themes: exploring data, planning a study, anticipating pattern and statistical inference. TI–83 or T-84 series and the computer will be used as tools to facilitate statistical testing.  All students are required to take the AP examination, contingent on a pre-examination test in the spring.
     Prerequisite: Algebra 2
    *Department permission required.
  • Calculus I

    Calculus I is a one-semester course following Pre-Calculus (Hon.) (Accel.) that begins preparing students to sit for the AP Calculus BC exam the following year. The course begins with a study of limits and continuity, which is foundational to both differential and integral calculus. The derivative is introduced, and applications include curve sketching, related rates, and optimation. The year concludes with an introduction to integral calculus. 
  • Geometry (Honors)

    This course provides, through deductive reasoning, a comprehensive study of theorems, postulates, solid and coordinate geometry. This course is offered to students who have completed Algebra 1 and is intended to broaden their skills and develop an aggressive, yet flexible approach to finding solutions to problems. Special attention is given to proofs and constructions in the Honors section, and students are challenged with problems of higher difficulty. 
    *Department permission required.
  • Geometry B

    This course provides a comprehensive study of the theorems, postulates, and definitions associated with plane, solid, and coordinate geometry. Specific topics include parallel lines, congruent and similar triangles, quadrilaterals and other polygons, circles, right triangles, and area and volume. Both inductive and deductive reasoning are applied, and students in the B sections will learn to write formal proofs. Algebra 1 is a prerequisite, as algebraic skills are utilized throughout the course.
  • Geometry C

    This course provides a comprehensive study of the theorems, postulates, and definitions associated with plane, solid, and coordinate geometry. Specific topics include parallel lines, congruent and similar triangles, quadrilaterals and other polygons, circles, right triangles, and area and volume. Both inductive and deductive reasoning are applied, but formal proofs will be less emphasized for students in the C sections. Algebra 1 is a prerequisite, as algebraic skills are utilized throughout the course.
  • Introduction to Calculus

    Introduction to Calculus is a course designed to teach not only the mechanics of differentiating and integrating polynomial, exponential, logarithmic and trigonometric functions but also to apply the principles learned to a variety of problems. Topics studied will include the following: solving for the maximum and minimum values of a function, curve sketching, related rates, and statistics. Applications include examples from physics, economics, social science, biology, chemistry, and probability.
    Prerequisite: Precalculus or Trig. and Functions.
  • Linear Algebra

    Linear Algebra is a full year course covering linear transformations, matrices, linear spaces, eigenvalues, and eigenvectors. Emphasis will be placed on analysis and proofs.
    This course is offered in alternate years.
    Prerequisite: BC Calculus
    *Department permission required.
  • Multi-Variable Calculus

    This course covers the topics of vectors and the geometry of space. We will study vector-valued functions, functions of several vari­ables, multiple integration, and vector analysis. Emphasis will be placed on graphing in three dimensions, including using polar, cylindrical, and spherical coordinate systems. Additional topics, including graph theory and topology, may be covered if time allows. This course is offered in alternate years.
    Prerequisite: BC Calculus.
    *Department permission required.
  • Pre-Calculus

    Pre-Calculus provides a solid preparation for the student who intends to continue the study of mathematics through Calculus. The initial portion of the course centers around an in­-depth study of the trigonometric functions. This includes both the right triangle and unit circle approaches and concludes with analytic trigonometry. With this background in place, students are then introduced to polar coordinates and parametric equations, vectors in two and three dimensions, conic sections, sequences, series, and probability.
    Prerequisite: High success in Geometry and Algebra II
    *Department permission required.
  • Pre-Calculus (Honors) (Accel.)

    Students will pursue an in-depth study of the trigonometric functions including graphing, identities, and solving equations. The study of parametric equations and polar forms will also be studied. The course will be followed by three semesters of BC Calculus. Students will be expected to cover the two-year sequence.
    *Department permission required.
  • Statistics

    Statistics is a year-long course that introduces students to the fundamentals of statistical analysis.  Students will make and use statistical models to analyze and interpret data.  Topics covered include descriptive statistics, displaying and describing categorical and quantitative data, the Normal model and its applications, linear regression, probability, and experimental design.  Time permitting, students will be introduced to statistical inference.  The class will be heavily project focused with students collecting and analyzing data in the real world.
  • Trigonometry & Functions

    This course begins with a review of important algebraic topics with an emphasis on the concept of functions. Special attention is given to exponential and logarithmic functions and their applications to a variety of problems. The circular and trigonometric functions are then introduced, becoming a central theme of the second semester. All the trigono­metric functions, the identities, graphing, and applications of these concepts will be studied. Trigonometry and Functions proceeds at a slower pace than the Pre­-Calculus course. 

Faculty

Hamden Hall Country Day School, located less than two miles from Yale University, is one of the best private schools in Connecticut to enroll elementary, middle, and high school students. Our nurturing and inclusive community provides a dynamic learning environment that promotes academic excellence by understanding each child and fostering their individual growth.