Upper School
US Curriculum

Mathematics

The Upper School math program strives to afford students a positive experience in math class while challenging them in classes in which they are well placed and poised to succeed so they can pursue their math education with confidence.
We work to assure appropriate placement in courses that best support students’ intellectual development so they can do well in math, be able to use it when necessary and appreciate it for its beauty as well as its uses. In addition, we want students to improve their logical and deductive reasoning skills and to have confidence in their ability to figure things out on their own. Students attain a solid, working knowledge of mathematics and are able to communicate mathematics effectively both in writing and when speaking. In addition, students learn to manage a myriad of details, organize their thoughts and reflect on their thinking processes. Our long-term goal is to help students become better problem-solvers, not just in math class, but in their everyday lives.

Mathematics Courses

List of 14 items.

  • Quadratic Topics in Algebra 1

    6 meetings per seven-day cycle/3 credits

    In this course, students build on their study of linear topics and begin to explore quadratic equations. Students quickly review the basics of simplifying algebraic expressions, solving one-variable linear equations and inequalities, and graphing linear equations. We then move on to study systems of linear equations before we tackle exponents, exponential functions, and quadratic equations. We will conclude our study with polynomials and factoring, rational equations and functions, and radicals and their relationship to geometry. The course stresses relevancy with an emphasis on real-life applications.

    Text: Larson, Boswell, Kanold and Stiff, Algebra 1
  • Geometry

    6 meetings per seven-day cycle/3 credits
    Prerequisite or co-requisite: Quadratic Topics 301 or the equivalent.

    In this Euclidean geometry course, the main emphasis is on plane geometry. The traditional topics are covered: parallel lines and planes, congruency, parallelograms, similarity, right triangle relationships, circles, polygons, and constructions. Direct and indirect proofs are taught as methods of reasoning. Non-Euclidean topics such as solid geometry, coordinate geometry, and transformational geometry are introduced.

    Text: Harold, Jacob, Geometry: Seeing, Doing, Understanding
  • Algebra II with Trigonometry

    6 meetings per seven-day cycle/3 credits
    Prerequisite: Quadratic Topics 301. Prerequisite or co-requisite: Geometry 302.

    Students in this course review the essentials of first-year algebra including functions and relations and algebraic and graphical solutions of linear and quadratic equations and inequalities. We move on to discuss complex numbers, conic sections, and trigonometric, exponential, and logarithmic functions.

    Students are required to have a calculator with graphing capabilities. The TI-89 is recommended.

    Text: Blitzer, Algebra 2 and Trigonometry
  • Advanced Algebra II with Trigonometry

    6 meetings per seven-day cycle/3 credits
    Prerequisite: “A-” or above in Quadratic Topics 301 and teacher recommendation. Prerequisite or co-requisite: Geometry 302.

    This course is designed for serious students who intend to go on to higher work in mathematics and who intend to do more than the minimum secondary school work in math and science. This is a fast-paced course that requires a strong background in Algebra I skills. Students in this course quickly review and expand upon the essentials of Algebra I and develop the structure and theory of the real number system. Topics include the concepts of function and relation, algebraic and graphical solutions of linear and quadratic equations and inequalities, polynomial equations and complex numbers, conic sections, exponential and logarithmic functions, and the study of trigonometry and circular functions.

    Students are required to have a calculator with graphics capabilities. The Texas Instruments TI-89 is recommended.

    Text: Blitzer, Algebra 2 and Trigonometry
  • Math 4: Pre-Calculus

    6 meetings per seven-day cycle/3 credits
    Prerequisite: Adv Alg 2/Trig 303, or “B” or above in Alg 2/Trig 365

    This course establishes a deeper knowledge of the topics covered in the Algebra II courses (303 and 365). It treats selected topics of algebra and trigonometry, including matrices, arithmetic and geometric sequences, mathematical induction, and the binomial expansion formula. It is also designed to provide the students with a deeper understanding of functions and to prepare the more able students to take AP Calculus AB 328 the following year.

    Students are required to have a calculator with graphics capabilities. The Texas Instruments TI-89 is recommended.

    Text: Stewart, PreCalculus
  • Math 5: Advanced Pre-Calculus

    6 meetings per seven-day cycle/3 credits
    Prerequisite: At least a “B+” average in Adv Alg 2/Trig 303, and teacher recommendation.

    Advanced Pre-Calculus is designed for students who enjoy math and want to push themselves daily. The course is very rigorous and demanding and prepares students for AP Calculus AB 328 or AP Calculus AB/BC 312. We study many topics including polynomials, inequalities, functions, exponents and logarithms, trigonometry, polar coordinates, vectors and determinants, parametric equations, sequences and series, combinatorics, and probability. Students are required to derive all formulas and there is a great emphasis on solving multi-step, multi-process problems.

    Students are required to have a calculator with graphics capabilities. The Texas Instruments TI-89 is recommended.

    Text: Brown, Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis
  • Statistics and Probability

    6 meetings per seven-day cycle/3 credits
    Prerequisite: Alg 2/Trig 365 or Adv Alg 2/Trig 303. Must be a junior or senior

    “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”. –H.G. Wells

    We live in the information age; raw data, graphs, rates, percentages, probabilities, averages, forecasts, and trend lines are an inescapable part of our everyday lives. Everyone who needs to collect and analyze data needs to understand statistics, including those involved in every branch of natural science, the social sciences (psychology, sociology, anthropology, etc.), business and economics, political science and government, and law and medicine.

    This course is designed to examine how data and statistics shape our world. Students will learn the importance of collecting and studying data in real-life situations. They will explore data analysis, data production, statistical inference, and probability and, in turn, are provided with the tools to make good decisions with data.
  • AP Statistics

    6 meetings per seven-day cycle/3 credits
    Prerequisite: “B” or above in Adv Pre-Calc 305 or AP Calc AB 328, and recommendation of teacher; or “B+” or above in Pre-Calc 304 and recommendation of teacher; or “A-“ or above in Adv Alg 2/Trig 303 and the recommendation of teacher. Occasionally, students with straight A’s in Alg 2/Trig 365 may be considered for AP Statistics by applying to the department chair.

    This course follows the curriculum recommended by the College Board for the Statistics Advanced Placement Exam. The purpose of the course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference.

    Students are required to have a calculator with graphing and statistical capabilities.

    Text: Yates, Moore, McCabe, The Practice of Statistics
  • Calculus-Based AP Statistics

    6 meetings per seven-day cycle/3 credits
    Pre-requisite: A- or better in AP Calc AB 328, B+ or better in Acc AP Calc AB 308, or B or better in AP Calc AB/BC 312. Co-requisite: AP Calc BC 310, unless BC Calculus (310 or 312) taken previously.

    In this course probability theory is used to make sense of randomness and uncertainty, and statistics is used to make intelligent judgments and informed decisions in the presence of uncertainty and variation. Calculus provides the methodological basis in both disciplines. Students will use quantitative methods to analyze data, make rational decisions under uncertainty, design experiments, and model randomness and variability in the social and natural sciences. This course is more mathematically rigorous than AP Statistics.

    Textbooks:
    Devore, Jay L., Berk, Kenneth N. Modern Mathematical Statistics with Applications
    Springer 2nd Edition 2012 (also available as an eBook)
    ISBN 978-1-4614-0391-3
  • AP Calculus I (AB)

    6 meetings per seven-day cycle/3 credits
    Prerequisite: Adv Pre-Calc 305 or a B+ or above in Pre-Calc 304, and teacher recommendation.

    This course will focus on gaining a conceptual understanding of calculus and discovering a wide variety of applications in the real world. Topics will include functions, limits, differentiation, and integration and applications from engineering, physics, life sciences, and economics. All AP topics will be covered.

    Students are required to have a calculator with graphing capabilities. The Texas Instruments TI-89 is recommended.

    Text: James Stewart, Single Variable Calculus: Concepts and Context
  • AP Calculus II (BC)

    6 meetings per seven-day cycle/3 credits
    Prerequisite: Acc AP Calc AB 308; or an A- or above in AP Calc AB 328.

    This course follows the curriculum recommended by the College Board for the Calculus BC Advanced Placement Exam. Applications of integration begun in AP Calculus AB are reviewed and additional applications including arc length and work are studied. Other topics include techniques of integration, infinite series, the calculus of polar coordinate functions, parametric equations, vector functions, improper integrals, and simple differential equations.

    Students are required to have a calculator with graphics capabilities. The Texas Instruments TI-89 is recommended. Some course time will be devoted to discussing the mathematics that the calculator might be using to perform the calculations.

    Text: Finney, Demana, Waits, Kennedy, Calculus Graphical, Numerical, Algebraic
  • AP Calculus (AB/BC)

    6 meetings per seven-day cycle/3 credits
    Prerequisite: An “A-” average in Adv Pre-Calc 305 and recommendation of the 305 instructor

    This is a fast-paced course for students who wish to cover all of the topics included on both the AB and BC Advanced Placement Examinations. In order to achieve this goal, students will be required to complete a summer self-study assignment. Students will be tested on this material and then we will move on to applications of derivatives, curve sketching, techniques of integration and its applications, infinite series, the calculus of polar coordinate functions, parametric equations, vector functions, improper integrals, and simple differential equations. This course is designed for students who have a passion for mathematics and want to challenge themselves daily. Because of the material to be covered, students will need to be independent, self-motivated learners. Rising juniors should only consider this course if they wish to continue on in math beyond the BC course during their senior year.

    Students are required to have a calculator with graphing capabilities. The Texas Instruments TI-89 is recommended.
  • Multivariable Calculus/Linear Algebra

    6 meetings per seven-day cycle/3 credits
    Prerequisite: B+ in AP Calculus BC 310 or AP Calculus AB/BC 312

    This course is open to students that have successfully completed BC Calculus (Math 310 or 312). The first half of this course covers vector and multi-variable calculus. Topics include vectors, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2D- and 3D-space. The second half covers matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, and eigenvalues. Students will be required to complete a short independent study on an application of these topics. This course follows MIT syllabi with free resources available to students through MIT OpenCourseWare.

    Textbooks:
    • Edwards and Penney, Multivariable Calculus.
    • Strang, Introduction to Linear Algebra.
  • Math Team

    1 meeting per seven-day cycle/0 credits
    Open to all Upper School students

    The Math Team class will provide students with an opportunity to prepare for participation in mathematics contests. Students will study a variety of problem solving techniques and they will practice using problems from previous contests. Any student can participate, regardless of what math class he or she is currently taking. The only requirement is that students have an interest in mathematics and a desire to stretch their mathematical thinking. Students who want to take part in interscholastic math competitions should sign up for this course if their schedule allows.