Mathematics

List of 15 items.

• Quadratic Topics in Algebra 1

  5 meetings per eight-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.

• Geometry

  5 meetings per eight-day cycle/3 credits
  Prerequisite: 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. Area and volumes are also covered. Direct and indirect proofs are taught as methods of reasoning throughout the course. Introductory statistics are taught focusing on qualitative and quantitative data, measures of center and spread, and reading and organizing data.

• Algebra II with Trigonometry

  5 meetings per eight-day cycle/3 credits
  Prerequisite: Quadratic Topics 301 and Geometry 302
  With departmental permission, Geometry 302 may be taken concurrently.
  
  

  Students in this course review the essentials of first-year algebra, including functions and relations, as well as 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.

• Advanced Algebra II with Trigonometry

  5 meetings per eight-day cycle/3 credits
  Prerequisite: “A-” or above in Quadratic Topics 301 and Geometry 302
  With departmental permission, Geometry 302 may be taken concurrently.
  
  

  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.

• Pre-Calculus

  5 meetings per eight-day cycle/3 credits
  Prerequisite: Adv Alg 2/Trig 303 or Alg 2/Trig 365
  
  This course is devoted to developing a toolkit of functions and other mathematical concepts that serve as a bridge between mathematics and the world it models. The toolkit includes explicitly, implicitly, and recursively defined functions, matrices, graph theory, probability, and statistics. Students will discover the power of these math concepts through modeling projects and lab activities that incorporate the use of graphing calculators and computer programs, such as Desmos, Google Sheets, and StatCrunch. Students will present their results in formal written reports. This course does not prepare students for AP Calculus.

• Advanced Pre-Calculus

  5 meetings per eight-day cycle/3 credits
  Prerequisite: “B-” or above in 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 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.

• Accelerated Pre-Calculus with and Intro to Calculus

  5 meetings per eight-day cycle/3 credits
  Prerequisite:“B+” or above in Adv Alg 2/Trig 303
  
  

  Accelerated 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.

• Statistics and Probability

  5 meetings per eight-day cycle/3 credits
  Prerequisite: Open only to seniors. Juniors need the permission of the department head.
  
  

  “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. In turn, they are provided with the tools to make good decisions with data.

• AP Statistics

  5 meetings per eight-day cycle/3 credits
  Prerequisite: Accelerated Pre-Calc with Intro to Calc; “B+” or above in Advanced Pre-Calc 304 or “A-” or above in Pre-Calc. Occasionally, rising seniors with straight “As” in Alg 2/Trig 365 may be considered for AP Statistics by applying to the department head. Open only to seniors. Juniors need the permission of the department head.
  
  

  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.

• Calculus-Based AP Statistics

  5 meetings per eight-day cycle/3 credits
  Prerequisite: “B+” or above in AP Calc AB 328 or “B” or above in AP Calc AB/BC 312
  
  

  In this course, probability theory is used to make sense of randomness and uncertainty, and statistics are 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.

• AP Calculus I (AB)

  5 meetings per eight-day cycle/3 credits
  Prerequisite: Accelerated Pre-Calc with Intro to Calc 305 or a "B+" or above in Advanced Pre-Calc 304
  
  

  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.

• AP Calculus II (BC)

  5 meetings per eight-day cycle/3 credits
  Prerequisite: “B+” 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.

• AP Calculus (AB/BC)

  5 meetings per eight-day cycle/3 credits
  Prerequisite: A “B+” average in Accelerated Pre-Calc with Intro to Calc 305
  
  

  This is a fast-paced course for students who wish to cover all 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

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

  This course is open to students who have successfully completed BC Calculus (Math 310 or 312). The first half of this course covers vector and multivariable calculus. Topics include vectors, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2-D and 3-D 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.

• Math Team

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

  The Math Team will provide students with an opportunity to prepare for participation in mathematics contests. Students will study a variety of problem-solving techniques and will practice using problems from previous contests. Any student can participate, regardless of what math class they are 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.