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Mathematics

The mission of Sage Hill School’s Mathematics Department is to strike a balance between the theory — the foundation, beauty, and precision — and the application of mathematics. Students are exposed to a strong theoretical foundation (using proper mathematical notation at all times) and hands-on projects that confirm, apply, and make more tangible the theory. Students also learn how to tackle real world problems using a variety of techniques and technologies.

While teachers try to point students in the right direction and challenge them, it is the students who have to produce results. Teachers do not cover the material but do their utmost to uncover it in order to provoke students’ thinking in a small, interactive classroom environment. All students are expected to take three consecutive years of mathematics following initial placement assessments, and they may choose from a variety of options depending on the pace and the scope of their course of study.

  • Statistics and Data Methods

    This course covers the basic principles of descriptive statistics, relationships in data, experimental design, and statistical inference in the contexts of real-life data and social issues. Statistical techniques are studied with an emphasis on their practicality for drawing conclusions from data. There will be a focus on collecting, analyzing, representing, and reporting data. Other topics include probability distributions, sampling techniques, and binomial distributions. The course covers the principles of hypothesis testing and confidence intervals. Students also measure the probability of events, interpret probability and use probability in decision-making. Recommended Preparation: Successful completion of Algebra II or Accelerated Algebra II and Trigonometry. This is a Sage Center Designated Course

  • Algebra I

    This course provides a strong foundation in the important concepts of Algebra I with particular emphasis on universal mathematical notation. Students develop the skills and confidence to establish the groundwork for subsequent courses. The course stresses analytical skills more than simple mechanical skills. Students work on many models represented by linear, quadratic and exponential functions as well as systems of equations.

  • Geometry

    This course explores basic elements of Euclidean geometry and employs primarily deductive methods of reasoning with basic two- and three-dimensional shapes and their properties. The course also helps students reinforce algebraic concepts in the course of solving geometric problems.

  • Honors Algebra II and Trigonometry

    This course covers all of the material taught in Algebra II and Precalculus at a greater level of difficulty and at an Honors pace. Students are expected to demonstrate a greater depth of understanding through problem solving as well as written explanation. Additional topics include: an introduction to matrices applied to linear programming, natural logarithms and base e, slant asymptotes of rational graphs, an introduction to series and sequences, systems and translations of quadratic relations.

  • Algebra II

    This course continues the development of algebraic skills and concepts and prepares students for study in Precalculus. In addition to topics discussed in Algebra I, this course covers topics such as linear models, quadratic models, exponential and logarithmic models, rational models, irrational models, and quadratic relations. Students also complete projects that apply concepts to model real-world phenomena.

  • Accelerated Algebra II and Trigonometry

    This course covers all of the material taught in Algebra II and Precalculus at a greater level of difficulty and at an accelerated pace. Students are expected to demonstrate a greater depth of understanding through problem solving as well as written explanation. Additional topics include: an introduction to matrices applied to linear programming, natural logarithms and base e, slant asymptotes of rational graphs, an introduction to series and sequences, systems and translations of quadratic relations. Recommended Preparation: Recommendation of the Mathematics Department, passing Geometry with a grade of A both semesters, and demonstrating mastery on an Accelerated Algebra II placement process.

  • Precalculus

    This course prepares students for Calculus through a thorough study of elementary functions including trigonometric functions, conic sections and sequences and series. Students also explore real-world applications over the course of the year.

  • Honors Precalculus

    This course covers all of the material taught in the Precalculus class at a greater level of difficulty and at an Honors pace. Students are expected to demonstrate a greater depth of understanding through problem solving as well as written explanation. Additional topics may include: matrices and linear programming, parametric equations, multiple angle identities, the polar coordinate system, the binomial theorem, and an introduction to calculus.

  • Calculus

    The goal of this course is to introduce students to the basic concepts of calculus, or the study of motion. Students study rates of change, differentiation, integration limits, and applications of these topics. Analytical and mechanical skills are stressed throughout the course and problems are solved algebraically, analytically and graphically.

  • AP Calculus AB

    This course introduces students to the basic concepts of calculus. Students learn to read the language of differential equations and to understand that the two principal divisions of calculus–differential (rate problems) and integral (accumulation problems)–are unified by the Fundamental Theorem of Calculus. The course introduces methods for determining derivatives and integrals of elementary functions, and students explore applications of the derivative and integral. Analytical and mechanical skills are stressed throughout the year.

  • AP Calculus BC

    This course introduces students to the concepts of calculus. In addition to learning to read the language of differential equations and understanding the Fundamental Theorem of Calculus, students learn methods for determining derivatives and integrals of elementary functions and explore applications of the derivative and integral. Additional topics include techniques of integration, differential equations and sequences and series, polar, parametric and vector functions.

  • Calculus C

    This course continues the study of single-variable calculus. This course will provide a deeper understanding of the concepts of limit, continuity, derivatives and integrals which were all covered in AP Calculus AB. The major topics covered in this course are parametric, polar, and vector functions; slope fields; Euler’s method; L’Hopital’s Rule; Improper Integrals; differential equations; Polynomial approximations and Series; and Taylor Series. Students enrolled in Calculus C are required to take AP Calculus BC exam.

  • Multivariable Calculus

    This course extends the concepts of single-variable calculus into three dimensions and completes the study of calculus. During the first semester, students learn vector-valued functions and operations, study functions and derivatives in three-space, limits and infinite series. During the second semester, students will further investigate functions and their derivatives in three dimensions, applications of multiple integrals (including rectangular, spherical and cylindrical coordinate systems), integration in vector fields, divergence theorem, Green’s Theorem and Stokes’ Theorem.

  • Advanced Topics in Mathematics

    This college level course covers post-calculus material at an introductory level. Many of these topics are seen in core mathematics major courses. The first semester consists of developing an understanding of proof in addition to the basics of set theory, symbolic logic, number theory, and group theory. The topics covered in second semester vary depending on the preferences of the class and build upon our foundation of algebraic structures. These concepts may include but are not limited to linear algebra, non-Euclidean geometry, graph theory, or complex analysis. This course prepares students for advanced study in mathematics and other related fields.

  • AP Computer Science

    This course is designed to teach students not only how to program in a high-level computer language, Java, but also about computing in general. The curriculum educates students to use programming methodology and problem-solving skills to produce computer-based solutions to problems by challenging them to take the lessons learned in class and apply them immediately to various exercises on the computer. After completing this course, students should be able to write high-level code in Java, understand the concepts of object-oriented programming, and use methodologies to analyze a problem and then implement a solution with Java on the computer.

  • AP Statistics

    The AP course in Statistics is the equivalent of a semester-long, college-level introductory statistics course and prepares students for the AP Statistics exam administered in the spring. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course focuses on four broad conceptual themes: describing patterns and graphical analysis; planning and conducting a study; exploring random phenomena using probability and simulation; and estimating population parameters and testing hypotheses using formal inference procedures. Students will also design and carry out a full-year APA-style research project.

  • Linear Algebra

    This course will focus on matrix theory, vector properties, systems of linear equations, subspaces, linear transformations, eigenvalues and eigenvectors, orthogonality, and vector spaces. The course will also focus on applications of vectors and matrices, including linear games, computer graphics, UPC codes and other real world applications. These concepts are extremely useful in physics, economics, social and natural sciences, and engineering. This elective is recommended for students wanting to pursue STEM in college.
  • Photo of Drew Ishii
    Drew Ishii
    Mathematics Department Chair and Teacher
    Bio
  • Photo of Mr. Anderson
    Mr. Anderson
    Mathematics Teacher
    Bio
  • Photo of Cecelia Angotti
    Cecelia Angotti
    Mathematics Teacher
    Bio
  • Photo of Derek Carlson
    Derek Carlson
    Mathematics Teacher
    Bio
  • Photo of Claire Cassidy
    Claire Cassidy
    Mathematics Teacher
    Bio
  • Photo of Rena Dear
    Rena Dear
    Mathematics Teacher
    Bio
  • Photo of Jim Lau
    Jim Lau
    Mathematics Teacher
    Bio
  • Photo of Kelly May
    Kelly May
    Mathematics Teacher
    Bio
  • Photo of Nate Miller
    Nate Miller
    Mathematics Teacher
    Bio
  • Photo of Dinh Nguyen
    Dinh Nguyen
    Mathematics Teacher
    Bio

Sage Hill School

20402 Newport Coast Drive, Newport Coast, CA 92657
Phone: 949.219.0100  |  Fax: 949.219.1399
Sage Hill School admits students of any race, color, national and ethnic origin to all the rights, privileges, programs and activities generally accorded or made available to students at the School. The School does not discriminate on the basis of race, color, national and ethnic origin in administration of its educational policies, admissions policies, scholarship programs, and athletic and other School administered programs.