Citizen, Scholar, Steward

Mathematics

KCD’s mathematics programs are designed to prepare students to succeed in college as well as to function productively in today’s world. The department offers both fundamental and enrichment mathematics necessary to challenge students to meet their potential and to develop the awareness that mathematics is both useful and exciting. Advanced level classes are available in Geometry, Algebra II, and Precalculus. We also offer AP courses in Calculus and Statistics.
 

  • Algebra l

    The skills and concepts that students learn in Algebra I serve as a foundation for the entire sequence of high school mathematics courses. Topics include operations on polynomials, factoring, operations on rational expressions, using properties of exponents (including negative exponents), graphing linear and quadratic equations, solving linear equations, solving various types of word problems, solving linear systems of equations, solving radical and quadratic equations, and simplifying radicals. Because the material for this course was designed by KCD’s math faculty, there is no textbook for this course.

  • Algebra II

    Because this course is an extension of Algebra I and Geometry, students’ success depends largely upon a solid understanding of the concepts in those courses. Initial instruction reviews and then extends these concepts and attendant skills. This class also includes an investigation into properties and operations with real numbers and later an emphasis on linear programming, modeling, absolute value equations and inequalities, quadratic equations, exponents, radicals, and real-life application problems. New topics include complex numbers, functions, exponential functions, logarithms, rational expressions, sequences and series, and conic sections. If time permits, the class will include a brief introduction to trigonometry.

  • Algebra II Advanced

    As an extension of Advanced Algebra I and Advanced Geometry, students are expected to have a broad and deep understanding of the fundamental concepts presented in those courses. In this advanced class, it is assumed that students have retained what they learned in previous courses. Some highlights of the year include the study of polynomials, inequalities, quadratics, systems, exponentials, series and patterns, radical expressions and equations, including complex numbers. Attention is then turned to studying a variety of functions, including graphing rational functions. Conic sections and logarithm progressions are also covered along with an introduction to matrices, Pascal’s Triangle and the Binomial Theorem. Students will learn about probability and statistics as well.  Throughout the year, students use a graphing calculator to improve their understanding of all concepts studied.
     

  • Geometry

    In this course, students study the properties of points, lines, planes, and other geometric figures. Students also begin to develop their logical and critical reasoning skills through the completion of both algebraic and geometric proofs. Through an emphasis on applying algebraic concepts to geometric ideas, students begin to appreciate the interrelationships between geometry and algebra. Throughout the year, students make use of the Geometer’s Sketchpad software, which allows students to interpret and explore many geometric relationships visually.

  • Geometry Advanced

    In this course, students study the same concepts as in regular Geometry; however, advanced students spend an entire year in proof writing and study longer, more complicated proofs. In addition to the use of more advanced algebraic concepts, students are also asked to analyze and prove many theorems that students not enrolled in the advanced course are simply asked to accept. Geometer’s Sketchpad software is employed in the course as a replacement for and improvement on the compass/straightedge constructions of past years.

  • Essentials of Precalculus

    This course is intended for juniors and seniors who have completed Algebra II but have not yet mastered the necessary skills to advance to the regular Precalculus course. During the first trimester, students complete an extensive review of concepts studied during Algebra I and Algebra II. They also study concepts tested on the SAT and ACT and have the opportunity to take practice tests. Throughout the second trimester, students learn the fundamentals of trigonometry. The class completes a brief introduction to statistical ideas including topics in sampling data, analyzing data, and the Normal distribution. During the last trimester, the focus is on real-life mathematics and applications of mathematics in the world. Throughout the year, students use a graphing calculator to improve their understanding of all the concepts studied.
     

  • Precalculus

    This course is for students who have completed Algebra I, Algebra II, and Geometry and who anticipate taking Calculus and/or AP Statistics in the future. It covers trigonometric functions and complex numbers, as well as logarithmic, exponential and composition of functions. It also reviews sequences and series, conic sections, and matrices in more depth. If time permits, students will study polar graphing, vectors, parametric equations, and probability.

  • Calculus

    Students who have successfully completed Precalculus may take this course to acquaint themselves with calculus concepts. It should be noted that any study of Calculus requires a significantly higher level of abstraction and command of concepts than Precalculus. Approximately one trimester of this course is devoted to an intensive review of algebra concepts, functions and their graphs, trigonometry, and analytic geometry. The remainder of the course is used to introduce students to the concepts of limits, continuity, derivatives and their applications, and integrals.

  • Precalculus Advanced

    This course is designed for students who have completed Advanced Algebra I, Advanced Algebra II, and Advanced Geometry and who anticipate taking either AP Calculus AB or BC the following year. In addition to reviewing and expanding topics from previous courses, it also covers trigonometric functions, complex numbers, matrices, logarithmic and exponential functions, analytic geometry, theory of equations, and sequences and series. The year is finished with an introduction to the polar coordinate system, parametric equations and their applications. It moves at a much faster pace than the Precalculus course.

  • AP Calculus AB

    This college-level course prepares students for the AB Advanced Placement Calculus Examination. Topics include analytic geometry; polynomial, rational, exponential, logarithmic, and trigonometric functions and their graphs; limits and continuity; techniques and applications of the derivatives of these functions; integration techniques and applications of the integral; the mean value theorem; and the fundamental theorem of calculus.

  • AP Calculus BC

    AP Calculus BC is offered as a second year of calculus to those students who have already completed AP Calculus AB. Some students may take this class directly after completion of Advanced Precalculus if prerequisite requirements are met. This intensive college-level course prepares students for the BC Advanced Placement exam and covers some additional topics that are typically encountered in university Calculus II courses. A review of material from the AB curriculum includes more demanding problems than previously encountered. Among the new topics introduced are hyperbolic functions; advanced techniques in integration; improper integrals; the calculus of polar and parametric equations, including vectors in the plane; an extension of first-order linear differential equations, including logistic functions; infinite series, including power series, Taylor and Maclaurin Series, and Taylor polynomials.

  • Multivariable Calculus

    Multivariable Calculus is offered to those students who have already completed AP Calculus BC. As its name suggests, multivariable calculus is the extension of calculus to more than one variable. Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, LaGrange multipliers, and vector calculus in 2-D and 3-D space.
    This intensive college level course prepares students for other upper level college mathematics courses such as differential equations and linear algebra.
     

  • Statistics

    This one-trimester elective course is designed to provide a sampling of the material encountered in one semester of an introductory college statistics class. Students will learn univariate and bivariate data analysis techniques (including least squares regression lines and correlation), the Normal distribution, and sampling distributions. Inferential statistics is encountered while constructing confidence intervals. The class will provide good background for any student wishing to major in the social sciences in college. Statistics is also an appropriate course to prepare for AP Statistics.
     

  • AP Statistics

    The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. The syllabus follows the outline of the College Board's course description and is meant to prepare all students for the Advanced Placements exam in May. The use of graphing calculators is an essential part of the course, and students will need to have a TI-83 or TI-84 (preferred) graphing calculator.

  • Statistics

    The purpose of the full-year course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference.  Students will use real-world data to practice analysis and inference methods.  Students will also be required to gather data through sampling and experimentation.  The class will prioritize collaboration, communication, critical thinking, and creativity through the use of multiple project-based assessments. The use of graphing calculators is an essential part of the course, and students will need to have a TI-83 or TI-84 (preferred) graphing calculator.

    Grades 11–12; Prerequisites: Algebra 2 or approval from Math Dept. Chair.

  • Statistics

    The purpose of the full year course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to 4 broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical interference. Students will use real-world data to practice analysis and interference methods.
    The use of graphing calculators is an essential part of the course and students will need to have a TI-83 or TI-84 graphing calculator.
    Grades 11-12
    Prerequisites: Algebra II or approval from math dept. chair

Grade/Dept

Our Faculty

  • Photo of Katharine Herman
    Katharine Herman
    Math Department Chair
    Yale University - B.S.
    Columbia University - M.A.
    At KCD since 2008
  • Photo of Elizabeth Andrews
    Elizabeth Andrews
    Fourth Grade Teacher
    Transylvania University - BA Computer Science
    University of Louisville - Masters in Elementary Education
    At KCD since 2018
  • Photo of Reed Cohen
    Reed Cohen
    Math Teacher
    At KCD since 2021
  • Photo of Sheila Erk
    Sheila Erk
    Math Teacher
    Bellarmine University - B.A., M.A.T.
    At KCD since 2007
  • Photo of Michael Goldberg
    Michael Goldberg
    Honors Program Director, Math Teacher
    Cornell University - B.A.
    University of Illinois - M.A., Ph.D.
    At KCD since 2001
  • Kristen Grogan
    Math Teacher
    Loyola University - B.A.
    LIU Post - M.S.
    At KCD since 2015
  • Photo of Michelle Paschal
    Michelle Paschal
    Math Teacher
    Indiana University Southeast - B.S.
    Indiana Wesleyan University - M.A.
    At KCD since 1989
  • Photo of Sarah Shartzer
    Sarah Shartzer
    Math Teacher, Blackbaud Manager
    College of William and Mary - B.A.
    Bellarmine University - M.A.T.
    University of the Cumberlands - Ed.D.
    At KCD since 2002
  • Thomas Sheehan
    US Physics and Math Teacher
    At KCD since 2024
  • Amena Shukairy
    US Math Teacher
    At KCD since 2024
  • Benjamin Studevent
    US Physics Teacher
    At KCD since 2025
  • Photo of Monica Whitehouse
    Monica Whitehouse
    JK-1 Learning Specialist
    University of South Carolina - B.A.
    University of Louisville - M.A.
    At KCD since 2008
  • Photo of Jennifer Williams
    Jennifer Williams
    Math Teacher
    University of Illinois - B.Ed., M.A.
    At KCD since 1999

KCD Connect

find us around the web
4100 Springdale Road • Louisville, KY 40241 • (502) 423-0440 • Fax (502) 423-0445
Kentucky Country Day School is a private JK–12, coeducational school located on a spacious 80+ acre campus in Louisville, KY. KCD combines a rigorous academic program with a wide variety of athletic and extracurricular programs. Our outstanding faculty creates an intimate learning environment that is both challenging and supportive.